Let $G \cong \Bbb{Z}_q \times \Bbb{Z}_q \times \Bbb{Z}_q \times \Bbb{Z}_q$ be an elementary abelian group. I want to know my following calculation is correct?
The number of subgroups of $G$ isomorphic to $\Bbb{Z}_q \times \Bbb{Z}_q$ is equal to $\frac{(q^4-1)(q^4-q)}{(q^2-1)(q^2-q)}$