Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
254 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 17. #65138 | C5 | direct (N × H) |
| 42. C4×C52 | Q16 | semidirect |
| 105. C52 | #462 | semidirect |
| 118. C4×C5 | Dic20 | semidirect |
| 119. C4×C5 | C5×Q16 | semidirect |
| 158. C5 | #65138 | direct (N × H) |
| 159. C5 | C5×#462 | semidirect |
| 165. C4 | C5×Dic20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic20 | 2 |
| C5×#4015 | 2 |
| C4×C5×Dic10 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3948 | 2 |
| C5×#462 | 5 |
| #65138 | 5 |