Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
243 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 243 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. #11716384 | C2 | semidirect |
| 5. #11716381 | C2 | semidirect |
| 7. #41×C25 | C4 | semidirect |
| 22. Q8×C25 | C2×C4 | semidirect |
| 25. D4×C25 | C2×C4 | semidirect |
| 91. C25 | #417 | semidirect |
| 105. #41 | Dic25 | semidirect |
| 124. Q8 | C2×Dic25 | semidirect |
| 127. D4 | C2×Dic25 | semidirect |
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 |
| #11716384 | 2 |
| #11716381 | 2 |
| #65521 | 5 |