Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
255 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C4×Dic25 | C2 | semidirect |
| 3. C2×#87716 | C2 | semidirect |
| 4. #11716385 | C2 | direct (N × H) |
| 7. #41×C25 | C4 | semidirect |
| 9. C2×Q8×C25 | C4 | semidirect |
| 11. C2×D4×C25 | C4 | semidirect |
| 16. C4×Dic25 | C22 | semidirect |
| 18. #87716 | C22 | semidirect |
| 24. Q8×C25 | C2×C4 | semidirect |
| 28. D4×C25 | C2×C4 | semidirect |
| 76. C2×C25 | #104 | semidirect |
| 102. C25 | C2×#104 | semidirect |
| 117. #41 | Dic25 | semidirect |
| 119. C2×Q8 | Dic25 | semidirect |
| 121. C2×D4 | Dic25 | semidirect |
| 138. Q8 | C2×Dic25 | semidirect |
| 142. D4 | C2×Dic25 | semidirect |
| 171. C2 | #11716385 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C25 | 2 |
| C2×C4×Dic25 | 2 |
| C2×#87716 | 2 |
| #11716385 | 2 |
| C2×#3969 | 5 |