Congruence condition on number of non-cyclic subgroups of prime-cube order for odd prime
In terms of universal congruence condition
Let be an odd prime. The collection of non-cyclic groups of order is a Collection of groups satisfying a universal congruence condition (?).
Statement with symbols
Let be an odd prime and be a finite -group (i.e., a group of prime power order where the underlying prime is ) containing a non-cyclic subgroup of order . Then, the total number of non-cyclic subgroups of order in is congruent to modulo .