Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
356 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10604037 | C2 | semidirect |
| 4. #10604011 | C2 | semidirect |
| 6. #10598594 | C2 | semidirect |
| 7. #10598589 | C2 | semidirect |
| 23. C5×#331 | C4 | semidirect |
| 24. #64764 | C4 | semidirect |
| 25. #64706 | C4 | semidirect |
| 26. #64702 | C4 | semidirect |
| 127. #331 | AGL(1,𝔽5) | semidirect |
| 313. C5 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604620 | 2 |
| #10604606 | 2 |
| #10604037 | 2 |
| #10604011 | 2 |
| #10599174 | 2 |
| #10598594 | 2 |
| #10598589 | 2 |
| #9592 | 5 |