Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
307 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 108 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. #11716845 | C2 | semidirect |
| 4. C5×#4002 | C2 | semidirect |
| 5. #11716752 | C2 | semidirect |
| 11. D5×#170 | C4 | semidirect |
| 28. #6032 | C2×C4 | semidirect |
| 29. C5×#170 | C2×C4 | semidirect |
| 36. #4002 | D5 | direct (N × H) |
| 75. C5×D5 | #97 | semidirect |
| 100. #170 | C4×D5 | semidirect |
| 108. C52 | C2×#97 | semidirect |
| 153. D5 | #4002 | direct (N × H) |
| 167. C5 | D5×#97 | semidirect |
| 168. C5 | C2×#4002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#170 | 2 |
| C4×D5×Dic5 | 2 |
| #11716845 | 2 |
| C5×#4002 | 2 |
| #11716752 | 2 |
| C2×#4002 | 5 |
| D5×#97 | 5 |