Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
608 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 608 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 |
|---|---|---|
| 3. D5⋊#824 | C2 | semidirect |
| 5. #11751712 | C2 | semidirect |
| 6. #11746765 | C2 | semidirect |
| 7. C3×#64897 | C2 | semidirect |
| 18. C2×#6706 | C4 | semidirect |
| 19. C2×C5×Dic12 | C4 | semidirect |
| 21. C2×#6663 | C4 | semidirect |
| 22. C2×#6660 | C4 | semidirect |
| 34. #64897 | D3 | semidirect |
| 147. C2×Dic12 | AGL(1,𝔽5) | semidirect |
| 396. C3×C5 | #1902 | semidirect |
| 454. C5 | #68725 | semidirect |
| 469. C3 | #10604851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756827 | 2 |
| C2×#91261 | 2 |
| D5⋊#824 | 2 |
| #11751723 | 2 |
| #11751712 | 2 |
| #11746765 | 2 |
| C3×#64897 | 2 |
| #10604851 | 3 |
| #68725 | 5 |