Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
808 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 379 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×#6029 | C2 | semidirect |
| 3. C22⋊#6029 | C2 | direct (N × H) |
| 11. C2×#6029 | C22 | semidirect |
| 15. C23×C52 | C8 | semidirect |
| 34. C22×C52 | C2×C8 | semidirect |
| 50. C2×C52 | C22⋊C8 | semidirect |
| 56. C23×C5 | #168 | semidirect |
| 70. C52 | C2×C22⋊C8 | semidirect |
| 75. C22×C5 | C2×#168 | semidirect |
| 91. C2×C5 | C22⋊#168 | semidirect |
| 97. C23 | #6029 | semidirect |
| 108. C5 | C2×C22⋊#168 | semidirect |
| 113. C22 | C2×#6029 | semidirect |
| 121. C2 | C22⋊#6029 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C22×#6029 | 2 |
| C22⋊#6029 | 2 |
| C2×C22⋊#168 | 5 |