Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
207 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 207 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 |
|---|---|---|
| 23. #6032 | Q8 | semidirect |
| 89. C52 | #446 | semidirect |
| 134. C5 | #65120 | semidirect |
| 135. C5 | #65709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716962 | 2 |
| C4×#6032 | 2 |
| C5×C4⋊#170 | 2 |
| #11716759 | 2 |
| #11716752 | 2 |
| #65709 | 5 |
| #65120 | 5 |