2-subnormal subgroup | | Normal subgroup Normal closure Normalizer of a subgroup Conjugate subgroups Normal core of normalizer Normal core Subnormal subgroup Subnormal depth Commutator of two subgroups |

3-subnormal subgroup | | Normal subgroup 2-subnormal subgroup |

4-subnormal subgroup | | Subnormal subgroup Subnormal depth 2-subnormal subgroup Normal subgroup 3-subnormal subgroup |

Abelian group | | Center Derived subgroup Normal subgroup Diagonal-in-square operator |

Abelian normal subgroup | | Normal subgroup Abelian group |

Abelian normal subgroup of maximum rank | | Abelian normal subgroup Abelian group Normal subgroup Rank of a p-group Normal rank of a p-group |

Almost normal subgroup | | Normal subgroup Subgroup of finite index Normalizer of a subgroup Index of a subgroup Conjugate subgroups |

Almost subnormal subgroup | | Normal subgroup Subgroup of finite index |

Automorph-conjugate subgroup | | Automorphic subgroups Conjugate subgroups Normal subgroup Normalizer of a subgroup |

Automorphism-faithful normal subgroup | | Automorphism-faithful subgroup Normal subgroup |

C-closed normal subgroup | | C-closed subgroup Normal subgroup |

Central factor | factor in central product product with centralizer is whole group quotient action by outer automorphisms is trivial every inner automorphism restricts to an inner automorphism | Inner automorphism Centralizer Normal subgroup Quotient group maps to outer automorphism group of normal subgroup Internal central product Image-potentially operator Direct factor Upper join-closure operator Cocentral subgroup |

Central factor of normal subgroup | | Central factor Normal subgroup Normal closure |

Centralizer-free normal subgroup | | Centralizer-free subgroup Normal subgroup |

Class two normal subgroup | | Normal subgroup Group of nilpotency class two |

Closed normal subgroup | | Closed subgroup of semitopological group Normal subgroup |

Commutator of a normal subgroup and a subset | | Normal subgroup Commutator of two subsets Commutator |

Commutator-in-center subgroup | | Normal subgroup Commutator-in-centralizer subgroup |

Complete direct factor | | Direct factor Complete group Normal subgroup Complemented normal subgroup |

Complete group | | Normal subgroup Direct factor |

Completely divisibility-closed normal subgroup | | Completely divisibility-closed subgroup Normal subgroup |

Conjugacy-closed normal subgroup | | Conjugacy-closed subgroup Normal subgroup |

Coprime automorphism-faithful normal subgroup | | Coprime automorphism-faithful subgroup Normal subgroup |

Coprime automorphism-invariant normal subgroup | | Coprime automorphism-invariant subgroup Normal subgroup |

Coprime automorphism-invariant normal subgroup of group of prime power order | | Coprime automorphism-invariant normal subgroup Group of prime power order Normal subgroup Normal subgroup of group of prime power order Coprime automorphism-invariant subgroup Coprime automorphism-invariant subgroup of group of prime power order |

Cyclic normal subgroup | | Normal subgroup Cyclic group |

Dedekind group | every subgroup is normal every cyclic subgroup is normal normal closure of element is cyclic | Normal subgroup Inner automorphism Power automorphism Normal closure Levi operator Cyclic group Hamiltonian operator |

Dedekind normal subgroup | | Normal subgroup Dedekind group |

Direct factor | factor in internal direct product normal with normal complement has centralizing complement | Internal direct product Normal subgroup Normal complement Retract |

Direct factor of normal subgroup | | Direct factor Normal subgroup Normal closure |

Divisible normal subgroup | | Normal subgroup Divisible group |

Elementary abelian normal subgroup | | Normal subgroup Elementary abelian group |

Finite normal subgroup | | Normal subgroup Finite group |

Finitely generated normal subgroup | | Normal subgroup Finitely generated group |

Group in which every automorphism is inner | | Normal subgroup Central factor Automorphism of a group Inner automorphism |

Group in which every nontrivial normal subgroup has finite index | | Normal subgroup Subgroup of finite index |

Group in which every normal subgroup is a central factor | | Normal subgroup Central factor |

Group in which every normal subgroup is a direct factor | | Normal subgroup Direct factor |

Group in which every normal subgroup is characteristic | | Normal subgroup Characteristic subgroup Transitively normal subgroup Automorphism of a group Normal automorphism |

Group in which every normal subgroup is fully invariant | | Normal subgroup Fully invariant subgroup |

Group in which every normal subgroup is powering-invariant | | Normal subgroup Powering-invariant subgroup |

Group in which every permutable subgroup is normal | | Permutable subgroup Normal subgroup |

Group in which every pronormal subgroup is normal | | Pronormal subgroup Normal subgroup |

Group in which every retract is a direct factor | | Normal subgroup Retract Direct factor |

Group in which every subgroup is pronormal | | Pronormal subgroup Normal subgroup Hamiltonian operator |

Group whose automorphism group is abelian | abelian automorphism group any two automorphisms commute | Automorphism group of a group Abelian group Normal subgroup Normal subgroup contained in centralizer of derived subgroup |

Group whose inner automorphism group is central in automorphism group | | Inner automorphism group Central subgroup Automorphism group of a group Inner automorphism Central automorphism Normal subgroup Commutator-in-center subgroup |

Groups embeddable as normal subgroups in a finite group with a common complement | | Normal subgroup Permutable complements Normal complement |

Hall subgroup of normal subgroup | | Hall subgroup Normal subgroup |

Hereditarily normal subgroup | | Transitively normal subgroup Dedekind group Normal subgroup Hereditarily operator |