Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
237 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 79 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. C25×#117 | C2 | semidirect |
| 3. #11716488 | C2 | semidirect |
| 4. #11716354 | C2 | semidirect |
| 11. C2×D100 | C4 | semidirect |
| 12. C2×C4×D25 | C4 | semidirect |
| 13. C2×Dic50 | C4 | semidirect |
| 99. #117 | D25 | semidirect |
| 101. C25 | #410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C25×#117 | 2 |
| #11716488 | 2 |
| #11716354 | 2 |
| #65295 | 5 |