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. #11750812 | C2 | semidirect |
| 2. C5×#4717 | C2 | semidirect |
| 4. C3×#64686 | C2 | semidirect |
| 5. #11745934 | C2 | semidirect |
| 6. #11745920 | C2 | semidirect |
| 7. #11745912 | C2 | semidirect |
| 20. #90945 | C4 | semidirect |
| 21. #90939 | C4 | semidirect |
| 29. #64686 | D3 | semidirect |
| 41. C5×Dic12 | C2×C4 | semidirect |
| 42. C5×D24 | C2×C4 | semidirect |
| 47. C3×#672 | C2×C4 | semidirect |
| 49. #4717 | D5 | semidirect |
| 114. #672 | C4×D3 | semidirect |
| 141. Dic12 | C4×D5 | semidirect |
| 144. D24 | C4×D5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #69091 | semidirect |
| 270. C3 | #10601722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750812 | 2 |
| C5×#4717 | 2 |
| #11747548 | 2 |
| C3×#64686 | 2 |
| #11745934 | 2 |
| #11745920 | 2 |
| #11745912 | 2 |
| #10601722 | 3 |
| #69091 | 5 |