Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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×#2177 | C2 | semidirect |
| 3. #10599878 | C2 | semidirect |
| 4. #10598316 | C2 | semidirect |
| 5. #10598071 | C2 | semidirect |
| 6. #10598070 | C2 | semidirect |
| 7. #10598010 | C2 | semidirect |
| 15. #64740 | C4 | semidirect |
| 16. #64739 | C4 | semidirect |
| 35. Dic40 | C2×C4 | semidirect |
| 37. D80 | C2×C4 | semidirect |
| 39. #3926 | C2×C4 | semidirect |
| 42. #2177 | D5 | semidirect |
| 160. C5 | #13658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2177 | 2 |
| #10602251 | 2 |
| #10599878 | 2 |
| #10598316 | 2 |
| #10598071 | 2 |
| #10598070 | 2 |
| #10598010 | 2 |
| #13658 | 5 |