Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 255. C5 | #9770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#487 | 2 |
| #10602568 | 2 |
| #10602567 | 2 |
| #10602566 | 2 |
| #10600584 | 2 |
| #10600517 | 2 |
| #9770 | 5 |