Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
696 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×#65676 | C2 | semidirect |
| 3. C2×#64927 | C2 | semidirect |
| 4. #10604177 | C2 | semidirect |
| 5. #10598722 | C2 | semidirect |
| 61. #4002 | D4 | semidirect |
| 255. C2×D5 | #329 | semidirect |
| 380. C5 | #9119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65676 | 2 |
| #10608393 | 2 |
| C2×#64927 | 2 |
| #10604177 | 2 |
| #10598722 | 2 |
| #9119 | 5 |