Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
338 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 88 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. D5×#681 | C2 | semidirect |
| 3. #11716703 | C2 | semidirect |
| 4. C5×#3968 | C2 | semidirect |
| 5. #11716599 | C2 | semidirect |
| 41. #3968 | D5 | semidirect |
| 119. C52 | #413 | semidirect |
| 177. C5 | #65040 | semidirect |
| 178. C5 | #65526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| D5×#681 | 2 |
| #11716703 | 2 |
| C5×#3968 | 2 |
| #11716599 | 2 |
| #65526 | 5 |
| #65040 | 5 |