Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 52 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. C3×D5×D8 | C2 | semidirect |
| 2. D5×D24 | C2 | semidirect |
| 3. #91110 | C2 | semidirect |
| 4. C5×#826 | C2 | semidirect |
| 5. #90938 | C2 | semidirect |
| 6. #90937 | C2 | semidirect |
| 7. D5×C3⋊C16 | C2 | semidirect |
| 11. C3×C5×D8 | C22 | semidirect |
| 12. D120 | C22 | semidirect |
| 13. C5×D24 | C22 | semidirect |
| 15. C3×D40 | C22 | semidirect |
| 18. C3⋊#672 | C22 | semidirect |
| 19. C5×C3⋊C16 | C22 | semidirect |
| 22. D5×D8 | D3 | semidirect |
| 44. #826 | D5 | direct (N × H) |
| 49. C5×D8 | C2×D3 | semidirect |
| 53. D40 | C2×D3 | semidirect |
| 71. C3×D8 | C2×D5 | semidirect |
| 75. D24 | C2×D5 | semidirect |
| 77. C3⋊C16 | C2×D5 | semidirect |
| 100. C3×D5 | D16 | semidirect |
| 129. D8 | D3×D5 | semidirect |
| 133. C3×C5 | C2×D16 | semidirect |
| 148. D5 | #826 | direct (N × H) |
| 166. C5 | C2×#826 | semidirect |
| 176. C3 | D5×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×D8 | 2 |
| D5×D24 | 2 |
| #91110 | 2 |
| C5×#826 | 2 |
| #90938 | 2 |
| #90937 | 2 |
| D5×C3⋊C16 | 2 |
| D5×D16 | 3 |
| C2×#826 | 5 |