Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 352 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. #11716616 | C2 | direct (N × H) |
| 12. C2×C5×#168 | C4 | semidirect |
| 25. C5×#168 | C2×C4 | semidirect |
| 64. C2×#168 | Dic5 | semidirect |
| 67. C2×C52 | #107 | semidirect |
| 97. #168 | C2×Dic5 | semidirect |
| 102. C52 | C2×#107 | semidirect |
| 142. C2×C5 | #3939 | semidirect |
| 143. C2×C5 | #3950 | semidirect |
| 161. C5 | C2×#3939 | semidirect |
| 162. C5 | C2×#3950 | semidirect |
| 172. C2 | #11716616 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1039 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C22×C5×#168 | 2 |
| #11716616 | 2 |
| C2×#3950 | 5 |
| C2×#3939 | 5 |