Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 1. #4092 | C2 | semidirect |
| 2. C2×#688 | C2 | semidirect |
| 3. C2×#676 | C2 | semidirect |
| 5. C5×#103 | C2 | semidirect |
| 6. #3953 | C2 | semidirect |
| 7. #3939 | C2 | semidirect |
| 37. #168 | D4 | semidirect |
| 43. #103 | D5 | semidirect |
| 92. C5 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4092 | 2 |
| C2×#688 | 2 |
| C2×#676 | 2 |
| #4041 | 2 |
| C5×#103 | 2 |
| #3953 | 2 |
| #3939 | 2 |
| #468 | 5 |