Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. C3×C5×#459 | C2 | semidirect |
| 2. #11751174 | C2 | semidirect |
| 3. #11751116 | C2 | semidirect |
| 4. #11751113 | C2 | semidirect |
| 5. #11746365 | C2 | semidirect |
| 6. #11746306 | C2 | semidirect |
| 7. #11746301 | C2 | semidirect |
| 25. C5×#459 | D3 | semidirect |
| 53. C3×#459 | D5 | semidirect |
| 101. C3⋊#168 | D8 | semidirect |
| 140. #459 | D15 | semidirect |
| 292. C3×C5 | #1687 | semidirect |
| 347. C5 | #71009 | semidirect |
| 364. C3 | #10601802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#459 | 2 |
| #11751174 | 2 |
| #11751116 | 2 |
| #11751113 | 2 |
| #11746365 | 2 |
| #11746306 | 2 |
| #11746301 | 2 |
| #10601802 | 3 |
| #71009 | 5 |