Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 3. #10601503 | C2 | semidirect |
| 5. #10601447 | C2 | semidirect |
| 6. C5×#1382 | C2 | semidirect |
| 7. #10598296 | C2 | semidirect |
| 21. C2×#3932 | C4 | semidirect |
| 39. C2×Dic20 | C2×C4 | semidirect |
| 51. C2×C5×C16 | C2×C4 | semidirect |
| 70. #1382 | D5 | semidirect |
| 194. C2×C16 | C4×D5 | semidirect |
| 300. C5 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3932 | 2 |
| #10610898 | 2 |
| #10601503 | 2 |
| C2×#64715 | 2 |
| #10601447 | 2 |
| C5×#1382 | 2 |
| #10598296 | 2 |
| #13019 | 5 |