Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
197 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 197 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 |
|---|---|---|
| 8. C5×#704 | C4 | semidirect |
| 10. C2×C5×#170 | C4 | semidirect |
| 15. #64867 | C5 | direct (N × H) |
| 49. #704 | C4×C5 | semidirect |
| 51. C2×#170 | C4×C5 | semidirect |
| 99. C52 | #344 | semidirect |
| 160. C5 | C5×#344 | semidirect |
| 161. C5 | #64867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#704 | 2 |
| C5×#4023 | 2 |
| #64867 | 5 |
| C5×#344 | 5 |