Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 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×#474 | C2 | semidirect |
| 2. #11751186 | C2 | semidirect |
| 4. #11751113 | C2 | semidirect |
| 5. #11746368 | C2 | semidirect |
| 6. #11746306 | C2 | semidirect |
| 7. #11746300 | C2 | semidirect |
| 25. C5×#474 | D3 | semidirect |
| 52. C3×#474 | D5 | semidirect |
| 97. C3⋊#168 | D8 | semidirect |
| 134. #474 | D15 | semidirect |
| 274. C3×C5 | #1685 | semidirect |
| 322. C5 | #71104 | semidirect |
| 337. C3 | #10601897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#474 | 2 |
| #11751186 | 2 |
| #11751116 | 2 |
| #11751113 | 2 |
| #11746368 | 2 |
| #11746306 | 2 |
| #11746300 | 2 |
| #10601897 | 3 |
| #71104 | 5 |