Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
998 conjugacy classes of subgroups; only the 303 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 303 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 | (C3⋊D3)⋊D5 |
| commutator, hypocenter | C32×C5 | C23×C4 |
| Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| 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×C5×C3⋊Dic3 | C2 | semidirect |
| 3. C22×C3×Dic15 | C2 | semidirect |
| 4. C2×#67154 | C2 | direct (N × H) |
| 8. C22×C3×D15 | C4 | semidirect |
| 10. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 11. C2×C3×Dic15 | C22 | semidirect |
| 12. #67154 | C22 | direct (N × H) |
| 16. C22×Dic15 | D3 | semidirect |
| 23. C22×C32×C5 | C2×C4 | semidirect |
| 25. C2×C3×D15 | C2×C4 | semidirect |
| 27. C5×C3⋊Dic3 | C23 | semidirect |
| 28. C3×Dic15 | C23 | semidirect |
| 31. C22×C3⋊Dic3 | D5 | semidirect |
| 37. C22×D15 | Dic3 | semidirect |
| 41. C2×Dic15 | C2×D3 | semidirect |
| 50. C2×C32×C5 | C22×C4 | semidirect |
| 52. C3×D15 | C22×C4 | semidirect |
| 60. C2×C3⋊Dic3 | C2×D5 | semidirect |
| 65. C22×C3×C5 | C4×D3 | semidirect |
| 66. C22×C3×C5 | C2×Dic3 | semidirect |
| 69. C2×D15 | C2×Dic3 | semidirect |
| 73. Dic15 | C22×D3 | semidirect |
| 87. C32×C5 | C23×C4 | semidirect |
| 94. C22×C32 | C4×D5 | semidirect |
| 98. C3⋊Dic3 | C22×D5 | semidirect |
| 103. C2×C3×C5 | C2×C4×D3 | semidirect |
| 104. C2×C3×C5 | C22×Dic3 | semidirect |
| 107. D15 | C22×Dic3 | semidirect |
| 123. C22×C5 | D3×Dic3 | semidirect |
| 129. C2×C32 | C2×C4×D5 | semidirect |
| 137. C3×C5 | C22×C4×D3 | semidirect |
| 138. C3×C5 | C23×Dic3 | semidirect |
| 143. C22×C3 | D5×Dic3 | semidirect |
| 144. C22×C3 | #1200 | semidirect |
| 154. C2×C5 | C2×D3×Dic3 | semidirect |
| 157. C32 | C22×C4×D5 | semidirect |
| 167. C2×C3 | C2×D5×Dic3 | semidirect |
| 168. C2×C3 | C2×#1200 | semidirect |
| 172. C5 | C22×D3×Dic3 | semidirect |
| 175. C22 | #67154 | direct (N × H) |
| 180. C3 | C22×D5×Dic3 | semidirect |
| 181. C3 | C22×#1200 | semidirect |
| 183. C2 | C2×#67154 | 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×C5×C3⋊Dic3 | 2 |
| C22×C3×Dic15 | 2 |
| C2×#67154 | 2 |
| C22×#1200 | 3 |
| C22×D5×Dic3 | 3 |
| C22×D3×Dic3 | 5 |