Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 96 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. C5×#4072 | C2 | semidirect |
| 3. #11716622 | C2 | semidirect |
| 8. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 10. C2×#6045 | C4 | semidirect |
| 31. #4072 | D5 | semidirect |
| 104. C52 | #410 | semidirect |
| 160. C5 | #65295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C5×#4072 | 2 |
| #11716622 | 2 |
| #65295 | 5 |