Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 70 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×C5×#687 | C2 | semidirect |
| 3. #11716985 | C2 | semidirect |
| 4. C2×#87774 | C2 | semidirect |
| 5. #11716594 | C2 | semidirect |
| 26. C5×#168 | D4 | semidirect |
| 32. C2×#687 | D5 | semidirect |
| 41. #1039 | SD16 | semidirect |
| 88. #168 | C22⋊D5 | semidirect |
| 94. C52 | #492 | semidirect |
| 141. C5 | #65464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717260 | 2 |
| C2×C5×#687 | 2 |
| #11716985 | 2 |
| C2×#87774 | 2 |
| #11716594 | 2 |
| #65464 | 5 |