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×C5×D3 | C2 | semidirect |
| 4. C3×C4×Dic15 | C2 | semidirect |
| 5. #10623814 | C2 | semidirect |
| 6. #10623813 | C2 | semidirect |
| 7. (C2×D3)⋊Dic15 | C2 | semidirect |
| 19. #67152 | C4 | direct (N × H) |
| 26. C2×C4×C5×D3 | D3 | semidirect |
| 31. C4×Dic15 | D3 | semidirect |
| 39. C2×C3⋊D15 | C2×C4 | semidirect |
| 42. C2×C3×C5×D3 | C2×C4 | semidirect |
| 43. C32×C4×C5 | D4 | semidirect |
| 46. C3×Dic15 | C2×C4 | semidirect |
| 50. C2×C3×C4×D3 | D5 | semidirect |
| 121. C2×C5×D3 | C4×D3 | semidirect |
| 124. C3×C4×C5 | D12 | semidirect |
| 125. C3×C4×C5 | #67 | semidirect |
| 130. Dic15 | C4×D3 | semidirect |
| 140. C2×C4×D3 | D15 | semidirect |
| 149. C32×C5 | C4×D4 | semidirect |
| 166. C2×C3×D3 | C4×D5 | semidirect |
| 167. C32×C4 | C22⋊D5 | semidirect |
| 219. C4×C5 | #626 | semidirect |
| 236. C3×C5 | C4×D12 | semidirect |
| 237. C3×C5 | C4×#67 | semidirect |
| 255. C2×D3 | C4×D15 | semidirect |
| 260. C3×C4 | #1203 | semidirect |
| 261. C3×C4 | #1220 | semidirect |
| 273. C32 | C4×C22⋊D5 | semidirect |
| 298. C5 | C4×#626 | semidirect |
| 310. C4 | #67152 | direct (N × H) |
| 312. C3 | C4×#1203 | semidirect |
| 313. C3 | C4×#1220 | 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×C5×D3 | 2 |
| C2×#67152 | 2 |
| C3×C4×Dic15 | 2 |
| #10623814 | 2 |
| #10623813 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| C4×#1220 | 3 |
| C4×#1203 | 3 |
| C4×#626 | 5 |