Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 107 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. C22×C3×Dic15 | C2 | semidirect |
| 3. C2×#67155 | C2 | semidirect |
| 4. C3×#6719 | C2 | semidirect |
| 5. #10623832 | C2 | semidirect |
| 6. #10623830 | C2 | semidirect |
| 7. #10623828 | C2 | semidirect |
| 12. C5×#638 | C4 | semidirect |
| 21. C22×Dic15 | D3 | semidirect |
| 28. #6719 | D3 | semidirect |
| 38. C22×C32×C5 | C2×C4 | semidirect |
| 42. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 43. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 47. C3×Dic15 | D4 | semidirect |
| 96. #638 | Dic5 | semidirect |
| 112. C22×C3×C5 | C4×D3 | semidirect |
| 113. C22×C3×C5 | C4×D3 | semidirect |
| 128. Dic15 | #67 | semidirect |
| 151. C32×C5 | C4×D4 | semidirect |
| 164. C22×C32 | C2×Dic5 | semidirect |
| 168. C2×C3⋊D3 | C2×Dic5 | semidirect |
| 169. C3⋊Dic3 | C2×Dic5 | semidirect |
| 219. C22×C5 | #624 | semidirect |
| 239. C3×C5 | #67⋊C4 | semidirect |
| 240. C3×C5 | C4×#67 | semidirect |
| 249. C22×C3 | D3×Dic5 | semidirect |
| 250. C22×C3 | D3×Dic5 | semidirect |
| 278. C32 | D4×Dic5 | semidirect |
| 304. C5 | #63952 | semidirect |
| 310. C22 | #67155 | semidirect |
| 318. C3 | Dic5×#67 | semidirect |
| 319. C3 | #67⋊Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C22×C3×Dic15 | 2 |
| C2×#67155 | 2 |
| C3×#6719 | 2 |
| #10623832 | 2 |
| #10623830 | 2 |
| #10623828 | 2 |
| #67⋊Dic5 | 3 |
| Dic5×#67 | 3 |
| #63952 | 5 |