# Classification of finite N-groups

## Statement

Any finite N-group that is not solvable is an almost simple group. In particular, it contains a simple normal centralizer-free subgroup isomorphic to one of the following:

1. The projective special linear group $PSL(2,q)$ for some prime power $q > 3$.
2. The Suzuki group $Sz(2^{2n + 1})$, $n \ge 1$.
3. The projective special linear group $PSL(3,3)$.
4. The Mathieu group $M_{11}$.
5. The alternating group of degree seven $A_7$.
6. The projective special unitary group $PSU(3,3)$.