Jordan-Holder Theorem
A composition series of a group G is a chain of subgroups of G satisfying  where  stands for normal subgroup such that the quotient group of each link in the chain is a simple group.
For a finite group G, such a composition series certainly exists; and the isomorphism classes of simple groups are unique, up to permutation. This is called the Jordan-Hölder theorem.
See also Normal series.
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