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. #11756512 | C2 | semidirect |
| 2. #11756511 | C2 | semidirect |
| 3. C3×C5×#504 | C2 | semidirect |
| 4. #11751010 | C2 | semidirect |
| 5. #11751009 | C2 | semidirect |
| 6. #11751005 | C2 | semidirect |
| 7. C2×#91084 | C2 | semidirect |
| 14. C2×Dic60 | C22 | semidirect |
| 16. #91793 | C22 | semidirect |
| 18. C3×C5×M32 | C22 | semidirect |
| 19. C2×C3×C5×C16 | C22 | semidirect |
| 20. Dic120 | C22 | semidirect |
| 21. #91084 | C22 | semidirect |
| 22. #91084 | C22 | semidirect |
| 23. #91084 | C22 | semidirect |
| 24. D240 | C22 | semidirect |
| 28. C5×#504 | D3 | semidirect |
| 56. C3×#504 | D5 | semidirect |
| 70. C5×M32 | C2×D3 | semidirect |
| 71. C2×C5×C16 | C2×D3 | semidirect |
| 104. C3×M32 | C2×D5 | semidirect |
| 105. C2×C3×C16 | C2×D5 | semidirect |
| 138. #504 | D15 | semidirect |
| 199. M32 | C2×D15 | semidirect |
| 200. C2×C16 | C2×D15 | semidirect |
| 251. C3×C5 | #3416 | semidirect |
| 285. C5 | #82014 | semidirect |
| 294. C3 | #10613745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756512 | 2 |
| #11756511 | 2 |
| C3×C5×#504 | 2 |
| #11751010 | 2 |
| #11751009 | 2 |
| #11751005 | 2 |
| C2×#91084 | 2 |
| #10613745 | 3 |
| #82014 | 5 |