Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 130 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. #11716759 | C2 | direct (N × H) |
| 19. C2×C5×Dic5 | C8 | semidirect |
| 41. C5×Dic5 | C2×C8 | semidirect |
| 64. C2×C52 | C4⋊C8 | semidirect |
| 83. C2×Dic5 | #170 | semidirect |
| 97. C52 | C2×C4⋊C8 | semidirect |
| 118. Dic5 | C2×#170 | semidirect |
| 134. C2×C5 | #3946 | semidirect |
| 135. C2×C5 | C4⋊#170 | semidirect |
| 154. C5 | C2×#3946 | semidirect |
| 155. C5 | C2×C4⋊#170 | semidirect |
| 165. C2 | #11716759 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6032 | 2 |
| C22×C5×#170 | 2 |
| C2×Dic52 | 2 |
| #11716759 | 2 |
| C2×C4⋊#170 | 5 |
| C2×#3946 | 5 |