Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
416 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 144 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. #11716607 | C2 | direct (N × H) |
| 10. C2×C5×Dic10 | C4 | semidirect |
| 29. C5×Dic10 | C2×C4 | semidirect |
| 63. C2×Dic10 | Dic5 | semidirect |
| 76. C2×C52 | #103 | semidirect |
| 110. Dic10 | C2×Dic5 | semidirect |
| 117. C52 | C2×#103 | semidirect |
| 159. C2×C5 | #3948 | semidirect |
| 160. C2×C5 | #3967 | semidirect |
| 181. C5 | C2×#3948 | semidirect |
| 182. C5 | C2×#3967 | semidirect |
| 192. C2 | #11716607 | 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×C4⋊#1039 | 2 |
| C22×C5×#168 | 2 |
| #11716607 | 2 |
| C2×#3967 | 5 |
| C2×#3948 | 5 |