Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
153 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 19. C5×Dic10 | C8 | semidirect |
| 70. Dic10 | #168 | semidirect |
| 78. C52 | Q8⋊C8 | semidirect |
| 125. C5 | Q8⋊#168 | semidirect |
| 126. C5 | #64872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4033 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| #64872 | 5 |
| Q8⋊#168 | 5 |