Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 1. C5×#2159 | C2 | semidirect |
| 3. C2×#64731 | C2 | semidirect |
| 4. #10601455 | C2 | semidirect |
| 7. #10598214 | C2 | semidirect |
| 57. #2159 | D5 | semidirect |
| 268. C5 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2159 | 2 |
| C2×#64736 | 2 |
| C2×#64731 | 2 |
| #10601455 | 2 |
| #10601445 | 2 |
| #10601421 | 2 |
| #10598214 | 2 |
| #13478 | 5 |