Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
315 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 315 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. C2×C22⋊#1035 | C2 | semidirect |
| 3. #11716429 | C2 | semidirect |
| 4. #11716421 | C2 | semidirect |
| 5. C23×D25 | C4 | semidirect |
| 8. C2×D4×C25 | C4 | semidirect |
| 9. C2×C22⋊D25 | C4 | semidirect |
| 14. C2×C4×D25 | C4 | semidirect |
| 16. C22⋊#1035 | C22 | semidirect |
| 19. C23×C25 | C2×C4 | semidirect |
| 25. C22×D25 | C2×C4 | semidirect |
| 32. C2×C4×C25 | C2×C4 | semidirect |
| 35. C2×Dic25 | C2×C4 | semidirect |
| 82. D25 | #99 | semidirect |
| 108. C25 | C2×#99 | semidirect |
| 135. C2×D4 | #1035 | semidirect |
| 158. C23 | C2×#1035 | semidirect |
| 168. C2×C4 | C2×#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 |
| C2×C22⋊#1035 | 2 |
| #11716429 | 2 |
| #11716421 | 2 |
| D5⋊#99 | 5 |