Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
736 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 6. #11716958 | C2 | direct (N × H) |
| 29. C2×C5×Dic5 | Q8 | semidirect |
| 49. C5×Dic5 | C2×Q8 | semidirect |
| 72. C2×C52 | C4⋊Q8 | semidirect |
| 94. C2×Dic5 | Dic10 | semidirect |
| 106. C52 | C2×C4⋊Q8 | semidirect |
| 123. Dic5 | C2×Dic10 | semidirect |
| 139. C2×C5 | #4034 | semidirect |
| 157. C5 | C2×#4034 | semidirect |
| 166. C2 | #11716958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C22×#6039 | 2 |
| C2×C5×#683 | 2 |
| C2×#87780 | 2 |
| C2×Dic52 | 2 |
| #11716958 | 2 |
| C2×#4034 | 5 |