Jordan–Hölder Theorem

A theorem stating that for any finite-length group or module, any two composition series have isomorphic simple factor modules up to reordering; equivalently, the multiset of composition factors (simple quotients) and the composition length are invariants of the object.

The theorem that any two composition series of a finite-length object (for example a finite group or a finite-length module) have isomorphic multisets of simple composition factors, possibly in different orders; the multiset of factors is therefore well-defined.