Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
190 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 4. #10598491 | C2 | direct (N × H) |
| 12. C2×C5×C32 | C4 | semidirect |
| 13. C2×#3926 | C4 | semidirect |
| 14. #64667 | C4 | semidirect |
| 30. C5×C32 | C2×C4 | semidirect |
| 31. #3926 | C2×C4 | semidirect |
| 59. C2×C32 | AGL(1,𝔽5) | semidirect |
| 92. C32 | C2×AGL(1,𝔽5) | semidirect |
| 119. C2×C5 | #1426 | semidirect |
| 137. C5 | C2×#1426 | semidirect |
| 149. C2 | #10598491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64852 | 2 |
| C2×#64850 | 2 |
| C2×#64667 | 2 |
| #10598491 | 2 |
| C2×#1426 | 5 |