Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
396 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 68 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×#6777 | C2 | semidirect |
| 2. C2×C3×D40 | C2 | semidirect |
| 3. #91465 | C2 | semidirect |
| 4. C2×#6652 | C2 | semidirect |
| 5. #91104 | C2 | semidirect |
| 6. C5×#821 | C2 | semidirect |
| 7. #90964 | C2 | semidirect |
| 13. C2×C3×D20 | C22 | semidirect |
| 18. C2×C3×C5×C8 | C22 | semidirect |
| 19. C2×C3⋊#168 | C22 | semidirect |
| 20. C5×C4⋊Dic3 | C22 | semidirect |
| 27. C2×D40 | D3 | semidirect |
| 45. C5×D12 | D4 | semidirect |
| 49. C3×D20 | D4 | semidirect |
| 59. #821 | D5 | semidirect |
| 68. C2×D20 | C2×D3 | semidirect |
| 70. C2×C5×C8 | C2×D3 | semidirect |
| 80. C2×D15 | D8 | semidirect |
| 105. C2×C3×C8 | C2×D5 | semidirect |
| 108. C4⋊Dic3 | C2×D5 | semidirect |
| 127. D20 | #67 | semidirect |
| 163. D12 | D20 | semidirect |
| 198. C2×C8 | D3×D5 | semidirect |
| 201. C3×C5 | #447 | semidirect |
| 256. C5 | #5156 | semidirect |
| 275. C3 | #65062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6777 | 2 |
| C2×C3×D40 | 2 |
| #91465 | 2 |
| C2×#6652 | 2 |
| #91104 | 2 |
| C5×#821 | 2 |
| #90964 | 2 |
| #65062 | 3 |
| #5156 | 5 |