Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
279 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 116 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×#4004 | C2 | semidirect |
| 4. C5×C4⋊#170 | C2 | semidirect |
| 14. #65758 | C5 | direct (N × H) |
| 32. #4004 | C2×C5 | semidirect |
| 33. C4⋊#170 | C2×C5 | semidirect |
| 41. C4×C52 | M16 | semidirect |
| 44. C5×Dic5 | M16 | semidirect |
| 103. C52 | #423 | semidirect |
| 125. C4×C5 | C5×M16 | semidirect |
| 126. C4×C5 | #704 | semidirect |
| 129. Dic5 | C5×M16 | semidirect |
| 166. C5 | C5×#423 | semidirect |
| 167. C5 | #65758 | direct (N × H) |
| 178. C4 | C5×#704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#704 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C5×#4004 | 2 |
| C5×C4⋊#170 | 2 |
| #65758 | 5 |
| C5×#423 | 5 |