Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
400 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 158 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. C5×#3948 | C2 | direct (N × H) |
| 10. C2×C5×Dic10 | C4 | semidirect |
| 17. C2×#3948 | C5 | direct (N × H) |
| 29. C5×Dic10 | C2×C4 | semidirect |
| 39. #3948 | C2×C5 | direct (N × H) |
| 62. C2×Dic10 | C4×C5 | semidirect |
| 75. C2×C52 | #103 | semidirect |
| 107. Dic10 | C2×C4×C5 | semidirect |
| 115. C52 | C2×#103 | semidirect |
| 156. C2×C5 | #3948 | direct (N × H) |
| 157. C2×C5 | C5×#103 | semidirect |
| 178. C5 | C2×#3948 | direct (N × H) |
| 179. C5 | C2×C5×#103 | semidirect |
| 189. C2 | C5×#3948 | 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 |
| C22×C52×C8 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×#3948 | 2 |
| C2×C5×#103 | 5 |
| C2×#3948 | 5 |