Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
792 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 294 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 |
|---|---|---|
| 2. C2×C32×C4×D5 | C2 | semidirect |
| 3. C32×C5×C22⋊C4 | C2 | semidirect |
| 4. C32×C22⋊Dic5 | C2 | semidirect |
| 5. C32×#685 | C2 | semidirect |
| 6. C3×D5×C22⋊C4 | C3 | direct (N × H) |
| 9. C22×C32×D5 | C4 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 13. C2×C32×Dic5 | C22 | semidirect |
| 17. C2×C3×C4×D5 | C2×C3 | semidirect |
| 18. C3×C5×C22⋊C4 | C2×C3 | semidirect |
| 19. C3×C22⋊Dic5 | C2×C3 | semidirect |
| 20. C3×#685 | C2×C3 | semidirect |
| 22. C22×C32×C5 | C2×C4 | semidirect |
| 27. C2×C32×D5 | C2×C4 | semidirect |
| 31. D5×C22⋊C4 | C32 | direct (N × H) |
| 36. C32×C22⋊C4 | D5 | direct (N × H) |
| 39. C22×C3×D5 | C3×C4 | semidirect |
| 42. C2×C3×C4×C5 | C22×C3 | semidirect |
| 43. C2×C3×Dic5 | C22×C3 | semidirect |
| 50. C32×D5 | C22⋊C4 | direct (N × H) |
| 52. C2×C4×D5 | C2×C32 | semidirect |
| 53. C5×C22⋊C4 | C2×C32 | semidirect |
| 54. C22⋊Dic5 | C2×C32 | semidirect |
| 55. #685 | C2×C32 | semidirect |
| 63. C2×C32×C4 | C2×D5 | semidirect |
| 65. C22×C3×C5 | C2×C3×C4 | semidirect |
| 70. C2×C3×D5 | C2×C3×C4 | semidirect |
| 78. C3×C22⋊C4 | C3×D5 | direct (N × H) |
| 79. C32×C5 | C2×C22⋊C4 | semidirect |
| 82. C22×D5 | C32×C4 | semidirect |
| 85. C2×C4×C5 | C22×C32 | semidirect |
| 86. C2×Dic5 | C22×C32 | semidirect |
| 94. C22×C32 | C4×D5 | semidirect |
| 103. C3×D5 | C3×C22⋊C4 | direct (N × H) |
| 111. C2×C3×C4 | C2×C3×D5 | semidirect |
| 113. C22×C5 | C2×C32×C4 | semidirect |
| 118. C2×D5 | C2×C32×C4 | semidirect |
| 131. C22⋊C4 | C32×D5 | direct (N × H) |
| 132. C3×C5 | C2×C3×C22⋊C4 | semidirect |
| 139. C22×C3 | C3×C4×D5 | semidirect |
| 147. D5 | C32×C22⋊C4 | direct (N × H) |
| 148. C32 | D5×C22⋊C4 | direct (N × H) |
| 156. C2×C4 | C2×C32×D5 | semidirect |
| 162. C5 | C2×C32×C22⋊C4 | semidirect |
| 169. C22 | C32×C4×D5 | semidirect |
| 173. C3 | C3×D5×C22⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×D5 | 2 |
| C2×C32×C4×D5 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C32×C22⋊Dic5 | 2 |
| C32×#685 | 2 |
| C3×D5×C22⋊C4 | 3 |
| C2×C32×C22⋊C4 | 5 |