Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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. C5×#2158 | C2 | semidirect |
| 5. #10598298 | C2 | semidirect |
| 6. #10598218 | C2 | semidirect |
| 7. #10598216 | C2 | semidirect |
| 54. #2158 | D5 | semidirect |
| 251. C5 | #13500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2158 | 2 |
| C2×#64728 | 2 |
| #10601458 | 2 |
| #10601457 | 2 |
| #10598298 | 2 |
| #10598218 | 2 |
| #10598216 | 2 |
| #13500 | 5 |