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. C3×C5×#117 | C2 | semidirect |
| 3. C2×C5×#208 | C2 | semidirect |
| 4. C5×#805 | C2 | semidirect |
| 10. C5×#235 | C4 | semidirect |
| 12. C2×C5×D12 | C4 | semidirect |
| 14. C2×C5×Dic6 | C4 | semidirect |
| 17. C3×C42×C5 | C22 | semidirect |
| 19. C5×#208 | C22 | semidirect |
| 21. #5005 | C5 | direct (N × H) |
| 24. C5×#117 | D3 | semidirect |
| 46. C3×#117 | C2×C5 | semidirect |
| 47. C2×#208 | C2×C5 | semidirect |
| 48. #805 | C2×C5 | semidirect |
| 63. C42×C5 | C2×D3 | semidirect |
| 81. #235 | C4×C5 | semidirect |
| 83. C2×D12 | C4×C5 | semidirect |
| 85. C2×Dic6 | C4×C5 | semidirect |
| 88. C3×C42 | C22×C5 | semidirect |
| 90. #208 | C22×C5 | semidirect |
| 113. #117 | C5×D3 | semidirect |
| 165. C42 | C2×C5×D3 | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | #5005 | 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 |
| C3×C5×#117 | 2 |
| C2×C5×#208 | 2 |
| C5×#805 | 2 |
| C5×#421 | 3 |
| #5005 | 5 |