Let p and q be distinct primes. How many mutually non-isomorphic Abelian groups are there of order $p^2q^4$. I think there are 6 of them:
$p^2q^4$ $q, qp, q^2p$ $q^2, q^2p^2$ $p, pq^3$ $pq, pq^3$ $q, q^3p^2$
in order that the former divides latter ones. The solution says 10. Any ideas?