Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
210 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 12. Q8⋊#168 | C5 | direct (N × H) |
| 14. C52×Q8 | C8 | semidirect |
| 64. C5×Q8 | #168 | semidirect |
| 65. C5×Q8 | C5×C8 | semidirect |
| 88. C52 | Q8⋊C8 | semidirect |
| 130. Q8 | C5×#168 | semidirect |
| 139. C5 | Q8⋊#168 | direct (N × H) |
| 140. C5 | C5×Q8⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C52×Q8 | 2 |
| C5×C4⋊#168 | 2 |
| C4×C5×#168 | 2 |
| C5×Q8⋊C8 | 5 |
| Q8⋊#168 | 5 |