Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
554 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 120 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. C23×C3×C5×D3 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×C5×#625 | C2 | semidirect |
| 4. C5×#3757 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 12. C22×C3×C5×D3 | C22 | semidirect |
| 13. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 15. C2×C3×C5×Dic3 | C22 | semidirect |
| 17. #63976 | C5 | direct (N × H) |
| 19. C23×C5×D3 | D3 | semidirect |
| 23. C2×C5×#67 | D3 | semidirect |
| 30. C22×C32×C5 | D4 | semidirect |
| 37. C2×C3×C5×D3 | D4 | semidirect |
| 41. C23×C3×D3 | C2×C5 | semidirect |
| 42. C2×C3×#67 | C2×C5 | semidirect |
| 43. C2×#625 | C2×C5 | semidirect |
| 44. #3757 | C2×C5 | semidirect |
| 45. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 56. C22×C5×D3 | C2×D3 | semidirect |
| 65. C2×C5×Dic3 | C2×D3 | semidirect |
| 82. C22×C3×D3 | C22×C5 | semidirect |
| 83. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 85. C2×C3×Dic3 | C22×C5 | semidirect |
| 98. C22×C3×C5 | #67 | semidirect |
| 99. C22×C3×C5 | #67 | semidirect |
| 107. C2×C5×D3 | #67 | semidirect |
| 114. C23×D3 | C5×D3 | semidirect |
| 118. C2×#67 | C5×D3 | semidirect |
| 124. C32×C5 | #120 | semidirect |
| 135. C22×C32 | C5×D4 | semidirect |
| 142. C2×C3×D3 | C5×D4 | semidirect |
| 169. C22×D3 | C2×C5×D3 | semidirect |
| 178. C2×Dic3 | C2×C5×D3 | semidirect |
| 186. C22×C5 | #625 | semidirect |
| 201. C3×C5 | #937 | semidirect |
| 202. C3×C5 | #953 | semidirect |
| 214. C22×C3 | C5×#67 | semidirect |
| 215. C22×C3 | C5×#67 | semidirect |
| 223. C2×D3 | C5×#67 | semidirect |
| 234. C32 | C5×#120 | semidirect |
| 257. C5 | #63976 | direct (N × H) |
| 265. C22 | C5×#625 | semidirect |
| 270. C3 | C5×#937 | semidirect |
| 271. C3 | C5×#953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C5×D3 | 2 |
| C2×C3×C5×#67 | 2 |
| C2×C5×#625 | 2 |
| C5×#3757 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#953 | 3 |
| C5×#937 | 3 |
| #63976 | 5 |