Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
618 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 199 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×#64674 | C2 | semidirect |
| 4. C5×#1273 | C2 | semidirect |
| 5. #10598144 | C2 | semidirect |
| 45. #1273 | D5 | semidirect |
| 77. C2×#168 | M16 | semidirect |
| 224. C5 | #8147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#676 | 2 |
| C4×#3952 | 2 |
| C2×#64674 | 2 |
| C5×#1273 | 2 |
| #10598144 | 2 |
| #8147 | 5 |