Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
255 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 63 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×C4×#1035 | C2 | semidirect |
| 3. C2×#87735 | C2 | semidirect |
| 4. #11716423 | C2 | direct (N × H) |
| 6. C2×D4×C25 | C4 | semidirect |
| 11. #87746 | C4 | semidirect |
| 14. C2×Dic50 | C4 | semidirect |
| 17. C4×#1035 | C22 | semidirect |
| 19. #87735 | C22 | semidirect |
| 26. D4×C25 | C2×C4 | semidirect |
| 39. Dic50 | C2×C4 | semidirect |
| 74. C2×C25 | #104 | semidirect |
| 102. C25 | C2×#104 | semidirect |
| 121. C2×D4 | #1035 | semidirect |
| 142. D4 | C2×#1035 | semidirect |
| 171. C2 | #11716423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87746 | 2 |
| C2×C4×#1035 | 2 |
| C2×#87735 | 2 |
| #11716423 | 2 |
| C2×#4008 | 5 |