Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×C4×C3⋊D15 | C2 | semidirect |
| 2. C2×C3×C4×D15 | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 5. Dic3⋊Dic15 | C2 | semidirect |
| 6. #10623813 | C2 | semidirect |
| 7. #10623811 | C2 | semidirect |
| 19. #67151 | C4 | direct (N × H) |
| 25. C2×C4×D15 | D3 | semidirect |
| 32. C4×C5×Dic3 | D3 | semidirect |
| 39. C2×C3⋊D15 | C2×C4 | semidirect |
| 42. C2×C3×D15 | C2×C4 | semidirect |
| 43. C32×C4×C5 | D4 | semidirect |
| 47. C3×C5×Dic3 | C2×C4 | semidirect |
| 52. C3×C4×Dic3 | D5 | semidirect |
| 118. C2×D15 | C4×D3 | semidirect |
| 125. C3×C4×C5 | D12 | semidirect |
| 126. C3×C4×C5 | #67 | semidirect |
| 133. C5×Dic3 | C4×D3 | semidirect |
| 148. C4×Dic3 | D15 | semidirect |
| 149. C32×C5 | C4×D4 | semidirect |
| 167. C32×C4 | D20 | semidirect |
| 171. C3×Dic3 | C4×D5 | semidirect |
| 220. C4×C5 | #626 | semidirect |
| 236. C3×C5 | C4×D12 | semidirect |
| 237. C3×C5 | C4×#67 | semidirect |
| 260. C3×C4 | #1202 | semidirect |
| 261. C3×C4 | D60 | semidirect |
| 267. Dic3 | C4×D15 | semidirect |
| 273. C32 | C4×D20 | semidirect |
| 298. C5 | C4×#626 | semidirect |
| 310. C4 | #67151 | direct (N × H) |
| 312. C3 | C4×#1202 | semidirect |
| 313. C3 | C4×D60 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D15 | 2 |
| C2×C3×C4×D15 | 2 |
| C2×#67151 | 2 |
| C3×C4×C5×Dic3 | 2 |
| Dic3⋊Dic15 | 2 |
| #10623813 | 2 |
| #10623811 | 2 |
| C4×D60 | 3 |
| C4×#1202 | 3 |
| C4×#626 | 5 |