Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
536 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 536 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. C5×#1009 | C2 | semidirect |
| 2. C3×C5×#131 | C2 | semidirect |
| 3. C5×#908 | C2 | semidirect |
| 4. C5×#904 | C2 | semidirect |
| 5. C2×C5×D24 | C2 | semidirect |
| 10. C5×#235 | C22 | semidirect |
| 11. C2×C5×D12 | C22 | semidirect |
| 12. C3×C5×M16 | C22 | semidirect |
| 13. C2×C3×C5×C8 | C22 | semidirect |
| 14. C5×Dic12 | C22 | semidirect |
| 15. C5×D24 | C22 | semidirect |
| 16. C5×D24 | C22 | semidirect |
| 17. C5×#204 | C22 | semidirect |
| 18. #5752 | C5 | direct (N × H) |
| 23. C5×#131 | D3 | semidirect |
| 35. #1009 | C2×C5 | semidirect |
| 36. C3×#131 | C2×C5 | semidirect |
| 37. #908 | C2×C5 | semidirect |
| 38. #904 | C2×C5 | semidirect |
| 39. C2×D24 | C2×C5 | semidirect |
| 49. C5×M16 | C2×D3 | semidirect |
| 50. C2×C5×C8 | C2×D3 | semidirect |
| 61. #235 | C22×C5 | semidirect |
| 62. C2×D12 | C22×C5 | semidirect |
| 63. C3×M16 | C22×C5 | semidirect |
| 64. C2×C3×C8 | C22×C5 | semidirect |
| 65. Dic12 | C22×C5 | semidirect |
| 66. D24 | C22×C5 | semidirect |
| 67. D24 | C22×C5 | semidirect |
| 68. #204 | C22×C5 | semidirect |
| 84. #131 | C5×D3 | semidirect |
| 114. M16 | C2×C5×D3 | semidirect |
| 115. C2×C8 | C2×C5×D3 | semidirect |
| 116. C3×C5 | #576 | semidirect |
| 140. C5 | #5752 | direct (N × H) |
| 147. C3 | C5×#576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1009 | 2 |
| C3×C5×#131 | 2 |
| C5×#908 | 2 |
| C5×#904 | 2 |
| C2×C5×D24 | 2 |
| C5×#576 | 3 |
| #5752 | 5 |