Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 2. D5×Dic24 | C2 | semidirect |
| 3. Dic240 | C2 | semidirect |
| 4. C5×#4449 | C2 | semidirect |
| 5. C3×#64667 | C2 | semidirect |
| 6. #11745829 | C2 | semidirect |
| 7. #11745825 | C2 | semidirect |
| 27. #64667 | D3 | semidirect |
| 45. #4449 | D5 | semidirect |
| 170. C3×C5 | #2264 | semidirect |
| 195. C5 | #69374 | semidirect |
| 203. C3 | #10600174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11746832 | 2 |
| D5×Dic24 | 2 |
| Dic240 | 2 |
| C5×#4449 | 2 |
| C3×#64667 | 2 |
| #11745829 | 2 |
| #11745825 | 2 |
| #10600174 | 3 |
| #69374 | 5 |