Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
311 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 104 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. C4×#6032 | C2 | semidirect |
| 4. C4×C5×#170 | C2 | semidirect |
| 5. #11716752 | C2 | semidirect |
| 11. #87829 | C4 | direct (N × H) |
| 28. #6032 | C2×C4 | semidirect |
| 29. C5×#170 | C2×C4 | semidirect |
| 36. C4×#170 | D5 | semidirect |
| 44. C4×C52 | M16 | semidirect |
| 48. C5×Dic5 | M16 | semidirect |
| 101. #170 | C4×D5 | semidirect |
| 109. C52 | C4×M16 | semidirect |
| 127. C4×C5 | #676 | semidirect |
| 128. C4×C5 | #700 | semidirect |
| 133. Dic5 | #676 | semidirect |
| 171. C5 | C4×#676 | semidirect |
| 172. C5 | C4×#700 | semidirect |
| 182. C4 | #87829 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87829 | 2 |
| C4×#6036 | 2 |
| C4×#6032 | 2 |
| C4×C5×#170 | 2 |
| #11716752 | 2 |
| C4×#700 | 5 |
| C4×#676 | 5 |