Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #11716783 | C2 | semidirect |
| 23. #6036 | C8 | semidirect |
| 40. C5×Dic5 | C2×C8 | semidirect |
| 59. C5⋊D5 | C4⋊C8 | semidirect |
| 83. C52 | C2×C4⋊C8 | semidirect |
| 101. Dic5 | D5⋊C8 | semidirect |
| 131. C5 | D5⋊(C4⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87862 | 2 |
| C2×#87855 | 2 |
| C4×#6036 | 2 |
| #11716783 | 2 |
| D5⋊(C4⋊C8) | 5 |