Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 88 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. C32×Q8×D5 | C2 | semidirect |
| 3. C3×#6717 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. C3×#6658 | C2 | semidirect |
| 6. C3×#6656 | C2 | semidirect |
| 7. C3×D5×C3⋊C8 | C2 | semidirect |
| 9. D5×#215 | C3 | direct (N × H) |
| 11. C32×C5×Q8 | C22 | semidirect |
| 17. C32×Dic10 | C22 | semidirect |
| 19. C3×C3⋊#168 | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 23. C3×Q8×D5 | D3 | semidirect |
| 24. C3×Q8×D5 | C2×C3 | semidirect |
| 28. #6717 | C2×C3 | semidirect |
| 29. C5×#215 | C2×C3 | semidirect |
| 34. #6658 | C2×C3 | semidirect |
| 35. #6656 | C2×C3 | semidirect |
| 36. D5×C3⋊C8 | C2×C3 | semidirect |
| 51. C3×#215 | D5 | direct (N × H) |
| 56. C3×C5×Q8 | C2×D3 | semidirect |
| 57. C3×C5×Q8 | C22×C3 | semidirect |
| 73. C3×Dic10 | C2×D3 | semidirect |
| 74. C3×Dic10 | C22×C3 | semidirect |
| 77. C3⋊#168 | C22×C3 | semidirect |
| 79. C5×C3⋊C8 | C22×C3 | semidirect |
| 85. C32×D5 | SD16 | semidirect |
| 86. Q8×D5 | C3×D3 | semidirect |
| 96. C32×Q8 | C2×D5 | semidirect |
| 103. C3×C3⋊C8 | C2×D5 | semidirect |
| 138. #215 | C3×D5 | direct (N × H) |
| 140. C32×C5 | C2×SD16 | semidirect |
| 142. C5×Q8 | C2×C3×D3 | semidirect |
| 149. Dic10 | C2×C3×D3 | semidirect |
| 168. C3×D5 | #215 | direct (N × H) |
| 169. C3×D5 | C3×SD16 | semidirect |
| 180. C3×Q8 | D3×D5 | semidirect |
| 181. C3×Q8 | C2×C3×D5 | semidirect |
| 197. C3⋊C8 | C2×C3×D5 | semidirect |
| 218. C3×C5 | C2×#215 | semidirect |
| 219. C3×C5 | C2×C3×SD16 | semidirect |
| 244. D5 | C3×#215 | direct (N × H) |
| 245. C32 | D5×SD16 | semidirect |
| 249. Q8 | C3×D3×D5 | semidirect |
| 267. C5 | C2×C3×#215 | semidirect |
| 277. C3 | D5×#215 | direct (N × H) |
| 278. C3 | C3×D5×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×D5 | 2 |
| C3×D5×D12 | 2 |
| C3×#6717 | 2 |
| C3×C5×#215 | 2 |
| C3×#6658 | 2 |
| C3×#6656 | 2 |
| C3×D5×C3⋊C8 | 2 |
| C3×D5×SD16 | 3 |
| D5×#215 | 3 |
| C2×C3×#215 | 5 |