Here is my numbers using Phenol notation. Note that numbers in asterisk are not by me.
Members: 218
(1*) Googol = 10[1]100
(2*) Googolplex = 10[1]10[1]100
(3*) Googolduplex = 10[1]10[1]10[1]100
(4*) Googoltriplex = 10[1]10[1]10[1]10[1]100
(5*) Googolquadriplex = 10[1]10[1]10[1]10[1]10[1]100
(6*) Googolquintiplex = 10[1]10[1]10[1]10[1]10[1]10[1]100
(7*) Googolsextiplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]100
(8*) Googolseptiplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100
(9*) Googoloctiplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100
(10*) Googolnoniplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100
(11*) Googoldeciplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100
(85*) Monologue = 10[2]1 = 10
(86*) Dialogue = 10[2]2 = 10[1]10 = 10^10 = 10,000,000,000
(87*) Trialogue = 10[2]3 = 10[1]10[1]10 = 10^10^10 = 10^10,000,000,000 = 10^^3
(88*) Tetralogue = 10[2]4 = 10[1]10[1]10[1]10 = 10^10^10^10 = 10^10^10,000,000,000 = 10^^4
(89*) Pentalogue = 10[2]5 = 10[1]10[1]10[1]10[1]10 = 10^10^10^10^10 = 10^^5
(90*) Hexalogue = 10[2]6 = 10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10 = 10^^6
(91*) Heptalogue = 10[2]7 = 10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10 = 10^^7
(92*) Octalogue = 10[2]8 = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10^10 = 10^^8
(93*) Ennalogue = 10[2]9 = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10^10^10 = 10^^9
(94*) Dekalogue = 10[2]10 = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10^10^10^10 = 10^^10
(95*) Endekalogue = 10[2]11 = 10^^11
(96*) Dodekalogue = 10[2]12 = 10^^12
(97*) Triadekalogue = 10[2]13 = 10^^13
(98*) Tetradekalogue = 10[2]14 = 10^^14
(99*) Icosalogue = 10[2]20 = 10^^20
(100*) Triantalogue = 10[2]30 = 10^^30
(101*) Terantalogue  = 10[2]40 = 10^^40
(102*) Hectalogue = 10[2]100 = 10^^100
(103*) Chilialogue = 10[2]1,000 = 10^^1,000
(104*) Myrialogue = 10[2]10,000 = 10^^10,000
(12) Doogol = 10[2]100 = 10^^100
(13) Doogolplex = 10[2]10[2]100
(14) Doogolduplex = 10[2]10[2]10[2]100
(15) Doogoltriplex = 10[2]10[2]10[2]10[2]100
(16) Doogolquadriplex = 10[2]10[2]10[2]10[2]10[2]100
(17) Doogolquintiplex = 10[2]10[2]10[2]10[2]10[2]10[2]100
(105*) Tria-taxis = 10[3]3 = 10[2]10[2]10 = 10^^10^^10 = 10^^^3
(106*) Tetra-taxis = 10[3]4 = 10[2]10[2]10[2]10 = 10^^10^^10^^10 = 10^^^4
(107*) Penta-taxis = 10[3]5 = 10^^^5
(108*) Hexa-taxis = 10[3]6 = 10^^^6
(109*) Hepta-taxis = 10[3]7 = 10^^^7
(110*) Octa-taxis = 10[3]8 = 10^^^8
(111*) Enna-taxis = 10[3]9 = 10^^^9
(112*) Deka-taxis = 10[3]10 = 10^^^10
(113*) Hecta-taxis = 10[3]100 = 10^^^100
(18) Troogol = 10[3]100
(19) Troogolplex = 10[3]10[3]100
(20) Troogolduplex = 10[3]10[3]10[3]100
(21) Troogoltriplex = 10[3]10[3]10[3]10[3]100
(114*) Tria-petaxis = 10[4]3 = 10[3]10[3]10 = 10^^^10^^^10 = 10^^^^3
(115*) Tetra-petaxis = 10[4]4 = 10[3]10[3]10[3]10 = 10^^^10^^^10^^^10 = 10^^^^4
(116*) Deka-petaxis = 10[4]10 = 10^^^^10
(117*) Hecta-petaxis = 10[4]100 = 10^^^^100
(22) Teroogol = 10[4]100
(23) Teroogolplex = 10[4]10[4]100
(24) Teroogolduplex = 10[4]10[4]10[4]100
(25) Teroogoltriplex = 10[4]10[4]10[4]10[4]100
(118*) Deka-exaxis = 10[5]10 = 10^^^^^10
(123*) Hecta-exaxis = 10[5]100 = 10^^^^^100
(26) Petoogol = 10[5]100
(27) Petoogolplex = 10[5]10[5]100
(28) Petoogolduplex = 10[5]10[5]10[5]100
(29) Petoogoltriplex = 10[5]10[5]10[5]10[5]100
(119*) Deka-eptaxis = 10[6]10 = 10^^^^^^10
(124*) Hecta-eptaxis = 10[7]10 = 10^^^^^^100
(30) Ectoogol = 10[6]100
(31) Ectoogolplex = 10[6]10[6]100
(32) Ectoogolduplex = 10[6]10[6]10[6]100
(33) Ectoogoltriplex = 10[6]10[6]10[6]10[6]100
(120*) Deka-octaxis = 10[7]10 = 10^^^^^^^10
(125*) Hecta-octaxis = 10[7]100 = 10^^^^^^^100
(34) Zettoogol = 10[7]100
(35) Zettoogolplex = 10[7]10[7]100
(36) Zettoogolduplex = 10[7]10[7]10[7]100
(37) Zettoogoltriplex = 10[7]10[7]10[7]10[7]100
(121*) Deka-ennaxis = 10[8]10 = 10^^^^^^^^10
(38) Yottoogol = 10[8]100
(39) Yottoogolplex = 10[8]10[8]100
(40) Yottoogolduplex = 10[8]10[8]10[8]100
(41) Yottoogoltriplex = 10[8]10[8]10[8]10[8]100
(122*) Deka-dekaxis = 10[9]10 = 10^^^^^^^^^10
There is the Cookie Fonster's extended SI prefix hoaxordinary realms...
(42) Brontoogol = 10[9]100
(43) Brontoogolplex = 10[9]10[9]100
(44) Brontoogolduplex = 10[9]10[9]10[9]100
(84) Decens = 10[10]10 = 10[0,1]10
(45) Geopoogol = 10[10]100
(46) Geopoogolplex = 10[10]10[10]100
(47) Geopoogolduplex = 10[10]10[10]10[10]100
(48) Gea'hepoogol = 10[11]100
(49) Gea'ottoogol = 10[12]100
(50) Gea'neatoogol = 10[13]100
(51) Gea'deatoogol = 10[14]100
(52) Gea'unatoogol = 10[15]100
(53) Gea'entoogol = 10[16]100
(54) Gea'fitoogol = 10[17]100
(55) Gea'sytoogol = 10[18]100
(56) Gea'brontoogol = 10[19]100
(57) Amosoogol = 10[20]100
(58) Ama'hepoogol = 10[21]100
(59) Ama'ottoogol = 10[22]100
(60) Ama'neatoogol = 10[23]100
(61) Ama'deatoogol = 10[24]100
(62) Ama'unatoogol = 10[25]100
(63) Ama'entoogol = 10[26]100
(64) Ama'fitoogol = 10[27]100
(65) Ama'sytoogol = 10[28]100
(66) Ama'brontoogol = 10[29]100
(67) Haproogol = 10[30]100
(68) Kyroogol = 10[40]100
(69) Pijoogol = 10[50]100
(70) Saganoogol = 10[60]100
(71) Pectroogol = 10[70]100
(72) Nisaboogol = 10[80]100
(73) Zotzoogol = 10[90]100
(74) Alphoogol = 10[100]100
(75) Betoogol = 10[200]100
(76) Gammoogol = 10[300]100
(77) Deltoogol = 10[400]100
(78) Thetoogol = 10[500]100
(79) Iotoogol = 10[600]100
(80) Kappoogol = 10[700]100
(81) Lambdoogol = 10[800]100
(82) Sigmoogol = 10[900]100
(83) Omegoogol = 10[1,000]100
(126) Hectens = 10[0,1]100 = 10[100]10
(127) Decensplex = 10[0,1]10[0,1]10 = 10[0,1]10[10]10 = 10[1,1]3
(128) Decensdulex = 10[0,1]10[0,1]10[0,1]10 = 10[1,1]4
(129) Hectensplex = 10[0,1]10[0,1]100 = 10[0,1]10[100]10
(130) Hectensduplex = 10[0,1]10[0,1]10[0,1]100
(131) Decenstriplex = 10[0,1]5
(132) Expandecens = 10[1,1]10
(133) Expandhectens = 10[1,1]100
(134) Expandecensplex = 10[1,1]10[1,1]10
(135) Expandhectensplex = 10[1,1]10[1,1]100
(136) Multiexpandecens = 10[2,1]10
(137) Powerexpandecens = 10[3,1]10
(138) Teraexpandecens = 10[4,1]10
(139) Petaexpandecens = 10[5,1]10
(140) Exaexpandecens = 10[6,1]10
(141) Zettaexpandecens = 10[7,1]10
(142) Yottaexpandecens = 10[8,1]10
(143) Duedecens = 10[0,2]10 = 10[10,1]10
(144) Duedecensplex = 10[0,2]10[0,2]10
(145) Exploduedecens = 10[1,2]10
(146) Multiexploduedecens = 10[2,2]10
(147) Powerexploduedecens = 10[3,2]10
(148) Teraexploduedecens = 10[4,2]10
(149) Tristo-decens = 10[0,3]10 = 10[10,2]10
(150) Detonatristo-decens = 10[1,3]10
(151) Multidetonatristo-decens = 10[2,3]10
(152) Teristo-decens = 10[0,4]10 = 10[10,3]10
(153) Detonateristo-decens = 10[1,4]10
(154) Petisto-decens = 10[0,5]10 = 10[10,4]10
(155) Ectisto-decens = 10[0,6]10 = 10[10,5]10
(156) Zettisto-decens = 10[0,7]10 = 10[10,6]10
(157) Yottisto-decens = 10[0,8]10 = 10[10,7]10
(158) Brontisto-decens = 10[0,9]10 = 10[10,8]10
(159) Geopisto-decens = 10[0,10]10 = 10[10,9]10
(160) Dis-decens = 10[0,0,1]10 = 10[0,10]10 = 10[10,9]10
(161) Dis-hectens = 10[0,0,1]100 = 10[0,100]10
(162) Dis-decensplex = 10[0,0,1]10[0,0,1]10
(163) Disya-hepe-decens = 10[1,0,1]10
(164) Disya-otte-decens = 10[2,0,1]10
(165) Disya-neate-decens = 10[3,0,1]10
(166) Disya-hapa-decens = 10[0,1,1]10 = 10[10,0,1]10
(167) Disya-hapa-hepe-decens = 10[1,1,1]10
(168) Disya-ottahapa-decens = 10[0,2,1]10 = 10[10,1,1]10
(169) Disya-neatahapa-decens = 10[0,3,1]10
(170) Disya-deatahapa-decens = 10[0,4,1]10
(171) Ottadis-decens = 10[0,0,2]10 = 10[0,10,1]10
(172) Ottadisya-hepe-decens = 10[1,0,2]10
(173) Ottadisya-hapa-decens = 10[0,1,2]10
(174) Ottadisya-ottehapa-decens = 10[0,2,2]10
(175) Neatadis-decens = 10[0,0,3]10 = 10[0,10,2]10
(176) Deatadis-decens = 10[0,0,4]10
(177) Unatadis-decens = 10[0,0,5]10
(178) Entadis-decens = 10[0,0,6]10
(179) Fitadis-decens = 10[0,0,7]10
(180) Sytadis-decens = 10[0,0,8]10
(181) Tris-decens = 10[0,0,0,1]10 = 10[0,0,10]10
(182) Tris-hectens = 10[0,0,0,1]100 = 10[0,0,100]10
(183) Tris-decensplex = 10[0,0,0,1]10[0,0,0,1]10
(184) Trisya-hepe-decens = 10[1,0,0,1]10
(185) Trisya-hapa-decens = 10[0,1,0,1]10
(186) Trisya-dis-decens = 10[0,0,1,1]10
(187) Ottetris-decens = 10[0,0,0,2]10
(188) Neatatris-decens = 10[0,0,0,3]10
(189) Deatatris-decens = 10[0,0,0,4]10
(190) Tetrakis-decens = 10[0,0,0,0,1]10
(191) Ottatetrakis-decens = 10[0,0,0,0,2]10
(192) Pentakis-decens = 10[0,0,0,0,0,1]10 = 10[0{1}1]5
(193) Hexakis-decens = 10[0,0,0,0,0,0,1]10 = 10[0{1}1]6
(194) Heptakis-decens = 10[0,0,0,0,0,0,0,1]10 = 10[0{1}1]7
(195) Octakis-decens = 10[0,0,0,0,0,0,0,0,1]10 = 10[0{1}1]8
(196) Enneakis-decens = 10[0,0,0,0,0,0,0,0,0,1]10 = 10[0{1}1]9
(197) Decakis-decens = 10[0,0,0,0,0,0,0,0,0,0,1]10 = 10[0{1}1]10
(198) Redonahlah = 10[0{1}1]10 = 10[0,0,0,0,0,0,0,0,0,0,1]10
(199) Redonahlah-hects = 10[0{1}1]100
(200) Redonahlahplex = 10[0{1}1]10[0{1}1]10
(201) Redonah-hep = 10[1{1}1]10
(202) Redonah-ott = 10[2{1}1]10
(203) Redonah-neat = 10[3{1}1]10
(204) Redonah-deat = 10[4{1}1]10
(205) Redonah-hapax = 10[0,1{1}1]10
(206) Redonah-hapa-hep = 10[1,1{1}1]10
(207) Redonah-ottapax = 10[0,2{1}1]10
(208) Redonah-neatapax = 10[0,3{1}1]10
(209) Redonah-dis = 10[0,0,1{1}1]10
(210) Redonah-ottadis = 10[0,0,2{1}1]10
(211) Redonah-tris = 10[0,0,0,1{1}1]10
(212) Redonah-tetrakis = 10[0,0,0,0,1{1}1]10
(213) Ottaredonahlah = 10[0{1}2]10
(214) Ottaredonah-hep = 10[1{1}2]10
(215) Ottaredonah-hapax = 10[0,1{1}2]10
(216) Ottaredonah-dis = 10[0,0,1{1}2]10
(217) Neataredonahlah = 10[0{1}3]10
(218) Deataredonahlah = 10[0{1}4]10