Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 201 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. C4×Q8×C25 | C2 | semidirect |
| 3. Q8×Dic25 | C2 | semidirect |
| 5. #11716449 | C2 | semidirect |
| 7. C4×Dic50 | C2 | semidirect |
| 9. Q8×D25 | C4 | direct (N × H) |
| 23. Q8×C25 | C2×C4 | semidirect |
| 32. C4×D25 | Q8 | direct (N × H) |
| 33. Dic50 | C2×C4 | semidirect |
| 47. C4×C25 | C2×Q8 | semidirect |
| 50. Dic25 | C2×Q8 | semidirect |
| 68. D25 | C4×Q8 | direct (N × H) |
| 85. C4×Q8 | D25 | direct (N × H) |
| 88. C25 | C2×C4×Q8 | semidirect |
| 118. Q8 | C4×D25 | direct (N × H) |
| 138. C4 | Q8×D25 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D25 | 2 |
| C4×Q8×C25 | 2 |
| Q8×Dic25 | 2 |
| C4⋊C4×D25 | 2 |
| #11716449 | 2 |
| C42×D25 | 2 |
| C4×Dic50 | 2 |
| C4×Q8×D5 | 5 |