Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
376 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 76 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. C3×#4070 | C2 | semidirect |
| 3. C2×#6658 | C2 | semidirect |
| 4. C5×#830 | C2 | semidirect |
| 5. #90968 | C2 | semidirect |
| 12. C2×C3×Dic10 | C22 | semidirect |
| 13. C2×C5×C3⋊C8 | C22 | semidirect |
| 15. C3×C4⋊Dic5 | C22 | semidirect |
| 20. #4070 | D3 | semidirect |
| 42. #830 | D5 | semidirect |
| 49. C2×Dic10 | C2×D3 | semidirect |
| 52. C4⋊Dic5 | C2×D3 | semidirect |
| 58. C22×C3×C5 | SD16 | semidirect |
| 78. C2×C3⋊C8 | C2×D5 | semidirect |
| 121. C22×C5 | #215 | semidirect |
| 142. C3×C5 | #450 | semidirect |
| 145. C22×C3 | #677 | semidirect |
| 180. C5 | #5046 | semidirect |
| 187. C22 | #6658 | semidirect |
| 193. C3 | #65020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D60 | 2 |
| C3×#4070 | 2 |
| C2×#6658 | 2 |
| C5×#830 | 2 |
| #90968 | 2 |
| #65020 | 3 |
| #5046 | 5 |