Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
234 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 22. C52×Q8 | Q8 | semidirect |
| 90. C5×Q8 | Dic10 | semidirect |
| 91. C5×Q8 | Dic10 | semidirect |
| 123. C52 | #477 | semidirect |
| 169. Q8 | #6039 | semidirect |
| 180. C5 | #65083 | semidirect |
| 181. C5 | #65310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| #11717036 | 2 |
| #11716702 | 2 |
| C5×#3967 | 2 |
| #11716617 | 2 |
| #11716616 | 2 |
| #11716612 | 2 |
| #65310 | 5 |
| #65083 | 5 |