Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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×C8×D5 | C2 | semidirect |
| 3. #4038 | C2 | semidirect |
| 4. C5×#102 | C2 | semidirect |
| 5. #3964 | C2 | semidirect |
| 6. #3948 | C2 | semidirect |
| 7. #3942 | C2 | semidirect |
| 12. #711 | C4 | semidirect |
| 46. #102 | D5 | semidirect |
| 96. C5 | #416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#711 | 2 |
| C2×C8×D5 | 2 |
| #4038 | 2 |
| C5×#102 | 2 |
| #3964 | 2 |
| #3948 | 2 |
| #3942 | 2 |
| #416 | 5 |