Isomorphic Cipher Hierarchy

We can think of the space of ciphers that produce isomorphs as a hierarchy. At the largest level are the ciphers that just produce isomorphs in general, which we call isomorphic ciphers. Within this space, there is a region of perfectly isomorphic ciphers. Within this are the group autokey (GAK) ciphers. Within this are the group ciphertext-autokey ciphers, which can be divided into regions for commutative and non-commutative groups. Within the commutative group-ciphertext autokey region, there is the smallest region in the hierarchy, the (classical) ciphertext-autokey (CTAK) ciphers, corresponding to cyclic groups.

Stated succinctly:

CTAK < GCTAK < GAK < Perfectly Isomorphic < Isomorphic

(It's currently unknown whether extended group-autokey (XGAK) covers all perfectly isomorphic ciphers, but it's definitely known that GAK < XGAK ≤ Perfectly Isomorphic.)

(It's also known that non-associative extensions of GCTAK/GAK based on loops and quasigroups end up not being perfectly isomorphic, this was proven.)

This categorization is very general, and doesn't only apply to the eyes or ciphers like them. For example, ciphers with 83 CT symbols are a tiny slice out of this entire space, spanning each of the regions (well, sort of, there are no non-commutative group-ciphertext autokey ciphers with 83 CT symbols because 83 is prime, so really there's a section of the CTAK region and a larger section of the GAK region).