Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 450 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 |
|---|---|---|
| 2. C5×#1546 | C2 | semidirect |
| 3. C2×#64767 | C2 | semidirect |
| 5. #10601313 | C2 | semidirect |
| 7. #10598235 | C2 | semidirect |
| 72. #1546 | D5 | semidirect |
| 343. C5 | #10550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614934 | 2 |
| C5×#1546 | 2 |
| C2×#64767 | 2 |
| #10601551 | 2 |
| #10601313 | 2 |
| #10601296 | 2 |
| #10598235 | 2 |
| #10550 | 5 |