Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
574 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 117 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. #10610994 | C2 | semidirect |
| 4. #10601321 | C2 | semidirect |
| 6. C5×#1303 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 71. #1303 | D5 | semidirect |
| 335. C5 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610994 | 2 |
| #10605443 | 2 |
| #10601567 | 2 |
| #10601321 | 2 |
| #10601295 | 2 |
| C5×#1303 | 2 |
| #10598111 | 2 |
| #9398 | 5 |