Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11750818 | C2 | semidirect |
| 2. C3×#65000 | C2 | semidirect |
| 4. C5×#4466 | C2 | semidirect |
| 5. #11745937 | C2 | semidirect |
| 6. #11745916 | C2 | semidirect |
| 7. #11745913 | C2 | semidirect |
| 20. #90942 | C4 | semidirect |
| 21. #90938 | C4 | semidirect |
| 25. #65000 | D3 | semidirect |
| 37. Dic60 | C2×C4 | semidirect |
| 38. D120 | C2×C4 | semidirect |
| 47. C5×C3⋊C16 | C2×C4 | semidirect |
| 54. #4466 | D5 | semidirect |
| 149. C3⋊C16 | C4×D5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #70918 | semidirect |
| 270. C3 | #10599884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750818 | 2 |
| C3×#65000 | 2 |
| #11747543 | 2 |
| C5×#4466 | 2 |
| #11745937 | 2 |
| #11745916 | 2 |
| #11745913 | 2 |
| #10599884 | 3 |
| #70918 | 5 |