Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 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×#689 | C2 | semidirect |
| 5. #3967 | C2 | semidirect |
| 6. #3942 | C2 | semidirect |
| 7. #3939 | C2 | semidirect |
| 46. C22×C5 | Q16 | semidirect |
| 87. C5 | #467 | semidirect |
| 90. C22 | #689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C22⋊Q8 | 2 |
| C2×#689 | 2 |
| #4070 | 2 |
| C22×#168 | 2 |
| #3967 | 2 |
| #3942 | 2 |
| #3939 | 2 |
| #467 | 5 |