Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 255. C5 | #9770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64970 | 2 |
| C5×#1450 | 2 |
| #10601573 | 2 |
| #10601572 | 2 |
| #10601571 | 2 |
| #10600584 | 2 |
| #9770 | 5 |