Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
319 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 138 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. #11716752 | C2 | direct (N × H) |
| 8. C2×#6032 | C4 | semidirect |
| 10. C2×C5×#170 | C4 | semidirect |
| 25. #6032 | C2×C4 | semidirect |
| 26. C5×#170 | C2×C4 | semidirect |
| 53. C2×#170 | Dic5 | semidirect |
| 64. C2×C52 | #97 | semidirect |
| 90. #170 | C2×Dic5 | semidirect |
| 97. C52 | C2×#97 | semidirect |
| 134. C2×C5 | #3947 | semidirect |
| 135. C2×C5 | #4002 | semidirect |
| 154. C5 | C2×#3947 | semidirect |
| 155. C5 | C2×#4002 | semidirect |
| 165. C2 | #11716752 | 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 |
| #11716752 | 2 |
| C2×#4002 | 5 |
| C2×#3947 | 5 |