Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 107 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×#1810 | C2 | semidirect |
| 3. #10602760 | C2 | semidirect |
| 4. #10600773 | C2 | semidirect |
| 6. #10600765 | C2 | semidirect |
| 11. C22×#677 | C4 | semidirect |
| 21. C2×#3953 | C4 | semidirect |
| 22. C2×#3949 | C4 | semidirect |
| 23. C2×#3948 | C4 | semidirect |
| 80. #1810 | D5 | semidirect |
| 399. C5 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65403 | 2 |
| C5×#1810 | 2 |
| #10602760 | 2 |
| #10600773 | 2 |
| #10600770 | 2 |
| #10600765 | 2 |
| #10600763 | 2 |
| #9816 | 5 |