Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11751171 | C2 | semidirect |
| 3. #11750943 | C2 | semidirect |
| 4. #11750939 | C2 | semidirect |
| 5. C3×C5×#331 | C2 | semidirect |
| 6. #11746302 | C2 | semidirect |
| 7. #11746300 | C2 | semidirect |
| 29. C5×#331 | D3 | semidirect |
| 54. C3×#331 | D5 | semidirect |
| 134. #331 | D15 | semidirect |
| 263. C3×C5 | #1697 | semidirect |
| 310. C5 | #68400 | semidirect |
| 325. C3 | #10599193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751173 | 2 |
| #11751171 | 2 |
| #11750943 | 2 |
| #11750939 | 2 |
| C3×C5×#331 | 2 |
| #11746302 | 2 |
| #11746300 | 2 |
| #10599193 | 3 |
| #68400 | 5 |