Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
248 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 16. #65369 | C5 | direct (N × H) |
| 24. C5×#168 | Q8 | semidirect |
| 89. #168 | C5×Q8 | semidirect |
| 95. C52 | #501 | semidirect |
| 142. C5 | #65369 | direct (N × H) |
| 143. C5 | C5×#501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C5×#4016 | 2 |
| C5×#3940 | 2 |
| C5×#3939 | 2 |
| C5×#3935 | 2 |
| C5×#501 | 5 |
| #65369 | 5 |