Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 86 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×C3×C5×SD16 | C2 | semidirect |
| 2. C5×#947 | C2 | semidirect |
| 3. C2×C5×#215 | C2 | semidirect |
| 4. C5×#940 | C2 | semidirect |
| 5. C2×C5×#213 | C2 | semidirect |
| 6. C2×C5×D24 | C2 | semidirect |
| 7. C5×#815 | C2 | semidirect |
| 22. #5176 | C5 | direct (N × H) |
| 24. C2×C5×SD16 | D3 | semidirect |
| 45. C3×C5×C8 | D4 | semidirect |
| 46. C5×C3⋊C8 | D4 | semidirect |
| 47. C2×C3×SD16 | C2×C5 | semidirect |
| 48. #947 | C2×C5 | semidirect |
| 49. C2×#215 | C2×C5 | semidirect |
| 50. #940 | C2×C5 | semidirect |
| 51. C2×#213 | C2×C5 | semidirect |
| 52. C2×D24 | C2×C5 | semidirect |
| 53. #815 | C2×C5 | semidirect |
| 108. C5×C8 | #67 | semidirect |
| 110. C2×SD16 | C5×D3 | semidirect |
| 136. C3×C8 | C5×D4 | semidirect |
| 137. C3⋊C8 | C5×D4 | semidirect |
| 162. C3×C5 | #496 | semidirect |
| 195. C8 | C5×#67 | semidirect |
| 201. C5 | #5176 | direct (N × H) |
| 213. C3 | C5×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD16 | 2 |
| C5×#947 | 2 |
| C2×C5×#215 | 2 |
| C5×#940 | 2 |
| C2×C5×#213 | 2 |
| C2×C5×D24 | 2 |
| C5×#815 | 2 |
| C5×#496 | 3 |
| #5176 | 5 |