Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 174 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×#3963 | C2 | semidirect |
| 6. C22×C4×C52 | C4 | semidirect |
| 11. #65500 | C5 | direct (N × H) |
| 27. #3963 | C2×C5 | semidirect |
| 45. C22×C4×C5 | Dic5 | semidirect |
| 46. C22×C4×C5 | C4×C5 | semidirect |
| 85. C52 | #381 | semidirect |
| 112. C22×C4 | C5×Dic5 | semidirect |
| 137. C5 | #65500 | direct (N × H) |
| 138. C5 | C5×#381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C5×#3963 | 2 |
| C5×#381 | 5 |
| #65500 | 5 |