Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
296 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 6. C52×C4⋊C4 | C4 | semidirect |
| 10. C4×C5×Dic5 | C4 | semidirect |
| 12. C5×#681 | C4 | semidirect |
| 15. #64752 | C5 | direct (N × H) |
| 53. C5×C4⋊C4 | Dic5 | semidirect |
| 54. C5×C4⋊C4 | C4×C5 | semidirect |
| 64. C4×Dic5 | C4×C5 | semidirect |
| 66. #681 | C4×C5 | semidirect |
| 106. C52 | #339 | semidirect |
| 141. C4⋊C4 | C5×Dic5 | semidirect |
| 170. C5 | #64752 | direct (N × H) |
| 171. C5 | C5×#339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#117 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C5×#681 | 2 |
| C5×#339 | 5 |
| #64752 | 5 |