Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 30. #6029 | Q8 | semidirect |
| 31. C5×#168 | Q8 | semidirect |
| 110. #168 | Dic10 | semidirect |
| 118. C52 | #498 | semidirect |
| 174. C5 | #65144 | semidirect |
| 175. C5 | #65368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4034 | 2 |
| #11717036 | 2 |
| #11716675 | 2 |
| C5×#3940 | 2 |
| #11716615 | 2 |
| #11716614 | 2 |
| Dic5×#168 | 2 |
| #65368 | 5 |
| #65144 | 5 |