Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10605120 | C2 | semidirect |
| 3. C5×#1963 | C2 | semidirect |
| 4. #10602607 | C2 | semidirect |
| 5. #10601295 | C2 | semidirect |
| 6. #10598204 | C2 | semidirect |
| 7. #10598105 | C2 | semidirect |
| 15. #65377 | C4 | semidirect |
| 16. #65362 | C4 | semidirect |
| 34. C5×C4⋊Q8 | C2×C4 | semidirect |
| 35. C5×#127 | C2×C4 | semidirect |
| 69. C4×#168 | C2×C4 | semidirect |
| 72. #1963 | D5 | semidirect |
| 119. C42×C5 | D8 | semidirect |
| 211. C4⋊Q8 | C4×D5 | semidirect |
| 216. #127 | C4×D5 | semidirect |
| 323. C42 | #686 | semidirect |
| 388. C5 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615033 | 2 |
| #10605120 | 2 |
| C5×#1963 | 2 |
| #10602607 | 2 |
| #10601295 | 2 |
| #10598204 | 2 |
| #10598105 | 2 |
| #9299 | 5 |