Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 103 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×#436 | C2 | semidirect |
| 3. #11751108 | C2 | semidirect |
| 4. #11750794 | C2 | semidirect |
| 5. #11746306 | C2 | semidirect |
| 6. #11746303 | C2 | semidirect |
| 7. #11746279 | C2 | semidirect |
| 25. C5×#436 | D3 | semidirect |
| 52. C3×#436 | D5 | semidirect |
| 95. C3×C5×C8 | D8 | semidirect |
| 136. #436 | D15 | semidirect |
| 194. C5×C8 | #213 | semidirect |
| 237. C3×C8 | #686 | semidirect |
| 274. C3×C5 | #1685 | semidirect |
| 316. C8 | #6715 | semidirect |
| 322. C5 | #70867 | semidirect |
| 337. C3 | #10601660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#436 | 2 |
| #11751116 | 2 |
| #11751108 | 2 |
| #11750794 | 2 |
| #11746306 | 2 |
| #11746303 | 2 |
| #11746279 | 2 |
| #10601660 | 3 |
| #70867 | 5 |