Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
203 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 8. C4×C5×AGL(1,𝔽5) | C4 | semidirect |
| 10. C5×D5⋊C8 | C4 | semidirect |
| 11. C42×C52 | C4 | semidirect |
| 14. C4×C5×Dic5 | C4 | semidirect |
| 15. #64863 | C5 | direct (N × H) |
| 50. C4×AGL(1,𝔽5) | C4×C5 | semidirect |
| 52. D5⋊C8 | C4×C5 | semidirect |
| 63. C42×C5 | C4×C5 | semidirect |
| 64. C42×C5 | AGL(1,𝔽5) | semidirect |
| 67. C4×Dic5 | C4×C5 | semidirect |
| 100. C52 | H(3,ℤ/4) | semidirect |
| 137. C42 | C5×AGL(1,𝔽5) | semidirect |
| 160. C5 | C5×H(3,ℤ/4) | semidirect |
| 161. C5 | #64863 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4130 | 2 |
| C5×D5⋊M16 | 2 |
| C5×#4018 | 2 |
| #64863 | 5 |
| C5×H(3,ℤ/4) | 5 |