Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
368 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 104 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×#87804 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. #11716601 | C2 | semidirect |
| 5. #11716599 | C2 | semidirect |
| 48. C2×#681 | D5 | semidirect |
| 155. C52 | #413 | semidirect |
| 235. C5 | #65421 | semidirect |
| 236. C5 | #65526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×#87804 | 2 |
| C2×C5×#681 | 2 |
| #11716601 | 2 |
| #11716599 | 2 |
| #65526 | 5 |
| #65421 | 5 |