Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×#6034 | C2 | semidirect |
| 3. C22×#6033 | C2 | semidirect |
| 4. #11716779 | C2 | direct (N × H) |
| 13. C2×#6034 | C22 | semidirect |
| 15. C2×#6033 | C22 | semidirect |
| 21. C22×C5×D5 | C8 | semidirect |
| 50. C2×C5×D5 | C2×C8 | semidirect |
| 81. C2×C52 | C22⋊C8 | semidirect |
| 95. C22×D5 | #170 | semidirect |
| 128. C52 | C2×C22⋊C8 | semidirect |
| 148. C2×D5 | C2×#170 | semidirect |
| 176. C2×C5 | #4003 | semidirect |
| 177. C2×C5 | C22⋊#170 | semidirect |
| 202. C5 | C2×#4003 | semidirect |
| 203. C5 | C2×C22⋊#170 | semidirect |
| 217. C2 | #11716779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×Dic5 | 2 |
| C22×#6034 | 2 |
| C22×#6033 | 2 |
| #11716779 | 2 |
| C2×C22⋊#170 | 5 |
| C2×#4003 | 5 |