Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
740 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 740 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. #11756511 | C2 | semidirect |
| 2. C3×C5×#504 | C2 | semidirect |
| 3. #11751009 | C2 | semidirect |
| 4. #11751005 | C2 | semidirect |
| 5. C2×D240 | C2 | semidirect |
| 10. #91793 | C22 | semidirect |
| 11. C2×D120 | C22 | semidirect |
| 12. C3×C5×M32 | C22 | semidirect |
| 13. C2×C3×C5×C16 | C22 | semidirect |
| 14. Dic120 | C22 | semidirect |
| 15. #91084 | C22 | semidirect |
| 16. D240 | C22 | semidirect |
| 17. D240 | C22 | semidirect |
| 20. C5×#504 | D3 | semidirect |
| 38. C3×#504 | D5 | semidirect |
| 47. C5×M32 | C2×D3 | semidirect |
| 48. C2×C5×C16 | C2×D3 | semidirect |
| 70. C3×M32 | C2×D5 | semidirect |
| 71. C2×C3×C16 | C2×D5 | semidirect |
| 93. #504 | D15 | semidirect |
| 133. M32 | C2×D15 | semidirect |
| 134. C2×C16 | C2×D15 | semidirect |
| 168. C3×C5 | #3415 | semidirect |
| 192. C5 | #82013 | semidirect |
| 199. C3 | #10613744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756511 | 2 |
| C3×C5×#504 | 2 |
| #11751009 | 2 |
| #11751005 | 2 |
| C2×D240 | 2 |
| #10613744 | 3 |
| #82013 | 5 |