Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
235 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 64 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. #87849 | C4 | semidirect |
| 10. C5×C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 12. C4×#1039 | C4 | semidirect |
| 13. C4×C5×Dic5 | C4 | semidirect |
| 52. C4⋊AGL(1,𝔽5) | Dic5 | semidirect |
| 65. C4×Dic5 | AGL(1,𝔽5) | semidirect |
| 103. C52 | #339 | semidirect |
| 164. C5 | #64752 | semidirect |
| 165. C5 | #64862 | 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 |
| C4×D5×Dic5 | 2 |
| #64862 | 5 |
| #64752 | 5 |