Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 87 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×#442 | C2 | semidirect |
| 3. #11750818 | C2 | semidirect |
| 4. #11746384 | C2 | semidirect |
| 5. #11746309 | C2 | semidirect |
| 6. #11746308 | C2 | semidirect |
| 7. #11746287 | C2 | semidirect |
| 16. #91111 | C4 | semidirect |
| 17. #91110 | C4 | semidirect |
| 23. C5×#442 | D3 | semidirect |
| 41. Dic60 | C2×C4 | semidirect |
| 42. D120 | C2×C4 | semidirect |
| 47. C3⋊#672 | C2×C4 | semidirect |
| 48. C3×#442 | D5 | semidirect |
| 117. #442 | D15 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #70918 | semidirect |
| 270. C3 | #10601711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#442 | 2 |
| #11751248 | 2 |
| #11750818 | 2 |
| #11746384 | 2 |
| #11746309 | 2 |
| #11746308 | 2 |
| #11746287 | 2 |
| #10601711 | 3 |
| #70918 | 5 |