Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
311 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 148 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. C5×#4002 | C2 | semidirect |
| 4. C4×C5×#170 | C2 | semidirect |
| 8. C5×#704 | C4 | direct (N × H) |
| 14. C4×#704 | C5 | direct (N × H) |
| 26. C5×#170 | C2×C4 | semidirect |
| 31. #4002 | C2×C5 | semidirect |
| 32. C4×#170 | C2×C5 | semidirect |
| 40. C4×C52 | M16 | semidirect |
| 43. C5×Dic5 | M16 | semidirect |
| 52. #704 | C4×C5 | direct (N × H) |
| 93. #170 | C2×C4×C5 | semidirect |
| 99. C52 | C4×M16 | semidirect |
| 120. C4×C5 | C5×M16 | semidirect |
| 121. C4×C5 | #704 | direct (N × H) |
| 124. Dic5 | C5×M16 | semidirect |
| 159. C5 | C4×C5×M16 | semidirect |
| 160. C5 | C4×#704 | direct (N × H) |
| 170. C4 | C5×#704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#704 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C5×#4002 | 2 |
| C4×C5×#170 | 2 |
| C4×#704 | 5 |
| C4×C5×M16 | 5 |