Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
237 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11716549 | C2 | semidirect |
| 3. #11716429 | C2 | semidirect |
| 4. #11716421 | C2 | semidirect |
| 5. C22×C4×C25 | C4 | semidirect |
| 6. C2×C22⋊D25 | C4 | semidirect |
| 11. C2×C4×D25 | C4 | semidirect |
| 13. C2×Dic50 | C4 | semidirect |
| 93. C25 | #410 | semidirect |
| 115. C22×C4 | #1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| #11716549 | 2 |
| #11716429 | 2 |
| #11716421 | 2 |
| #65745 | 5 |