Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
483 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 483 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×Q8×D25 | C2 | semidirect |
| 3. C25×C22⋊Q8 | C2 | semidirect |
| 4. #11716508 | C2 | semidirect |
| 5. #11716486 | C2 | semidirect |
| 6. #11716459 | C2 | semidirect |
| 7. #11716458 | C2 | semidirect |
| 8. C4⋊C4×D25 | C2 | semidirect |
| 9. C4⋊C4×D25 | C2 | semidirect |
| 11. #11716440 | C2 | semidirect |
| 13. C2×Q8×C25 | C22 | semidirect |
| 24. C2×Dic50 | C22 | semidirect |
| 25. C2×Dic50 | C22 | semidirect |
| 26. C4⋊C4×C25 | C22 | semidirect |
| 27. C4⋊C4×C25 | C22 | semidirect |
| 32. C4⋊Dic25 | C22 | semidirect |
| 33. C4⋊Dic25 | C22 | semidirect |
| 34. #87718 | C22 | semidirect |
| 35. #87718 | C22 | semidirect |
| 36. #87718 | C22 | semidirect |
| 41. C22×D25 | Q8 | semidirect |
| 76. C22×C25 | C2×Q8 | semidirect |
| 83. C2×D25 | C2×Q8 | semidirect |
| 124. D25 | C22⋊Q8 | direct (N × H) |
| 157. C22⋊Q8 | D25 | direct (N × H) |
| 161. C25 | C2×C22⋊Q8 | semidirect |
| 185. C2×Q8 | C2×D25 | semidirect |
| 200. C4⋊C4 | C2×D25 | semidirect |
| 201. C4⋊C4 | C2×D25 | semidirect |
| 247. C22 | Q8×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D25 | 2 |
| C22×C4×D25 | 2 |
| C25×C22⋊Q8 | 2 |
| #11716508 | 2 |
| #11716486 | 2 |
| #11716459 | 2 |
| #11716458 | 2 |
| C4⋊C4×D25 | 2 |
| C22⋊C4×D25 | 2 |
| #11716440 | 2 |
| D5×C22⋊Q8 | 5 |