Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 56 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. #11746838 | C2 | semidirect |
| 2. D3×D80 | C2 | semidirect |
| 3. D480 | C2 | semidirect |
| 4. C5×#4447 | C2 | semidirect |
| 5. C3×#64669 | C2 | semidirect |
| 6. #11745824 | C2 | semidirect |
| 7. #11745819 | C2 | semidirect |
| 12. D240 | C22 | semidirect |
| 14. C3×Dic40 | C22 | semidirect |
| 18. C3×C5×C32 | C22 | semidirect |
| 19. C5×C3⋊C32 | C22 | semidirect |
| 25. #64669 | D3 | semidirect |
| 45. #4447 | D5 | semidirect |
| 49. Dic40 | C2×D3 | semidirect |
| 56. C5×C32 | C2×D3 | semidirect |
| 78. C3×C32 | C2×D5 | semidirect |
| 79. C3⋊C32 | C2×D5 | semidirect |
| 138. C32 | D3×D5 | semidirect |
| 174. C3×C5 | #2263 | semidirect |
| 204. C5 | #69380 | semidirect |
| 213. C3 | #10600166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11746838 | 2 |
| D3×D80 | 2 |
| D480 | 2 |
| C5×#4447 | 2 |
| C3×#64669 | 2 |
| #11745824 | 2 |
| #11745819 | 2 |
| #10600166 | 3 |
| #69380 | 5 |