Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
400 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×C5×Dic5 | C4 | semidirect |
| 12. Dic52 | C4 | semidirect |
| 52. C4×Dic5 | AGL(1,𝔽5) | semidirect |
| 83. C52 | #382 | semidirect |
| 134. C5 | #65689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1044 | 2 |
| C2×C4⋊#1043 | 2 |
| C4×#6036 | 2 |
| #11716776 | 2 |
| #65689 | 5 |