Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
206 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10598490 | C2 | direct (N × H) |
| 8. C2×C5×C32 | C4 | semidirect |
| 9. C2×#3926 | C4 | semidirect |
| 10. D5×C32 | C4 | semidirect |
| 23. C5×C32 | C2×C4 | semidirect |
| 24. #3926 | C2×C4 | semidirect |
| 47. C2×C32 | AGL(1,𝔽5) | semidirect |
| 74. C32 | C2×AGL(1,𝔽5) | semidirect |
| 98. C2×C5 | #1424 | semidirect |
| 100. D5 | #1424 | semidirect |
| 115. C5 | C2×#1424 | semidirect |
| 127. C2 | #10598490 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64849 | 2 |
| C2×D5×C32 | 2 |
| #10598490 | 2 |
| C2×#1424 | 5 |