Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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. #4090 | C2 | semidirect |
| 3. C2×#689 | C2 | semidirect |
| 6. C2×Dic20 | C2 | semidirect |
| 7. #3947 | C2 | semidirect |
| 86. C5 | #497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×SD16 | 2 |
| #4090 | 2 |
| C2×#689 | 2 |
| #4082 | 2 |
| C2×#687 | 2 |
| C2×Dic20 | 2 |
| #3947 | 2 |
| #497 | 5 |