Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 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. C5×#2221 | C2 | semidirect |
| 2. C2×#64739 | C2 | semidirect |
| 3. #10602247 | C2 | semidirect |
| 4. #10602244 | C2 | semidirect |
| 5. #10598316 | C2 | semidirect |
| 6. #10598074 | C2 | semidirect |
| 7. #10598072 | C2 | semidirect |
| 47. #2221 | D5 | semidirect |
| 172. C5 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2221 | 2 |
| C2×#64739 | 2 |
| #10602247 | 2 |
| #10602244 | 2 |
| #10598316 | 2 |
| #10598074 | 2 |
| #10598072 | 2 |
| #13700 | 5 |