Definition:Decomposable Group

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

Then $\left({G, \circ}\right)$ is decomposable there exists a decomposition of $\left({G, \circ}\right)$.

That is, $\left({G, \circ}\right)$ is the internal direct product of two (or more) proper subgroups of $G$.