Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 1. C5×#1707 | C2 | semidirect |
| 2. #10602178 | C2 | semidirect |
| 5. #10602103 | C2 | semidirect |
| 7. C8×#672 | C2 | semidirect |
| 50. #1707 | D5 | semidirect |
| 76. #672 | SD16 | semidirect |
| 108. C5×C8 | SD32 | semidirect |
| 188. C8 | #3960 | semidirect |
| 191. C5 | #12505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1707 | 2 |
| #10602178 | 2 |
| #10602174 | 2 |
| #10602106 | 2 |
| #10602103 | 2 |
| #10598851 | 2 |
| C8×#672 | 2 |
| #12505 | 5 |