Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 224 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. #11717036 | C2 | direct (N × H) |
| 21. C2×C4×C52 | Q8 | semidirect |
| 27. C2×C5×Dic5 | Q8 | semidirect |
| 49. C4×C52 | C2×Q8 | semidirect |
| 53. C5×Dic5 | C2×Q8 | semidirect |
| 80. C2×C52 | C4⋊Q8 | semidirect |
| 95. C2×C4×C5 | Dic10 | semidirect |
| 96. C2×C4×C5 | Dic10 | semidirect |
| 106. C2×Dic5 | Dic10 | semidirect |
| 119. C52 | C2×C4⋊Q8 | semidirect |
| 136. C4×C5 | C2×Dic10 | semidirect |
| 137. C4×C5 | C2×Dic10 | semidirect |
| 142. Dic5 | C2×Dic10 | semidirect |
| 159. C2×C5 | #4015 | semidirect |
| 160. C2×C5 | #4034 | semidirect |
| 177. C2×C4 | #6039 | semidirect |
| 180. C5 | C2×#4015 | semidirect |
| 181. C5 | C2×#4034 | semidirect |
| 190. C4 | C2×#6039 | semidirect |
| 191. C2 | #11717036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6039 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87780 | 2 |
| #11717036 | 2 |
| C2×#4034 | 5 |
| C2×#4015 | 5 |