Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
320 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 20. #64712 | C4 | semidirect |
| 242. C5 | #13141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64737 | 2 |
| #10601453 | 2 |
| #10601447 | 2 |
| #10601368 | 2 |
| C2×#64707 | 2 |
| C5×#1386 | 2 |
| #10598302 | 2 |
| #13141 | 5 |