Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 158 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×C5×#681 | C2 | semidirect |
| 3. C5×C22⋊#168 | C2 | semidirect |
| 11. C2×C5×#168 | C22 | semidirect |
| 13. #65496 | C5 | direct (N × H) |
| 30. C2×#681 | C2×C5 | semidirect |
| 32. C22⋊#168 | C2×C5 | semidirect |
| 38. C22×C52 | M16 | semidirect |
| 64. C2×#168 | C22×C5 | semidirect |
| 108. C52 | #407 | semidirect |
| 124. C22×C5 | #681 | semidirect |
| 127. C22×C5 | C5×M16 | semidirect |
| 172. C5 | #65496 | direct (N × H) |
| 173. C5 | C5×#407 | semidirect |
| 178. C22 | C5×#681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C2×C5×#681 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#407 | 5 |
| #65496 | 5 |