Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
1324 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 200 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. C23×D3×D5 | C2 | semidirect |
| 2. C22×D60 | C2 | semidirect |
| 3. C22×#1203 | C2 | semidirect |
| 4. C22×#1202 | C2 | semidirect |
| 5. C2×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C2×C3×#685 | C2 | semidirect |
| 7. C2×#6667 | C2 | semidirect |
| 8. #91476 | C2 | direct (N × H) |
| 11. C23×D15 | C22 | semidirect |
| 17. C22×D3×D5 | C22 | semidirect |
| 18. C22×C3×C4×C5 | C22 | semidirect |
| 20. C2×D60 | C22 | semidirect |
| 21. C22×C5×Dic3 | C22 | semidirect |
| 22. C22×C3×Dic5 | C22 | semidirect |
| 24. C2×#1203 | C22 | semidirect |
| 26. C2×#1202 | C22 | semidirect |
| 27. C5×(C2×D3)⋊C4 | C22 | semidirect |
| 28. C3×#685 | C22 | semidirect |
| 29. #6667 | C22 | semidirect |
| 37. C2×#685 | D3 | semidirect |
| 45. C22×D15 | D4 | semidirect |
| 47. C22×D15 | C23 | semidirect |
| 50. C22×C5×D3 | D4 | semidirect |
| 54. C22×C3×D5 | D4 | semidirect |
| 61. C2×C3×C4×C5 | C23 | semidirect |
| 64. C2×C5×Dic3 | C23 | semidirect |
| 66. C2×C3×Dic5 | C23 | semidirect |
| 75. C2×(C2×D3)⋊C4 | D5 | semidirect |
| 86. C22×C4×C5 | C2×D3 | semidirect |
| 89. C22×Dic5 | C2×D3 | semidirect |
| 96. #685 | C2×D3 | semidirect |
| 109. C2×D15 | C2×D4 | semidirect |
| 113. C2×C5×D3 | C2×D4 | semidirect |
| 117. C2×C3×D5 | C2×D4 | semidirect |
| 131. C22×C3×C4 | C2×D5 | semidirect |
| 134. C22×Dic3 | C2×D5 | semidirect |
| 141. (C2×D3)⋊C4 | C2×D5 | semidirect |
| 161. C22×D5 | D12 | semidirect |
| 166. C2×C4×C5 | C22×D3 | semidirect |
| 169. C2×Dic5 | C22×D3 | semidirect |
| 180. C2×C3×C5 | #120 | semidirect |
| 207. C22×D3 | D20 | semidirect |
| 212. C2×C3×C4 | C22×D5 | semidirect |
| 215. C2×Dic3 | C22×D5 | semidirect |
| 238. C2×D5 | C2×D12 | semidirect |
| 258. C22×C4 | D3×D5 | semidirect |
| 262. C3×C5 | C2×#120 | semidirect |
| 283. C2×D3 | C2×D20 | semidirect |
| 288. C2×C5 | #882 | semidirect |
| 324. C2×C4 | C2×D3×D5 | semidirect |
| 326. C2×C3 | #4028 | semidirect |
| 333. C5 | C2×#882 | semidirect |
| 358. C3 | C2×#4028 | semidirect |
| 363. C2 | #91476 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D3×D5 | 2 |
| C22×D60 | 2 |
| C22×#1203 | 2 |
| C22×#1202 | 2 |
| C2×C5×(C2×D3)⋊C4 | 2 |
| C2×C3×#685 | 2 |
| C2×#6667 | 2 |
| #91476 | 2 |
| C2×#4028 | 3 |
| C2×#882 | 5 |