Subset Product of Subgroups

Theorem
Let $\left({G, \circ}\right)$ be a group.

Let $H, K$ be subgroups of $G$.

Then $H \circ K$ is a subgroup of $G$ iff $H$ and $K$ are permutable.

That is:

$H \circ K$ is a subgroup of $G$ iff:
 * $H \circ K = K \circ H$

where $H \circ K$ denotes subset product.