Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10611044 | C2 | semidirect |
| 5. #10601317 | C2 | semidirect |
| 6. #10600655 | C2 | semidirect |
| 7. C5×#1299 | C2 | semidirect |
| 83. #1299 | D5 | semidirect |
| 337. C5 | #10107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611044 | 2 |
| #10610796 | 2 |
| #10610269 | 2 |
| #10601554 | 2 |
| #10601317 | 2 |
| #10600655 | 2 |
| C5×#1299 | 2 |
| #10107 | 5 |