Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. C5×#1570 | C2 | semidirect |
| 4. #10601286 | C2 | semidirect |
| 5. #10601239 | C2 | semidirect |
| 7. #10598228 | C2 | semidirect |
| 54. #1570 | D5 | semidirect |
| 237. C5 | #10666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1570 | 2 |
| #10601551 | 2 |
| #10601306 | 2 |
| #10601286 | 2 |
| #10601239 | 2 |
| #10601219 | 2 |
| #10598228 | 2 |
| #10666 | 5 |