Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2161 | C2 | semidirect |
| 4. Dic5×#108 | C2 | semidirect |
| 6. #10598301 | C2 | semidirect |
| 7. #10598224 | C2 | semidirect |
| 20. #64737 | C4 | semidirect |
| 21. #64736 | C4 | semidirect |
| 57. #2161 | D5 | semidirect |
| 264. C5 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2161 | 2 |
| #10602235 | 2 |
| #10601489 | 2 |
| Dic5×#108 | 2 |
| #10601483 | 2 |
| #10598301 | 2 |
| #10598224 | 2 |
| #13137 | 5 |