Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
235 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 72 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. C5×C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 10. C5×#700 | C4 | semidirect |
| 12. C42×C52 | C4 | semidirect |
| 14. C4×C5×Dic5 | C4 | semidirect |
| 15. #64862 | C5 | direct (N × H) |
| 52. C4⋊AGL(1,𝔽5) | C4×C5 | semidirect |
| 54. #700 | C4×C5 | semidirect |
| 65. C42×C5 | C4×C5 | semidirect |
| 66. C42×C5 | AGL(1,𝔽5) | semidirect |
| 68. C4×Dic5 | C4×C5 | semidirect |
| 103. C52 | #339 | semidirect |
| 140. C42 | C5×AGL(1,𝔽5) | semidirect |
| 164. C5 | C5×#339 | semidirect |
| 165. C5 | #64862 | 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 |
| C42×C5×D5 | 2 |
| #64862 | 5 |
| C5×#339 | 5 |