Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
998 conjugacy classes of subgroups; only the 456 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 456 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×C5 | D32 |
| commutator, hypocenter | C32 | C23×C4×C5 |
| Frattini | C2 | C22×C5×D32 |
| Fitting, socle | C23×C32×C5 | C22 |
| prime radical | C23×C3×C5×D3 | C2 |
| cosocle | C2×C32 | C24×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C5 | |
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×C5×Dic3 | C2 | semidirect |
| 4. C2×C5×D3×Dic3 | C2 | direct (N × H) |
| 8. C22×C3×C5×D3 | C4 | semidirect |
| 10. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 11. C2×C3×C5×Dic3 | C22 | semidirect |
| 12. C5×D3×Dic3 | C22 | direct (N × H) |
| 13. C22×D3×Dic3 | C5 | direct (N × H) |
| 21. C22×C5×Dic3 | D3 | direct (N × H) |
| 23. C22×C32×C5 | C2×C4 | semidirect |
| 25. C2×C3×C5×D3 | C2×C4 | semidirect |
| 27. C5×C3⋊Dic3 | C23 | semidirect |
| 28. C3×C5×Dic3 | C23 | semidirect |
| 31. C22×C3⋊Dic3 | C2×C5 | semidirect |
| 32. C22×C3×Dic3 | C2×C5 | semidirect |
| 33. C2×D3×Dic3 | C2×C5 | direct (N × H) |
| 39. C22×C5×D3 | Dic3 | direct (N × H) |
| 46. C2×C5×Dic3 | C2×D3 | direct (N × H) |
| 50. C2×C32×C5 | C22×C4 | semidirect |
| 52. C3×C5×D3 | C22×C4 | semidirect |
| 58. C22×C3×D3 | C4×C5 | semidirect |
| 60. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 61. C2×C3×Dic3 | C22×C5 | semidirect |
| 62. D3×Dic3 | C22×C5 | direct (N × H) |
| 67. C22×C3×C5 | C4×D3 | semidirect |
| 68. C22×C3×C5 | C2×Dic3 | semidirect |
| 71. C2×C5×D3 | C2×Dic3 | direct (N × H) |
| 77. C5×Dic3 | C22×D3 | direct (N × H) |
| 85. C22×Dic3 | C5×D3 | direct (N × H) |
| 87. C32×C5 | C23×C4 | semidirect |
| 94. C22×C32 | C2×C4×C5 | semidirect |
| 96. C2×C3×D3 | C2×C4×C5 | semidirect |
| 98. C3⋊Dic3 | C23×C5 | semidirect |
| 99. C3×Dic3 | C23×C5 | semidirect |
| 104. C2×C3×C5 | C2×C4×D3 | semidirect |
| 105. C2×C3×C5 | C22×Dic3 | semidirect |
| 108. C5×D3 | C22×Dic3 | direct (N × H) |
| 114. C22×D3 | C5×Dic3 | direct (N × H) |
| 121. C2×Dic3 | C2×C5×D3 | direct (N × H) |
| 125. C22×C5 | D3×Dic3 | direct (N × H) |
| 129. C2×C32 | C22×C4×C5 | semidirect |
| 131. C3×D3 | C22×C4×C5 | semidirect |
| 137. C3×C5 | C22×C4×D3 | semidirect |
| 138. C3×C5 | C23×Dic3 | semidirect |
| 143. C22×C3 | C4×C5×D3 | semidirect |
| 144. C22×C3 | C2×C5×Dic3 | semidirect |
| 147. C2×D3 | C2×C5×Dic3 | direct (N × H) |
| 153. Dic3 | C22×C5×D3 | direct (N × H) |
| 155. C2×C5 | C2×D3×Dic3 | direct (N × H) |
| 157. C32 | C23×C4×C5 | semidirect |
| 167. C2×C3 | C2×C4×C5×D3 | semidirect |
| 168. C2×C3 | C22×C5×Dic3 | semidirect |
| 171. D3 | C22×C5×Dic3 | direct (N × H) |
| 172. C5 | C22×D3×Dic3 | direct (N × H) |
| 175. C22 | C5×D3×Dic3 | direct (N × H) |
| 180. C3 | C22×C4×C5×D3 | semidirect |
| 181. C3 | C23×C5×Dic3 | semidirect |
| 183. C2 | C2×C5×D3×Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C5×D3 | 2 |
| C22×C5×C3⋊Dic3 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C2×C5×D3×Dic3 | 2 |
| C23×C5×Dic3 | 3 |
| C22×C4×C5×D3 | 3 |
| C22×D3×Dic3 | 5 |