The International Cloud Atlas states that there are 5 main types of cirrus clouds. There's cirrus castellanus, cirrus fibratus, cirrus floccus, cirrus spissatus, and cirrus uncinus. These are the main shapes they can take, and they come in four varieties. These varieties are intortus, radiatus, vertebratus, and duplicatus.
If clouds have a question mark next to them I couldn't find photos them, or they don't exist. If anyone explains why a certain cloud subtype can't exist I'll put that under it's description.
For image sources, just click on the images.
Cirrus fibratus are defined by being made of very long straight streaks that resemble pulled fibers. They are easily mistaken for cirrus uncinus, however uncinus will have curled tails at the end.
Cirrus Fibratus Intortus?
Fibratus that form straight intersecting lines, often in chaotic ways
Might not exist.
Cirrus floccus resembles wool, like castellanus it can be mistaken for altocumulus very easily, however these clouds are mostly transparent, and will often have virga precipitation tails with them.
Cirrus spissatus is a type of cirrus is defined by being very dense. They are capable of blocking the sun if it winds up in front of it. These clouds like to hang out around cumulonimbus.
Cirrus Unicus are defined by their curls. Very similar to fibratus, but are often a bit shorter and more sparsley populated in the sky. These are often a sign that a storm is coming.
Cirrus Uncinus Intortus?
Uncinus that's scattered about unpredictably, like a pile of fluffy fish hooks.
Might not exist.
Cirrus Uncinus Radiatus?
Uncinus that radiates out from a point in the distance.
.Cirrus Uncinus Vertebratus?
Exists in theory, but I have no idea what it would look like.
Might not exist.
Cirrus Castellanus is a subset of cirrus clouds that are defined by cumuliform tops that trickle up like the crenellations of a castle.
Cirrus Castellanus Intortus?
Castellanus that form chaotic intersections. They resemble a field of wispy spikes.
Might not exist.
Cirrus Castellanus Radiatus?
Castellanus that streak out from a point in the distance, like the highways of a city that meet at some point far away but are cut off before the meeting point
Might not exist.
Cirrus Castellanus Vertebratus?
Castellanus that streaks out from a center line.
Might not exist.