Congruence condition on number of abelian subgroups of order sixteen and exponent dividing eight

Statement in terms of universal congruence condition
The collection of abelian groups of order $$2^4 = 16$$ and exponent dividing $$2^3 = 8$$ (in other words, the abelian non-cyclic groups) is a fact about::collection of groups satisfying a universal congruence condition.

Related facts
For a summary of information, refer collection of groups satisfying a universal congruence condition.


 * Congruence condition on number of abelian subgroups of prime-cube order
 * Congruence condition on number of abelian subgroups of prime-fourth order
 * Congruence condition on number of abelian subgroups of order eight and exponent dividing four
 * Jonah-Konvisser congruence condition on number of abelian subgroups of small prime power order for odd prime
 * Congruence condition on number of abelian subgroups of small prime power order and bounded exponent for odd prime
 * Jonah-Konvisser congruence condition on number of elementary abelian subgroups of small prime power order for odd prime