Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #10611060 | C2 | semidirect |
| 3. #10601621 | C2 | semidirect |
| 4. #10601597 | C2 | semidirect |
| 5. #10601591 | C2 | semidirect |
| 6. C5×#1307 | C2 | semidirect |
| 7. #10598201 | C2 | semidirect |
| 89. #1307 | D5 | semidirect |
| 386. C5 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611060 | 2 |
| #10610789 | 2 |
| #10601621 | 2 |
| #10601597 | 2 |
| #10601591 | 2 |
| C5×#1307 | 2 |
| #10598201 | 2 |
| #9350 | 5 |