Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
228 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 20. #65143 | C5 | direct (N × H) |
| 30. C5×Dic10 | Q8 | semidirect |
| 108. Dic10 | C5×Q8 | semidirect |
| 121. C52 | #475 | semidirect |
| 178. C5 | #65143 | direct (N × H) |
| 179. C5 | C5×#475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4034 | 2 |
| C5×#4033 | 2 |
| C52×#106 | 2 |
| C5×#3948 | 2 |
| C5×#3946 | 2 |
| C5×#3942 | 2 |
| C5×#3940 | 2 |
| C5×#475 | 5 |
| #65143 | 5 |