Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11716613 | C2 | semidirect |
| 89. C52 | #424 | semidirect |
| 137. C5 | #65391 | semidirect |
| 138. C5 | #65408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717246 | 2 |
| C2×C5×#681 | 2 |
| C22×C5×#168 | 2 |
| #11716613 | 2 |
| #65408 | 5 |
| #65391 | 5 |