Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. C5×#2248 | C2 | semidirect |
| 2. #10602106 | C2 | semidirect |
| 3. #10602091 | C2 | semidirect |
| 4. #10602084 | C2 | semidirect |
| 6. #10599854 | C2 | semidirect |
| 7. C16×#168 | C2 | semidirect |
| 47. #2248 | D5 | semidirect |
| 72. C5×C16 | D8 | semidirect |
| 73. #672 | D8 | semidirect |
| 105. #168 | SD32 | semidirect |
| 160. C16 | #686 | semidirect |
| 184. C5 | #12517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2248 | 2 |
| #10602106 | 2 |
| #10602091 | 2 |
| #10602084 | 2 |
| #10602069 | 2 |
| #10599854 | 2 |
| C16×#168 | 2 |
| #12517 | 5 |