Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
688 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 208 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 |
|---|---|---|
| 5. #11717037 | C2 | direct (N × H) |
| 17. C2×C4×C52 | Q8 | semidirect |
| 20. C2×#1039 | Q8 | semidirect |
| 37. C4×C52 | C2×Q8 | semidirect |
| 39. #1039 | C2×Q8 | semidirect |
| 57. C2×C52 | C4⋊Q8 | semidirect |
| 67. C2×C4×C5 | Dic10 | semidirect |
| 85. C52 | C2×C4⋊Q8 | semidirect |
| 96. C4×C5 | C2×Dic10 | semidirect |
| 115. C2×C5 | #4034 | semidirect |
| 127. C2×C4 | #6039 | semidirect |
| 130. C5 | C2×#4034 | semidirect |
| 138. C4 | C2×#6039 | semidirect |
| 139. C2 | #11717037 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6039 | 2 |
| C2×C4×#1039 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×#87781 | 2 |
| #11717037 | 2 |
| C2×#4034 | 5 |