An Example of a Relatively Maximal Nonpronormal Subgroup of Odd Order in a Finite Simple Group

Abstract We prove the existence of a triple (X, G, H), where X is a class of finite groups consisting of groups of odd order which is complete (i. e. , closed under subgroups, homomorphic images, and extensions), G is a finite simple group, H is an X -maximal subgroup in G, and H is not pronormal in G.