In Neukirch/Schmidt/Wingberg, "Cohomology of Number Fields", the following sentence is part of the proof of Proposition 3.5.7. (here $E$ is a finite group, and $\Phi(E)$ is the Frattini subgroup):
Let $N$ be a minimal normal subgroup of $E$ and assume that $N\subset\Phi(E)$. Since $\Phi(E)$ is nilpotent, the group $N$ is abelian.
I don't understand why this follows. If $N$ were minimal normal in $\Phi(E)$, it would certainly be true, but I don't see why that should be the case.