Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4126 conjugacy classes of subgroups; only the 2795 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2795 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 |
|---|---|---|
| 3. C22×#3935 | C2 | direct (N × H) |
| 8. C23×#168 | C4 | semidirect |
| 10. C2×#3935 | C22 | direct (N × H) |
| 20. C22×#168 | C2×C4 | semidirect |
| 22. #3935 | C23 | direct (N × H) |
| 37. C2×#168 | C22×C4 | semidirect |
| 46. C23×C5 | #97 | semidirect |
| 56. #168 | C23×C4 | semidirect |
| 68. C22×C5 | C2×#97 | semidirect |
| 88. C2×C5 | C22×#97 | semidirect |
| 91. C23 | #3935 | direct (N × H) |
| 102. C5 | C23×#97 | semidirect |
| 103. C22 | C2×#3935 | direct (N × H) |
| 110. C2 | C22×#3935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C5 | 2 |
| C24×#168 | 2 |
| C22×#3935 | 2 |
| C23×#97 | 5 |