Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 223. C5 | #9792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65167 | 2 |
| #10604698 | 2 |
| #10604688 | 2 |
| #10604299 | 2 |
| #10604266 | 2 |
| #9792 | 5 |