Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4⋊C4 | C2 | semidirect |
| 5. C2×#683 | C2 | semidirect |
| 6. #3963 | C2 | semidirect |
| 7. #3963 | C2 | semidirect |
| 20. #685 | C4 | semidirect |
| 38. C2×C4×C5 | C2×C4 | semidirect |
| 47. C2×Dic5 | C2×C4 | semidirect |
| 52. C2×C4⋊C4 | D5 | semidirect |
| 70. C2×D5 | C4⋊C4 | semidirect |
| 124. C2×C4 | C4×D5 | semidirect |
| 126. C5 | #385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D5 | 2 |
| C2×C5×C4⋊C4 | 2 |
| C2×#685 | 2 |
| C2×#683 | 2 |
| #3963 | 2 |
| #385 | 5 |