On Finite Groups Whose All Maximal Subgroups Are Isomorphic

Let G be a finite group.One of the most important and effective ways is that the structure of G is investigated by its maximal subgroups.A group is said to be an MI group if all of its maximal subgroups are isomorphic.As we know from the Sylow theorem,such groups can only be finite p-groups.First of all,we classify the MI groups of order p~3 and p~4.And then we give the completely classification of regular MI groups of order p~5 and p~6,respectively.Lastly,we determine the nonabelian MI groups of order 2~5.