Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
198 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 47 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. C22×D20 | C2 | semidirect |
| 2. #4076 | C2 | semidirect |
| 3. C2×D40 | C2 | semidirect |
| 4. C5×C22⋊C8 | C2 | semidirect |
| 5. #3953 | C2 | semidirect |
| 12. C2×D20 | C22 | semidirect |
| 13. C2×C5×C8 | C22 | semidirect |
| 15. C4⋊Dic5 | C22 | semidirect |
| 32. D20 | D4 | semidirect |
| 38. C22⋊C8 | D5 | semidirect |
| 41. C22×C5 | D8 | semidirect |
| 61. C2×C8 | C2×D5 | semidirect |
| 86. C5 | #447 | semidirect |
| 96. C22 | D40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D20 | 2 |
| #4076 | 2 |
| C2×D40 | 2 |
| C5×C22⋊C8 | 2 |
| #3953 | 2 |
| #447 | 5 |