Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 144. C4×C5 | #368 | semidirect |
| 206. C5 | #13179 | semidirect |
| 217. C4 | #64851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64851 | 2 |
| #10603859 | 2 |
| C4×#3996 | 2 |
| D5×C4⋊C16 | 2 |
| #10598667 | 2 |
| #13179 | 5 |