Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 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×C5×SD16 | C2 | semidirect |
| 3. #4092 | C2 | semidirect |
| 4. C2×#688 | C2 | semidirect |
| 5. #3964 | C2 | semidirect |
| 6. #3953 | C2 | semidirect |
| 7. #3952 | C2 | semidirect |
| 9. C2×C5×Q8 | C22 | semidirect |
| 17. C2×C5×C8 | C22 | semidirect |
| 20. C4⋊Dic5 | C22 | semidirect |
| 22. C2×#168 | C22 | semidirect |
| 47. C2×SD16 | D5 | semidirect |
| 62. C2×D5 | SD16 | semidirect |
| 69. C2×Q8 | C2×D5 | semidirect |
| 79. C2×C8 | C2×D5 | semidirect |
| 110. C5 | #450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D5 | 2 |
| C2×C5×SD16 | 2 |
| #4092 | 2 |
| C2×#688 | 2 |
| #3964 | 2 |
| #3953 | 2 |
| #3952 | 2 |
| #450 | 5 |