Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
273 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11716845 | C2 | semidirect |
| 5. C4×#6032 | C2 | semidirect |
| 10. #87849 | C4 | semidirect |
| 11. D5⋊#168 | C4 | semidirect |
| 100. C52 | #405 | semidirect |
| 154. C5 | #65286 | 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×#87849 | 2 |
| C2×D5⋊#168 | 2 |
| C5×#4038 | 2 |
| #11716845 | 2 |
| C4×#6032 | 2 |
| #65701 | 5 |
| #65286 | 5 |