Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
550 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 108 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. #10604722 | C2 | semidirect |
| 4. #10598764 | C2 | semidirect |
| 5. C22×C8×D5 | C4 | semidirect |
| 11. C2×C4×C5×C8 | C4 | semidirect |
| 12. C2×#3952 | C4 | semidirect |
| 14. C2×C4⋊#168 | C4 | semidirect |
| 104. C2×C4×C8 | AGL(1,𝔽5) | semidirect |
| 115. C22×D5 | #106 | semidirect |
| 128. C2×C4×C5 | #106 | semidirect |
| 144. C5×C8 | #99 | semidirect |
| 278. C2×C4 | #3993 | semidirect |
| 285. C8 | #3999 | semidirect |
| 286. C5 | #8608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D20 | 2 |
| #10604722 | 2 |
| #10604167 | 2 |
| #10598764 | 2 |
| #8608 | 5 |