Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11747870 | C2 | semidirect |
| 5. C5×#4512 | C2 | semidirect |
| 6. C3×#64737 | C2 | semidirect |
| 7. #11745938 | C2 | semidirect |
| 20. #90947 | C4 | semidirect |
| 21. #90943 | C4 | semidirect |
| 28. #64737 | D3 | semidirect |
| 53. #4512 | D5 | semidirect |
| 217. C3×C5 | #2180 | semidirect |
| 246. C5 | #69264 | semidirect |
| 255. C3 | #10599883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11748069 | 2 |
| #11747870 | 2 |
| #11747560 | 2 |
| #11746339 | 2 |
| C5×#4512 | 2 |
| C3×#64737 | 2 |
| #11745938 | 2 |
| #10599883 | 3 |
| #69264 | 5 |