Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
512 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C5×#3230 | C2 | semidirect |
| 4. #10602634 | C2 | semidirect |
| 5. #10602571 | C2 | semidirect |
| 7. #10598235 | C2 | semidirect |
| 78. #3230 | D5 | semidirect |
| 352. C5 | #10202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3230 | 2 |
| #10615094 | 2 |
| #10614930 | 2 |
| #10602634 | 2 |
| #10602571 | 2 |
| #10601582 | 2 |
| #10598235 | 2 |
| #10202 | 5 |