Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
471 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 168 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. C22×C5×#170 | C2 | semidirect |
| 3. C5×C22⋊#170 | C2 | direct (N × H) |
| 11. C2×C5×#170 | C22 | semidirect |
| 12. C2×C22⋊#170 | C5 | direct (N × H) |
| 16. C23×C52 | C8 | semidirect |
| 29. C22×#170 | C2×C5 | semidirect |
| 31. C22⋊#170 | C2×C5 | direct (N × H) |
| 38. C22×C52 | C2×C8 | semidirect |
| 58. C2×#170 | C22×C5 | semidirect |
| 63. C2×C52 | C22⋊C8 | semidirect |
| 76. C23×C5 | C5×C8 | semidirect |
| 77. C23×C5 | #170 | semidirect |
| 101. C52 | C2×C22⋊C8 | semidirect |
| 118. C22×C5 | C2×C5×C8 | semidirect |
| 121. C22×C5 | C2×#170 | semidirect |
| 147. C2×C5 | C5×C22⋊C8 | semidirect |
| 148. C2×C5 | C22⋊#170 | direct (N × H) |
| 157. C23 | C5×#170 | semidirect |
| 169. C5 | C2×C5×C22⋊C8 | semidirect |
| 170. C5 | C2×C22⋊#170 | direct (N × H) |
| 175. C22 | C2×C5×#170 | semidirect |
| 183. C2 | C5×C22⋊#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×Dic5 | 2 |
| C22×C5×#170 | 2 |
| C5×C22⋊#170 | 2 |
| C2×C22⋊#170 | 5 |
| C2×C5×C22⋊C8 | 5 |