Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
163 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 33 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. C22×C4×C52 | C4 | semidirect |
| 8. C5×C22⋊Dic5 | C4 | semidirect |
| 39. C22×C4×C5 | Dic5 | semidirect |
| 40. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 48. C22⋊Dic5 | Dic5 | semidirect |
| 81. C52 | #352 | semidirect |
| 105. C22×C4 | #1042 | semidirect |
| 132. C5 | #64759 | semidirect |
| 133. C5 | #64916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4075 | 2 |
| #11716856 | 2 |
| #11716854 | 2 |
| #64916 | 5 |
| #64759 | 5 |