Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5699 | C2 | semidirect |
| 2. #11751168 | C2 | semidirect |
| 4. #11746915 | C2 | semidirect |
| 5. C3×#64763 | C2 | semidirect |
| 6. #11745850 | C2 | semidirect |
| 7. #11745847 | C2 | semidirect |
| 34. #64763 | D3 | semidirect |
| 65. #5699 | D5 | semidirect |
| 322. C3×C5 | #1657 | semidirect |
| 369. C5 | #68371 | semidirect |
| 385. C3 | #10602748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5699 | 2 |
| #11751168 | 2 |
| #11747032 | 2 |
| #11746915 | 2 |
| C3×#64763 | 2 |
| #11745850 | 2 |
| #11745847 | 2 |
| #10602748 | 3 |
| #68371 | 5 |