Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
450 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 80 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. #11717244 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 4. C5×C22⋊#168 | C2 | semidirect |
| 5. #11716604 | C2 | semidirect |
| 8. C2×#6045 | C22 | semidirect |
| 13. C4⋊#1039 | C22 | semidirect |
| 15. C2×C5×#168 | C22 | semidirect |
| 43. C22⋊#168 | D5 | semidirect |
| 47. C22×C52 | SD16 | semidirect |
| 82. C2×#168 | C2×D5 | semidirect |
| 132. C52 | #450 | semidirect |
| 145. C22×C5 | #677 | semidirect |
| 146. C22×C5 | #687 | semidirect |
| 206. C5 | #65020 | semidirect |
| 207. C5 | #65507 | semidirect |
| 214. C22 | #87773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| #11717244 | 2 |
| C2×#87773 | 2 |
| C5×C22⋊#168 | 2 |
| #11716604 | 2 |
| #65507 | 5 |
| #65020 | 5 |