Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
230 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 16. #65140 | C5 | direct (N × H) |
| 25. C5×Dic10 | Q8 | semidirect |
| 90. Dic10 | C5×Q8 | semidirect |
| 99. C52 | #475 | semidirect |
| 150. C5 | #65140 | direct (N × H) |
| 151. C5 | C5×#475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4015 | 2 |
| C4×C5×Dic10 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3949 | 2 |
| C5×#3948 | 2 |
| C5×#475 | 5 |
| #65140 | 5 |