Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 2. C3×#65729 | C2 | semidirect |
| 3. #11751824 | C2 | semidirect |
| 6. #11746773 | C2 | semidirect |
| 7. #11746525 | C2 | semidirect |
| 26. #91109 | C4 | semidirect |
| 27. C5×#825 | C4 | semidirect |
| 28. #90980 | C4 | semidirect |
| 29. #90978 | C4 | semidirect |
| 33. #65729 | D3 | semidirect |
| 155. #825 | AGL(1,𝔽5) | semidirect |
| 397. C3×C5 | #1861 | semidirect |
| 459. C5 | #70735 | semidirect |
| 476. C3 | #10604008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756823 | 2 |
| C3×#65729 | 2 |
| #11751824 | 2 |
| #11751717 | 2 |
| D5×#825 | 2 |
| #11746773 | 2 |
| #11746525 | 2 |
| #10604008 | 3 |
| #70735 | 5 |