Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #10610222 | C2 | semidirect |
| 3. #10601583 | C2 | semidirect |
| 4. #10601567 | C2 | semidirect |
| 5. #10600616 | C2 | semidirect |
| 6. C5×#1275 | C2 | semidirect |
| 7. #10598229 | C2 | semidirect |
| 23. #64984 | C4 | semidirect |
| 24. #64983 | C4 | semidirect |
| 75. #1275 | D5 | semidirect |
| 110. C2×C5×C8 | D8 | semidirect |
| 296. C2×C8 | D40 | semidirect |
| 360. C5 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611034 | 2 |
| #10610222 | 2 |
| #10601583 | 2 |
| #10601567 | 2 |
| #10600616 | 2 |
| C5×#1275 | 2 |
| #10598229 | 2 |
| #9293 | 5 |