Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
212 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 212 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 |
|---|---|---|
| 1. C5×#4912 | C2 | semidirect |
| 2. #11746835 | C2 | semidirect |
| 3. #11746341 | C2 | semidirect |
| 4. C3×#64739 | C2 | semidirect |
| 5. #11745829 | C2 | semidirect |
| 6. #11745821 | C2 | semidirect |
| 7. D3×#3926 | C2 | semidirect |
| 26. #64739 | D3 | semidirect |
| 40. #4912 | D5 | semidirect |
| 171. C3×C5 | #2262 | semidirect |
| 198. C5 | #69376 | semidirect |
| 206. C3 | #10602301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4912 | 2 |
| #11746835 | 2 |
| #11746341 | 2 |
| C3×#64739 | 2 |
| #11745829 | 2 |
| #11745821 | 2 |
| D3×#3926 | 2 |
| #10602301 | 3 |
| #69376 | 5 |