Exceptional subgroup (awaiting review)

An exceptional subgroup of $\GL_2(\F_p)$ does not contain $\SL_2(\F_p)$ and is not contained in a Borel subgroup or in the normalizer of a Cartan subgroup.

Exceptional subgroups are classified according to their image in $\PGL_2(\F_p)$, which must be isomorphic to one of the alternating groups $A_4$ or $A_5$, or to the symmetric group $S_4$. These groups are labelled using identifiers containing one of the strings A4, A5, S4, as described in [MR:3482279 ].