Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
998 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 248 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 |
|---|---|---|
| 1. C22×C5×D32 | C2 | semidirect |
| 2. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 3. C2×C3×C5×D12 | C2 | semidirect |
| 4. C2×C5×#625 | C2 | semidirect |
| 5. C5×#3802 | C2 | direct (N × H) |
| 8. C22×C3×C5×D3 | C22 | semidirect |
| 10. C2×C5×D32 | C22 | semidirect |
| 11. C2×C32×C4×C5 | C22 | semidirect |
| 12. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 13. C4×C5×C3⋊D3 | C22 | semidirect |
| 14. C3×C5×D12 | C22 | semidirect |
| 15. C5×#625 | C22 | semidirect |
| 16. C2×#3802 | C5 | direct (N × H) |
| 21. C2×C5×D12 | D3 | semidirect |
| 25. C2×C5×C3⋊D3 | D4 | semidirect |
| 28. C2×C3×C5×D3 | C23 | semidirect |
| 30. C32×C4×C5 | C23 | semidirect |
| 31. C5×C3⋊Dic3 | C23 | semidirect |
| 33. C22×D32 | C2×C5 | semidirect |
| 34. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 35. C2×C3×D12 | C2×C5 | semidirect |
| 36. C2×#625 | C2×C5 | semidirect |
| 37. #3802 | C2×C5 | direct (N × H) |
| 43. C22×C5×D3 | C2×D3 | semidirect |
| 46. C2×C3×C4×C5 | C2×D3 | semidirect |
| 50. C5×D12 | C2×D3 | semidirect |
| 54. C2×C32×C5 | C2×D4 | semidirect |
| 56. C5×C3⋊D3 | C2×D4 | semidirect |
| 64. C22×C3×D3 | C22×C5 | semidirect |
| 66. C2×D32 | C22×C5 | semidirect |
| 67. C2×C32×C4 | C22×C5 | semidirect |
| 68. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 69. C4×C3⋊D3 | C22×C5 | semidirect |
| 70. C3×D12 | C22×C5 | semidirect |
| 71. #625 | C22×C5 | semidirect |
| 82. C2×C5×D3 | C22×D3 | semidirect |
| 84. C3×C4×C5 | C22×D3 | semidirect |
| 91. C2×D12 | C5×D3 | semidirect |
| 94. C32×C5 | C22×D4 | semidirect |
| 103. C2×C4×C5 | D32 | semidirect |
| 105. C2×C3⋊D3 | C5×D4 | semidirect |
| 108. C2×C3×D3 | C23×C5 | semidirect |
| 110. C32×C4 | C23×C5 | semidirect |
| 111. C3⋊Dic3 | C23×C5 | semidirect |
| 116. C2×C3×C5 | D3×D4 | semidirect |
| 126. C22×D3 | C2×C5×D3 | semidirect |
| 129. C2×C3×C4 | C2×C5×D3 | semidirect |
| 133. D12 | C2×C5×D3 | semidirect |
| 143. C4×C5 | C2×D32 | semidirect |
| 144. C2×C32 | C2×C5×D4 | semidirect |
| 146. C3⋊D3 | C2×C5×D4 | semidirect |
| 154. C3×C5 | C2×D3×D4 | semidirect |
| 165. C2×D3 | C22×C5×D3 | semidirect |
| 167. C3×C4 | C22×C5×D3 | semidirect |
| 172. C2×C5 | #3802 | direct (N × H) |
| 174. C32 | C22×C5×D4 | semidirect |
| 183. C2×C4 | C5×D32 | semidirect |
| 187. C2×C3 | C5×D3×D4 | semidirect |
| 192. C5 | C2×#3802 | direct (N × H) |
| 200. C4 | C2×C5×D32 | semidirect |
| 202. C3 | C2×C5×D3×D4 | semidirect |
| 205. C2 | C5×#3802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D32 | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×C5×#625 | 2 |
| C5×#3802 | 2 |
| C2×C5×D3×D4 | 3 |
| C2×#3802 | 5 |