Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. C2×#64731 | C2 | semidirect |
| 4. #10601399 | C2 | semidirect |
| 6. C5×#1387 | C2 | semidirect |
| 7. #10598223 | C2 | semidirect |
| 20. #65184 | C4 | semidirect |
| 69. #1387 | D5 | semidirect |
| 103. Dic20 | C4⋊C4 | semidirect |
| 105. D40 | C4⋊C4 | semidirect |
| 292. C5 | #12821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65184 | 2 |
| #10602232 | 2 |
| C2×#64731 | 2 |
| #10601399 | 2 |
| #10601391 | 2 |
| C5×#1387 | 2 |
| #10598223 | 2 |
| #12821 | 5 |