Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 130 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. C5×#3828 | C2 | semidirect |
| 2. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C32×C5×M16 | C2 | semidirect |
| 4. C5×#3745 | C2 | semidirect |
| 5. C5×#3744 | C2 | semidirect |
| 12. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 14. C5×#634 | C22 | semidirect |
| 15. C32×C5×C8 | C22 | semidirect |
| 16. #64117 | C5 | direct (N × H) |
| 19. C3×C5×M16 | D3 | semidirect |
| 30. #3828 | C2×C5 | semidirect |
| 31. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 32. C32×M16 | C2×C5 | semidirect |
| 33. #3745 | C2×C5 | semidirect |
| 34. #3744 | C2×C5 | semidirect |
| 43. C3×C5×C8 | C2×D3 | semidirect |
| 53. C5×M16 | C3⋊D3 | semidirect |
| 59. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 61. #634 | C22×C5 | semidirect |
| 62. C32×C8 | C22×C5 | semidirect |
| 72. C3×M16 | C5×D3 | semidirect |
| 75. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 84. C5×C8 | C2×C3⋊D3 | semidirect |
| 105. C3×C8 | C2×C5×D3 | semidirect |
| 121. M16 | C5×C3⋊D3 | semidirect |
| 122. C3×C5 | #908 | semidirect |
| 134. C32 | C5×AGL(1,ℤ/8) | semidirect |
| 143. C8 | C2×C5×C3⋊D3 | semidirect |
| 148. C5 | #64117 | direct (N × H) |
| 156. C3 | C5×#908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C32×C5×M16 | 2 |
| C5×#3745 | 2 |
| C5×#3744 | 2 |
| C5×#908 | 3 |
| #64117 | 5 |