Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 420 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. #10604639 | C2 | semidirect |
| 4. #10604628 | C2 | semidirect |
| 6. #10598533 | C2 | semidirect |
| 7. #10598528 | C2 | semidirect |
| 17. C5×#492 | C4 | semidirect |
| 20. #65370 | C4 | semidirect |
| 21. #65359 | C4 | semidirect |
| 23. #64971 | C4 | semidirect |
| 117. #492 | AGL(1,𝔽5) | semidirect |
| 296. C5 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617365 | 2 |
| #10613485 | 2 |
| #10604639 | 2 |
| #10604628 | 2 |
| #10604595 | 2 |
| #10598533 | 2 |
| #10598528 | 2 |
| #9415 | 5 |