Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 5. #87853 | C4 | semidirect |
| 11. C2×#6029 | C4 | semidirect |
| 12. C2×C5×#168 | C4 | semidirect |
| 63. C2×#168 | AGL(1,𝔽5) | semidirect |
| 98. C52 | #344 | semidirect |
| 153. C5 | #64753 | semidirect |
| 154. C5 | #64894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#681 | 2 |
| C5×#4130 | 2 |
| C2×#87768 | 2 |
| #64894 | 5 |
| #64753 | 5 |