Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
230 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 230 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. C4⋊#1042 | C4 | semidirect |
| 10. C4×C5×AGL(1,𝔽5) | C4 | semidirect |
| 11. #87804 | C4 | semidirect |
| 12. C5×#681 | C4 | semidirect |
| 53. C4×AGL(1,𝔽5) | Dic5 | semidirect |
| 64. #681 | AGL(1,𝔽5) | semidirect |
| 102. C52 | #339 | semidirect |
| 160. C5 | #64743 | semidirect |
| 161. C5 | #64900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717425 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| D5×#681 | 2 |
| #64900 | 5 |
| #64743 | 5 |