Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
302 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. C5×#1416 | C2 | semidirect |
| 5. #10598317 | C2 | semidirect |
| 6. #10598088 | C2 | semidirect |
| 7. #10598069 | C2 | semidirect |
| 12. D5×Q32 | C4 | semidirect |
| 32. C5×Q32 | C2×C4 | semidirect |
| 40. Dic40 | C2×C4 | semidirect |
| 51. #1416 | D5 | direct (N × H) |
| 120. Q32 | C4×D5 | semidirect |
| 167. D5 | #1416 | direct (N × H) |
| 187. C5 | C2×#1416 | 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×D5×C32 | 2 |
| D5×#366 | 2 |
| C5×#1416 | 2 |
| #10598317 | 2 |
| #10598088 | 2 |
| #10598069 | 2 |
| C2×#1416 | 5 |