In this paper,groups of order pn in which the number of subgroups of possible order is less than or equal to p3 ale classified.It turns out that if p>2,n≥ 5,then the classification of groups of order pn in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order pn with a cyclic subgroup of index p2 ale the same.