Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
465 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
| 4. #11716455 | C2 | semidirect |
| 5. #11716454 | C2 | semidirect |
| 6. C4×D100 | C2 | semidirect |
| 7. C42×D25 | C2 | semidirect |
| 9. #87748 | C4 | direct (N × H) |
| 23. Q8×C25 | C2×C4 | semidirect |
| 30. D100 | C2×C4 | semidirect |
| 33. C4×D25 | C2×C4 | semidirect |
| 47. C4×C25 | #41 | semidirect |
| 50. Dic25 | #41 | semidirect |
| 83. C4×Q8 | D25 | semidirect |
| 88. C25 | C4×#41 | semidirect |
| 117. Q8 | C4×D25 | semidirect |
| 138. C4 | #87748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87748 | 2 |
| C4×Q8×C25 | 2 |
| Q8×Dic25 | 2 |
| #11716455 | 2 |
| #11716454 | 2 |
| C4×D100 | 2 |
| C42×D25 | 2 |
| C4×#713 | 5 |