Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
370 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C5×#689 | C2 | semidirect |
| 5. C5×#3942 | C2 | semidirect |
| 18. #65339 | C5 | direct (N × H) |
| 38. C2×#689 | C2×C5 | semidirect |
| 42. #3942 | C2×C5 | semidirect |
| 45. C22×C52 | Q16 | semidirect |
| 122. C52 | #451 | semidirect |
| 131. C22×C5 | #689 | semidirect |
| 132. C22×C5 | C5×Q16 | semidirect |
| 186. C5 | #65339 | direct (N × H) |
| 187. C5 | C5×#451 | semidirect |
| 190. C22 | C5×#689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic10 | 2 |
| C52×C22⋊Q8 | 2 |
| C2×C5×#689 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#3942 | 2 |
| C5×#451 | 5 |
| #65339 | 5 |