Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 78 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×#65158 | C2 | semidirect |
| 2. #11748063 | C2 | semidirect |
| 4. #11746308 | C2 | semidirect |
| 5. C5×#4488 | C2 | semidirect |
| 6. #11745916 | C2 | semidirect |
| 7. #11745876 | C2 | semidirect |
| 20. #90940 | C4 | semidirect |
| 21. #90937 | C4 | semidirect |
| 25. #65158 | D3 | semidirect |
| 36. C5×Dic12 | C2×C4 | semidirect |
| 37. C5×D24 | C2×C4 | semidirect |
| 46. C3⋊#672 | C2×C4 | semidirect |
| 52. #4488 | D5 | semidirect |
| 143. Dic12 | C4×D5 | semidirect |
| 144. D24 | C4×D5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #70918 | semidirect |
| 270. C3 | #10600042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65158 | 2 |
| #11748063 | 2 |
| #11747539 | 2 |
| #11746308 | 2 |
| C5×#4488 | 2 |
| #11745916 | 2 |
| #11745876 | 2 |
| #10600042 | 3 |
| #70918 | 5 |