What is the number of homomorphisms from $\mathbb{Z}_{10}\times \mathbb{Z}_{25}\to S_4$
From searching similar questions I know that if $\phi:\mathbb{Z}_{10}\times \mathbb{Z}_{25}\to S_4$ is a homomorphism then the order of $\phi(x)$ divides the order of $x$, but I fail to see how to apply this here. I also know $\mathbb{Z}_{10}\times \mathbb{Z}_{25}$ is not a cyclic group.
Hints, answers are appreciated, thank you in advance.