Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
688 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 4. #11716962 | C2 | semidirect |
| 7. C2×#6045 | C4 | semidirect |
| 76. C52 | #519 | semidirect |
| 113. C5 | #65850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C5×#4072 | 2 |
| #11717075 | 2 |
| #11716962 | 2 |
| #65850 | 5 |