Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
948 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 114 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×#64907 | C2 | semidirect |
| 3. #10604722 | C2 | semidirect |
| 4. #10604706 | C2 | semidirect |
| 6. C22×C5×Q16 | C4 | semidirect |
| 11. C2×#4065 | C4 | semidirect |
| 13. C22×D40 | C4 | semidirect |
| 16. C2×#3993 | C22 | semidirect |
| 17. C2×#3990 | C22 | semidirect |
| 103. C5×Q16 | C22⋊C4 | semidirect |
| 114. D40 | C22⋊C4 | semidirect |
| 126. C22×Q16 | AGL(1,𝔽5) | semidirect |
| 220. C22×C5 | #360 | semidirect |
| 274. Q16 | C22⋊AGL(1,𝔽5) | semidirect |
| 343. C5 | #12735 | semidirect |
| 357. C22 | #64907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4065 | 2 |
| C2×#64907 | 2 |
| #10604722 | 2 |
| #10604706 | 2 |
| #12735 | 5 |