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. C5×D3×D16 | C2 | semidirect |
| 2. #11746835 | C2 | semidirect |
| 3. #11746341 | C2 | semidirect |
| 4. C3×#64739 | C2 | semidirect |
| 5. #11745825 | C2 | semidirect |
| 6. #11745818 | C2 | semidirect |
| 7. #11745816 | C2 | semidirect |
| 12. Dic120 | C22 | semidirect |
| 16. C3×D80 | C22 | semidirect |
| 18. C3⋊#3926 | C22 | semidirect |
| 19. C3×#3926 | C22 | semidirect |
| 26. #64739 | D3 | semidirect |
| 40. D3×D16 | D5 | semidirect |
| 54. D80 | C2×D3 | semidirect |
| 56. #3926 | C2×D3 | semidirect |
| 174. C3×C5 | #2263 | semidirect |
| 204. C5 | #69377 | semidirect |
| 213. C3 | #10602251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×D16 | 2 |
| #11746835 | 2 |
| #11746341 | 2 |
| C3×#64739 | 2 |
| #11745825 | 2 |
| #11745818 | 2 |
| #11745816 | 2 |
| #10602251 | 3 |
| #69377 | 5 |