Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #11716800 | C2 | semidirect |
| 7. #87862 | C4 | semidirect |
| 17. #6034 | C2×C4 | semidirect |
| 38. C5⋊D5 | #106 | semidirect |
| 56. C52 | C2×#106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87862 | 2 |
| #11717018 | 2 |
| #11716800 | 2 |
| C2×#106 | 25 |