Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10611002 | C2 | semidirect |
| 4. #10601586 | C2 | semidirect |
| 6. #10600615 | C2 | semidirect |
| 7. C5×#1281 | C2 | semidirect |
| 83. #1281 | D5 | semidirect |
| 337. C5 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611002 | 2 |
| #10610999 | 2 |
| #10610228 | 2 |
| #10601586 | 2 |
| #10601583 | 2 |
| #10600615 | 2 |
| C5×#1281 | 2 |
| #10226 | 5 |