Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
394 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 122 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⋊(C3⋊Dic15) | C2 | semidirect |
| 4. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 5. #10623814 | C2 | semidirect |
| 12. C3×C4×D15 | C4 | semidirect |
| 25. C5×C4⋊Dic3 | D3 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 33. C3×Dic15 | C2×C4 | semidirect |
| 39. C3×C4⋊Dic3 | D5 | semidirect |
| 52. C4×D15 | Dic3 | semidirect |
| 62. C3×D15 | C4⋊C4 | semidirect |
| 86. C3×C4×C5 | C4×D3 | semidirect |
| 87. C3×C4×C5 | C2×Dic3 | semidirect |
| 91. Dic15 | C2×Dic3 | semidirect |
| 103. C4⋊Dic3 | D15 | direct (N × H) |
| 105. C32×C5 | C2×C4⋊C4 | semidirect |
| 117. C32×C4 | C4×D5 | semidirect |
| 131. D15 | C4⋊Dic3 | direct (N × H) |
| 154. C4×C5 | D3×Dic3 | semidirect |
| 167. C3×C5 | D3×C4⋊C4 | semidirect |
| 168. C3×C5 | C2×C4⋊Dic3 | semidirect |
| 181. C3×C4 | D5×Dic3 | semidirect |
| 182. C3×C4 | C4×D15 | semidirect |
| 192. C32 | D5×C4⋊C4 | semidirect |
| 211. C5 | D3×C4⋊Dic3 | semidirect |
| 219. C4 | Dic3×D15 | semidirect |
| 221. C3 | D5×C4⋊Dic3 | semidirect |
| 222. C3 | C4⋊C4×D15 | 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×Dic3×D15 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| #10623814 | 2 |
| C4⋊C4×D15 | 3 |
| D5×C4⋊Dic3 | 3 |
| D3×C4⋊Dic3 | 5 |