Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1234 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1234 conjugacy classes of subgroups — too many to draw. Only its 232 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×#65684 | C2 | semidirect |
| 3. C2×#64927 | C2 | semidirect |
| 4. #10604638 | C2 | direct (N × H) |
| 19. #65684 | C22 | semidirect |
| 20. #64927 | C22 | semidirect |
| 235. C2×C5 | #1536 | semidirect |
| 271. C5 | C2×#1536 | semidirect |
| 290. C2 | #10604638 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66059 | 2 |
| C2×#65684 | 2 |
| C2×#64927 | 2 |
| #10604638 | 2 |
| C2×#1536 | 5 |