Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 94 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×#41 | C2 | semidirect |
| 2. C2×C5×#215 | C2 | semidirect |
| 3. C2×C5×#213 | C2 | semidirect |
| 4. C5×#930 | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 6. C5×#832 | C2 | semidirect |
| 7. C5×#830 | C2 | semidirect |
| 24. #5238 | C5 | direct (N × H) |
| 25. C2×C5×#41 | D3 | semidirect |
| 36. C3×C5×Q8 | D4 | semidirect |
| 39. C3×C5×D4 | D4 | semidirect |
| 52. C2×C3×#41 | C2×C5 | semidirect |
| 53. C2×#215 | C2×C5 | semidirect |
| 54. C2×#213 | C2×C5 | semidirect |
| 55. #930 | C2×C5 | semidirect |
| 56. #835 | C2×C5 | semidirect |
| 57. #832 | C2×C5 | semidirect |
| 58. #830 | C2×C5 | semidirect |
| 109. C5×Q8 | #67 | semidirect |
| 115. C5×D4 | #67 | semidirect |
| 125. C2×#41 | C5×D3 | semidirect |
| 142. C3×Q8 | C5×D4 | semidirect |
| 145. C3×D4 | C5×D4 | semidirect |
| 188. C3×C5 | #449 | semidirect |
| 214. Q8 | C5×#67 | semidirect |
| 220. D4 | C5×#67 | semidirect |
| 236. C5 | #5238 | direct (N × H) |
| 252. C3 | C5×#449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#41 | 2 |
| C2×C5×#215 | 2 |
| C2×C5×#213 | 2 |
| C5×#930 | 2 |
| C5×#835 | 2 |
| C5×#832 | 2 |
| C5×#830 | 2 |
| C5×#449 | 3 |
| #5238 | 5 |