Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 1. C5×#131 | C2 | semidirect |
| 3. #4047 | C2 | semidirect |
| 4. #3969 | C2 | semidirect |
| 5. #3957 | C2 | semidirect |
| 6. #3954 | C2 | semidirect |
| 7. #3947 | C2 | semidirect |
| 14. #689 | C4 | semidirect |
| 15. #688 | C4 | semidirect |
| 16. #687 | C4 | semidirect |
| 17. #686 | C4 | semidirect |
| 42. #131 | D5 | semidirect |
| 90. C5 | #444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#131 | 2 |
| #4096 | 2 |
| #4047 | 2 |
| #3969 | 2 |
| #3957 | 2 |
| #3954 | 2 |
| #3947 | 2 |
| #444 | 5 |