Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 88 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. C5×#5012 | C2 | semidirect |
| 3. C3×#65297 | C2 | semidirect |
| 4. #11746910 | C2 | semidirect |
| 5. #11745869 | C2 | semidirect |
| 6. #11745861 | C2 | semidirect |
| 7. #11745854 | C2 | semidirect |
| 27. #65297 | D3 | semidirect |
| 53. #5012 | D5 | semidirect |
| 263. C3×C5 | #1697 | semidirect |
| 310. C5 | #71138 | semidirect |
| 325. C3 | #10601662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751116 | 2 |
| C5×#5012 | 2 |
| C3×#65297 | 2 |
| #11746910 | 2 |
| #11745869 | 2 |
| #11745861 | 2 |
| #11745854 | 2 |
| #10601662 | 3 |
| #71138 | 5 |