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Intermediate notions between [[closure-characteristic subgroup]] and [[Hall subgroup]] | Intermediate notions between [[closure-characteristic subgroup]] and [[Hall subgroup]]# |
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Join of Sylow subgroups | Join of Sylow subgroups |

Join of automorph-conjugate subgroups | Join of automorph-conjugate subgroups |

Subgroup whose normal closure is fully invariant | Subgroup whose normal closure is fully invariant |

Subgroup whose normal closure is homomorph-containing | Subgroup whose normal closure is homomorph-containing |