Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
456 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 16. #65268 | C5 | direct (N × H) |
| 24. C2×C4×C52 | Q8 | semidirect |
| 30. C2×C5×Dic5 | Q8 | semidirect |
| 108. C2×C4×C5 | Dic10 | semidirect |
| 111. C2×C4×C5 | C5×Q8 | semidirect |
| 117. C2×Dic5 | C5×Q8 | semidirect |
| 124. C52 | #395 | semidirect |
| 190. C2×C4 | C5×Dic10 | semidirect |
| 193. C5 | #65268 | direct (N × H) |
| 194. C5 | C5×#395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic10 | 2 |
| C2×C52×C4⋊C4 | 2 |
| C2×C5×#683 | 2 |
| C5×#3963 | 2 |
| C5×#395 | 5 |
| #65268 | 5 |