Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
471 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 122 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×#6032 | C2 | semidirect |
| 3. C22×C5×#170 | C2 | semidirect |
| 4. #11716754 | C2 | direct (N × H) |
| 13. C2×#6032 | C22 | semidirect |
| 15. C2×C5×#170 | C22 | semidirect |
| 21. C22×C5⋊D5 | C8 | semidirect |
| 37. C22×#170 | D5 | semidirect |
| 49. C2×C5⋊D5 | C2×C8 | semidirect |
| 72. C2×#170 | C2×D5 | semidirect |
| 78. C2×C52 | C22⋊C8 | semidirect |
| 124. C52 | C2×C22⋊C8 | semidirect |
| 172. C2×C5 | #3952 | semidirect |
| 173. C2×C5 | #4003 | semidirect |
| 200. C5 | C2×#3952 | semidirect |
| 201. C5 | C2×#4003 | semidirect |
| 215. C2 | #11716754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6036 | 2 |
| C22×#6032 | 2 |
| C22×C5×#170 | 2 |
| #11716754 | 2 |
| C2×#4003 | 5 |
| C2×#3952 | 5 |