Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C2×#681 | C2 | semidirect |
| 3. C2×#676 | C2 | semidirect |
| 4. C5×C22⋊C8 | C2 | semidirect |
| 5. #3952 | C2 | semidirect |
| 6. #3946 | C2 | semidirect |
| 7. C8×Dic5 | C2 | semidirect |
| 37. #168 | D4 | semidirect |
| 43. C22⋊C8 | D5 | semidirect |
| 57. Dic5 | M16 | semidirect |
| 92. C5 | #436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊D5 | 2 |
| C2×#681 | 2 |
| C2×#676 | 2 |
| C5×C22⋊C8 | 2 |
| #3952 | 2 |
| #3946 | 2 |
| C8×Dic5 | 2 |
| #436 | 5 |