Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
201 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 73 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. C4×D100 | C2 | semidirect |
| 3. C4×C8×C25 | C2 | semidirect |
| 4. #11716369 | C2 | semidirect |
| 5. #11716367 | C2 | semidirect |
| 13. D200 | C4 | direct (N × H) |
| 21. D100 | C2×C4 | semidirect |
| 24. C8×C25 | C2×C4 | semidirect |
| 35. C4×C25 | D8 | semidirect |
| 66. C4×C8 | D25 | semidirect |
| 67. C25 | C4×D8 | semidirect |
| 98. C8 | C4×D25 | semidirect |
| 106. C4 | D200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D200 | 2 |
| C4×D100 | 2 |
| C4×C8×C25 | 2 |
| #11716369 | 2 |
| #11716367 | 2 |
| C4×D40 | 5 |