Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#87829 | C2 | semidirect |
| 3. C22⋊#6032 | C2 | semidirect |
| 4. C5×C22⋊#170 | C2 | semidirect |
| 5. #11716754 | C2 | semidirect |
| 14. C2×#6032 | C22 | semidirect |
| 15. C2×C5×#170 | C22 | semidirect |
| 42. C22⋊#170 | D5 | semidirect |
| 49. C22×C52 | M16 | semidirect |
| 57. C2×C5⋊D5 | M16 | semidirect |
| 80. C2×#170 | C2×D5 | semidirect |
| 139. C52 | #407 | semidirect |
| 148. C22×C5 | #676 | semidirect |
| 149. C22×C5 | #700 | semidirect |
| 229. C5 | #65015 | semidirect |
| 230. C5 | #65756 | semidirect |
| 240. C22 | #87829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6036 | 2 |
| C2×#87829 | 2 |
| C22⋊#6032 | 2 |
| C5×C22⋊#170 | 2 |
| #11716754 | 2 |
| #65756 | 5 |
| #65015 | 5 |