Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
462 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D3×D15 |
| commutator, hypocenter | C32×C5 | C2×C42 |
| Frattini | C22 | C2×D3×D15 |
| Fitting | C2×C32×C4×C5 | C22 |
| socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C22×C3×D15 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C3⋊Dic15 | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 5. Dic3×Dic15 | C2 | semidirect |
| 12. C3×C4×D15 | C4 | semidirect |
| 14. Dic3×D15 | C4 | direct (N × H) |
| 25. C4×C5×Dic3 | D3 | semidirect |
| 30. C32×C4×C5 | C2×C4 | semidirect |
| 31. C3⋊Dic15 | C2×C4 | semidirect |
| 32. C3×Dic15 | C2×C4 | semidirect |
| 33. C3×C5×Dic3 | C2×C4 | semidirect |
| 38. C3×C4×Dic3 | D5 | semidirect |
| 51. C4×D15 | Dic3 | direct (N × H) |
| 60. C3×D15 | C42 | semidirect |
| 82. C3×C4×C5 | C4×D3 | semidirect |
| 83. C3×C4×C5 | C2×Dic3 | semidirect |
| 87. Dic15 | C2×Dic3 | semidirect |
| 89. C5×Dic3 | C4×D3 | semidirect |
| 100. C4×Dic3 | D15 | direct (N × H) |
| 101. C32×C5 | C2×C42 | semidirect |
| 112. C32×C4 | C4×D5 | semidirect |
| 115. C3×Dic3 | C4×D5 | semidirect |
| 123. D15 | C4×Dic3 | direct (N × H) |
| 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 | C4×D15 | semidirect |
| 175. Dic3 | C4×D15 | direct (N × H) |
| 179. C32 | C42×D5 | semidirect |
| 195. C5 | C4×D3×Dic3 | semidirect |
| 202. C4 | Dic3×D15 | direct (N × H) |
| 204. C3 | C4×D5×Dic3 | semidirect |
| 205. C3 | C42×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×C4×C5×Dic3 | 2 |
| Dic3×Dic15 | 2 |
| C42×D15 | 3 |
| C4×D5×Dic3 | 3 |
| C4×D3×Dic3 | 5 |