Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
562 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 168 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. C2×C5×D3×Dic3 | C2 | semidirect |
| 3. C5×#3757 | C2 | semidirect |
| 4. C3×C5×#217 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 10. C22×C3×C5×D3 | C4 | semidirect |
| 13. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 14. C2×C3×C5×Dic3 | C22 | semidirect |
| 16. D3×#217 | C5 | direct (N × H) |
| 26. C5×#217 | D3 | direct (N × H) |
| 29. C22×C32×C5 | C2×C4 | semidirect |
| 34. C2×C3×C5×D3 | C2×C4 | semidirect |
| 40. C2×D3×Dic3 | C2×C5 | semidirect |
| 41. #3757 | C2×C5 | semidirect |
| 42. C3×#217 | C2×C5 | semidirect |
| 43. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 52. C22×C5×D3 | Dic3 | semidirect |
| 60. C2×C5×Dic3 | C2×D3 | semidirect |
| 68. C3×C5×D3 | C22⋊C4 | semidirect |
| 76. C22×C3×D3 | C4×C5 | semidirect |
| 79. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 80. C2×C3×Dic3 | C22×C5 | semidirect |
| 92. C22×C3×C5 | C4×D3 | semidirect |
| 93. C22×C3×C5 | C2×Dic3 | semidirect |
| 99. C2×C5×D3 | C2×Dic3 | semidirect |
| 115. #217 | C5×D3 | direct (N × H) |
| 117. C32×C5 | C2×C22⋊C4 | semidirect |
| 127. C22×C32 | C2×C4×C5 | semidirect |
| 132. C2×C3×D3 | C2×C4×C5 | semidirect |
| 149. C5×D3 | #217 | direct (N × H) |
| 158. C22×D3 | C5×Dic3 | semidirect |
| 166. C2×Dic3 | C2×C5×D3 | semidirect |
| 174. C22×C5 | D3×Dic3 | semidirect |
| 182. C3×D3 | C5×C22⋊C4 | semidirect |
| 189. C3×C5 | D3×C22⋊C4 | semidirect |
| 190. C3×C5 | C2×#217 | semidirect |
| 201. C22×C3 | C4×C5×D3 | semidirect |
| 202. C22×C3 | C2×C5×Dic3 | semidirect |
| 208. C2×D3 | C2×C5×Dic3 | semidirect |
| 220. C32 | C2×C5×C22⋊C4 | semidirect |
| 241. D3 | C5×#217 | direct (N × H) |
| 242. C5 | D3×#217 | direct (N × H) |
| 249. C22 | C5×D3×Dic3 | semidirect |
| 254. C3 | C5×D3×C22⋊C4 | semidirect |
| 255. C3 | C2×C5×#217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C5×D3 | 2 |
| C2×C5×D3×Dic3 | 2 |
| C5×#3757 | 2 |
| C3×C5×#217 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C2×C5×#217 | 3 |
| C5×D3×C22⋊C4 | 3 |
| D3×#217 | 5 |