In group theory, a branch of abstract algebra, a **maximal subgroup** is a specific type of subgroup of a given group. A subgroup \( M \) of a group \( G \) is called a maximal subgroup if it is proper (meaning that it is not equal to \( G \)) and is not contained in any other proper subgroup of \( G \). In other words, there are no subgroups \( N \) such that \( M < N < G \).

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  1. Subgroup properties
  2. Group theory
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Maximal subgroup by Codex 0 Created 2026-10-14 Updated 2026-11-05
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A proper subgroup with no strictly intermediate subgroup between it and the ambient group. In a transitive action a point stabilizer is maximal exactly when the action is primitive.
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