Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 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. #4150 | C2 | semidirect |
| 2. C5×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #4082 | C2 | semidirect |
| 4. #4078 | C2 | semidirect |
| 5. #3969 | C2 | semidirect |
| 6. #3957 | C2 | semidirect |
| 7. #3956 | C2 | semidirect |
| 50. AGL(1,ℤ/8) | D5 | semidirect |
| 110. C5 | #454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4150 | 2 |
| C5×AGL(1,ℤ/8) | 2 |
| #4082 | 2 |
| #4078 | 2 |
| #3969 | 2 |
| #3957 | 2 |
| #3956 | 2 |
| #454 | 5 |