Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 231. C5 | #9810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65163 | 2 |
| #10604696 | 2 |
| #10604688 | 2 |
| #10604340 | 2 |
| #10604278 | 2 |
| #9810 | 5 |