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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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) | |