Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
1078 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D15 |
| commutator, hypocenter | C32×C5 | C23×C4 |
| Frattini | C2 | C22×D3×D15 |
| Fitting, socle | C23×C32×C5 | C22 |
| prime radical | C23×C3⋊D15 | C2 |
| cosocle | C2×C32×C5 | C24 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3×Dic15 | C2 | semidirect |
| 3. C22×C3×C5×Dic3 | C2 | semidirect |
| 4. C2×#67149 | C2 | direct (N × H) |
| 8. C22×C3⋊D15 | C4 | semidirect |
| 10. C2×C3×Dic15 | C22 | semidirect |
| 11. C2×C3×C5×Dic3 | C22 | semidirect |
| 12. #67149 | C22 | direct (N × H) |
| 18. C22×Dic15 | D3 | semidirect |
| 20. C22×C5×Dic3 | D3 | semidirect |
| 23. C22×C32×C5 | C2×C4 | semidirect |
| 25. C2×C3⋊D15 | C2×C4 | semidirect |
| 27. C3×Dic15 | C23 | semidirect |
| 28. C3×C5×Dic3 | C23 | semidirect |
| 32. C22×C3×Dic3 | D5 | semidirect |
| 44. C2×Dic15 | C2×D3 | semidirect |
| 46. C2×C5×Dic3 | C2×D3 | semidirect |
| 51. C2×C32×C5 | C22×C4 | semidirect |
| 53. C3⋊D15 | C22×C4 | semidirect |
| 62. C2×C3×Dic3 | C2×D5 | semidirect |
| 66. C22×C3×C5 | C4×D3 | semidirect |
| 67. C22×C3×C5 | C4×D3 | semidirect |
| 77. Dic15 | C22×D3 | semidirect |
| 79. C5×Dic3 | C22×D3 | semidirect |
| 86. C22×Dic3 | D15 | semidirect |
| 89. C32×C5 | C23×C4 | semidirect |
| 96. C22×C32 | C4×D5 | semidirect |
| 101. C3×Dic3 | C22×D5 | semidirect |
| 105. C2×C3×C5 | C2×C4×D3 | semidirect |
| 106. C2×C3×C5 | C2×C4×D3 | semidirect |
| 124. C2×Dic3 | C2×D15 | semidirect |
| 127. C22×C5 | #624 | semidirect |
| 133. C2×C32 | C2×C4×D5 | semidirect |
| 141. C3×C5 | C22×C4×D3 | semidirect |
| 142. C3×C5 | C22×C4×D3 | semidirect |
| 145. C22×C3 | #1200 | semidirect |
| 146. C22×C3 | C4×D15 | semidirect |
| 158. Dic3 | C22×D15 | semidirect |
| 159. C2×C5 | C2×#624 | semidirect |
| 162. C32 | C22×C4×D5 | semidirect |
| 171. C2×C3 | C2×#1200 | semidirect |
| 172. C2×C3 | C2×C4×D15 | semidirect |
| 178. C5 | C22×#624 | semidirect |
| 181. C22 | #67149 | direct (N × H) |
| 186. C3 | C22×#1200 | semidirect |
| 187. C3 | C22×C4×D15 | semidirect |
| 189. C2 | C2×#67149 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊D15 | 2 |
| C22×C3×Dic15 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C2×#67149 | 2 |
| C22×C4×D15 | 3 |
| C22×#1200 | 3 |
| C22×#624 | 5 |