Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
233 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 233 conjugacy classes of subgroups — too many to draw. Only its 76 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×#700 | C4 | semidirect |
| 11. C52×C4⋊C4 | C4 | semidirect |
| 13. C5×C4⋊Dic5 | C4 | semidirect |
| 15. #64875 | C5 | direct (N × H) |
| 54. C4×AGL(1,𝔽5) | C4×C5 | semidirect |
| 56. #700 | C4×C5 | semidirect |
| 62. C5×C4⋊C4 | C4×C5 | semidirect |
| 63. C5×C4⋊C4 | AGL(1,𝔽5) | semidirect |
| 69. C4⋊Dic5 | C4×C5 | semidirect |
| 108. C52 | #339 | semidirect |
| 143. C4⋊C4 | C5×AGL(1,𝔽5) | semidirect |
| 175. C5 | C5×#339 | semidirect |
| 176. C5 | #64875 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×C5×#700 | 2 |
| C5×#4038 | 2 |
| #64875 | 5 |
| C5×#339 | 5 |