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

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) |

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 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) |

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 | | |

Grigorchuk group | | Underlying prime of p-group (2) Minimum size of generating set (3) |

Group of unit quaternions | | Dimension of an algebraic group (3) Dimension of a real Lie group (3) |

Higman-Sims group | | Order of a group (44,352,000) Number of conjugacy classes (24) |

Holomorph of Z9 | 54 (6) | Order of a group (54) Exponent of a group (18) Frattini length (2) Fitting length (2) Derived length (2) Minimum size of generating set (2) Subgroup rank of a group (2) |

Infinite dihedral group | | Derived length (2) Fitting length (2) Frattini length (1) Subgroup rank of a group (2) |

Inner automorphism group of wreath product of Z2 and A5 | 960 (11358) | |

Janko group:J2 | | Order of a group (604,800) Number of conjugacy classes (21) |

Mathieu group:M10 | 720 (765) | Order of a group (720) Exponent of a group (120) Frattini length (1) |

Mathieu group:M11 | | Order of a group (7,920) Exponent of a group (1,320) Frattini length (1) |

Mathieu group:M12 | | Order of a group (95,040) Exponent of a group (1,320) |

Mathieu group:M22 | | Order of a group (443,520) Exponent of a group (9,240) Number of conjugacy classes (12) |

Mathieu group:M23 | | Order of a group (10,200,960) Exponent of a group (212,520) Number of conjugacy classes (17) |

Mathieu group:M24 | | Order of a group (244,823,040) Exponent of a group (212,520) Number of conjugacy classes (26) |

Mathieu group:M9 | 72 (41) | Order of a group (72) Exponent of a group (12) Derived length (3) Frattini length (1) Fitting length (2) Minimum size of generating set (2) Subgroup rank of a group (2) Max-length of a group (5) Number of subgroups (68) Number of conjugacy classes (6) Number of conjugacy classes of subgroups (14) |

Metaplectic group:Mp(2,R) | | Composition length (3) Chief length (3) Dimension of a real Lie group (3) |

Projective special linear group:PSL(2,11) | 660 (13) | Order of a group (660) Exponent of a group (330) Frattini length (1) Chief length (1) Composition length (1) Number of conjugacy classes (8) Number of equivalence classes under rational conjugacy (6) Number of conjugacy classes of subgroups (16) Number of subgroups (620) Number of automorphism classes of subgroups (14) |

Projective special linear group:PSL(2,13) | 1,092 (25) | Order of a group (1,092) Exponent of a group (546) Frattini length (1) Chief length (1) Composition length (1) Number of conjugacy classes (9) Number of equivalence classes under rational conjugacy (6) Number of conjugacy classes of subgroups (16) Number of subgroups (942) |

Projective special linear group:PSL(2,17) | | Order of a group (2,448) Exponent of a group (1,224) Number of conjugacy classes (11) Number of conjugacy classes of subgroups (22) Number of subgroups:2420 (?) |