Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 102 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×#67149 | C2 | semidirect |
| 3. C3×C4×Dic15 | C2 | semidirect |
| 4. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 5. #10623813 | C2 | semidirect |
| 10. C4⋊(C3⋊D15) | C4 | semidirect |
| 23. C4×Dic15 | D3 | semidirect |
| 24. C5×C4⋊Dic3 | D3 | semidirect |
| 30. C2×C3⋊D15 | C2×C4 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 33. C3×Dic15 | D4 | semidirect |
| 38. C3×C4⋊Dic3 | D5 | semidirect |
| 90. C3×C4×C5 | C4×D3 | semidirect |
| 91. C3×C4×C5 | C4×D3 | semidirect |
| 93. Dic15 | D12 | semidirect |
| 106. C4⋊Dic3 | D15 | semidirect |
| 108. C32×C5 | C4×D4 | semidirect |
| 120. C32×C4 | C4×D5 | semidirect |
| 159. C4×C5 | #624 | semidirect |
| 172. C3×C5 | C4×D12 | semidirect |
| 173. C3×C5 | #893 | semidirect |
| 190. C3×C4 | #1200 | semidirect |
| 191. C3×C4 | C4×D15 | semidirect |
| 199. C32 | #4039 | semidirect |
| 219. C5 | #63894 | semidirect |
| 227. C4 | #67149 | semidirect |
| 229. C3 | #91418 | semidirect |
| 230. C3 | #91782 | 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×#67149 | 2 |
| C3×C4×Dic15 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| #10623813 | 2 |
| #91782 | 3 |
| #91418 | 3 |
| #63894 | 5 |