Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
462 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 4. C3×C4×Dic15 | C2 | semidirect |
| 5. #10623828 | C2 | semidirect |
| 13. C3×C4×D15 | C4 | semidirect |
| 14. #67154 | C4 | direct (N × H) |
| 20. C4×Dic15 | D3 | semidirect |
| 30. C32×C4×C5 | C2×C4 | semidirect |
| 31. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 32. C3×Dic15 | C2×C4 | semidirect |
| 33. C3×Dic15 | C2×C4 | semidirect |
| 37. C4×C3⋊Dic3 | D5 | semidirect |
| 47. C4×D15 | Dic3 | semidirect |
| 60. C3×D15 | C42 | semidirect |
| 81. C3×C4×C5 | C4×D3 | semidirect |
| 82. C3×C4×C5 | C2×Dic3 | semidirect |
| 83. Dic15 | C4×D3 | semidirect |
| 84. Dic15 | C2×Dic3 | semidirect |
| 101. C32×C5 | C2×C42 | semidirect |
| 112. C32×C4 | C4×D5 | semidirect |
| 113. C3⋊Dic3 | C4×D5 | semidirect |
| 123. D15 | C4×Dic3 | semidirect |
| 145. C4×C5 | D3×Dic3 | semidirect |
| 157. C3×C5 | C42×D3 | semidirect |
| 158. C3×C5 | C2×C4×Dic3 | semidirect |
| 169. C3×C4 | D5×Dic3 | semidirect |
| 170. C3×C4 | #1200 | semidirect |
| 179. C32 | C42×D5 | semidirect |
| 195. C5 | C4×D3×Dic3 | semidirect |
| 202. C4 | #67154 | direct (N × H) |
| 204. C3 | C4×D5×Dic3 | semidirect |
| 205. C3 | C4×#1200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C2×#67154 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×C4×Dic15 | 2 |
| #10623828 | 2 |
| C4×#1200 | 3 |
| C4×D5×Dic3 | 3 |
| C4×D3×Dic3 | 5 |