Direct factor implies normal

Statement
Suppose $$G$$ is an internal direct product of subgroups $$H$$ and $$K$$, so that both $$H$$ and $$K$$ are direct factors of $$G$$. Then, both $$H$$ and $$K$$ are normal subgroups of $$G$$.

Intermediate properties

 * Central factor
 * Complemented normal subgroup

Proof
The proof is direct from the definition.