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×#65203 | C2 | semidirect |
| 2. #10613530 | C2 | semidirect |
| 3. D5×#493 | C2 | semidirect |
| 4. C5×#2248 | C2 | semidirect |
| 5. #10602274 | C2 | semidirect |
| 6. #10602106 | C2 | semidirect |
| 7. #10602083 | C2 | semidirect |
| 8. #10599853 | C2 | semidirect |
| 9. C4×#3930 | C2 | semidirect |
| 16. C2×C5×SD32 | C22 | semidirect |
| 17. C5×#494 | C22 | semidirect |
| 20. #65480 | C22 | semidirect |
| 21. C2×#3960 | C22 | semidirect |
| 24. C2×#3958 | C22 | semidirect |
| 28. C2×D80 | C22 | semidirect |
| 31. #64984 | C22 | semidirect |
| 33. C4×C5×C16 | C22 | semidirect |
| 34. #64722 | C22 | semidirect |
| 35. C4×#672 | C22 | semidirect |
| 78. #3930 | D4 | semidirect |
| 84. #2248 | D5 | semidirect |
| 130. C5×C16 | C2×D4 | semidirect |
| 131. #672 | C2×D4 | semidirect |
| 140. C2×SD32 | C2×D5 | semidirect |
| 146. #494 | C2×D5 | semidirect |
| 157. C4×C16 | C2×D5 | semidirect |
| 244. C4×C5 | #509 | semidirect |
| 292. C16 | D4×D5 | semidirect |
| 332. C5 | #33717 | semidirect |
| 346. C4 | #65203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65203 | 2 |
| #10613530 | 2 |
| D5×#493 | 2 |
| C5×#2248 | 2 |
| #10602274 | 2 |
| #10602106 | 2 |
| #10602083 | 2 |
| #10599853 | 2 |
| C4×#3930 | 2 |
| #33717 | 5 |