Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 206 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 |
|---|---|---|
| 6. #87853 | C4 | semidirect |
| 11. #87804 | C4 | semidirect |
| 12. C5×#681 | C4 | semidirect |
| 63. #681 | AGL(1,𝔽5) | semidirect |
| 103. C52 | #343 | semidirect |
| 163. C5 | #64750 | semidirect |
| 164. C5 | #64899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#681 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| D5×#681 | 2 |
| #64899 | 5 |
| #64750 | 5 |