Find the number of subgroups of $\mathbb{Z}_{100}\times\mathbb{Z}_{500}$ are isomorphic with $\mathbb{Z}_{25}\times\mathbb{Z}_{25}$.
Using the order of elements in $\mathbb{Z}_{100}\times\mathbb{Z}_{500}$, it was so tedious work for me.
Is there an another way to solve the above problem?