Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. #11716563 | C2 | semidirect |
| 2. C2×D8×C25 | C2 | semidirect |
| 3. #11716495 | C2 | semidirect |
| 4. #11716474 | C2 | semidirect |
| 5. #11716473 | C2 | semidirect |
| 6. D8×D25 | C2 | semidirect |
| 7. #11716467 | C2 | semidirect |
| 8. #11716464 | C2 | semidirect |
| 9. C2×D4×C25 | C22 | semidirect |
| 12. #87746 | C22 | semidirect |
| 14. D4×D25 | C22 | semidirect |
| 16. #87744 | C22 | semidirect |
| 17. D8×C25 | C22 | semidirect |
| 18. D8×C25 | C22 | semidirect |
| 19. C2×C8×C25 | C22 | semidirect |
| 20. #87722 | C22 | semidirect |
| 21. #87721 | C22 | semidirect |
| 22. #87716 | C22 | semidirect |
| 23. D200 | C22 | semidirect |
| 24. #87713 | C22 | semidirect |
| 25. #87712 | C22 | semidirect |
| 26. C8×D25 | C22 | semidirect |
| 27. Dic100 | C22 | semidirect |
| 116. C2×D8 | D25 | semidirect |
| 118. C25 | #576 | semidirect |
| 136. C2×D4 | C2×D25 | semidirect |
| 142. D8 | C2×D25 | semidirect |
| 143. D8 | C2×D25 | semidirect |
| 147. C2×C8 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716563 | 2 |
| C2×D8×C25 | 2 |
| #11716495 | 2 |
| #11716474 | 2 |
| #11716473 | 2 |
| D8×D25 | 2 |
| #11716467 | 2 |
| #11716464 | 2 |
| #66091 | 5 |