Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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×C5×Q64 | C2 | semidirect |
| 4. C2×#64742 | C2 | semidirect |
| 5. #10598317 | C2 | semidirect |
| 6. #10598088 | C2 | semidirect |
| 50. C2×Q64 | D5 | semidirect |
| 142. C2×D5 | Q64 | semidirect |
| 199. C5 | #13665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q32 | 2 |
| C2×C5×Q64 | 2 |
| #10602297 | 2 |
| C2×#64742 | 2 |
| #10598317 | 2 |
| #10598088 | 2 |
| #10598085 | 2 |
| #13665 | 5 |