Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
155 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 155 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 4. C2×C5×Dic10 | C4 | semidirect |
| 6. C42×C52 | C4 | semidirect |
| 8. #64854 | C5 | direct (N × H) |
| 31. C2×Dic10 | C4×C5 | semidirect |
| 36. C42×C5 | C4×C5 | semidirect |
| 37. C42×C5 | AGL(1,𝔽5) | semidirect |
| 61. C52 | #354 | semidirect |
| 83. C42 | C5×AGL(1,𝔽5) | semidirect |
| 100. C5 | C5×#354 | semidirect |
| 101. C5 | #64854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4021 | 2 |
| C5×#3999 | 2 |
| #64854 | 5 |
| C5×#354 | 5 |