Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
684 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 2. C22×D3×Dic5 | C2 | semidirect |
| 3. C2×#6719 | C2 | semidirect |
| 4. C2×C3×C22⋊Dic5 | C2 | semidirect |
| 5. #91555 | C2 | direct (N × H) |
| 6. C2×#6669 | C2 | semidirect |
| 7. C2×#6668 | C2 | semidirect |
| 8. C2×(C2×D3)⋊Dic5 | C2 | semidirect |
| 20. C2×D3×Dic5 | C22 | semidirect |
| 21. #6719 | C22 | semidirect |
| 22. C3×C22⋊Dic5 | C22 | semidirect |
| 23. #6669 | C22 | semidirect |
| 24. #6668 | C22 | semidirect |
| 25. (C2×D3)⋊Dic5 | C22 | semidirect |
| 31. C2×C22⋊Dic5 | D3 | semidirect |
| 77. C22⋊Dic5 | C2×D3 | semidirect |
| 144. C2×C3×C5 | #123 | semidirect |
| 203. C3×C5 | C2×#123 | semidirect |
| 223. C2×C5 | #883 | semidirect |
| 249. C2×C3 | #4081 | semidirect |
| 254. C5 | C2×#883 | semidirect |
| 272. C3 | C2×#4081 | semidirect |
| 275. C2 | #91555 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#67 | 2 |
| C22×D3×Dic5 | 2 |
| C2×#6719 | 2 |
| C2×C3×C22⋊Dic5 | 2 |
| #91555 | 2 |
| C2×#6669 | 2 |
| C2×#6668 | 2 |
| C2×(C2×D3)⋊Dic5 | 2 |
| C2×#4081 | 3 |
| C2×#883 | 5 |