Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 91 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×#6705 | C2 | semidirect |
| 3. C3×C4×C5×C8 | C2 | semidirect |
| 4. #91104 | C2 | semidirect |
| 5. C4⋊(C3⋊#168) | C2 | semidirect |
| 19. C4×C5×C8 | D3 | semidirect |
| 31. C3×C5×C8 | D4 | semidirect |
| 35. C3×C4×C8 | D5 | semidirect |
| 53. C3×C4×C5 | M16 | semidirect |
| 75. C5×C8 | D12 | semidirect |
| 81. C4×C8 | D15 | semidirect |
| 95. C3×C8 | D20 | semidirect |
| 102. C4×C5 | ΓL(1,𝔽25) | semidirect |
| 115. C3×C5 | #436 | semidirect |
| 121. C3×C4 | #676 | semidirect |
| 139. C8 | D60 | semidirect |
| 144. C5 | #4688 | semidirect |
| 151. C4 | #6705 | semidirect |
| 154. C3 | #64977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6705 | 2 |
| C4×D60 | 2 |
| C3×C4×C5×C8 | 2 |
| #91104 | 2 |
| C4⋊(C3⋊#168) | 2 |
| #64977 | 3 |
| #4688 | 5 |