Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
688 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 318 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. C5×#4015 | C2 | direct (N × H) |
| 13. C2×#4015 | C5 | direct (N × H) |
| 16. C2×C4×C52 | Q8 | semidirect |
| 30. #4015 | C2×C5 | direct (N × H) |
| 35. C4×C52 | C2×Q8 | semidirect |
| 55. C2×C52 | C4⋊Q8 | semidirect |
| 68. C2×C4×C5 | Dic10 | semidirect |
| 71. C2×C4×C5 | C5×Q8 | semidirect |
| 83. C52 | C2×C4⋊Q8 | semidirect |
| 96. C4×C5 | C2×Dic10 | semidirect |
| 99. C4×C5 | C2×C5×Q8 | semidirect |
| 111. C2×C5 | #4015 | direct (N × H) |
| 112. C2×C5 | C5×C4⋊Q8 | semidirect |
| 121. C2×C4 | C5×Dic10 | semidirect |
| 126. C5 | C2×#4015 | direct (N × H) |
| 127. C5 | C2×C5×C4⋊Q8 | semidirect |
| 132. C4 | C2×C5×Dic10 | semidirect |
| 134. C2 | C5×#4015 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic10 | 2 |
| C2×C42×C52 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×#4015 | 2 |
| C2×C5×C4⋊Q8 | 5 |
| C2×#4015 | 5 |