Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#87863 | C2 | semidirect |
| 3. C2×#87855 | C2 | semidirect |
| 4. C2×#87834 | C2 | semidirect |
| 5. C2×D5⋊#170 | C2 | semidirect |
| 6. #11717358 | C2 | direct (N × H) |
| 15. #87863 | C22 | semidirect |
| 18. #87855 | C22 | semidirect |
| 19. #87834 | C22 | semidirect |
| 20. D5⋊#170 | C22 | semidirect |
| 93. C2×C52 | #131 | semidirect |
| 140. C52 | C2×#131 | semidirect |
| 182. C2×C5 | #4131 | semidirect |
| 183. C2×C5 | #4133 | semidirect |
| 206. C5 | C2×#4131 | semidirect |
| 207. C5 | C2×#4133 | semidirect |
| 219. C2 | #11717358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| C2×#87863 | 2 |
| C2×#87855 | 2 |
| C2×#87834 | 2 |
| C2×D5⋊#170 | 2 |
| #11717358 | 2 |
| C2×#4133 | 5 |
| C2×#4131 | 5 |