Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. C2×C16×AGL(1,𝔽5) | C2 | semidirect |
| 4. #10604075 | C2 | semidirect |
| 6. #10598664 | C2 | semidirect |
| 7. #10598619 | C2 | semidirect |
| 21. C5×#357 | C4 | semidirect |
| 22. #64782 | C4 | semidirect |
| 23. #64729 | C4 | semidirect |
| 24. #64711 | C4 | semidirect |
| 126. #357 | AGL(1,𝔽5) | semidirect |
| 328. C5 | #13147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604802 | 2 |
| C2×#64904 | 2 |
| C2×C16×AGL(1,𝔽5) | 2 |
| #10604075 | 2 |
| D5×#357 | 2 |
| #10598664 | 2 |
| #10598619 | 2 |
| #13147 | 5 |