Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
236 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 24. C5×#168 | Q8 | semidirect |
| 90. #168 | Dic10 | semidirect |
| 96. C52 | #501 | semidirect |
| 144. C5 | #64991 | semidirect |
| 145. C5 | #65369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717190 | 2 |
| C5×#4015 | 2 |
| C5×#3935 | 2 |
| #11716616 | 2 |
| #11716614 | 2 |
| #65369 | 5 |
| #64991 | 5 |