Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
754 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 11. C2×C5×Dic20 | C4 | semidirect |
| 12. C2×#87775 | C4 | semidirect |
| 80. C2×Dic20 | AGL(1,𝔽5) | semidirect |
| 201. C52 | #1971 | semidirect |
| 277. C5 | #10604849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716920 | 2 |
| C2×#11716886 | 2 |
| C2×#11716860 | 2 |
| C2×#11716768 | 2 |
| #13103880 | 2 |
| #10604849 | 5 |