Congruence condition on number of non-cyclic subgroups of prime-cube order for odd prime

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Statement

In terms of universal congruence condition

Let p be an odd prime. The collection of non-cyclic groups of order p^3 is a Collection of groups satisfying a universal congruence condition (?).

Statement with symbols

Let p be an odd prime and P be a finite p-group (i.e., a group of prime power order where the underlying prime is p) containing a non-cyclic subgroup of order p^3. Then, the total number of non-cyclic subgroups of order p^3 in P is congruent to 1 modulo p.