Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
246 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 21. C5×#108 | C8 | semidirect |
| 92. #108 | #168 | semidirect |
| 156. C5 | #7176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#108 | 2 |
| C4×#3944 | 2 |
| C2×#64678 | 2 |
| #7176 | 5 |