Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #4095 | C2 | semidirect |
| 3. #4094 | C2 | semidirect |
| 4. C2×#686 | C2 | semidirect |
| 5. #3965 | C2 | semidirect |
| 6. #3955 | C2 | semidirect |
| 7. #3954 | C2 | semidirect |
| 41. AGL(1,ℤ/8) | D5 | semidirect |
| 92. C5 | #472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×AGL(1,ℤ/8) | 2 |
| #4095 | 2 |
| #4094 | 2 |
| C2×#686 | 2 |
| #3965 | 2 |
| #3955 | 2 |
| #3954 | 2 |
| #472 | 5 |