Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×C5×Dic3⋊C4 | C2 | semidirect |
| 3. C32×C4×Dic5 | C2 | semidirect |
| 4. C3×Dic3⋊Dic5 | C2 | semidirect |
| 5. C3×#6669 | C2 | semidirect |
| 9. #91387 | C3 | direct (N × H) |
| 20. C5×Dic3⋊C4 | C2×C3 | semidirect |
| 27. C3×C4×Dic5 | D3 | semidirect |
| 28. C3×C4×Dic5 | C2×C3 | semidirect |
| 29. Dic3⋊Dic5 | C2×C3 | semidirect |
| 30. #6669 | C2×C3 | semidirect |
| 50. C3×Dic3⋊C4 | D5 | semidirect |
| 80. C4×Dic5 | C3×D3 | semidirect |
| 126. Dic3⋊C4 | C3×D5 | semidirect |
| 127. C32×C5 | #126 | semidirect |
| 196. C3×C5 | #876 | semidirect |
| 197. C3×C5 | C3×#126 | semidirect |
| 226. C32 | #4044 | semidirect |
| 245. C5 | C3×#876 | semidirect |
| 257. C3 | #91387 | direct (N × H) |
| 258. C3 | C3×#4044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6714 | 2 |
| C3×C5×Dic3⋊C4 | 2 |
| C32×C4×Dic5 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#6669 | 2 |
| C3×#6667 | 2 |
| C3×#4044 | 3 |
| #91387 | 3 |
| C3×#876 | 5 |