Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
153 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 11. #64872 | C5 | direct (N × H) |
| 19. C5×Dic10 | C8 | semidirect |
| 70. Dic10 | C5×C8 | semidirect |
| 78. C52 | Q8⋊C8 | semidirect |
| 125. C5 | C5×Q8⋊C8 | semidirect |
| 126. C5 | #64872 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4033 | 2 |
| C5×C4⋊#170 | 2 |
| C4×C5×#170 | 2 |
| #64872 | 5 |
| C5×Q8⋊C8 | 5 |