Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
206 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #11716891 | C2 | semidirect |
| 3. #11716866 | C2 | semidirect |
| 4. #11716775 | C2 | semidirect |
| 5. D5⋊#674 | C2 | semidirect |
| 13. #87765 | C22 | semidirect |
| 14. #87764 | C22 | semidirect |
| 71. C5×D5 | M32 | semidirect |
| 102. C52 | C2×M32 | semidirect |
| 140. D5 | #3998 | semidirect |
| 153. C5 | D5⋊M32 | semidirect |
| 154. C5 | C2×#3998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#168 | 2 |
| #11716891 | 2 |
| #11716866 | 2 |
| #11716775 | 2 |
| D5⋊#674 | 2 |
| C2×#3998 | 5 |
| D5⋊M32 | 5 |