Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
319 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11716736 | C2 | semidirect |
| 5. C2×#6045 | C4 | semidirect |
| 7. C2×C5×Dic10 | C4 | semidirect |
| 12. D5×Dic10 | C4 | semidirect |
| 78. C2×Dic10 | AGL(1,𝔽5) | semidirect |
| 142. C52 | #419 | semidirect |
| 214. C5 | #65293 | semidirect |
| 215. C5 | #65782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic10 | 2 |
| D5⋊#681 | 2 |
| C5×#4130 | 2 |
| #11716736 | 2 |
| #65782 | 5 |
| #65293 | 5 |