Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 112 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. #11716601 | C2 | direct (N × H) |
| 90. C2×C52 | #101 | semidirect |
| 136. C52 | C2×#101 | semidirect |
| 185. C2×C5 | #3956 | semidirect |
| 186. C2×C5 | #3968 | semidirect |
| 206. C5 | C2×#3956 | semidirect |
| 207. C5 | C2×#3968 | semidirect |
| 219. C2 | #11716601 | 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×#87804 | 2 |
| C2×C5×#681 | 2 |
| #11716601 | 2 |
| C2×#3968 | 5 |
| C2×#3956 | 5 |