Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
465 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 159 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. Q8×#1035 | C2 | semidirect |
| 3. D4×#1035 | C2 | semidirect |
| 4. #11716549 | C2 | semidirect |
| 5. C2×C4×#1035 | C2 | semidirect |
| 7. #41×C25 | C4 | semidirect |
| 8. #87748 | C4 | semidirect |
| 10. #87746 | C4 | semidirect |
| 12. #87744 | C4 | semidirect |
| 24. Q8×C25 | C2×C4 | semidirect |
| 25. D4×C25 | C2×C4 | semidirect |
| 26. C2×C4×C25 | C2×C4 | semidirect |
| 27. C22⋊D25 | C2×C4 | semidirect |
| 28. C2×Dic25 | C2×C4 | semidirect |
| 29. D100 | C2×C4 | semidirect |
| 30. C4×D25 | C2×C4 | semidirect |
| 31. C4×D25 | C2×C4 | semidirect |
| 34. Dic50 | C2×C4 | semidirect |
| 45. #1035 | #41 | direct (N × H) |
| 88. C25 | C4×#41 | semidirect |
| 102. #41 | #1035 | direct (N × H) |
| 118. Q8 | C2×#1035 | semidirect |
| 121. D4 | C2×#1035 | semidirect |
| 130. C2×C4 | C2×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D25 | 2 |
| Q8×#1035 | 2 |
| D4×#1035 | 2 |
| #11716549 | 2 |
| C2×C4×#1035 | 2 |
| #41×AGL(1,𝔽5) | 5 |