Let $G$ and $H$ be finite groups then proof that $l(G \times H) = l(G) + l(H)$ and $fact(G \times H) = fact(G) \cup fact(H)$. Where $l$ is the length of any of its composition series and $fact$ are the factors of any of its composition series.
I don't really see how I would build a composition series for the product.