Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
663 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 663 conjugacy classes of subgroups — too many to draw. Only its 312 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×C5×#704 | C2 | direct (N × H) |
| 3. C22×C5×#170 | C2 | semidirect |
| 9. C5×#704 | C22 | direct (N × H) |
| 10. C2×C5×#170 | C22 | semidirect |
| 11. C22×#704 | C5 | direct (N × H) |
| 21. C5×#170 | C23 | semidirect |
| 24. C2×#704 | C2×C5 | direct (N × H) |
| 25. C22×#170 | C2×C5 | semidirect |
| 29. C22×C52 | M16 | semidirect |
| 46. #704 | C22×C5 | direct (N × H) |
| 47. C2×#170 | C22×C5 | semidirect |
| 52. C2×C52 | C2×M16 | semidirect |
| 73. #170 | C23×C5 | semidirect |
| 78. C52 | C22×M16 | semidirect |
| 85. C22×C5 | C5×M16 | semidirect |
| 86. C22×C5 | #704 | direct (N × H) |
| 109. C2×C5 | C2×C5×M16 | semidirect |
| 110. C2×C5 | C2×#704 | direct (N × H) |
| 123. C5 | C22×C5×M16 | semidirect |
| 124. C5 | C22×#704 | direct (N × H) |
| 126. C22 | C5×#704 | direct (N × H) |
| 133. C2 | C2×C5×#704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×Dic5 | 2 |
| C2×C5×#704 | 2 |
| C22×C5×#170 | 2 |
| C22×#704 | 5 |
| C22×C5×M16 | 5 |