Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
198 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 67 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. C25×#97 | C2 | semidirect |
| 4. #11716369 | C2 | semidirect |
| 5. #11716366 | C2 | semidirect |
| 13. D200 | C4 | semidirect |
| 20. D100 | C2×C4 | semidirect |
| 23. C8×C25 | C2×C4 | semidirect |
| 62. #97 | D25 | semidirect |
| 63. C25 | #442 | semidirect |
| 91. C8 | C4×D25 | semidirect |
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 |
| C25×#97 | 2 |
| #11716369 | 2 |
| #11716366 | 2 |
| #65000 | 5 |