Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
199 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 199 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 |
|---|---|---|
| 7. C4×#1042 | C4 | semidirect |
| 10. C4×C5×AGL(1,𝔽5) | C4 | semidirect |
| 11. C2×#6029 | C4 | semidirect |
| 12. C2×C5×#168 | C4 | semidirect |
| 51. C4×AGL(1,𝔽5) | Dic5 | semidirect |
| 64. C2×#168 | AGL(1,𝔽5) | semidirect |
| 99. C52 | H(3,ℤ/4) | semidirect |
| 156. C5 | #64751 | semidirect |
| 157. C5 | #64895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717425 | 2 |
| C5×#4130 | 2 |
| C2×#87768 | 2 |
| #64895 | 5 |
| #64751 | 5 |