Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
834 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 834 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 |
|---|---|---|
| 2. C2×#64913 | C2 | semidirect |
| 3. #10598823 | C2 | direct (N × H) |
| 13. #64913 | C22 | semidirect |
| 21. C22×C5×D4 | C8 | semidirect |
| 61. C2×C5×D4 | C2×C8 | semidirect |
| 148. C22×D4 | #170 | semidirect |
| 211. C2×D4 | C2×#170 | semidirect |
| 241. C2×C5 | #1318 | semidirect |
| 290. C5 | C2×#1318 | semidirect |
| 321. C2 | #10598823 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65510 | 2 |
| C2×#64913 | 2 |
| #10598823 | 2 |
| C2×#1318 | 5 |