Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
471 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 157 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×#6032 | C2 | semidirect |
| 3. C22⋊#6032 | C2 | direct (N × H) |
| 11. C2×#6032 | C22 | semidirect |
| 16. C23×C52 | C8 | semidirect |
| 38. C22×C52 | C2×C8 | semidirect |
| 63. C2×C52 | C22⋊C8 | semidirect |
| 76. C23×C5 | #168 | semidirect |
| 77. C23×C5 | #170 | semidirect |
| 101. C52 | C2×C22⋊C8 | semidirect |
| 117. C22×C5 | C2×#168 | semidirect |
| 121. C22×C5 | C2×#170 | semidirect |
| 147. C2×C5 | C22⋊#168 | semidirect |
| 148. C2×C5 | C22⋊#170 | semidirect |
| 157. C23 | #6032 | semidirect |
| 169. C5 | C2×C22⋊#168 | semidirect |
| 170. C5 | C2×C22⋊#170 | semidirect |
| 175. C22 | C2×#6032 | semidirect |
| 183. C2 | C22⋊#6032 | 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×#6032 | 2 |
| C22⋊#6032 | 2 |
| C2×C22⋊#170 | 5 |
| C2×C22⋊#168 | 5 |