Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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×C5×D4 | C2 | semidirect |
| 2. C2×#686 | C2 | semidirect |
| 3. #4076 | C2 | semidirect |
| 4. #3964 | C2 | semidirect |
| 5. C22⋊#168 | C2 | semidirect |
| 12. C2×D20 | C22 | semidirect |
| 15. C4⋊Dic5 | C22 | semidirect |
| 16. C2×#168 | C22 | semidirect |
| 26. C5×D4 | D4 | semidirect |
| 34. C22×D4 | D5 | semidirect |
| 45. C22×C5 | D8 | semidirect |
| 80. D4 | C22⋊D5 | semidirect |
| 86. C5 | #447 | semidirect |
| 96. C22 | #686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D4 | 2 |
| C2×#686 | 2 |
| #4076 | 2 |
| #3964 | 2 |
| C22⋊#168 | 2 |
| #447 | 5 |