Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#65204 | C2 | semidirect |
| 2. D5×#494 | C2 | semidirect |
| 4. C5×#2248 | C2 | semidirect |
| 5. #10602275 | C2 | semidirect |
| 6. #10602105 | C2 | semidirect |
| 7. #10602084 | C2 | semidirect |
| 8. #10599859 | C2 | semidirect |
| 9. C4×#3930 | C2 | semidirect |
| 78. #3930 | D4 | semidirect |
| 84. #2248 | D5 | semidirect |
| 234. C4×C5 | #510 | semidirect |
| 317. C5 | #33718 | semidirect |
| 328. C4 | #65204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65204 | 2 |
| D5×#494 | 2 |
| #10613513 | 2 |
| C5×#2248 | 2 |
| #10602275 | 2 |
| #10602105 | 2 |
| #10602084 | 2 |
| #10599859 | 2 |
| C4×#3930 | 2 |
| #33718 | 5 |