Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
640 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 640 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 |
|---|---|---|
| 2. C22×C5×#168 | C2 | semidirect |
| 3. #11716598 | C2 | direct (N × H) |
| 11. C2×C5×#168 | C22 | semidirect |
| 16. C22×C5⋊D5 | C8 | semidirect |
| 29. C22×#168 | D5 | semidirect |
| 38. C2×C5⋊D5 | C2×C8 | semidirect |
| 58. C2×#168 | C2×D5 | semidirect |
| 60. C2×C52 | C22⋊C8 | semidirect |
| 96. C52 | C2×C22⋊C8 | semidirect |
| 132. C2×C5 | #3952 | semidirect |
| 152. C5 | C2×#3952 | semidirect |
| 165. C2 | #11716598 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C22×C5×#168 | 2 |
| #11716598 | 2 |
| C2×#3952 | 5 |