Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #10600326 | C2 | semidirect |
| 5. #10600322 | C2 | semidirect |
| 6. #10598119 | C2 | semidirect |
| 7. #10598117 | C2 | semidirect |
| 23. #65329 | C4 | semidirect |
| 24. #65322 | C4 | semidirect |
| 36. C22×Dic10 | C2×C4 | semidirect |
| 55. C2×C4⋊Dic5 | C2×C4 | semidirect |
| 75. C22⋊#168 | C2×C4 | semidirect |
| 418. C5 | #9341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2377 | 2 |
| #10614362 | 2 |
| #10602466 | 2 |
| #10600326 | 2 |
| #10600322 | 2 |
| #10598119 | 2 |
| #10598117 | 2 |
| #9341 | 5 |