Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1022 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 224 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. C2×#65733 | C2 | semidirect |
| 2. #10617361 | C2 | semidirect |
| 4. #10604798 | C2 | semidirect |
| 5. #10604611 | C2 | semidirect |
| 6. #10603858 | C2 | semidirect |
| 7. C4×#3992 | C2 | semidirect |
| 22. C5×#493 | C4 | semidirect |
| 23. #65444 | C4 | semidirect |
| 24. #65365 | C4 | semidirect |
| 25. #64988 | C4 | semidirect |
| 55. #3992 | D4 | semidirect |
| 104. #493 | AGL(1,𝔽5) | semidirect |
| 178. C4×C5 | #444 | semidirect |
| 244. C5 | #21706 | semidirect |
| 255. C4 | #65733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65733 | 2 |
| #10617361 | 2 |
| #10613513 | 2 |
| #10604798 | 2 |
| #10604611 | 2 |
| #10603858 | 2 |
| C4×#3992 | 2 |
| #21706 | 5 |