All composition series for a finite group G have the same length and the same set of composition factors. For example, the three composition series for C12 = {e,g,…,g11} are
which have composition factors C2, C2, C3 in some order. But knowledge of the composition factors says relatively little about the structure of G. For example, all five groups of order 12 have composition factors C2, C2, C3.