Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×D160 | C2 | semidirect |
| 2. C2×#64667 | C2 | semidirect |
| 3. #10600120 | C2 | semidirect |
| 4. C5×#1424 | C2 | semidirect |
| 5. #10598068 | C2 | semidirect |
| 27. C5×C32 | D4 | semidirect |
| 32. #1424 | D5 | semidirect |
| 82. C32 | D20 | semidirect |
| 124. C5 | #13697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D160 | 2 |
| C2×#64667 | 2 |
| #10600120 | 2 |
| C5×#1424 | 2 |
| #10598068 | 2 |
| #13697 | 5 |