Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
552 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 225 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. #11717428 | C2 | semidirect |
| 3. #11717426 | C2 | semidirect |
| 4. D5⋊#681 | C2 | semidirect |
| 5. C2×D5⋊#168 | C2 | semidirect |
| 13. #87853 | C22 | semidirect |
| 14. C2×#6032 | C22 | semidirect |
| 15. #87849 | C22 | semidirect |
| 18. D5⋊#168 | C22 | semidirect |
| 84. C5×D5 | #131 | semidirect |
| 121. C52 | C2×#131 | semidirect |
| 163. D5 | #4094 | semidirect |
| 179. C5 | C2×#4094 | semidirect |
| 180. C5 | D5⋊#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×#41 | 2 |
| #11717428 | 2 |
| #11717426 | 2 |
| D5⋊#681 | 2 |
| C2×D5⋊#168 | 2 |
| D5⋊#131 | 5 |
| C2×#4094 | 5 |