Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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. C22×C5×C8 | C2 | semidirect |
| 3. C22×#168 | C2 | semidirect |
| 4. #3952 | C2 | direct (N × H) |
| 13. C2×C5×C8 | C22 | semidirect |
| 15. C2×#168 | C22 | semidirect |
| 20. C22×D5 | C8 | semidirect |
| 35. C22×C8 | D5 | semidirect |
| 44. C2×D5 | C2×C8 | semidirect |
| 59. C2×C8 | C2×D5 | semidirect |
| 60. C2×C5 | C22⋊C8 | semidirect |
| 81. C5 | C2×C22⋊C8 | semidirect |
| 95. C2 | #3952 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D5 | 2 |
| C22×C5×C8 | 2 |
| C22×#168 | 2 |
| #3952 | 2 |
| C2×C22⋊C8 | 5 |