Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#687 | C2 | semidirect |
| 3. #4070 | C2 | semidirect |
| 4. C22×#168 | C2 | semidirect |
| 5. #3964 | C2 | semidirect |
| 6. #3942 | C2 | semidirect |
| 7. #3940 | C2 | semidirect |
| 37. #168 | D4 | semidirect |
| 50. C22×C5 | SD16 | semidirect |
| 92. C5 | #465 | semidirect |
| 98. C22 | #687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#121 | 2 |
| C2×#687 | 2 |
| #4070 | 2 |
| C22×#168 | 2 |
| #3964 | 2 |
| #3942 | 2 |
| #3940 | 2 |
| #465 | 5 |