On the type of conjugacy classes and the set of indices of maximal subgroups

Let G be a nite group. By MT(G) = (m1...mk) we denote the type of conjugacy classes of maximal subgroups of G, which implies that G has exactly k conjugacy classes of maximal subgroups and m1≤...≤ mk are the numbers of conjugates of maximal subgroups of G, where m1 mk. In this paper, we give some new characterizations of nite groups by the type of conjugacy classes of maximal subgroups. By п_t(G) we denote the set of indices of all maximal subgroups of G. We also investigate the in uence of the set of indices of all maximal subgroups on the structure of nite groups.