Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 19. #64681 | C4 | semidirect |
| 20. C4×#672 | C4 | semidirect |
| 195. C5 | #12893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1833 | 2 |
| #10600689 | 2 |
| #10600674 | 2 |
| #10598222 | 2 |
| #10598220 | 2 |
| #10598216 | 2 |
| #10598215 | 2 |
| #12893 | 5 |