Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 118 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×C3×C5×M16 | C2 | semidirect |
| 3. C5×#926 | C2 | semidirect |
| 4. C5×#825 | C2 | semidirect |
| 10. C5×#235 | C4 | semidirect |
| 12. C2×C5×D12 | C4 | semidirect |
| 14. C2×C5×Dic6 | C4 | semidirect |
| 16. C3×C5×M16 | C22 | semidirect |
| 20. C4×C5×Dic3 | C22 | semidirect |
| 21. #5139 | C5 | direct (N × H) |
| 23. C2×C5×M16 | D3 | semidirect |
| 46. C2×C3×M16 | C2×C5 | semidirect |
| 47. #926 | C2×C5 | semidirect |
| 48. #825 | C2×C5 | semidirect |
| 59. C5×M16 | C2×D3 | semidirect |
| 81. #235 | C4×C5 | semidirect |
| 83. C2×D12 | C4×C5 | semidirect |
| 85. C2×Dic6 | C4×C5 | semidirect |
| 87. C3×M16 | C22×C5 | semidirect |
| 91. C4×Dic3 | C22×C5 | semidirect |
| 112. C2×M16 | C5×D3 | semidirect |
| 161. M16 | C2×C5×D3 | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | #5139 | direct (N × H) |
| 221. C3 | C5×#421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#235 | 2 |
| C2×C3×C5×M16 | 2 |
| C5×#926 | 2 |
| C5×#825 | 2 |
| C5×#421 | 3 |
| #5139 | 5 |