Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 23. C5×#332 | C4 | semidirect |
| 24. #64767 | C4 | semidirect |
| 25. #64706 | C4 | semidirect |
| 26. #64702 | C4 | semidirect |
| 140. #332 | AGL(1,𝔽5) | semidirect |
| 343. C5 | #9566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604674 | 2 |
| #10604667 | 2 |
| #10604033 | 2 |
| #10604030 | 2 |
| D5×#332 | 2 |
| #10598587 | 2 |
| #10598586 | 2 |
| #9566 | 5 |