Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#64762 | C2 | semidirect |
| 3. C2×#64761 | C2 | semidirect |
| 4. #10598289 | C2 | semidirect |
| 5. #10598288 | C2 | semidirect |
| 8. C5×#532 | C4 | semidirect |
| 10. C5×#497 | C4 | semidirect |
| 12. C5×#496 | C4 | semidirect |
| 16. C4×C5×M16 | C4 | semidirect |
| 40. C5×C4⋊Q8 | C2×C4 | semidirect |
| 41. C5×#127 | C2×C4 | semidirect |
| 54. C5×#97 | C2×C4 | semidirect |
| 55. C5×#97 | C2×C4 | semidirect |
| 118. #532 | Dic5 | semidirect |
| 120. #497 | Dic5 | semidirect |
| 122. #496 | Dic5 | semidirect |
| 128. C4×M16 | Dic5 | semidirect |
| 189. C4⋊Q8 | C2×Dic5 | semidirect |
| 190. #127 | C2×Dic5 | semidirect |
| 206. #97 | C2×Dic5 | semidirect |
| 207. #97 | C2×Dic5 | semidirect |
| 325. C5 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3153 | 2 |
| C2×#64762 | 2 |
| C2×#64761 | 2 |
| #10598289 | 2 |
| #10598288 | 2 |
| #13578 | 5 |