Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
650 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 103 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×#65482 | C2 | semidirect |
| 2. C2×#64984 | C2 | semidirect |
| 3. C5×#1974 | C2 | semidirect |
| 4. C2×#64715 | C2 | semidirect |
| 5. #10598149 | C2 | semidirect |
| 27. C2×C5×Q16 | D4 | semidirect |
| 29. C2×C5×D8 | D4 | semidirect |
| 52. #3944 | D4 | semidirect |
| 57. #1974 | D5 | semidirect |
| 151. C2×Q16 | D20 | semidirect |
| 162. C2×D8 | D20 | semidirect |
| 272. C5 | #13331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65482 | 2 |
| C2×#64984 | 2 |
| C5×#1974 | 2 |
| C2×#64715 | 2 |
| #10598149 | 2 |
| #13331 | 5 |