Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
538 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 538 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. C2×#65000 | C2 | semidirect |
| 3. C5×#1975 | C2 | semidirect |
| 4. C2×#64786 | C2 | semidirect |
| 5. C2×#64715 | C2 | semidirect |
| 6. #10598221 | C2 | semidirect |
| 7. #10598154 | C2 | semidirect |
| 17. C2×#3960 | C4 | semidirect |
| 18. C2×#3958 | C4 | semidirect |
| 35. C2×C5×Q16 | C2×C4 | semidirect |
| 37. C2×C5×D8 | C2×C4 | semidirect |
| 68. C2×#672 | C2×C4 | semidirect |
| 73. #1975 | D5 | semidirect |
| 188. C2×Q16 | C4×D5 | semidirect |
| 196. C2×D8 | C4×D5 | semidirect |
| 332. C5 | #13037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65482 | 2 |
| C2×#65000 | 2 |
| C5×#1975 | 2 |
| C2×#64786 | 2 |
| C2×#64715 | 2 |
| #10598221 | 2 |
| #10598154 | 2 |
| #13037 | 5 |