Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 7. C4×#1039 | C4 | semidirect |
| 9. C5×C4⋊Dic5 | C4 | semidirect |
| 12. C5×#681 | C4 | semidirect |
| 57. C4⋊Dic5 | Dic5 | semidirect |
| 66. #681 | Dic5 | semidirect |
| 107. C52 | #339 | semidirect |
| 171. C5 | #64752 | semidirect |
| 172. C5 | #64775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C5×#4072 | 2 |
| C2×C5×#681 | 2 |
| #64775 | 5 |
| #64752 | 5 |