Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 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×#65208 | C2 | semidirect |
| 2. #10613530 | C2 | semidirect |
| 3. C5×#2247 | C2 | semidirect |
| 4. #10602293 | C2 | semidirect |
| 5. #10602106 | C2 | semidirect |
| 6. #10599853 | C2 | semidirect |
| 7. C4×D5×C16 | C2 | semidirect |
| 52. D5×C16 | D4 | semidirect |
| 57. #2247 | D5 | semidirect |
| 159. C4×C5 | #508 | semidirect |
| 217. C5 | #33713 | semidirect |
| 226. C4 | #65208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65208 | 2 |
| #10613530 | 2 |
| C5×#2247 | 2 |
| #10602293 | 2 |
| #10602106 | 2 |
| #10599853 | 2 |
| C4×D5×C16 | 2 |
| #33713 | 5 |