Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 156 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×C32×Dic5 | C2 | semidirect |
| 3. C2×C3⋊D3×Dic5 | C2 | semidirect |
| 4. #10623913 | C2 | semidirect |
| 5. #10623775 | C2 | semidirect |
| 6. #10623771 | C2 | semidirect |
| 7. Dic5×C3⋊Dic3 | C2 | semidirect |
| 13. C5×#638 | C4 | semidirect |
| 21. C22×C3×Dic5 | D3 | semidirect |
| 29. C22×C32×C5 | C2×C4 | semidirect |
| 33. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 36. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 38. C32×Dic5 | D4 | semidirect |
| 65. C22×Dic5 | C3⋊D3 | semidirect |
| 75. #638 | Dic5 | direct (N × H) |
| 82. C22×C3×C5 | C4×D3 | semidirect |
| 90. C3×Dic5 | #67 | semidirect |
| 99. C32×C5 | C4×D4 | semidirect |
| 112. C22×C32 | C2×Dic5 | semidirect |
| 116. C2×C3⋊D3 | C2×Dic5 | semidirect |
| 121. C3⋊Dic3 | C2×Dic5 | semidirect |
| 143. C22×C5 | C4×C3⋊D3 | semidirect |
| 149. Dic5 | #638 | direct (N × H) |
| 162. C3×C5 | C4×#67 | semidirect |
| 165. C22×C3 | D3×Dic5 | semidirect |
| 180. C32 | D4×Dic5 | semidirect |
| 196. C5 | C4×#638 | semidirect |
| 202. C22 | C3⋊D3×Dic5 | semidirect |
| 209. C3 | Dic5×#67 | 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×C32×Dic5 | 2 |
| C2×C3⋊D3×Dic5 | 2 |
| #10623913 | 2 |
| #10623775 | 2 |
| #10623771 | 2 |
| Dic5×C3⋊Dic3 | 2 |
| Dic5×#67 | 3 |
| C4×#638 | 5 |