Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
736 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 286 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 |
|---|---|---|
| 3. C5×#4090 | C2 | direct (N × H) |
| 17. C2×#4090 | C5 | direct (N × H) |
| 25. C2×C5×Dic5 | Q8 | semidirect |
| 37. #4090 | C2×C5 | direct (N × H) |
| 46. C5×Dic5 | C2×Q8 | semidirect |
| 72. C2×C52 | C4⋊Q8 | semidirect |
| 99. C2×Dic5 | C5×Q8 | semidirect |
| 108. C52 | C2×C4⋊Q8 | semidirect |
| 127. Dic5 | C2×C5×Q8 | semidirect |
| 141. C2×C5 | #4090 | direct (N × H) |
| 142. C2×C5 | C5×C4⋊Q8 | semidirect |
| 159. C5 | C2×#4090 | direct (N × H) |
| 160. C5 | C2×C5×C4⋊Q8 | semidirect |
| 168. C2 | C5×#4090 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C22×C5×Dic10 | 2 |
| C5×#4090 | 2 |
| C2×C5×#683 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C5×C4⋊Q8 | 5 |
| C2×#4090 | 5 |