Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#65200 | C2 | semidirect |
| 2. #10613513 | C2 | semidirect |
| 3. D5×#493 | C2 | semidirect |
| 4. C5×#2246 | C2 | semidirect |
| 5. #10602259 | C2 | semidirect |
| 6. #10602084 | C2 | semidirect |
| 7. #10602083 | C2 | semidirect |
| 8. #10599854 | C2 | semidirect |
| 9. C4×#3930 | C2 | semidirect |
| 16. C2×C5×D16 | C22 | semidirect |
| 18. C5×#493 | C22 | semidirect |
| 20. #65444 | C22 | semidirect |
| 23. C2×#3959 | C22 | semidirect |
| 24. C2×#3958 | C22 | semidirect |
| 28. C2×#3932 | C22 | semidirect |
| 30. #64988 | C22 | semidirect |
| 33. C4×C5×C16 | C22 | semidirect |
| 34. #64722 | C22 | semidirect |
| 35. C4×#672 | C22 | semidirect |
| 78. #3930 | D4 | semidirect |
| 86. #2246 | D5 | semidirect |
| 130. C5×C16 | C2×D4 | semidirect |
| 131. #672 | C2×D4 | semidirect |
| 142. C2×D16 | C2×D5 | semidirect |
| 152. #493 | C2×D5 | semidirect |
| 157. C4×C16 | C2×D5 | semidirect |
| 243. C4×C5 | #509 | semidirect |
| 292. C16 | D4×D5 | semidirect |
| 332. C5 | #33717 | semidirect |
| 346. C4 | #65200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65200 | 2 |
| #10613513 | 2 |
| D5×#493 | 2 |
| C5×#2246 | 2 |
| #10602259 | 2 |
| #10602084 | 2 |
| #10602083 | 2 |
| #10599854 | 2 |
| C4×#3930 | 2 |
| #33717 | 5 |