Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
406 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 107 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×#67154 | C2 | semidirect |
| 3. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 4. C3×C4⋊Dic15 | C2 | semidirect |
| 5. #10623829 | C2 | semidirect |
| 13. C3×D60 | C4 | semidirect |
| 20. C4⋊Dic15 | D3 | semidirect |
| 30. C2×C3×D15 | C2×C4 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 33. C5×C3⋊Dic3 | D4 | semidirect |
| 38. C4×C3⋊Dic3 | D5 | semidirect |
| 47. D60 | Dic3 | semidirect |
| 81. C2×D15 | C2×Dic3 | semidirect |
| 86. C3×C4×C5 | C4×D3 | semidirect |
| 87. C3×C4×C5 | C2×Dic3 | semidirect |
| 107. C32×C5 | C4×D4 | semidirect |
| 119. C32×C4 | C4×D5 | semidirect |
| 121. C3⋊Dic3 | D20 | semidirect |
| 158. C4×C5 | D3×Dic3 | semidirect |
| 170. C3×C5 | #893 | semidirect |
| 171. C3×C5 | D4×Dic3 | semidirect |
| 183. C3×C4 | D5×Dic3 | semidirect |
| 184. C3×C4 | #1200 | semidirect |
| 196. C32 | C4×D20 | semidirect |
| 215. C5 | #63898 | semidirect |
| 223. C4 | #67154 | semidirect |
| 225. C3 | Dic3×D20 | semidirect |
| 226. C3 | #91428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×#67154 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×C4⋊Dic15 | 2 |
| #10623829 | 2 |
| #91428 | 3 |
| Dic3×D20 | 3 |
| #63898 | 5 |