Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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. #4097 | C2 | semidirect |
| 3. #4055 | C2 | semidirect |
| 4. #4015 | C2 | semidirect |
| 5. C5×#104 | C2 | semidirect |
| 6. #3956 | C2 | semidirect |
| 7. #3937 | C2 | semidirect |
| 53. #104 | D5 | semidirect |
| 108. C5 | #456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4150 | 2 |
| #4097 | 2 |
| #4055 | 2 |
| #4015 | 2 |
| C5×#104 | 2 |
| #3956 | 2 |
| #3937 | 2 |
| #456 | 5 |