Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
199 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 199 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 |
|---|---|---|
| 6. C4×C5×AGL(1,𝔽5) | C4 | semidirect |
| 7. C2×C52×C8 | C4 | semidirect |
| 8. C2×C5×#168 | C4 | semidirect |
| 10. #64895 | C5 | direct (N × H) |
| 35. C4×AGL(1,𝔽5) | C4×C5 | semidirect |
| 39. C2×C5×C8 | C4×C5 | semidirect |
| 40. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 44. C2×#168 | C4×C5 | semidirect |
| 70. C52 | H(3,ℤ/4) | semidirect |
| 91. C2×C8 | C5×AGL(1,𝔽5) | semidirect |
| 112. C5 | C5×H(3,ℤ/4) | semidirect |
| 113. C5 | #64895 | 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 |
| C2×C5×#676 | 2 |
| #64895 | 5 |
| C5×H(3,ℤ/4) | 5 |