Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 284 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×SD16 | C2 | semidirect |
| 2. C5×#944 | C2 | semidirect |
| 3. C2×C5×#215 | C2 | semidirect |
| 5. C2×C5×#214 | C2 | semidirect |
| 6. C2×C5×#204 | C2 | semidirect |
| 7. C5×C8×Dic3 | C2 | semidirect |
| 22. #5175 | C5 | direct (N × H) |
| 26. 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. #944 | C2×C5 | semidirect |
| 49. C2×#215 | C2×C5 | semidirect |
| 51. C2×#214 | C2×C5 | semidirect |
| 52. C2×#204 | C2×C5 | semidirect |
| 53. C8×Dic3 | C2×C5 | semidirect |
| 77. C5×Dic3 | SD16 | semidirect |
| 107. C5×C8 | #67 | semidirect |
| 111. C2×SD16 | C5×D3 | semidirect |
| 134. C3×C8 | C5×D4 | semidirect |
| 135. C3⋊C8 | C5×D4 | semidirect |
| 159. C3×C5 | #492 | semidirect |
| 169. Dic3 | C5×SD16 | semidirect |
| 190. C8 | C5×#67 | semidirect |
| 195. C5 | #5175 | direct (N × H) |
| 206. C3 | C5×#492 | 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×#944 | 2 |
| C2×C5×#215 | 2 |
| C5×#940 | 2 |
| C2×C5×#214 | 2 |
| C2×C5×#204 | 2 |
| C5×C8×Dic3 | 2 |
| C5×#492 | 3 |
| #5175 | 5 |