Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11750995 | C2 | semidirect |
| 3. #11750970 | C2 | semidirect |
| 4. C3×C5×#365 | C2 | semidirect |
| 5. #11746333 | C2 | semidirect |
| 6. #11746316 | C2 | semidirect |
| 7. #11746309 | C2 | semidirect |
| 20. #91084 | C4 | semidirect |
| 21. D240 | C4 | semidirect |
| 26. C5×#365 | D3 | semidirect |
| 39. Dic60 | C2×C4 | semidirect |
| 42. D120 | C2×C4 | semidirect |
| 46. C3×C5×C16 | C2×C4 | semidirect |
| 51. C3×#365 | D5 | semidirect |
| 113. C5×C16 | C4×D3 | semidirect |
| 118. #365 | D15 | semidirect |
| 148. C3×C16 | C4×D5 | semidirect |
| 224. C16 | C4×D15 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #69310 | semidirect |
| 270. C3 | #10600103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751009 | 2 |
| #11750995 | 2 |
| #11750970 | 2 |
| C3×C5×#365 | 2 |
| #11746333 | 2 |
| #11746316 | 2 |
| #11746309 | 2 |
| #10600103 | 3 |
| #69310 | 5 |