Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 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. #4094 | C2 | semidirect |
| 3. #4053 | C2 | semidirect |
| 4. C5×#104 | C2 | semidirect |
| 5. #3954 | C2 | semidirect |
| 6. #3937 | C2 | semidirect |
| 7. C4×#168 | C2 | semidirect |
| 12. #689 | C4 | semidirect |
| 13. #688 | C4 | semidirect |
| 14. #687 | C4 | semidirect |
| 15. #686 | C4 | semidirect |
| 45. #104 | D5 | semidirect |
| 90. C5 | #443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4096 | 2 |
| #4094 | 2 |
| #4053 | 2 |
| C5×#104 | 2 |
| #3954 | 2 |
| #3937 | 2 |
| C4×#168 | 2 |
| #443 | 5 |