Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
760 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 760 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. C2×#87799 | C2 | semidirect |
| 3. C52×C22⋊C8 | C2 | semidirect |
| 4. C22⋊#6029 | C2 | semidirect |
| 5. #11716687 | C2 | semidirect |
| 14. C2×C52×C8 | C22 | semidirect |
| 15. C2×#6029 | C22 | semidirect |
| 38. C5×C22⋊C8 | D5 | semidirect |
| 43. C22×C52 | M16 | semidirect |
| 51. C2×C5⋊D5 | M16 | semidirect |
| 64. C2×C5×C8 | C2×D5 | semidirect |
| 96. C22⋊C8 | C5⋊D5 | semidirect |
| 97. C52 | #407 | semidirect |
| 100. C22×C5 | #676 | semidirect |
| 123. C2×C8 | C2×C5⋊D5 | semidirect |
| 148. C5 | #65015 | semidirect |
| 158. C22 | #87799 | 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×#87799 | 2 |
| C52×C22⋊C8 | 2 |
| C22⋊#6029 | 2 |
| #11716687 | 2 |
| #65015 | 5 |