proposition: Lemma norm_sub_max_pgroup pi H M G : [max M | pi.-subgroup(G) M] -> pi.-group H -> H \subset G -> H \subset 'N(M) -> H \subset M.
proof: Proof. by move=> maxM piH sHG /normC; apply: comm_sub_max_pgroup piH sHG. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)