Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1350 conjugacy classes of subgroups; only the 504 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 504 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. #10604190 | C2 | semidirect |
| 41. C42×C5 | M16 | semidirect |
| 86. C4×C5 | #423 | semidirect |
| 105. C42 | #700 | semidirect |
| 124. C5 | #20791 | semidirect |
| 132. C4 | #65681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65681 | 2 |
| C43×D5 | 2 |
| #10604190 | 2 |
| #20791 | 5 |