Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 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. #4072 | C2 | semidirect |
| 3. #3964 | C2 | semidirect |
| 4. #3964 | C2 | semidirect |
| 5. C22⋊#168 | C2 | semidirect |
| 6. #3940 | C2 | semidirect |
| 7. #3939 | C2 | semidirect |
| 84. C5 | #482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#121 | 2 |
| #4072 | 2 |
| #3964 | 2 |
| C22⋊#168 | 2 |
| #3940 | 2 |
| #3939 | 2 |
| #482 | 5 |