Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11751689 | C2 | semidirect |
| 2. #11751686 | C2 | semidirect |
| 4. #11746715 | C2 | semidirect |
| 5. C3×#64851 | C2 | semidirect |
| 6. #11746461 | C2 | semidirect |
| 7. #11746460 | C2 | semidirect |
| 19. #91084 | C4 | semidirect |
| 20. C5×#800 | C4 | semidirect |
| 22. #90948 | C4 | semidirect |
| 23. #90939 | C4 | semidirect |
| 30. #64851 | D3 | semidirect |
| 104. #800 | AGL(1,𝔽5) | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #69358 | semidirect |
| 282. C3 | #10604129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751689 | 2 |
| #11751686 | 2 |
| #11746833 | 2 |
| #11746715 | 2 |
| C3×#64851 | 2 |
| #11746461 | 2 |
| #11746460 | 2 |
| #10604129 | 3 |
| #69358 | 5 |