Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
328 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 83 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×#1574 | C2 | semidirect |
| 4. #10601546 | C2 | semidirect |
| 5. #10601541 | C2 | semidirect |
| 7. #10598203 | C2 | semidirect |
| 59. #1574 | D5 | semidirect |
| 268. C5 | #10611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1574 | 2 |
| #10601567 | 2 |
| #10601546 | 2 |
| #10601541 | 2 |
| #10601295 | 2 |
| #10598203 | 2 |
| #10611 | 5 |