Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 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. D5×C4⋊C4 | C2 | semidirect |
| 3. C5×#106 | C2 | semidirect |
| 4. #3953 | C2 | semidirect |
| 5. #3952 | C2 | semidirect |
| 6. #3941 | C2 | semidirect |
| 7. #3940 | C2 | semidirect |
| 38. #106 | D5 | semidirect |
| 86. C5 | #481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4041 | 2 |
| D5×C4⋊C4 | 2 |
| C5×#106 | 2 |
| #3953 | 2 |
| #3952 | 2 |
| #3941 | 2 |
| #3940 | 2 |
| #481 | 5 |