Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 4. C5×#4490 | C2 | semidirect |
| 5. C3×#64709 | C2 | semidirect |
| 6. #11745944 | C2 | semidirect |
| 7. #11745939 | C2 | semidirect |
| 20. #90933 | C4 | semidirect |
| 28. #64709 | D3 | semidirect |
| 50. #4490 | D5 | semidirect |
| 202. C3×C5 | #2158 | semidirect |
| 234. C5 | #69325 | semidirect |
| 246. C3 | #10600138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750981 | 2 |
| #11747690 | 2 |
| C2×#90933 | 2 |
| C5×#4490 | 2 |
| C3×#64709 | 2 |
| #11745944 | 2 |
| #11745939 | 2 |
| #10600138 | 3 |
| #69325 | 5 |