Below are some examples of a proper nontrivial subgroup that satisfy the property [[{{{1}}}]] in a group that satisfies the property [[{{{2}}}]].

| Group part | Subgroup part | Quotient part |
---|

2-Sylow subgroup of general linear group:GL(2,3) | General linear group:GL(2,3) | Semidihedral group:SD16 | |

A3 in A4 | Alternating group:A4 | Cyclic group:Z3 | |

A3 in A5 | Alternating group:A5 | Cyclic group:Z3 | |

A3 in S3 | Symmetric group:S3 | Cyclic group:Z3 | Cyclic group:Z2 |

A3 in S4 | Symmetric group:S4 | Cyclic group:Z3 | |

A4 in A5 | Alternating group:A5 | Alternating group:A4 | |

A4 in S4 | Symmetric group:S4 | Alternating group:A4 | Cyclic group:Z2 |

Center of M16 | M16 | Cyclic group:Z4 | Klein four-group |

Center of dihedral group:D16 | Dihedral group:D16 | Cyclic group:Z2 | Dihedral group:D8 |

Center of dihedral group:D8 | Dihedral group:D8 | Cyclic group:Z2 | Klein four-group |

Center of direct product of D8 and Z2 | Direct product of D8 and Z2 | Klein four-group | Klein four-group |

Center of quaternion group | Quaternion group | Cyclic group:Z2 | Klein four-group |

Center of semidihedral group:SD16 | Semidihedral group:SD16 | Cyclic group:Z2 | Dihedral group:D8 |

Center of special linear group:SL(2,3) | Special linear group:SL(2,3) | Cyclic group:Z2 | Alternating group:A4 |

Center of special linear group:SL(2,5) | Special linear group:SL(2,5) | Cyclic group:Z2 | Alternating group:A5 |

Cyclic four-subgroups of symmetric group:S4 | Symmetric group:S4 | Cyclic group:Z4 | |

Cyclic maximal subgroup of dihedral group:D16 | Dihedral group:D16 | Cyclic group:Z8 | Cyclic group:Z2 |

Cyclic maximal subgroup of dihedral group:D8 | Dihedral group:D8 | Cyclic group:Z4 | Cyclic group:Z2 |

Cyclic maximal subgroup of semidihedral group:SD16 | Semidihedral group:SD16 | Cyclic group:Z8 | Cyclic group:Z2 |

Cyclic maximal subgroups of quaternion group | Quaternion group | Cyclic group:Z4 | Cyclic group:Z2 |

D8 in A6 | Alternating group:A6 | Dihedral group:D8 | |

D8 in D16 | Dihedral group:D16 | Dihedral group:D8 | Cyclic group:Z2 |

D8 in S4 | Symmetric group:S4 | Dihedral group:D8 | |

D8 in SD16 | Semidihedral group:SD16 | Dihedral group:D8 | Cyclic group:Z2 |

Derived subgroup of M16 | M16 | Cyclic group:Z2 | Direct product of Z4 and Z2 |

Derived subgroup of dihedral group:D16 | Dihedral group:D16 | Cyclic group:Z4 | Klein four-group |

Diagonally embedded Z4 in direct product of Z8 and Z2 | Direct product of Z8 and Z2 | Cyclic group:Z4 | Cyclic group:Z4 |

Direct product of Z4 and Z2 in M16 | M16 | Direct product of Z4 and Z2 | Cyclic group:Z2 |

First agemo subgroup of direct product of Z4 and Z2 | Direct product of Z4 and Z2 | Cyclic group:Z2 | Klein four-group |

First omega subgroup of direct product of Z4 and Z2 | Direct product of Z4 and Z2 | Klein four-group | Cyclic group:Z2 |

Klein four-subgroup of M16 | M16 | Klein four-group | Cyclic group:Z4 |

Klein four-subgroup of alternating group:A4 | Alternating group:A4 | Klein four-group | Cyclic group:Z3 |

Klein four-subgroup of alternating group:A5 | Alternating group:A5 | Klein four-group | |

Klein four-subgroups of dihedral group:D8 | Dihedral group:D8 | Klein four-group | Cyclic group:Z2 |

Non-central Z4 in M16 | M16 | Cyclic group:Z4 | Cyclic group:Z4 |

Non-characteristic order two subgroups of direct product of Z4 and Z2 | Direct product of Z4 and Z2 | Cyclic group:Z2 | Cyclic group:Z4 |

Non-normal Klein four-subgroups of symmetric group:S4 | Symmetric group:S4 | Klein four-group | |

Non-normal subgroups of M16 | M16 | Cyclic group:Z2 | |

Non-normal subgroups of dihedral group:D8 | Dihedral group:D8 | Cyclic group:Z2 | |

Normal Klein four-subgroup of symmetric group:S4 | Symmetric group:S4 | Klein four-group | Symmetric group:S3 |

Q8 in SD16 | Semidihedral group:SD16 | Quaternion group | Cyclic group:Z2 |

S2 in S3 | Symmetric group:S3 | Cyclic group:Z2 | |

S2 in S4 | Symmetric group:S4 | Cyclic group:Z2 | |

S3 in S4 | Symmetric group:S4 | Symmetric group:S3 | |

S4 in S5 | Symmetric group:S5 | Symmetric group:S4 | |

SL(2,3) in GL(2,3) | General linear group:GL(2,3) | Special linear group:SL(2,3) | Cyclic group:Z2 |

Subgroup generated by double transposition in symmetric group:S4 | Symmetric group:S4 | Cyclic group:Z2 | |

Twisted S3 in A5 | Alternating group:A5 | Symmetric group:S3 | |

Z2 in V4 | Klein four-group | Cyclic group:Z2 | Cyclic group:Z2 |

Z4 in direct product of Z4 and Z2 | Direct product of Z4 and Z2 | Cyclic group:Z4 | Cyclic group:Z2 |

- Property "Satisfies property" (as page type) with input value "{{{1}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
- Property "Satisfies property" (as page type) with input value "{{{2}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
- Property "Stronger than" (as page type) with input value "{{{1}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.

Below are some examples of a proper nontrivial subgroup that *does not* satisfy the property [[{{{1}}}]] in a group that satisfies the property [[{{{2}}}]].

- Property "Dissatisfies property" (as page type) with input value "{{{1}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
- Property "Satisfies property" (as page type) with input value "{{{2}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
- Property "Weaker than" (as page type) with input value "{{{1}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.