Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
319 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. C5×#4005 | C2 | direct (N × H) |
| 14. C2×#4005 | C5 | direct (N × H) |
| 34. #4005 | C2×C5 | direct (N × H) |
| 68. C2×C52 | #101 | semidirect |
| 105. C52 | C2×#101 | semidirect |
| 145. C2×C5 | C5×#101 | semidirect |
| 146. C2×C5 | #4005 | direct (N × H) |
| 164. C5 | C2×C5×#101 | semidirect |
| 165. C5 | C2×#4005 | direct (N × H) |
| 176. C2 | C5×#4005 | 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×C5×#704 | 2 |
| C5×#4005 | 2 |
| C2×#4005 | 5 |
| C2×C5×#101 | 5 |