Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 128 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. #10598688 | C2 | direct (N × H) |
| 22. C2×C42×C5 | C8 | semidirect |
| 65. C42×C5 | C2×C8 | semidirect |
| 130. C2×C42 | #170 | semidirect |
| 186. C42 | C2×#170 | semidirect |
| 190. C2×C5 | #1324 | semidirect |
| 227. C5 | C2×#1324 | semidirect |
| 251. C2 | #10598688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65225 | 2 |
| C2×#64913 | 2 |
| #10598688 | 2 |
| C2×#1324 | 5 |