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 $$PSU(3,3)$$.

Related facts

 * Classification of finite minimal simple groups
 * Classification of finite simple groups