Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10604119 | C2 | semidirect |
| 4. AGL(1,𝔽5)×#108 | C2 | semidirect |
| 6. #10598670 | C2 | semidirect |
| 7. #10598631 | C2 | semidirect |
| 23. C5×#361 | C4 | semidirect |
| 24. #64783 | C4 | semidirect |
| 25. #64737 | C4 | semidirect |
| 26. #64716 | C4 | semidirect |
| 128. #361 | AGL(1,𝔽5) | semidirect |
| 288. C5 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604797 | 2 |
| #10604788 | 2 |
| #10604119 | 2 |
| AGL(1,𝔽5)×#108 | 2 |
| #10600049 | 2 |
| #10598670 | 2 |
| #10598631 | 2 |
| #13137 | 5 |