Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
159 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. C2×#87763 | C2 | semidirect |
| 23. C22×C52 | C16 | semidirect |
| 65. C52 | C22⋊C16 | semidirect |
| 74. C22×C5 | #672 | semidirect |
| 75. C22×C5 | #674 | semidirect |
| 112. C5 | C22⋊#672 | semidirect |
| 113. C5 | C22⋊#674 | semidirect |
| 116. C22 | #87763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#168 | 2 |
| C2×#87763 | 2 |
| C22⋊#674 | 5 |
| C22⋊#672 | 5 |