Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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. C5×#2159 | C2 | semidirect |
| 3. C2×#64738 | C2 | semidirect |
| 4. C2×#64734 | C2 | semidirect |
| 5. #10601424 | C2 | semidirect |
| 6. #10601391 | C2 | semidirect |
| 7. #10598217 | C2 | semidirect |
| 60. C5×M32 | D4 | semidirect |
| 78. #2159 | D5 | semidirect |
| 238. M32 | D20 | semidirect |
| 384. C5 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610912 | 2 |
| C5×#2159 | 2 |
| C2×#64738 | 2 |
| C2×#64734 | 2 |
| #10601424 | 2 |
| #10601391 | 2 |
| #10598217 | 2 |
| #13386 | 5 |