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. C5×#4717 | C2 | semidirect |
| 2. C3×#65000 | C2 | semidirect |
| 4. #11746287 | C2 | semidirect |
| 5. #11745935 | C2 | semidirect |
| 6. #11745915 | C2 | semidirect |
| 7. #11745911 | C2 | semidirect |
| 20. #90940 | C4 | semidirect |
| 21. #90937 | C4 | semidirect |
| 25. #65000 | D3 | semidirect |
| 37. C5×Dic12 | C2×C4 | semidirect |
| 38. C5×D24 | C2×C4 | semidirect |
| 47. C3⋊#672 | C2×C4 | semidirect |
| 50. #4717 | 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 | #10601722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4717 | 2 |
| C3×#65000 | 2 |
| #11747539 | 2 |
| #11746287 | 2 |
| #11745935 | 2 |
| #11745915 | 2 |
| #11745911 | 2 |
| #10601722 | 3 |
| #70918 | 5 |