Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
454 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 132 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. C2×D5×#168 | C2 | semidirect |
| 3. C22⋊#6029 | C2 | semidirect |
| 4. C5×C22⋊#168 | C2 | semidirect |
| 5. #11716597 | C2 | semidirect |
| 14. C2×#6029 | C22 | semidirect |
| 15. C2×C5×#168 | C22 | semidirect |
| 22. C22×C5×D5 | C8 | semidirect |
| 46. C22⋊#168 | D5 | direct (N × H) |
| 50. C22×C52 | C2×C8 | semidirect |
| 57. C2×C5×D5 | C2×C8 | semidirect |
| 85. C2×#168 | C2×D5 | semidirect |
| 93. C5×D5 | C22⋊C8 | semidirect |
| 104. C22×D5 | #168 | semidirect |
| 140. C52 | C2×C22⋊C8 | semidirect |
| 156. C22×C5 | C8×D5 | semidirect |
| 157. C22×C5 | C2×#168 | semidirect |
| 164. C2×D5 | C2×#168 | semidirect |
| 203. D5 | C22⋊#168 | direct (N × H) |
| 223. C5 | D5×C22⋊C8 | semidirect |
| 224. C5 | C2×C22⋊#168 | semidirect |
| 234. C22 | D5×#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×D5×#168 | 2 |
| C22⋊#6029 | 2 |
| C5×C22⋊#168 | 2 |
| #11716597 | 2 |
| C2×C22⋊#168 | 5 |
| D5×C22⋊C8 | 5 |