Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
448 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 142 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×#3968 | C2 | direct (N × H) |
| 14. C2×#3968 | C5 | direct (N × H) |
| 32. #3968 | C2×C5 | direct (N × H) |
| 67. C2×C52 | #101 | semidirect |
| 104. C52 | C2×#101 | semidirect |
| 143. C2×C5 | #3968 | direct (N × H) |
| 144. C2×C5 | C5×#101 | semidirect |
| 159. C5 | C2×#3968 | direct (N × H) |
| 160. C5 | C2×C5×#101 | semidirect |
| 170. C2 | C5×#3968 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×C5×#681 | 2 |
| C5×#3968 | 2 |
| C2×C5×#101 | 5 |
| C2×#3968 | 5 |