Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 90 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×D3×Q8 | C2 | semidirect |
| 2. C2×C5×#215 | C2 | semidirect |
| 3. C2×C5×#204 | C2 | semidirect |
| 5. C3×C5×#103 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C5×#810 | C2 | semidirect |
| 24. #4806 | C5 | direct (N × H) |
| 30. C5×#103 | D3 | semidirect |
| 35. C3×C5×Q8 | D4 | semidirect |
| 49. C5×Dic6 | D4 | semidirect |
| 52. C2×D3×Q8 | C2×C5 | semidirect |
| 53. C2×#215 | C2×C5 | semidirect |
| 54. C2×#204 | C2×C5 | semidirect |
| 56. C3×#103 | C2×C5 | semidirect |
| 57. (C2×D3)⋊C8 | C2×C5 | semidirect |
| 58. #810 | C2×C5 | semidirect |
| 81. C2×C5×D3 | SD16 | semidirect |
| 109. C5×Q8 | D12 | semidirect |
| 128. #103 | C5×D3 | semidirect |
| 138. C3×Q8 | C5×D4 | semidirect |
| 152. Dic6 | C5×D4 | semidirect |
| 183. C3×C5 | #448 | semidirect |
| 190. C2×D3 | C5×SD16 | semidirect |
| 208. Q8 | C5×D12 | semidirect |
| 227. C5 | #4806 | direct (N × H) |
| 241. C3 | C5×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| C2×C5×#215 | 2 |
| C2×C5×#204 | 2 |
| C5×#895 | 2 |
| C3×C5×#103 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×#810 | 2 |
| C5×#448 | 3 |
| #4806 | 5 |