Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 207 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. C3×C5×#576 | C2 | semidirect |
| 2. #11756512 | C2 | semidirect |
| 3. #11751296 | C2 | semidirect |
| 4. #11751295 | C2 | semidirect |
| 5. C2×#91111 | C2 | semidirect |
| 6. #11751248 | C2 | semidirect |
| 7. #11751241 | C2 | semidirect |
| 16. C2×Dic60 | C22 | semidirect |
| 17. #91793 | C22 | semidirect |
| 18. #91113 | C22 | semidirect |
| 19. #91112 | C22 | semidirect |
| 20. #91111 | C22 | semidirect |
| 21. #91111 | C22 | semidirect |
| 22. #91110 | C22 | semidirect |
| 23. #91096 | C22 | semidirect |
| 24. C2×C3⋊#672 | C22 | semidirect |
| 26. C5×#576 | D3 | semidirect |
| 54. C3×#576 | D5 | semidirect |
| 133. #576 | D15 | semidirect |
| 251. C3×C5 | #3416 | semidirect |
| 285. C5 | #84008 | semidirect |
| 294. C3 | #10615739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#576 | 2 |
| #11756512 | 2 |
| #11751296 | 2 |
| #11751295 | 2 |
| C2×#91111 | 2 |
| #11751248 | 2 |
| #11751241 | 2 |
| #10615739 | 3 |
| #84008 | 5 |