Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
177 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 177 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 |
|---|---|---|
| 2. C4⋊#6032 | C2 | semidirect |
| 3. C4×#6032 | C2 | semidirect |
| 19. C5×D20 | C8 | semidirect |
| 77. D20 | #168 | semidirect |
| 87. C52 | D4⋊C8 | semidirect |
| 142. C5 | D4⋊#168 | semidirect |
| 143. C5 | #64871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4039 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| #64871 | 5 |
| D4⋊#168 | 5 |