Definition
A subgroup of a group is termed conjugacy-closed if any two elements of the subgroup that are conjugate in the whole group are also conjugate in the subgroup.
An automorphism ζ ∈ Aut(H) of a group H is termed a class-preserving automorphism if it takes each element to within its conjugacy class, i.e. ζ(h) = hx for some x ∈ H. Let us call Cp(H) this subgroup of automorphims such that
References
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Group: C2
Aut(G): 1
Inn(G): 1
Class Preserving sub(G):1
Group: C3
Aut(G): C2
Inn(G): 1
Class Preserving sub(G):1
Group: C4
Aut(G): C2
Inn(G): 1
Class Preserving sub(G):1
Group: C2 x C2
Aut(G): S3
Inn(G): 1
Class Preserving sub(G):1
Group: C5
Aut(G): C4
Inn(G): 1
Class Preserving sub(G):1
Group: S3
Aut(G): S3
Inn(G): S3
Class Preserving sub(G):S3
Group: C6
Aut(G): C2
Inn(G): 1
Class Preserving sub(G):1
Group: C7
Aut(G): C6
Inn(G): 1
Class Preserving sub(G):1
Group: C8
Aut(G): C2 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: C4 x C2
Aut(G): D8
Inn(G): 1
Class Preserving sub(G):1
Group: D8
Aut(G): D8
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: Q8
Aut(G): S4
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: C2 x C2 x C2
Aut(G): PSL(3,2)
Inn(G): 1
Class Preserving sub(G):1
Group: C9
Aut(G): C6
Inn(G): 1
Class Preserving sub(G):1
Group: C3 x C3
Aut(G): GL(2,3)
Inn(G): 1
Class Preserving sub(G):1
Group: D10
Aut(G): C5 : C4
Inn(G): D10
Class Preserving sub(G):D10
Group: C10
Aut(G): C4
Inn(G): 1
Class Preserving sub(G):1
Group: C11
Aut(G): C10
Inn(G): 1
Class Preserving sub(G):1
Group: C3 : C4
Aut(G): D12
Inn(G): S3
Class Preserving sub(G):S3
Group: C12
Aut(G): C2 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: A4
Aut(G): S4
Inn(G): A4
Class Preserving sub(G):A4
Group: D12
Aut(G): D12
Inn(G): S3
Class Preserving sub(G):S3
Group: C6 x C2
Aut(G): D12
Inn(G): 1
Class Preserving sub(G):1
Group: C13
Aut(G): C12
Inn(G): 1
Class Preserving sub(G):1
Group: D14
Aut(G): (C7 : C3) : C2
Inn(G): D14
Class Preserving sub(G):D14
Group: C14
Aut(G): C6
Inn(G): 1
Class Preserving sub(G):1
Group: C15
Aut(G): C4 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: C16
Aut(G): C4 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: C4 x C4
Aut(G): (C2 x C2 x A4) : C2
Inn(G): 1
Class Preserving sub(G):1
Group: (C4 x C2) : C2
Aut(G): (C2 x C2 x C2 x C2) : C2
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: C4 : C4
Aut(G): (C2 x C2 x C2 x C2) : C2
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: C8 x C2
Aut(G): C2 x D8
Inn(G): 1
Class Preserving sub(G):1
Group: C8 : C2
Aut(G): C2 x D8
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: D16
Aut(G): (C2 x D8) : C2
Inn(G): D8
Class Preserving sub(G):D8
Group: QD16
Aut(G): C2 x D8
Inn(G): D8
Class Preserving sub(G):D8
Group: Q16
Aut(G): (C2 x D8) : C2
Inn(G): D8
Class Preserving sub(G):D8
Group: C4 x C2 x C2
Aut(G): (((C2 x D8) : C2) : C3) : C2
Inn(G): 1
Class Preserving sub(G):1
Group: C2 x D8
Aut(G): (((C4 x C2) : C2) : C2) : C2
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: C2 x Q8
Aut(G): (((C2 x C2 x C2 x C2) : C3) : C2) : C2
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: (C4 x C2) : C2
Aut(G): C2 x S4
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: C2 x C2 x C2 x C2
Aut(G): A8
Inn(G): 1
Class Preserving sub(G):1
Group: C17
Aut(G): C16
Inn(G): 1
Class Preserving sub(G):1
Group: D18
Aut(G): (C9 : C3) : C2
Inn(G): D18
Class Preserving sub(G):D18
Group: C18
Aut(G): C6
Inn(G): 1
Class Preserving sub(G):1
Group: C3 x S3
Aut(G): D12
Inn(G): S3
Class Preserving sub(G):S3
Group: (C3 x C3) : C2
Aut(G): (((C3 x C3) : Q8) : C3) : C2
Inn(G): (C3 x C3) : C2
Class Preserving sub(G):(C3 x C3) : C2
Group: C6 x C3
Aut(G): GL(2,3)
Inn(G): 1
Class Preserving sub(G):1
Group: C19
Aut(G): C18
Inn(G): 1
Class Preserving sub(G):1
Group: C5 : C4
Aut(G): C2 x (C5 : C4)
Inn(G): D10
Class Preserving sub(G):D10
Group: C20
Aut(G): C4 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: C5 : C4
Aut(G): C5 : C4
Inn(G): C5 : C4
Class Preserving sub(G):C5 : C4
Group: D20
Aut(G): C2 x (C5 : C4)
Inn(G): D10
Class Preserving sub(G):D10
Group: C10 x C2
Aut(G): C4 x S3
Inn(G): 1
Class Preserving sub(G):1
Group: C7 : C3
Aut(G): (C7 : C3) : C2
Inn(G): C7 : C3
Class Preserving sub(G):C7 : C3
Group: C21
Aut(G): C6 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: D22
Aut(G): (C11 : C5) : C2
Inn(G): D22
Class Preserving sub(G):D22
Group: C22
Aut(G): C10
Inn(G): 1
Class Preserving sub(G):1
Group: C23
Aut(G): C22
Inn(G): 1
Class Preserving sub(G):1
Group: C3 : C8
Aut(G): C2 x C2 x S3
Inn(G): S3
Class Preserving sub(G):S3
Group: C24
Aut(G): C2 x C2 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: SL(2,3)
Aut(G): S4
Inn(G): A4
Class Preserving sub(G):A4
Group: C3 : Q8
Aut(G): D8 x S3
Inn(G): D12
Class Preserving sub(G):D12
Group: C4 x S3
Aut(G): C2 x C2 x S3
Inn(G): S3
Class Preserving sub(G):S3
Group: D24
Aut(G): D8 x S3
Inn(G): D12
Class Preserving sub(G):D12
Group: C2 x (C3 : C4)
Aut(G): D8 x S3
Inn(G): S3
Class Preserving sub(G):S3
Group: (C6 x C2) : C2
Aut(G): C2 x C2 x S3
Inn(G): D12
Class Preserving sub(G):D12
Group: C12 x C2
Aut(G): C2 x D8
Inn(G): 1
Class Preserving sub(G):1
Group: C3 x D8
Aut(G): C2 x D8
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: C3 x Q8
Aut(G): C2 x S4
Inn(G): C2 x C2
Class Preserving sub(G):C2 x C2
Group: S4
Aut(G): S4
Inn(G): S4
Class Preserving sub(G):S4
Group: C2 x A4
Aut(G): S4
Inn(G): A4
Class Preserving sub(G):A4
Group: C2 x C2 x S3
Aut(G): S3 x S4
Inn(G): S3
Class Preserving sub(G):S3
Group: C6 x C2 x C2
Aut(G): C2 x PSL(3,2)
Inn(G): 1
Class Preserving sub(G):1
Group: C25
Aut(G): C20
Inn(G): 1
Class Preserving sub(G):1
Group: C5 x C5
Aut(G): GL(2,5)
Inn(G): 1
Class Preserving sub(G):1
Group: D26
Aut(G): (C13 : C4) : C3
Inn(G): D26
Class Preserving sub(G):D26
Group: C26
Aut(G): C12
Inn(G): 1
Class Preserving sub(G):1
Group: C27
Aut(G): C18
Inn(G): 1
Class Preserving sub(G):1
Group: C9 x C3
Aut(G): C2 x (((C3 x C3) : C3) : C2)
Inn(G): 1
Class Preserving sub(G):1
Group: (C3 x C3) : C3
Aut(G): (((C3 x C3) : Q8) : C3) : C2
Inn(G): C3 x C3
Class Preserving sub(G):C3 x C3
Group: C9 : C3
Aut(G): ((C3 x C3) : C3) : C2
Inn(G): C3 x C3
Class Preserving sub(G):C3 x C3
Group: C3 x C3 x C3
Aut(G): GL(3,3)
Inn(G): 1
Class Preserving sub(G):1
Group: C7 : C4
Aut(G): C2 x ((C7 : C3) : C2)
Inn(G): D14
Class Preserving sub(G):D14
Group: C28
Aut(G): C6 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: D28
Aut(G): C2 x ((C7 : C3) : C2)
Inn(G): D14
Class Preserving sub(G):D14
Group: C14 x C2
Aut(G): C6 x S3
Inn(G): 1
Class Preserving sub(G):1
Group: C29
Aut(G): C28
Inn(G): 1
Class Preserving sub(G):1
Group: C5 x S3
Aut(G): C4 x S3
Inn(G): S3
Class Preserving sub(G):S3
Group: C3 x D10
Aut(G): C2 x (C5 : C4)
Inn(G): D10
Class Preserving sub(G):D10
Group: D30
Aut(G): (C5 : C4) x S3
Inn(G): D30
Class Preserving sub(G):D30
Group: C30
Aut(G): C4 x C2
Inn(G): 1
Class Preserving sub(G):1
Group: C31
Aut(G): C30
Inn(G): 1
Class Preserving sub(G):1
-----------------------------------
Group: C32
Aut(G) es: C8 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: (C4 x C2) : C4
Aut(G) es: (C2 x C2 x ((C2 x C2 x C2 x C2) : C3)) : C2
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C8 x C4
Aut(G) es: (C2 x (((C4 x C2) : C2) : C2)) : C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C8 : C4
Aut(G) es: (C2 x (((C4 x C2) : C2) : C2)) : C2
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: (C8 x C2) : C2
Aut(G) es: C2 x ((C2 x C2 x C2 x C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: ((C4 x C2) : C2) : C2
Aut(G) es: (((C4 x C2) : C2) : C2) : C2
Inn(G): (C4 x C2) : C2
Class Preserving subgroup: (C4 x C2) : C2
Group: (C8 : C2) : C2
Aut(G) es: (D8 x D8) : C2
Inn(G): (C4 x C2) : C2
Class Preserving subgroup: (C4 x C2) : C2
Group: C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2)
Aut(G) es: (D8 x D8) : C2
Inn(G): (C4 x C2) : C2
Class Preserving subgroup: (C4 x C2) : C2
Group: (C8 x C2) : C2
Aut(G) es: C2 x C2 x C2 x D8
Inn(G): D8
Class Preserving subgroup: D8
Group: Q8 : C4
Aut(G) es: C2 x C2 x C2 x D8
Inn(G): D8
Class Preserving subgroup: D8
Group: (C4 x C4) : C2
Aut(G) es: C2 x C2 x D8
Inn(G): D8
Class Preserving subgroup: D8
Group: C4 : C8
Aut(G) es: C2 x ((C2 x C2 x C2 x C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C8 : C4
Aut(G) es: (C2 x C2 x C2 x D8) : C2
Inn(G): D8
Class Preserving subgroup: D8
Group: C8 : C4
Aut(G) es: (C2 x C2 x C2 x D8) : C2
Inn(G): D8
Class Preserving subgroup: D8
Group: C4 . D8 = C4 . (C4 x C2)
Aut(G) es: C2 x ((C2 x D8) : C2)
Inn(G): D8
Class Preserving subgroup: D8
Group: C16 x C2
Aut(G) es: C2 x ((C4 x C2) : C2)
Inn(G): 1
Class Preserving subgroup: 1
Group: C16 : C2
Aut(G) es: C2 x ((C4 x C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: D32
Aut(G) es: (C16 : C4) : C2
Inn(G): D16
Class Preserving subgroup: D16
Group: QD32
Aut(G) es: (C4 x D8) : C2
Inn(G): D16
Class Preserving subgroup: D16
Group: Q32
Aut(G) es: (C16 : C4) : C2
Inn(G): D16
Class Preserving subgroup: D16
Group: C4 x C4 x C2
Aut(G) es: (((C2 x C2 x ((C2 x C2 x C2 x C2) : C2)) : C2) : C3) : C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C2 x ((C4 x C2) : C2)
Aut(G) es: ((C2 x (((C4 x C2) : C2) : C2)) : C4) : C2
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C2 x (C4 : C4)
Aut(G) es: (((C2 x C2 x ((C4 x C2) : C2)) : C2) : C2) : C2
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: (C4 x C4) : C2
Aut(G) es: (C2 x C2 x ((C2 x C2 x C2 x C2) : C2)) : C2
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C4 x D8
Aut(G) es: C2 x C2 x ((C2 x C2 x C2 x C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C4 x Q8
Aut(G) es: C2 x C2 x (((C2 x C2 x C2 x C2) : C3) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: (C2 x C2 x C2 x C2) : C2
Aut(G) es: (C2 x C2 x ((C2 x C2 x C2 x C2) : C3)) : C2
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: (C4 x C2 x C2) : C2
Aut(G) es: C2 x C2 x ((C2 x C2 x C2 x C2) : C2)
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: (C2 x Q8) : C2
Aut(G) es: C2 x C2 x ((C2 x C2 x C2 x C2) : C2)
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: (C4 x C2 x C2) : C2
Aut(G) es: (C2 x C2 x C2 x C2 x C2 x C2) : C2
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: (C4 x C4) : C2
Aut(G) es: (C2 x C2 x ((C2 x C2 x C2 x C2) : C2)) : C2
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: (C2 x C2) . (C2 x C2 x C2)
Aut(G) es: (C2 x ((((C4 x C2) : C2) : C2) : C2)) : C2
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: (C4 x C4) : C2
Aut(G) es: C2 x C2 x ((C2 x C2 x C2 x C2) : C3)
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: (C4 x C4) : C2
Aut(G) es: ((((((C4 x C4) : C2) : C2) : C3) : C2) : C2) : C2
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: C4 : Q8
Aut(G) es: ((C2 x (((C8 : C2) : C2) : C2)) : C2) : C2
Inn(G): C2 x C2 x C2
Class Preserving subgroup: C2 x C2 x C2
Group: C8 x C2 x C2
Aut(G) es: C2 x ((((C2 x D8) : C2) : C3) : C2)
Inn(G): 1
Class Preserving subgroup: 1
Group: C2 x (C8 : C2)
Aut(G) es: C2 x ((((C4 x C2) : C2) : C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: (C8 x C2) : C2
Aut(G) es: C2 x C2 x S4
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C2 x D16
Aut(G) es: ((C2 x ((C2 x D8) : C2)) : C2) : C2
Inn(G): D8
Class Preserving subgroup: D8
Group: C2 x QD16
Aut(G) es: (C2 x C2 x C2 x D8) : C2
Inn(G): D8
Class Preserving subgroup: D8
Group: C2 x Q16
-----THIS WAS THE END FOR GAP!
Group: C33
Aut(G):C10 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: D34
Aut(G):C17 : C16
Inn(G): D34
Class Preserving subgroup: D34
Group: C34
Aut(G):C16
Inn(G): 1
Class Preserving subgroup: 1
Group: C35
Aut(G):C12 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C9 : C4
Aut(G):C2 x ((C9 : C3) : C2)
Inn(G): D18
Class Preserving subgroup: D18
Group: C36
Aut(G):C6 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: (C2 x C2) : C9
Aut(G):C3 x S4
Inn(G): A4
Class Preserving subgroup: A4
Group: D36
Aut(G):C2 x ((C9 : C3) : C2)
Inn(G): D18
Class Preserving subgroup: D18
Group: C18 x C2
Aut(G):C6 x S3
Inn(G): 1
Class Preserving subgroup: 1
Group: C3 x (C3 : C4)
Aut(G):C2 x C2 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: (C3 x C3) : C4
Aut(G):C2 x ((((C3 x C3) : Q8) : C3) : C2)
Inn(G): (C3 x C3) : C2
Class Preserving subgroup: (C3 x C3) : C2
Group: C12 x C3
Aut(G):C2 x GL(2,3)
Inn(G): 1
Class Preserving subgroup: 1
Group: (C3 x C3) : C4
Aut(G):((C3 x C3) : C8) : C2
Inn(G): (C3 x C3) : C4
Class Preserving subgroup: (C3 x C3) : C4
Group: S3 x S3
Aut(G):(S3 x S3) : C2
Inn(G): S3 x S3
Class Preserving subgroup: S3 x S3
Group: C3 x A4
Aut(G):S4 x S3
Inn(G): A4
Class Preserving subgroup: A4
Group: C6 x S3
Aut(G):C2 x C2 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C2 x ((C3 x C3) : C2)
Aut(G):C2 x ((((C3 x C3) : Q8) : C3) : C2)
Inn(G): (C3 x C3) : C2
Class Preserving subgroup: (C3 x C3) : C2
Group: C6 x C6
Aut(G):GL(2,3) x S3
Inn(G): 1
Class Preserving subgroup: 1
Group: C37
Aut(G):C36
Inn(G): 1
Class Preserving subgroup: 1
Group: D38
Aut(G):(C19 : C9) : C2
Inn(G): D38
Class Preserving subgroup: D38
Group: C38
Aut(G):C18
Inn(G): 1
Class Preserving subgroup: 1
Group: C13 : C3
Aut(G):(C13 : C4) : C3
Inn(G): C13 : C3
Class Preserving subgroup: C13 : C3
Group: C39
Aut(G):C12 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C5 : C8
Aut(G):C2 x C2 x (C5 : C4)
Inn(G): D10
Class Preserving subgroup: D10
Group: C40
Aut(G):C4 x C2 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C5 : C8
Aut(G):C2 x (C5 : C4)
Inn(G): C5 : C4
Class Preserving subgroup: C5 : C4
Group: C5 : Q8
Aut(G):(C5 : C4) x D8
Inn(G): D20
Class Preserving subgroup: D20
Group: C4 x D10
Aut(G):C2 x C2 x (C5 : C4)
Inn(G): D10
Class Preserving subgroup: D10
Group: D40
Aut(G):(C5 : C4) x D8
Inn(G): D20
Class Preserving subgroup: D20
Group: C2 x (C5 : C4)
Aut(G):(C5 : C4) x D8
Inn(G): D10
Class Preserving subgroup: D10
Group: (C10 x C2) : C2
Aut(G):C2 x C2 x (C5 : C4)
Inn(G): D20
Class Preserving subgroup: D20
Group: C20 x C2
Aut(G):C4 x D8
Inn(G): 1
Class Preserving subgroup: 1
Group: C5 x D8
Aut(G):C4 x D8
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C5 x Q8
Aut(G):C4 x S4
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C2 x (C5 : C4)
Aut(G):C2 x (C5 : C4)
Inn(G): C5 : C4
Class Preserving subgroup: C5 : C4
Group: C2 x C2 x D10
Aut(G):(C5 : C4) x S4
Inn(G): D10
Class Preserving subgroup: D10
Group: C10 x C2 x C2
Aut(G):C4 x PSL(3,2)
Inn(G): 1
Class Preserving subgroup: 1
Group: C41
Aut(G):C40
Inn(G): 1
Class Preserving subgroup: 1
Group: (C7 : C3) : C2
Aut(G):(C7 : C3) : C2
Inn(G): (C7 : C3) : C2
Class Preserving subgroup: (C7 : C3) : C2
Group: C2 x (C7 : C3)
Aut(G):(C7 : C3) : C2
Inn(G): C7 : C3
Class Preserving subgroup: C7 : C3
Group: C7 x S3
Aut(G):C6 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C3 x D14
Aut(G):C2 x ((C7 : C3) : C2)
Inn(G): D14
Class Preserving subgroup: D14
Group: D42
Aut(G):((C7 : C3) : C2) x S3
Inn(G): D42
Class Preserving subgroup: D42
Group: C42
Aut(G):C6 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C43
Aut(G):C42
Inn(G): 1
Class Preserving subgroup: 1
Group: C11 : C4
Aut(G):C2 x ((C11 : C5) : C2)
Inn(G): D22
Class Preserving subgroup: D22
Group: C44
Aut(G):C10 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: D44
Aut(G):C2 x ((C11 : C5) : C2)
Inn(G): D22
Class Preserving subgroup: D22
Group: C22 x C2
Aut(G):C10 x S3
Inn(G): 1
Class Preserving subgroup: 1
Group: C45
Aut(G):C12 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C15 x C3
Aut(G):C4 x GL(2,3)
Inn(G): 1
Class Preserving subgroup: 1
Group: D46
Aut(G):(C23 : C11) : C2
Inn(G): D46
Class Preserving subgroup: D46
Group: C46
Aut(G):C22
Inn(G): 1
Class Preserving subgroup: 1
Group: C47
Aut(G):C46
Inn(G): 1
Class Preserving subgroup: 1
Group: C3 : C16
Aut(G):C2 x C4 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C48
Aut(G):C4 x C2 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: (C4 x C4) : C3
Aut(G):((((C4 x C4) : C3) : C2) : C2) : C2
Inn(G): (C4 x C4) : C3
Class Preserving subgroup: (C4 x C4) : C3
Group: C8 x S3
Aut(G):C2 x C2 x C2 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C24 : C2
Aut(G):C2 x C2 x C2 x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: C24 : C2
Aut(G):C2 x D8 x S3
Inn(G): D24
Class Preserving subgroup: D24
Group: D48
Aut(G):((C2 x D8) : C2) x S3
Inn(G): D24
Class Preserving subgroup: D24
Group: C3 : Q16
Aut(G):((C2 x D8) : C2) x S3
Inn(G): D24
Class Preserving subgroup: D24
Group: C2 x (C3 : C8)
Aut(G):C2 x D8 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: (C3 : C8) : C2
Aut(G):C2 x D8 x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: C4 x (C3 : C4)
Aut(G):((C2 x C2 x C2 x C2) : C2) x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: (C3 : C4) : C4
Aut(G):C2 x C2 x C2 x C2 x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: C12 : C4
Aut(G):((C2 x C2 x C2 x C2) : C2) x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: (C12 x C2) : C2
Aut(G):C2 x C2 x C2 x C2 x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: (C3 x D8) : C2
Aut(G):C2 x D8 x S3
Inn(G): (C6 x C2) : C2
Class Preserving subgroup: (C6 x C2) : C2
Group: (C3 : C8) : C2
Aut(G):C2 x D8 x S3
Inn(G): (C6 x C2) : C2
Class Preserving subgroup: (C6 x C2) : C2
Group: (C3 x Q8) : C2
Aut(G):C2 x D8 x S3
Inn(G): (C6 x C2) : C2
Class Preserving subgroup: (C6 x C2) : C2
Group: C3 : Q16
Aut(G):C2 x D8 x S3
Inn(G): (C6 x C2) : C2
Class Preserving subgroup: (C6 x C2) : C2
Group: (C2 x (C3 : C4)) : C2
Aut(G):((C2 x C2 x C2 x C2) : C2) x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: C12 x C4
Aut(G):C2 x ((C2 x C2 x A4) : C2)
Inn(G): 1
Class Preserving subgroup: 1
Group: C3 x ((C4 x C2) : C2)
Aut(G):C2 x ((C2 x C2 x C2 x C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C3 x (C4 : C4)
Aut(G):C2 x ((C2 x C2 x C2 x C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C24 x C2
Aut(G):C2 x C2 x D8
Inn(G): 1
Class Preserving subgroup: 1
Group: C3 x (C8 : C2)
Aut(G):C2 x C2 x D8
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C3 x D16
Aut(G):C2 x ((C2 x D8) : C2)
Inn(G): D8
Class Preserving subgroup: D8
Group: C3 x QD16
Aut(G):C2 x C2 x D8
Inn(G): D8
Class Preserving subgroup: D8
Group: C3 x Q16
Aut(G):C2 x ((C2 x D8) : C2)
Inn(G): D8
Class Preserving subgroup: D8
Group: C2 . S4 = SL(2,3) . C2
Aut(G):C2 x S4
Inn(G): S4
Class Preserving subgroup: S4
Group: GL(2,3)
Aut(G):C2 x S4
Inn(G): S4
Class Preserving subgroup: S4
Group: A4 : C4
Aut(G):C2 x S4
Inn(G): S4
Class Preserving subgroup: S4
Group: C4 x A4
Aut(G):C2 x S4
Inn(G): A4
Class Preserving subgroup: A4
Group: C2 x SL(2,3)
Aut(G):C2 x S4
Inn(G): A4
Class Preserving subgroup: A4
Group: SL(2,3) : C2
Aut(G):C2 x S4
Inn(G): A4
Class Preserving subgroup: A4
Group: C2 x (C3 : Q8)
Aut(G):S3 x ((((C4 x C2) : C2) : C2) : C2)
Inn(G): D12
Class Preserving subgroup: D12
Group: C2 x C4 x S3
Aut(G):((C2 x C2 x C2 x C2) : C2) x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C2 x D24
Aut(G):S3 x ((((C4 x C2) : C2) : C2) : C2)
Inn(G): D12
Class Preserving subgroup: D12
Group: (C12 x C2) : C2
Aut(G):C2 x D8 x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: D8 x S3
Aut(G):C2 x D8 x S3
Inn(G): C2 x C2 x S3
Class Preserving subgroup: C2 x C2 x S3
Group: (C2 x (C3 : C4)) : C2
Aut(G):C2 x D8 x S3
Inn(G): C2 x C2 x S3
Class Preserving subgroup: C2 x C2 x S3
Group: Q8 x S3
Aut(G):C2 x S3 x S4
Inn(G): C2 x C2 x S3
Class Preserving subgroup: C2 x C2 x S3
Group: (C4 x S3) : C2
Aut(G):C2 x S3 x S4
Inn(G): C2 x C2 x S3
Class Preserving subgroup: C2 x C2 x S3
Group: C2 x C2 x (C3 : C4)
Aut(G):((((C2 x D8) : C2) : C3) : C2) x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C2 x ((C6 x C2) : C2)
Aut(G):((C2 x C2 x C2 x C2) : C2) x S3
Inn(G): D12
Class Preserving subgroup: D12
Group: C12 x C2 x C2
Aut(G):C2 x ((((C2 x D8) : C2) : C3) : C2)
Inn(G): 1
Class Preserving subgroup: 1
Group: C6 x D8
Aut(G):C2 x ((((C4 x C2) : C2) : C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C6 x Q8
Aut(G):C2 x ((((C2 x C2 x C2 x C2) : C3) : C2) : C2)
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C3 x ((C4 x C2) : C2)
Aut(G):C2 x C2 x S4
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C2 x S4
Aut(G):C2 x S4
Inn(G): S4
Class Preserving subgroup: S4
Group: C2 x C2 x A4
Aut(G):S4 x S3
Inn(G): A4
Class Preserving subgroup: A4
Group: (C2 x C2 x C2 x C2) : C3
Aut(G):(((C2 x C2 x C2 x C2) : A5) : C3) : C2
Inn(G): (C2 x C2 x C2 x C2) : C3
Class Preserving subgroup: (C2 x C2 x C2 x C2) : C3
Group: C2 x C2 x C2 x S3
Aut(G):S3 x ((C2 x C2 x C2) : PSL(3,2))
Inn(G): S3
Class Preserving subgroup: S3
Group: C6 x C2 x C2 x C2
Aut(G):C2 x A8
Inn(G): 1
Class Preserving subgroup: 1
Group: C49
Aut(G):C42
Inn(G): 1
Class Preserving subgroup: 1
Group: C7 x C7
Aut(G):GL(2,7)
Inn(G): 1
Class Preserving subgroup: 1
Group: D50
Aut(G):(C25 : C5) : C4
Inn(G): D50
Class Preserving subgroup: D50
Group: C50
Aut(G):C20
Inn(G): 1
Class Preserving subgroup: 1
Group: C5 x D10
Aut(G):C4 x (C5 : C4)
Inn(G): D10
Class Preserving subgroup: D10
Group: (C5 x C5) : C2
Aut(G):((C5 x C5) : SL(2,5)) : C4
Inn(G): (C5 x C5) : C2
Class Preserving subgroup: (C5 x C5) : C2
Group: C10 x C5
Aut(G):GL(2,5)
Inn(G): 1
Class Preserving subgroup: 1
Group: C51
Aut(G):C16 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C13 : C4
Aut(G):C2 x ((C13 : C4) : C3)
Inn(G): D26
Class Preserving subgroup: D26
Group: C52
Aut(G):C12 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C13 : C4
Aut(G):(C13 : C4) : C3
Inn(G): C13 : C4
Class Preserving subgroup: C13 : C4
Group: D52
Aut(G):C2 x ((C13 : C4) : C3)
Inn(G): D26
Class Preserving subgroup: D26
Group: C26 x C2
Aut(G):C12 x S3
Inn(G): 1
Class Preserving subgroup: 1
Group: C53
Aut(G):C52
Inn(G): 1
Class Preserving subgroup: 1
Group: D54
Aut(G):(C27 : C9) : C2
Inn(G): D54
Class Preserving subgroup: D54
Group: C54
Aut(G):C18
Inn(G): 1
Class Preserving subgroup: 1
Group: C3 x D18
Aut(G):C2 x ((C9 : C3) : C2)
Inn(G): D18
Class Preserving subgroup: D18
Group: C9 x S3
Aut(G):C6 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: ((C3 x C3) : C3) : C2
Aut(G):(((C3 x C3) : C3) : C2) : C2
Inn(G): ((C3 x C3) : C3) : C2
Class Preserving subgroup: ((C3 x C3) : C3) : C2
Group: (C9 : C3) : C2
Aut(G):(C9 : C3) : C2
Inn(G): (C9 : C3) : C2
Class Preserving subgroup: (C9 : C3) : C2
Group: (C9 x C3) : C2
Aut(G):(((C3 x ((C3 x C3 x C3) : C3)) : C3) : C2) : C2
Inn(G): (C9 x C3) : C2
Class Preserving subgroup: (C9 x C3) : C2
Group: ((C3 x C3) : C3) : C2
Aut(G):(((C3 x C3) : Q8) : C3) : C2
Inn(G): (C3 x C3) : C2
Class Preserving subgroup: (C3 x C3) : C2
Group: C18 x C3
Aut(G):C2 x (((C3 x C3) : C3) : C2)
Inn(G): 1
Class Preserving subgroup: 1
Group: C2 x ((C3 x C3) : C3)
Aut(G):(((C3 x C3) : Q8) : C3) : C2
Inn(G): C3 x C3
Class Preserving subgroup: C3 x C3
Group: C2 x (C9 : C3)
Aut(G):((C3 x C3) : C3) : C2
Inn(G): C3 x C3
Class Preserving subgroup: C3 x C3
Group: C3 x C3 x S3
Aut(G):GL(2,3) x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C3 x ((C3 x C3) : C2)
Aut(G):C2 x ((((C3 x C3) : Q8) : C3) : C2)
Inn(G): (C3 x C3) : C2
Class Preserving subgroup: (C3 x C3) : C2
Group: (C3 x C3 x C3) : C2
Aut(G):((C3 x C3 x C3) : PSL(3,3)) : C2
Inn(G): (C3 x C3 x C3) : C2
Class Preserving subgroup: (C3 x C3 x C3) : C2
Group: C6 x C3 x C3
Aut(G):GL(3,3)
Inn(G): 1
Class Preserving subgroup: 1
Group: C11 : C5
Aut(G):(C11 : C5) : C2
Inn(G): C11 : C5
Class Preserving subgroup: C11 : C5
Group: C55
Aut(G):C20 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C7 : C8
Aut(G):C2 x C2 x ((C7 : C3) : C2)
Inn(G): D14
Class Preserving subgroup: D14
Group: C56
Aut(G):C6 x C2 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: C7 : Q8
Aut(G):((C7 : C3) : C2) x D8
Inn(G): D28
Class Preserving subgroup: D28
Group: C4 x D14
Aut(G):C2 x C2 x ((C7 : C3) : C2)
Inn(G): D14
Class Preserving subgroup: D14
Group: D56
Aut(G):((C7 : C3) : C2) x D8
Inn(G): D28
Class Preserving subgroup: D28
Group: C2 x (C7 : C4)
Aut(G):((C7 : C3) : C2) x D8
Inn(G): D14
Class Preserving subgroup: D14
Group: (C14 x C2) : C2
Aut(G):C2 x C2 x ((C7 : C3) : C2)
Inn(G): D28
Class Preserving subgroup: D28
Group: C28 x C2
Aut(G):C6 x D8
Inn(G): 1
Class Preserving subgroup: 1
Group: C7 x D8
Aut(G):C6 x D8
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: C7 x Q8
Aut(G):C6 x S4
Inn(G): C2 x C2
Class Preserving subgroup: C2 x C2
Group: (C2 x C2 x C2) : C7
Aut(G):((C2 x C2 x C2) : C7) : C3
Inn(G): (C2 x C2 x C2) : C7
Class Preserving subgroup: (C2 x C2 x C2) : C7
Group: C2 x C2 x D14
Aut(G):((C7 : C3) : C2) x S4
Inn(G): D14
Class Preserving subgroup: D14
Group: C14 x C2 x C2
Aut(G):C6 x PSL(3,2)
Inn(G): 1
Class Preserving subgroup: 1
Group: C19 : C3
Aut(G):(C19 : C9) : C2
Inn(G): C19 : C3
Class Preserving subgroup: C19 : C3
Group: C57
Aut(G):C18 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: D58
Aut(G):(C29 : C7) : C4
Inn(G): D58
Class Preserving subgroup: D58
Group: C58
Aut(G):C28
Inn(G): 1
Class Preserving subgroup: 1
Group: C59
Aut(G):C58
Inn(G): 1
Class Preserving subgroup: 1
Group: C5 x (C3 : C4)
Aut(G):C2 x C4 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: C3 x (C5 : C4)
Aut(G):C2 x C2 x (C5 : C4)
Inn(G): D10
Class Preserving subgroup: D10
Group: C15 : C4
Aut(G):C2 x ((C5 : C4) x S3)
Inn(G): D30
Class Preserving subgroup: D30
Group: C60
Aut(G):C4 x C2 x C2
Inn(G): 1
Class Preserving subgroup: 1
Group: A5
Aut(G):S5
Inn(G): A5
Class Preserving subgroup: A5
Group: C3 x (C5 : C4)
Aut(G):C2 x (C5 : C4)
Inn(G): C5 : C4
Class Preserving subgroup: C5 : C4
Group: C15 : C4
Aut(G):(C5 : C4) x S3
Inn(G): C15 : C4
Class Preserving subgroup: C15 : C4
Group: S3 x D10
Aut(G):S3 x (C5 : C4)
Inn(G): S3 x D10
Class Preserving subgroup: S3 x D10
Group: C5 x A4
Aut(G):C4 x S4
Inn(G): A4
Class Preserving subgroup: A4
Group: C6 x D10
Aut(G):C2 x C2 x (C5 : C4)
Inn(G): D10
Class Preserving subgroup: D10
Group: C10 x S3
Aut(G):C2 x C4 x S3
Inn(G): S3
Class Preserving subgroup: S3
Group: D60
Aut(G):C2 x ((C5 : C4) x S3)
Inn(G): D30
Class Preserving subgroup: D30
Group: C30 x C2
Aut(G):C2 x C4 x S3
Inn(G): 1
Class Preserving subgroup: 1
Group: C61
Aut(G):C60
Inn(G): 1
Class Preserving subgroup: 1
Group: D62
Aut(G):((C31 : C5) : C3) : C2
Inn(G): D62
Class Preserving subgroup: D62
Group: C62
Aut(G):C30
Inn(G): 1
Class Preserving subgroup: 1
Group: C7 : C9
Aut(G):C3 x ((C7 : C3) : C2)
Inn(G): C7 : C3
Class Preserving subgroup: C7 : C3
Group: C63
Aut(G):C6 x C6
Inn(G): 1
Class Preserving subgroup: 1
Group: C3 x (C7 : C3)
Aut(G):((C7 : C3) : C2) x S3
Inn(G): C7 : C3
Class Preserving subgroup: C7 : C3
Group: C21 x C3
Aut(G):C6 x GL(2,3)
Inn(G): 1
Class Preserving subgroup: 1