Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 192 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. C2×#87776 | C2 | direct (N × H) |
| 13. #87776 | C22 | direct (N × H) |
| 35. C22×C52 | Q16 | semidirect |
| 64. C2×C52 | C2×Q16 | semidirect |
| 96. C52 | C22×Q16 | semidirect |
| 99. C22×C5 | Dic20 | semidirect |
| 100. C22×C5 | #689 | semidirect |
| 125. C2×C5 | C2×Dic20 | semidirect |
| 126. C2×C5 | C2×#689 | semidirect |
| 140. C5 | C22×Dic20 | semidirect |
| 141. C5 | C22×#689 | semidirect |
| 142. C22 | #87776 | direct (N × H) |
| 148. C2 | C2×#87776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C22×C5×Dic10 | 2 |
| C22×C5×#168 | 2 |
| C2×#87776 | 2 |
| C22×#689 | 5 |
| C22×Dic20 | 5 |