Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10613740 | C2 | semidirect |
| 2. C5×#2218 | C2 | semidirect |
| 3. #10602251 | C2 | semidirect |
| 4. #10598300 | C2 | semidirect |
| 5. #10598071 | C2 | semidirect |
| 7. C2×C5×D16 | C22 | semidirect |
| 14. C5×#367 | C22 | semidirect |
| 18. #64719 | C22 | semidirect |
| 38. Dic40 | D4 | semidirect |
| 42. D80 | D4 | semidirect |
| 46. #2218 | D5 | semidirect |
| 81. C2×D16 | C2×D5 | semidirect |
| 87. #367 | C2×D5 | semidirect |
| 204. C5 | #13667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613740 | 2 |
| C5×#2218 | 2 |
| #10602251 | 2 |
| #10598300 | 2 |
| #10598071 | 2 |
| #13667 | 5 |