Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 1. C5×#3206 | C2 | semidirect |
| 3. #10614990 | C2 | semidirect |
| 4. #10602604 | C2 | semidirect |
| 5. #10602567 | C2 | semidirect |
| 6. #10601549 | C2 | semidirect |
| 7. #10598237 | C2 | semidirect |
| 79. #3206 | D5 | semidirect |
| 111. C2×D20 | SD16 | semidirect |
| 400. C5 | #10240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3206 | 2 |
| #10615028 | 2 |
| #10614990 | 2 |
| #10602604 | 2 |
| #10602567 | 2 |
| #10601549 | 2 |
| #10598237 | 2 |
| #10240 | 5 |