Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
340 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#6758 | C2 | semidirect |
| 3. C2×C3×C4×AGL(1,𝔽5) | C2 | semidirect |
| 4. #91156 | C2 | direct (N × H) |
| 7. C2×Dic30 | C4 | semidirect |
| 8. C2×C5×D12 | C4 | semidirect |
| 14. #6772 | C4 | semidirect |
| 18. #6758 | C22 | semidirect |
| 20. C3×C4×AGL(1,𝔽5) | C22 | semidirect |
| 23. C2×C4×AGL(1,𝔽5) | D3 | semidirect |
| 33. Dic30 | C2×C4 | semidirect |
| 35. C5×D12 | C2×C4 | semidirect |
| 62. C4×AGL(1,𝔽5) | C2×D3 | semidirect |
| 85. C2×D12 | AGL(1,𝔽5) | semidirect |
| 117. C2×C3×C5 | #104 | semidirect |
| 136. D12 | C2×AGL(1,𝔽5) | semidirect |
| 169. C3×C5 | C2×#104 | semidirect |
| 183. C2×C5 | #805 | semidirect |
| 209. C2×C3 | #4008 | semidirect |
| 212. C5 | C2×#805 | semidirect |
| 225. C3 | C2×#4008 | semidirect |
| 229. C2 | #91156 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6772 | 2 |
| C2×#6758 | 2 |
| C2×C3×C4×AGL(1,𝔽5) | 2 |
| #91156 | 2 |
| C2×#4008 | 3 |
| C2×#805 | 5 |