subgroups of $G\times H$ in terms of subgroups of $G$ and $H$. Let's denote all subgroups of a group $G$ by $\text{sub}(G)$.
Let $G$ and $H$ be groups. Can $\text{sub}(G\times H)$ be determined in terms of $\text{sub}(G)$ and $\text{sub}(H)$?
$G\times H$ is the direct product.

See Goursat's lemma (http://en.wikipedia.org/wiki/Goursat's_lemma).
