Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
516 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10617422 | C2 | semidirect |
| 3. #10604806 | C2 | semidirect |
| 4. D5⋊#361 | C2 | semidirect |
| 5. #10604786 | C2 | semidirect |
| 6. #10598665 | C2 | semidirect |
| 7. #10598662 | C2 | semidirect |
| 20. C2×C5×D16 | C4 | semidirect |
| 21. C2×#3958 | C4 | semidirect |
| 22. C2×#3958 | C4 | semidirect |
| 25. C2×D80 | C4 | semidirect |
| 40. C2×C5×D8 | C2×C4 | semidirect |
| 52. C2×D40 | C2×C4 | semidirect |
| 67. C2×C5×C16 | C2×C4 | semidirect |
| 70. C2×#672 | C2×C4 | semidirect |
| 141. C2×D16 | AGL(1,𝔽5) | semidirect |
| 207. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 226. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 356. C5 | #13017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617422 | 2 |
| C2×D5×D16 | 2 |
| #10604806 | 2 |
| D5⋊#361 | 2 |
| #10604786 | 2 |
| #10598665 | 2 |
| #10598662 | 2 |
| #13017 | 5 |