Alternating group:A4 | 12 (3) | Order of a group (12) Exponent of a group (6) Derived length (2) Frattini length (1) Minimum size of generating set (2) Subgroup rank of a group (2) Max-length of a group (3) Composition length (3) Chief length (2) Number of conjugacy classes (4) Number of orbits under automorphism group (3) Number of equivalence classes under real conjugacy (3) Number of equivalence classes under rational conjugacy (3) Number of conjugacy classes of real elements (2) Number of conjugacy classes of rational elements (2) Number of conjugacy classes of subgroups (5) Number of subgroups (10) |

Alternating group:A5 | 60 (5) | Order of a group (60) Exponent of a group (30) Frattini length (1) Minimum size of generating set (2) Subgroup rank of a group (2) Max-length of a group (4) Composition length (1) Chief length (1) Number of subgroups (59) Number of conjugacy classes (5) Number of conjugacy classes of subgroups (9) |

Alternating group:A6 | 360 (118) | Order of a group (360) Exponent of a group (60) Frattini length (1) Minimum size of generating set (2) Subgroup rank of a group (2) Max-length of a group (5) Number of subgroups (501) Number of conjugacy classes (7) Number of conjugacy classes of subgroups (22) |

Alternating group:A7 | | Order of a group (2,520) Exponent of a group (420) Frattini length (1) Minimum size of generating set (2) Number of subgroups (3,786) Number of conjugacy classes (9) Number of conjugacy classes of subgroups (40) |

Amalgamated free product of Z and Z over 2Z | | |

Baumslag-Solitar group:BS(1,2) | | |

Binary octahedral group | 48 (28) | Order of a group (48) Exponent of a group (24) Derived length (4) Frattini length (2) Minimum size of generating set (2) Subgroup rank of a group (2) Max-length of a group (5) Number of conjugacy classes (8) Number of subgroups (35) Number of conjugacy classes of subgroups (13) |

Braid group:B3 | | |

Central product of D8 and Q8 | 32 (50) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (4) Subgroup rank of a group (4) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) |

Central product of D8 and Z4 | 16 (13) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) |

Central product of D8 and Z8 | 32 (38) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (2) Derived length (2) Frattini length (3) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) |

Central product of SL(2,5) and SL(2,7) | | Order of a group (20,160) |

Central product of UT(3,3) and Z9 | 81 (14) | Order of a group (81) Prime-base logarithm of order (4) Exponent of a group (9) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Fitting length (1) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) |

Central product of UT(3,Z) and Q | | Nilpotency class (2) Derived length (2) |

Central product of UT(3,Z) and Z identifying center with 2Z | | Nilpotency class (2) Derived length (2) Frattini length (2) Hirsch length of a polycyclic group (3) Polycyclic breadth (3) |

Dicyclic group:Dic20 | 20 (1) | Order of a group (20) Exponent of a group (10) Frattini length (2) Derived length (2) Minimum size of generating set (2) Subgroup rank of a group (2) |

Dihedral group:D10 | 10 (1) | Order of a group (10) Exponent of a group (10) Fitting length (2) Frattini length (1) Derived length (2) |

Dihedral group:D16 | 16 (7) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (3) Derived length (2) Frattini length (3) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (1) Characteristic rank of a p-group (1) Number of conjugacy classes (7) Number of equivalence classes under rational conjugacy (6) Number of conjugacy classes of rational elements (5) |

Dihedral group:D20 | 20 (4) | Order of group (20) Order of a group (10) Frattini length (1) Fitting length (1) Derived length (2) |

Dihedral group:D32 | 32 (18) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (16) Prime-base logarithm of exponent (4) Nilpotency class (4) Derived length (2) Frattini length (4) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (1) Characteristic rank of a p-group (1) |

Dihedral group:D8 | 8 (3) | Underlying prime of p-group (2) Order of a group (8) Prime-base logarithm of order (3) Max-length of a group (3) Chief length (3) Composition length (3) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Fitting length (1) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) Number of conjugacy classes (5) Number of equivalence classes under real conjugacy (5) Number of conjugacy classes of real elements (5) Number of equivalence classes under rational conjugacy (5) Number of conjugacy classes of rational elements (5) Number of subgroups (10) Number of conjugacy classes of subgroups (8) Number of normal subgroups (6) Number of automorphism classes of subgroups (6) Number of characteristic subgroups (4) |

Direct product of A4 and Z2 | 24 (13) | Order of a group (24) Exponent of a group (12) Derived length (2) Frattini length (1) Minimum size of generating set (2) Subgroup rank of a group (3) |

Direct product of A5 and SL(2,7) | | Order of a group (20,160) |

Direct product of A5 and Z2 | 120 (35) | Order of a group (120) Exponent of a group (30) Composition length (2) Chief length (2) Max-length of a group (5) Frattini length (1) |

Direct product of D16 and Z2 | 32 (39) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (3) Derived length (2) Frattini length (3) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (3) Normal rank of a p-group (2) Characteristic rank of a p-group (2) |

Direct product of D8 and V4 | 32 (46) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (4) Subgroup rank of a group (4) Rank of a p-group (4) Normal rank of a p-group (4) Characteristic rank of a p-group (3) |

Direct product of D8 and Z2 | 16 (11) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Fitting length (1) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (2) |

Direct product of D8 and Z3 | 24 (10) | Order of a group (24) Exponent of a group (12) Frattini length (2) Fitting length (1) Derived length (2) Nilpotency class (2) |

Direct product of Q8 and Z2 | 16 (12) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (2) |

Direct product of SL(2,5) and PSL(3,2) | | Order of a group (20,160) |

Direct product of SL(2,5) and SL(2,7) | | Order of a group (40,320) |

Direct product of prime-cube order group:U(3,3) and Z3 | 81 (12) | |

Faithful semidirect product of E8 and Z4 | 32 (6) | Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (3) Derived length (2) Frattini length (2) Minimum size of generating set (2) Subgroup rank of a group (3) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (3) |

Finitary alternating group of countable degree | | |

Finitary symmetric group of countable degree | | |

Free group:F2 | | |

GAPlus(1,R) | | |

General affine group of degree one | | |

General affine group:GA(1,5) | 20 (3) | Order of a group (20) Exponent of a group (20) Frattini length (1) Fitting length (2) Derived length (2) Minimum size of generating set (2) Subgroup rank of a group (2) |

General affine group:GA(1,7) | 42 (1) | Order of a group (42) Exponent of a group (42) Frattini length (1) Fitting length (2) Derived length (2) Subgroup rank of a group (2) Minimum size of generating set (2) |

General affine group:GA(1,8) | 56 (11) | Order of a group (56) Exponent of a group (14) Frattini length (1) Fitting length (2) Derived length (2) Minimum size of generating set (2) Subgroup rank of a group (3) |

General affine group:GA(1,9) | 72 (39) | Order of a group (72) Exponent of a group (24) Frattini length (1) Fitting length (2) Minimum size of generating set (2) Subgroup rank of a group (2) |

General affine group:GA(1,Q) | | |

General linear group over reals | | |

General linear group:GL(2,3) | 48 (29) | Order of a group (48) Exponent of a group (24) Derived length (4) Frattini length (2) Minimum size of generating set (2) Subgroup rank of a group (2) Max-length of a group (5) Composition length (5) Chief length (4) Number of subgroups (55) Number of conjugacy classes (8) Number of conjugacy classes of subgroups (16) |

General linear group:GL(2,R) | | Dimension of an algebraic group (4) Dimension of a real Lie group (4) |

General linear group:GL(2,Z) | | |

Generalized dihedral group for 2-quasicyclic group | | |

Generalized dihedral group for additive group of 2-adic integers | | |

Generalized dihedral group for direct product of Z4 and Z4 | 32 (34) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (2) |