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. C2×C32×C5×D4 | C2 | semidirect |
| 2. C5×#3828 | C2 | semidirect |
| 3. C5×#3754 | C2 | semidirect |
| 4. C5×#3753 | C2 | semidirect |
| 5. C5×#3748 | C2 | semidirect |
| 12. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 14. C5×#634 | C22 | semidirect |
| 15. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 16. #64141 | C5 | direct (N × H) |
| 17. C2×C3×C5×D4 | D3 | semidirect |
| 30. C2×C32×D4 | C2×C5 | semidirect |
| 31. #3828 | C2×C5 | semidirect |
| 32. #3754 | C2×C5 | semidirect |
| 33. #3753 | C2×C5 | semidirect |
| 34. #3748 | C2×C5 | semidirect |
| 50. C2×C5×D4 | C3⋊D3 | semidirect |
| 59. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 61. #634 | C22×C5 | semidirect |
| 62. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 70. C2×C3×D4 | C5×D3 | semidirect |
| 75. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 118. C2×D4 | C5×C3⋊D3 | semidirect |
| 122. C3×C5 | #932 | semidirect |
| 134. C32 | C5×AGL(1,ℤ/8) | semidirect |
| 148. C5 | #64141 | direct (N × H) |
| 156. C3 | C5×#932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C5×#3828 | 2 |
| C5×#3754 | 2 |
| C5×#3753 | 2 |
| C5×#3748 | 2 |
| C5×#932 | 3 |
| #64141 | 5 |