Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
658 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 4. #13099875 | C2 | semidirect |
| 28. #87767 | C8 | semidirect |
| 46. C5×#168 | C2×C8 | semidirect |
| 104. C5⋊D5 | #322 | semidirect |
| 130. #168 | D5⋊C8 | semidirect |
| 141. C52 | C2×#322 | semidirect |
| 197. C5 | #10603807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#87862 | 2 |
| C4×#87855 | 2 |
| C4×#87767 | 2 |
| #13099875 | 2 |
| #10603807 | 5 |