Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 144 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×D3×Dic10 | C2 | semidirect |
| 3. C2×Dic60 | C2 | semidirect |
| 4. C2×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C2×C3×#677 | C2 | semidirect |
| 6. C2×#6662 | C2 | semidirect |
| 7. C2×#6657 | C2 | semidirect |
| 8. #91274 | C2 | direct (N × H) |
| 20. D3×Dic10 | C22 | semidirect |
| 24. Dic60 | C22 | semidirect |
| 26. C5×ΓL(1,𝔽25) | C22 | semidirect |
| 27. C3×#677 | C22 | semidirect |
| 28. #6662 | C22 | semidirect |
| 29. #6657 | C22 | semidirect |
| 38. C2×#677 | D3 | semidirect |
| 69. C2×ΓL(1,𝔽25) | D5 | semidirect |
| 89. #677 | C2×D3 | semidirect |
| 121. ΓL(1,𝔽25) | C2×D5 | semidirect |
| 153. C2×C3×C5 | #137 | semidirect |
| 211. C3×C5 | C2×#137 | semidirect |
| 224. C2×C5 | #915 | semidirect |
| 251. C2×C3 | #4055 | semidirect |
| 254. C5 | C2×#915 | semidirect |
| 266. C3 | C2×#4055 | semidirect |
| 269. C2 | #91274 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic10 | 2 |
| C2×#6765 | 2 |
| C2×Dic60 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| C2×C3×#677 | 2 |
| C2×#6662 | 2 |
| C2×#6657 | 2 |
| #91274 | 2 |
| C2×#4055 | 3 |
| C2×#915 | 5 |