Abstract Algebra
《Abstract Algebra》 · 第 103 页 · Section 3.4「Composition Series and the Hölder Program」，Theorem 22
Theorem 22. (Jordan–Hölder) Let $G$ be a finite group with $G\neq 1$. Then (1) $G$ has a composition series and (2) The composition factors in a composition series are unique, namely, if $1=N_0\leq N_1\leq\cdots\leq N_r=G$ and $1=M_0\leq M_1\leq\cdots\leq M_s=G$ are two composition series for $G$, then $r=s$ and there is some permutation, $\pi$, of $\{1,2,\ldots,r\}$ such that $M_{\pi(i)}/M_{\pi(i)-1}\cong N_i/N_{i-1}$, $1\leq i\leq r$.