Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 5. C2×C5×Dic10 | C4 | semidirect |
| 10. C4×C5×Dic5 | C4 | semidirect |
| 12. #64693 | C5 | direct (N × H) |
| 43. C2×Dic10 | C4×C5 | semidirect |
| 54. C4×Dic5 | C4×C5 | semidirect |
| 86. C52 | #354 | semidirect |
| 143. C5 | #64693 | direct (N × H) |
| 144. C5 | C5×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4082 | 2 |
| C52×#99 | 2 |
| C5×#3966 | 2 |
| C5×#354 | 5 |
| #64693 | 5 |