Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
262 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 23. #6045 | Q8 | semidirect |
| 105. C52 | #475 | semidirect |
| 158. C5 | #65140 | semidirect |
| 159. C5 | #65383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C5×#4015 | 2 |
| C5×C4⋊#168 | 2 |
| #11716614 | 2 |
| #11716608 | 2 |
| #65383 | 5 |
| #65140 | 5 |