Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 199 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. C22×#6034 | C2 | semidirect |
| 3. C22×#6033 | C2 | semidirect |
| 4. C2×#87834 | C2 | direct (N × H) |
| 10. C2×#6034 | C22 | semidirect |
| 11. C2×#6033 | C22 | semidirect |
| 12. #87834 | C22 | direct (N × H) |
| 23. #6034 | C23 | semidirect |
| 24. #6033 | C23 | semidirect |
| 34. C22×C52 | M16 | semidirect |
| 60. C2×C52 | C2×M16 | semidirect |
| 91. C52 | C22×M16 | semidirect |
| 96. C22×C5 | #700 | semidirect |
| 97. C22×C5 | #704 | semidirect |
| 121. C2×C5 | C2×#700 | semidirect |
| 122. C2×C5 | C2×#704 | semidirect |
| 137. C5 | C22×#700 | semidirect |
| 138. C5 | C22×#704 | semidirect |
| 141. C22 | #87834 | direct (N × H) |
| 147. C2 | C2×#87834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×Dic5 | 2 |
| C22×#6034 | 2 |
| C22×#6033 | 2 |
| C2×#87834 | 2 |
| C22×#704 | 5 |
| C22×#700 | 5 |