I have encountered the following statement which I cannot prove:
A finite group $G$ is not solvable if and only if there is a NORMAL series with
$$ 1\lhd H \lhd N \lhd G $$
such that $N/H$ is a nonabelian simple group or product of isomorphic nonabelian simple groups.
I guess by a normal series is meant the usual, that any term of the series is normal in the whole group $G$.
Any help would be greatly appreciated.