Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 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. C5×D4×Dic3 | C2 | semidirect |
| 3. Dic3×D20 | C2 | semidirect |
| 4. #91116 | C2 | semidirect |
| 5. #90988 | C2 | semidirect |
| 6. #90964 | C2 | semidirect |
| 7. Dic3×#168 | C2 | semidirect |
| 18. C3×#686 | C4 | semidirect |
| 32. C3×C5×D4 | C2×C4 | semidirect |
| 40. C3×D20 | C2×C4 | semidirect |
| 43. C3×#168 | C2×C4 | semidirect |
| 46. D4×Dic3 | D5 | semidirect |
| 58. #686 | Dic3 | direct (N × H) |
| 76. C5×Dic3 | D8 | semidirect |
| 92. C5×D4 | C2×Dic3 | semidirect |
| 100. D20 | C2×Dic3 | semidirect |
| 103. #168 | C2×Dic3 | semidirect |
| 121. C3×D4 | C4×D5 | semidirect |
| 156. C3×C5 | C4×D8 | semidirect |
| 169. Dic3 | #686 | direct (N × H) |
| 180. D4 | D5×Dic3 | semidirect |
| 195. C5 | Dic3×D8 | semidirect |
| 209. C3 | C4×#686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Dic3 | 2 |
| C2×C3×#686 | 2 |
| Dic3×D20 | 2 |
| #91116 | 2 |
| #90988 | 2 |
| #90964 | 2 |
| Dic3×#168 | 2 |
| C4×#686 | 3 |
| Dic3×D8 | 5 |