Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 59 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. D25⋊M16 | C2 | semidirect |
| 4. #11716424 | C2 | semidirect |
| 6. C2×D4×C25 | C4 | semidirect |
| 10. D4×D25 | C4 | semidirect |
| 12. C2×D100 | C4 | semidirect |
| 16. C4⋊#1035 | C22 | semidirect |
| 19. D25⋊C8 | C22 | semidirect |
| 106. C25 | #418 | semidirect |
| 129. C2×D4 | #1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D25 | 2 |
| #11716549 | 2 |
| D25⋊M16 | 2 |
| #11716424 | 2 |
| #65767 | 5 |