Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 99. C52 | #341 | semidirect |
| 157. C5 | #64778 | semidirect |
| 158. C5 | #64896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87849 | 2 |
| C2×C5×#700 | 2 |
| C2×D5×#168 | 2 |
| #64896 | 5 |
| #64778 | 5 |