Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
279 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 84 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. C4⋊#6032 | C2 | semidirect |
| 4. C5×C4⋊#170 | C2 | semidirect |
| 5. #11716759 | C2 | semidirect |
| 37. C4⋊#170 | D5 | semidirect |
| 45. C4×C52 | M16 | semidirect |
| 49. C5×Dic5 | M16 | semidirect |
| 113. C52 | #423 | semidirect |
| 132. C4×C5 | #676 | semidirect |
| 133. C4×C5 | #700 | semidirect |
| 138. Dic5 | #700 | semidirect |
| 178. C5 | #65126 | semidirect |
| 179. C5 | #65681 | semidirect |
| 190. C4 | #87829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87829 | 2 |
| C4×#6036 | 2 |
| C4⋊#6032 | 2 |
| C5×C4⋊#170 | 2 |
| #11716759 | 2 |
| #65681 | 5 |
| #65126 | 5 |