Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
504 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C42×C5 | C22 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #560 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #91765 | C2 | semidirect |
| 2. C5×#874 | C2 | semidirect |
| 3. C3×#4022 | C2 | semidirect |
| 4. #91475 | C2 | semidirect |
| 5. #91453 | C2 | semidirect |
| 6. #91423 | C2 | semidirect |
| 7. #91416 | C2 | semidirect |
| 11. C2×C5×D12 | C22 | semidirect |
| 14. C2×D3×Dic5 | C22 | semidirect |
| 15. C3×C42×C5 | C22 | semidirect |
| 17. #6712 | C22 | semidirect |
| 19. C3×#683 | C22 | semidirect |
| 21. (C2×D3)⋊Dic5 | C22 | semidirect |
| 29. #4022 | D3 | semidirect |
| 49. #874 | D5 | semidirect |
| 56. C42×C5 | C2×D3 | semidirect |
| 62. #683 | C2×D3 | semidirect |
| 79. C2×D12 | C2×D5 | semidirect |
| 83. C3×C42 | C2×D5 | semidirect |
| 149. C42 | D3×D5 | semidirect |
| 150. C3×C5 | #560 | semidirect |
| 185. C5 | #5711 | semidirect |
| 197. C3 | #66054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91765 | 2 |
| C5×#874 | 2 |
| C3×#4022 | 2 |
| #91475 | 2 |
| #91453 | 2 |
| #91423 | 2 |
| #91416 | 2 |
| #66054 | 3 |
| #5711 | 5 |