Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
135 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 135 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 |
|---|---|---|
| 8. #64855 | C5 | direct (N × H) |
| 58. C52 | #356 | semidirect |
| 91. C5 | C5×#356 | semidirect |
| 92. C5 | #64855 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4015 | 2 |
| C5×#4005 | 2 |
| #64855 | 5 |
| C5×#356 | 5 |