2-subnormality is not transitive | There exist subgroups of arbitrarily large subnormal depth | 2-subnormal subgroup (1) Transitive subgroup property (2) |

Automorph-conjugacy is transitive | | Automorph-conjugate subgroup (1) Transitive subgroup property (2) |

Balanced implies transitive | Composition rule for function restriction | Balanced subgroup property (function restriction formalism) (?) Transitive subgroup property (?) |

Base of a wreath product is transitive | Wreath product is associative | Base of a wreath product (1) Transitive subgroup property (2) |

Central factor is transitive | | Central factor (1) Transitive subgroup property (2) |

Characteristically complemented characteristic is transitive | Characteristicity is transitive Characteristicity is strongly join-closed | Characteristically complemented characteristic subgroup (1) Transitive subgroup property (2) |

Characteristicity is transitive | | Characteristic subgroup (1) Transitive subgroup property (2) |

Cocentrality is transitive | | Cocentral subgroup (1) Transitive subgroup property (2) |

Cofactorial automorphism-invariance is not transitive | P-automorphism-invariant not implies characteristic | Cofactorial automorphism-invariant subgroup (1) Transitive subgroup property (2) |

Complete divisibility-closedness is transitive | | Completely divisibility-closed subgroup (1) Transitive subgroup property (2) |

Conjugacy-closedness is transitive | | Conjugacy-closed subgroup (1) Transitive subgroup property (2) |

Conjugate-denseness is transitive | | Conjugate-dense subgroup (1) Transitive subgroup property (2) |

Contranormality is transitive | | Contranormal subgroup (1) Transitive subgroup property (2) |

Direct factor is transitive | | Direct factor (1) Transitive subgroup property (2) |

Divisibility-closedness is transitive | | Divisibility-closed subgroup (1) Transitive subgroup property (2) |

Endomorphism kernel is not transitive | | Endomorphism kernel (1) Transitive subgroup property (2) |

Finite direct power-closed characteristic is transitive | | Finite direct power-closed characteristic subgroup (1) Transitive subgroup property (2) |

Finite-relative-intersection-closed implies transitive | | Finite-relative-intersection-closed subgroup property (?) Transitive subgroup property (?) |

Full invariance is transitive | Balanced implies transitive | Fully invariant subgroup (1) Transitive subgroup property (2) |

Hall is transitive | Index is multiplicative Lagrange's theorem | Hall subgroup (1) Transitive subgroup property (2) |

Homomorph-containment is not transitive | | Homomorph-containing subgroup (1) Transitive subgroup property (2) |

Index is multiplicative | Subgroup containment implies coset containment | Subgroup of finite index (1) Transitive subgroup property (2) Index of a subgroup (1) |

Intermediate characteristicity is not transitive | | Intermediately characteristic subgroup (1) Transitive subgroup property (2) |

Isomorph-freeness is not transitive | | Isomorph-free subgroup (1) Transitive subgroup property (2) Isomorph-containing subgroup (1) |

Lattice-complemented is not transitive | | Lattice-complemented subgroup (1) Transitive subgroup property (2) |

Local powering-invariance is transitive | | Local powering-invariant subgroup (1) Transitive subgroup property (2) |

No common composition factor with quotient group is transitive | No common composition factor with quotient group implies characteristic Characteristic of normal implies normal Third isomorphism theorem | Normal subgroup having no common composition factor with its quotient group (1) Transitive subgroup property (2) |

No nontrivial homomorphism to quotient group is not transitive | | Normal subgroup having no nontrivial homomorphism to its quotient group (1) Transitive subgroup property (2) |

Normality is not transitive | | Normal subgroup (1) Transitive subgroup property (2) Base of a wreath product (?) |

Permutability is not transitive | | Permutable subgroup (1) Transitive subgroup property (2) |

Permutably complemented is not transitive | | Permutably complemented subgroup (1) Transitive subgroup property (2) |

Powering-invariance is transitive | | Powering-invariant subgroup (1) Transitive subgroup property (2) |

Pronormality is not transitive | Normal implies pronormal Pronormal and subnormal implies normal Normality is not transitive | Pronormal subgroup (1) Transitive subgroup property (2) |

Pure definability is transitive | | Purely definable subgroup (1) Transitive subgroup property (2) |

Retract is transitive | | Retract (1) Transitive subgroup property (2) |

Subgroup property between normal and subnormal-to-normal is not transitive | Normality is not transitive | Normal subgroup (?) Subnormal-to-normal subgroup (?) Transitive subgroup property (?) |

Subhomomorph-containment is transitive | | Subhomomorph-containing subgroup (1) Transitive subgroup property (2) |

Transfer condition operator preserves transitivity | | Transitive subgroup property (?) Transfer condition operator-preserved subgroup metaproperty (?) Transfer condition operator (?) |

Transfer-closed characteristicity is transitive | Characteristicity is transitive Transfer condition operator preserves transitivity | Transfer-closed characteristic subgroup (1) Transitive subgroup property (2) |

Transitive and transfer condition implies finite-intersection-closed | Transitive and transfer condition implies finite-relative-intersection-closed Finite-relative-intersection-closed implies finite-intersection-closed | Transitive subgroup property (?) Transfer condition (?) Finite-intersection-closed subgroup property (?) |

Transitive and transfer condition implies finite-relative-intersection-closed | | Transitive subgroup property (?) Transfer condition (?) Finite-relative-intersection-closed subgroup property (?) |

Transitive normality is transitive | | Transitively normal subgroup (1) Transitive subgroup property (2) |

Verbality is transitive | | Verbal subgroup (1) Transitive subgroup property (2) |