general/subgroup-properties

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Quasinormal subgroup
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Subnormal subgroup
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Malnormal subgroup
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Maximal subgroup

Term in mathematics

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Conjugate-permutable subgroup
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Transitively normal subgroup

Property of a subgroup in mathematics

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Seminormal subgroup
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Pure subgroup
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Characteristic subgroup

Subgroup mapped to itself under every automorphism of the parent group

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Normal subgroup

Subgroup invariant under conjugation

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Special abelian subgroup
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Paranormal subgroup
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