Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
399 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 159 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×#87739 | C2 | semidirect |
| 3. C22×#6016 | C2 | semidirect |
| 4. #11716550 | C2 | direct (N × H) |
| 5. C2×#87735 | C2 | semidirect |
| 6. C2×D25⋊C8 | C2 | semidirect |
| 14. #87739 | C22 | semidirect |
| 18. C2×#6016 | C22 | semidirect |
| 19. #87735 | C22 | semidirect |
| 20. D25⋊C8 | C22 | semidirect |
| 68. C2×C25 | #131 | semidirect |
| 92. C25 | C2×#131 | semidirect |
| 147. C2 | #11716550 | 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×#87739 | 2 |
| C22×#6016 | 2 |
| #11716550 | 2 |
| C2×#87735 | 2 |
| C2×D25⋊C8 | 2 |
| C2×#4131 | 5 |