Find all non-trivial submodules of a direct sum of two non-isomorphic simple modules

Question

Let $R$ be a ring with $1$. Let $M_1$ and $M_2$ be two non-isomorphic simple (nonzero) $R$-modules. Find all non-trivial submodules of $M_1 \bigoplus M_2$.

Solution: $M_1 \bigoplus M_2 \cong M_1 \times M_2$. The submodules of $M_1 \times M_2$ are $M_1 \times \{0\}$, $\{0\} \times M_2$, $M_1 \times M_2$ and $\{0\} \times \{0\}$