Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
232 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 99 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. C5×#1370 | C2 | semidirect |
| 5. #10598046 | C2 | semidirect |
| 6. #10598045 | C2 | semidirect |
| 7. #10597930 | C2 | semidirect |
| 50. #1370 | D5 | semidirect |
| 109. C5×C8 | M32 | semidirect |
| 116. #168 | M32 | semidirect |
| 201. C8 | #3930 | semidirect |
| 204. C5 | #12017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10600077 | 2 |
| #10600068 | 2 |
| C8×#676 | 2 |
| C5×#1370 | 2 |
| #10598046 | 2 |
| #10598045 | 2 |
| #10597930 | 2 |
| #12017 | 5 |