Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11756442 | C2 | semidirect |
| 2. C3×C5×#496 | C2 | semidirect |
| 3. #11751175 | C2 | semidirect |
| 4. #11746361 | C2 | semidirect |
| 5. #11746285 | C2 | semidirect |
| 9. C3×C5×#127 | C22 | semidirect |
| 18. C3×C5×#97 | C22 | semidirect |
| 19. #91087 | C22 | semidirect |
| 22. C5×#496 | D3 | semidirect |
| 49. C3×#496 | D5 | semidirect |
| 55. C5×#127 | C2×D3 | semidirect |
| 64. C5×#97 | C2×D3 | semidirect |
| 90. C3×#127 | C2×D5 | semidirect |
| 99. C3×#97 | C2×D5 | semidirect |
| 125. #496 | D15 | semidirect |
| 188. #127 | C2×D15 | semidirect |
| 196. #97 | C2×D15 | semidirect |
| 258. C3×C5 | #1655 | semidirect |
| 303. C5 | #71326 | semidirect |
| 317. C3 | #10602119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756442 | 2 |
| C3×C5×#496 | 2 |
| #11751175 | 2 |
| #11746361 | 2 |
| #11746285 | 2 |
| #10602119 | 3 |
| #71326 | 5 |