Finite p-Groups in Which the Number of Subgroups of Possible Order is Less Than or Equal to $p^3 $

In this paper, groups of order p ⁿ in which the number of subgroups of possible order is less than or equal to p ³ are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order p ⁿ in which the number of subgroups of possible order is less than or equal to p ³ and the classification of groups of order p ⁿ with a cyclic subgroup of index p ² are the same.