Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
516 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11749173 | C2 | semidirect |
| 3. #11746366 | C2 | semidirect |
| 4. C3×#64765 | C2 | semidirect |
| 5. #11746010 | C2 | semidirect |
| 7. C2×C5×#237 | C4 | semidirect |
| 11. C5×#936 | C4 | semidirect |
| 14. C42×C5×D3 | C4 | semidirect |
| 15. C5×#869 | C4 | semidirect |
| 24. #64765 | D3 | semidirect |
| 95. C2×#237 | Dic5 | semidirect |
| 99. #936 | Dic5 | semidirect |
| 103. C42×D3 | Dic5 | semidirect |
| 104. #869 | Dic5 | semidirect |
| 288. C3×C5 | #2126 | semidirect |
| 340. C5 | #69151 | semidirect |
| 357. C3 | #10602612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5716 | 2 |
| #11749173 | 2 |
| #11746366 | 2 |
| C3×#64765 | 2 |
| #11746010 | 2 |
| #10602612 | 3 |
| #69151 | 5 |