Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
276 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 240. C5 | #10613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10601301 | 2 |
| #10601300 | 2 |
| #10601299 | 2 |
| #10601288 | 2 |
| C5×#1309 | 2 |
| #10613 | 5 |