Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
559 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 229 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×#87853 | C2 | semidirect |
| 3. C22×#6032 | C2 | semidirect |
| 4. #11717426 | C2 | direct (N × H) |
| 5. C2×#87849 | C2 | semidirect |
| 6. C2×D5⋊#168 | C2 | semidirect |
| 14. #87853 | C22 | semidirect |
| 18. C2×#6032 | C22 | semidirect |
| 19. #87849 | C22 | semidirect |
| 20. D5⋊#168 | C22 | semidirect |
| 90. C2×C52 | #131 | semidirect |
| 132. C52 | C2×#131 | semidirect |
| 175. C2×C5 | #4094 | semidirect |
| 176. C2×C5 | #4131 | semidirect |
| 196. C5 | C2×#4094 | semidirect |
| 197. C5 | C2×#4131 | semidirect |
| 209. C2 | #11717426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C2×#87853 | 2 |
| C22×#6032 | 2 |
| #11717426 | 2 |
| C2×#87849 | 2 |
| C2×D5⋊#168 | 2 |
| C2×#4131 | 5 |
| C2×#4094 | 5 |