Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. C23×Dic5 | C2 | semidirect |
| 3. C2×C5×C22⋊C4 | C2 | semidirect |
| 4. C2×#685 | C2 | semidirect |
| 5. #3963 | C2 | semidirect |
| 11. C2×C22⋊D5 | C4 | semidirect |
| 29. C22×D5 | C2×C4 | semidirect |
| 39. C2×Dic5 | C2×C4 | semidirect |
| 40. C2×Dic5 | D4 | semidirect |
| 44. C2×C22⋊C4 | D5 | semidirect |
| 50. C22×C5 | C22⋊C4 | semidirect |
| 105. C5 | #386 | semidirect |
| 115. C22 | #685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D5 | 2 |
| C23×Dic5 | 2 |
| C2×C5×C22⋊C4 | 2 |
| C2×#685 | 2 |
| #3963 | 2 |
| #386 | 5 |