Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 4. #11716612 | C2 | direct (N × H) |
| 22. C2×C5×Dic5 | C8 | semidirect |
| 44. C5×Dic5 | C2×C8 | semidirect |
| 67. C2×C52 | C4⋊C8 | semidirect |
| 91. C2×Dic5 | #168 | semidirect |
| 103. C52 | C2×C4⋊C8 | semidirect |
| 128. Dic5 | C2×#168 | semidirect |
| 142. C2×C5 | C4⋊#168 | semidirect |
| 143. C2×C5 | #3946 | semidirect |
| 162. C5 | C2×C4⋊#168 | semidirect |
| 163. C5 | C2×#3946 | semidirect |
| 173. C2 | #11716612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6029 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C22×C5×#168 | 2 |
| #11716612 | 2 |
| C2×#3946 | 5 |
| C2×C4⋊#168 | 5 |