Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1146 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 1. C2×C5×#493 | C2 | semidirect |
| 2. C2×#65362 | C2 | semidirect |
| 3. C2×#65359 | C2 | semidirect |
| 4. C2×#64982 | C2 | semidirect |
| 5. #10602073 | C2 | direct (N × H) |
| 6. C2×#64675 | C2 | semidirect |
| 14. C5×#493 | C22 | semidirect |
| 18. #65362 | C22 | semidirect |
| 20. #65359 | C22 | semidirect |
| 23. #64982 | C22 | semidirect |
| 24. #64675 | C22 | semidirect |
| 58. C2×#493 | D5 | semidirect |
| 87. C2×C5×C8 | D8 | semidirect |
| 107. #493 | C2×D5 | semidirect |
| 144. C5×C8 | C2×D8 | semidirect |
| 220. C2×C8 | #686 | semidirect |
| 228. C2×C5 | #1721 | semidirect |
| 261. C8 | C2×#686 | semidirect |
| 262. C5 | C2×#1721 | semidirect |
| 280. C2 | #10602073 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#493 | 2 |
| C2×#65362 | 2 |
| C2×#65359 | 2 |
| C2×#64982 | 2 |
| #10602073 | 2 |
| C2×#64675 | 2 |
| C2×#1721 | 5 |