Composition series of a group

Let \(G\) be a group. A composition series of \(G\) is a finite sequence of subgroups \[ 1=N_{0} \leq N_{1} \leq \cdots \leq N_{k-1} \leq N_{k}=G \] such that \(N_i \normal N_{i+1}\) and \(N_{i+1}/N_i\) is simple for \(0\leq i<k\). The quotients \(N_{i+1}/N_i\) are the composition factors of the series.