Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1936 conjugacy classes of subgroups; only the 608 normal subgroups are shown.
This group has 1936 conjugacy classes of subgroups — too many to draw. Only its 608 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×C5×Dic10 | C2 | semidirect |
| 3. C22×#6039 | C2 | semidirect |
| 5. C2×#87872 | C2 | direct (N × H) |
| 11. C2×C5×Dic10 | C22 | semidirect |
| 12. C2×#6039 | C22 | semidirect |
| 14. #87872 | C22 | direct (N × H) |
| 17. C22×C5⋊D5 | Q8 | semidirect |
| 23. C5×Dic10 | C23 | semidirect |
| 24. #6039 | C23 | semidirect |
| 32. C22×Dic10 | D5 | semidirect |
| 33. C22×C52 | C2×Q8 | semidirect |
| 35. C2×C5⋊D5 | C2×Q8 | semidirect |
| 54. C2×Dic10 | C2×D5 | semidirect |
| 56. C2×C52 | C22×Q8 | semidirect |
| 58. C5⋊D5 | C22×Q8 | semidirect |
| 76. Dic10 | C22×D5 | semidirect |
| 82. C52 | C23×Q8 | semidirect |
| 85. C22×C5 | Q8×D5 | semidirect |
| 108. C2×C5 | C2×Q8×D5 | semidirect |
| 123. C5 | C22×Q8×D5 | semidirect |
| 126. C22 | #87872 | direct (N × H) |
| 132. C2 | C2×#87872 | 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×C5×Dic10 | 2 |
| C22×#6039 | 2 |
| C22×#6036 | 2 |
| C2×#87872 | 2 |
| C22×Q8×D5 | 5 |