Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 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. C5×C22⋊Q8 | C2 | semidirect |
| 3. C2×#688 | C2 | semidirect |
| 4. C22⋊#168 | C2 | semidirect |
| 5. #3941 | C2 | semidirect |
| 7. C2×C5×Q8 | C22 | semidirect |
| 13. C5×C4⋊C4 | C22 | semidirect |
| 16. C2×#168 | C22 | semidirect |
| 35. C22⋊Q8 | D5 | semidirect |
| 40. C22×C5 | SD16 | semidirect |
| 51. C2×Q8 | C2×D5 | semidirect |
| 59. C4⋊C4 | C2×D5 | semidirect |
| 81. C5 | #450 | semidirect |
| 88. C22 | #688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D20 | 2 |
| C5×C22⋊Q8 | 2 |
| C2×#688 | 2 |
| C22⋊#168 | 2 |
| #3941 | 2 |
| #450 | 5 |