Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
214 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 59 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×D5×C32 | C2 | semidirect |
| 3. #10600120 | C2 | semidirect |
| 4. C5×#1423 | C2 | semidirect |
| 5. #10598068 | C2 | semidirect |
| 27. C5×C32 | D4 | semidirect |
| 32. #1423 | D5 | semidirect |
| 82. C32 | D20 | semidirect |
| 89. C2×D5 | D32 | semidirect |
| 126. C5 | #13694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D160 | 2 |
| C2×D5×C32 | 2 |
| #10600120 | 2 |
| C5×#1423 | 2 |
| #10598068 | 2 |
| #13694 | 5 |