Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
213 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C25×#97 | C2 | semidirect |
| 4. C8×Dic25 | C2 | semidirect |
| 5. #11716351 | C2 | semidirect |
| 13. #87712 | C4 | semidirect |
| 22. C8×C25 | C2×C4 | semidirect |
| 23. #6014 | C2×C4 | semidirect |
| 35. Dic25 | M16 | semidirect |
| 60. #97 | D25 | semidirect |
| 62. C25 | C4×M16 | semidirect |
| 89. C8 | C4×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87712 | 2 |
| C42×D25 | 2 |
| C25×#97 | 2 |
| C8×Dic25 | 2 |
| #11716351 | 2 |
| #64996 | 5 |