Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #10602654 | C2 | semidirect |
| 3. #10602653 | C2 | semidirect |
| 4. #10598283 | C2 | semidirect |
| 5. #10598275 | C2 | semidirect |
| 6. C5×#540 | C4 | semidirect |
| 8. C5×#496 | C4 | semidirect |
| 11. C5×#488 | C4 | semidirect |
| 16. C5×#433 | C4 | semidirect |
| 30. C5×#127 | C2×C4 | semidirect |
| 33. C5×#125 | C2×C4 | semidirect |
| 51. C5×#97 | C2×C4 | semidirect |
| 52. C4×C5×C8 | C2×C4 | semidirect |
| 101. #540 | Dic5 | semidirect |
| 103. #496 | Dic5 | semidirect |
| 106. #488 | Dic5 | semidirect |
| 111. #433 | Dic5 | semidirect |
| 159. #127 | C2×Dic5 | semidirect |
| 162. #125 | C2×Dic5 | semidirect |
| 184. #97 | C2×Dic5 | semidirect |
| 185. C4×C8 | C2×Dic5 | semidirect |
| 289. C5 | #13609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3220 | 2 |
| #10602654 | 2 |
| #10602653 | 2 |
| #10598283 | 2 |
| #10598275 | 2 |
| #13609 | 5 |