Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
274 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 69 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×#2207 | C2 | semidirect |
| 3. #10601707 | C2 | semidirect |
| 4. Q16×#168 | C2 | semidirect |
| 5. #10598281 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10598046 | C2 | semidirect |
| 48. #2207 | D5 | semidirect |
| 62. C5×Q16 | D8 | semidirect |
| 124. #168 | SD32 | semidirect |
| 170. Q16 | #686 | semidirect |
| 223. C5 | #12425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2207 | 2 |
| #10602069 | 2 |
| #10601707 | 2 |
| Q16×#168 | 2 |
| #10598281 | 2 |
| #10598051 | 2 |
| #10598046 | 2 |
| #12425 | 5 |