Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
273 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 4. #11716752 | C2 | semidirect |
| 5. Dic5×#170 | C2 | semidirect |
| 9. D5⋊#168 | C4 | semidirect |
| 11. C5×#700 | C4 | semidirect |
| 52. #700 | Dic5 | semidirect |
| 100. C52 | #405 | semidirect |
| 154. C5 | #65411 | semidirect |
| 155. C5 | #65701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊#168 | 2 |
| C2×C5×#700 | 2 |
| #11716959 | 2 |
| #11716752 | 2 |
| Dic5×#170 | 2 |
| #65701 | 5 |
| #65411 | 5 |