Complement for a minimal normal subgroup in a solvable group

Question

Let $G$ be a solvable group, $N$ a minimal normal subgroup of $G$ and suppose that exist $H$ a proper subgroup of $G$ such that $G=NH$. I want to prove that there is a complement of $N$ in $G$.

Right now I don't know how to start with this. Any hints?

Answer 1

Hints:

What does '$G$ is solvable' tell you about the structure of a minimal normal subgroup $N$ of $G$?

Use this to show $N\cap H$ is normal in $G$.