Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
468 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 154 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. C22×C32×C4×C5 | C2 | semidirect |
| 3. C5×#3757 | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 5. C5×#3750 | C2 | semidirect |
| 14. #64138 | C5 | direct (N × H) |
| 15. C22×C3×C4×C5 | D3 | semidirect |
| 29. C22×C32×C4 | C2×C5 | semidirect |
| 31. #3757 | C2×C5 | semidirect |
| 32. #3752 | C2×C5 | semidirect |
| 33. #3750 | C2×C5 | semidirect |
| 47. C22×C4×C5 | C3⋊D3 | semidirect |
| 66. C22×C3×C4 | C5×D3 | semidirect |
| 71. C32×C5 | #123 | semidirect |
| 112. C22×C4 | C5×C3⋊D3 | semidirect |
| 116. C3×C5 | #929 | semidirect |
| 129. C32 | C5×#123 | semidirect |
| 141. C5 | #64138 | direct (N × H) |
| 150. C3 | C5×#929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C2×C5×#638 | 2 |
| C5×#3757 | 2 |
| C5×#3752 | 2 |
| C5×#3750 | 2 |
| C5×#929 | 3 |
| #64138 | 5 |