Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
226 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 102 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. #65117 | C5 | direct (N × H) |
| 32. C5×#168 | Q8 | semidirect |
| 114. #168 | C5×Q8 | semidirect |
| 122. C52 | #446 | semidirect |
| 179. C5 | #65117 | direct (N × H) |
| 180. C5 | C5×#446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Dic10 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3947 | 2 |
| C5×#3946 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#3935 | 2 |
| C5×#446 | 5 |
| #65117 | 5 |