Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 256 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×Q8×Dic3 | C2 | semidirect |
| 3. C2×C5×#215 | C2 | semidirect |
| 5. C5×#832 | C2 | semidirect |
| 6. C5×#821 | C2 | semidirect |
| 7. C5×Dic3⋊C8 | C2 | semidirect |
| 22. #5163 | C5 | direct (N × H) |
| 24. C2×C5×SD16 | D3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 47. C2×C3×SD16 | C2×C5 | semidirect |
| 48. Q8×Dic3 | C2×C5 | semidirect |
| 49. C2×#215 | C2×C5 | semidirect |
| 51. #832 | C2×C5 | semidirect |
| 52. #821 | C2×C5 | semidirect |
| 53. Dic3⋊C8 | C2×C5 | semidirect |
| 80. C5×Dic3 | SD16 | semidirect |
| 97. C5×Q8 | #67 | semidirect |
| 112. C2×SD16 | C5×D3 | semidirect |
| 126. C3×Q8 | C5×D4 | semidirect |
| 166. C3×C5 | #460 | semidirect |
| 179. Dic3 | C5×SD16 | semidirect |
| 188. Q8 | C5×#67 | semidirect |
| 207. C5 | #5163 | direct (N × H) |
| 221. C3 | C5×#460 | 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×Q8×Dic3 | 2 |
| C2×C5×#215 | 2 |
| C5×#940 | 2 |
| C5×#832 | 2 |
| C5×#821 | 2 |
| C5×Dic3⋊C8 | 2 |
| C5×#460 | 3 |
| #5163 | 5 |