Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 272 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×#6029 | C2 | semidirect |
| 3. C22×C5×#168 | C2 | semidirect |
| 4. C2×#87768 | C2 | direct (N × H) |
| 10. C2×#6029 | C22 | semidirect |
| 11. C2×C5×#168 | C22 | semidirect |
| 12. #87768 | C22 | direct (N × H) |
| 23. #6029 | C23 | semidirect |
| 24. C5×#168 | C23 | semidirect |
| 32. C22×#168 | D5 | semidirect |
| 34. C22×C52 | M16 | semidirect |
| 57. C2×#168 | C2×D5 | semidirect |
| 60. C2×C52 | C2×M16 | semidirect |
| 86. #168 | C22×D5 | semidirect |
| 91. C52 | C22×M16 | semidirect |
| 96. C22×C5 | #676 | semidirect |
| 97. C22×C5 | #681 | semidirect |
| 121. C2×C5 | C2×#676 | semidirect |
| 122. C2×C5 | C2×#681 | semidirect |
| 137. C5 | C22×#676 | semidirect |
| 138. C5 | C22×#681 | semidirect |
| 141. C22 | #87768 | direct (N × H) |
| 147. C2 | C2×#87768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C22×#6029 | 2 |
| C22×C5×#168 | 2 |
| C2×#87768 | 2 |
| C22×#681 | 5 |
| C22×#676 | 5 |