Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
524 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#235 | C2 | semidirect |
| 2. C2×C3×C5×M16 | C2 | semidirect |
| 3. C5×#909 | C2 | semidirect |
| 4. C5×#908 | C2 | semidirect |
| 5. C5×#904 | C2 | semidirect |
| 12. C5×#235 | C22 | semidirect |
| 13. C2×C5×D12 | C22 | semidirect |
| 15. C2×C5×Dic6 | C22 | semidirect |
| 16. C3×C5×M16 | C22 | semidirect |
| 17. C2×C3×C5×C8 | C22 | semidirect |
| 18. C5×Dic12 | C22 | semidirect |
| 19. C5×D24 | C22 | semidirect |
| 20. C5×#204 | C22 | semidirect |
| 21. #5748 | C5 | direct (N × H) |
| 26. C2×C5×M16 | D3 | semidirect |
| 43. C2×#235 | C2×C5 | semidirect |
| 44. C2×C3×M16 | C2×C5 | semidirect |
| 45. #909 | C2×C5 | semidirect |
| 46. #908 | C2×C5 | semidirect |
| 47. #904 | C2×C5 | semidirect |
| 60. C5×M16 | C2×D3 | semidirect |
| 61. C2×C5×C8 | C2×D3 | semidirect |
| 77. #235 | C22×C5 | semidirect |
| 78. C2×D12 | C22×C5 | semidirect |
| 80. C2×Dic6 | C22×C5 | semidirect |
| 81. C3×M16 | C22×C5 | semidirect |
| 82. C2×C3×C8 | C22×C5 | semidirect |
| 83. Dic12 | C22×C5 | semidirect |
| 84. D24 | C22×C5 | semidirect |
| 85. #204 | C22×C5 | semidirect |
| 106. C2×M16 | C5×D3 | semidirect |
| 148. M16 | C2×C5×D3 | semidirect |
| 149. C2×C8 | C2×C5×D3 | semidirect |
| 150. C3×C5 | #575 | semidirect |
| 184. C5 | #5748 | direct (N × H) |
| 194. C3 | C5×#575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#235 | 2 |
| C2×C3×C5×M16 | 2 |
| C5×#909 | 2 |
| C5×#908 | 2 |
| C5×#904 | 2 |
| C5×#575 | 3 |
| #5748 | 5 |