Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. C2×#64733 | C2 | semidirect |
| 5. #10600612 | C2 | semidirect |
| 6. C5×#1375 | C2 | semidirect |
| 7. #10598308 | C2 | semidirect |
| 23. #64729 | C4 | semidirect |
| 24. #64723 | C4 | semidirect |
| 67. #1375 | D5 | semidirect |
| 100. Dic20 | C4⋊C4 | semidirect |
| 102. D40 | C4⋊C4 | semidirect |
| 288. C5 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65006 | 2 |
| C2×#64738 | 2 |
| #10602232 | 2 |
| C2×#64733 | 2 |
| #10600612 | 2 |
| C5×#1375 | 2 |
| #10598308 | 2 |
| #12955 | 5 |