Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
486 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. C2×#64850 | C2 | semidirect |
| 5. #10598664 | C2 | semidirect |
| 17. C5×C22⋊C16 | C4 | semidirect |
| 18. C22⋊#672 | C4 | semidirect |
| 19. #64727 | C4 | semidirect |
| 44. C2×C5×C16 | C2×C4 | semidirect |
| 45. C2×#672 | C2×C4 | semidirect |
| 104. C22⋊C16 | AGL(1,𝔽5) | semidirect |
| 167. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 176. C22×C5 | #367 | semidirect |
| 184. C2×D5 | #367 | semidirect |
| 289. C5 | #12920 | semidirect |
| 305. C22 | #64850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3994 | 2 |
| #10604723 | 2 |
| C2×#64850 | 2 |
| D5×C22⋊C16 | 2 |
| #10598664 | 2 |
| #12920 | 5 |