Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. C22×#6033 | C2 | semidirect |
| 2. C2×D5⋊#170 | C2 | semidirect |
| 4. C22⋊#6034 | C2 | semidirect |
| 5. #11716783 | C2 | semidirect |
| 6. #11716779 | C2 | semidirect |
| 7. #11716777 | C2 | semidirect |
| 29. C5×C22⋊D5 | C8 | semidirect |
| 38. #6033 | D4 | semidirect |
| 56. C22×C52 | C2×C8 | semidirect |
| 60. C2×C5×D5 | C2×C8 | semidirect |
| 66. C5×Dic5 | C2×C8 | semidirect |
| 112. C22⋊D5 | #170 | semidirect |
| 149. C52 | C8×D4 | semidirect |
| 161. C22×C5 | D5⋊C8 | semidirect |
| 162. C22×C5 | C2×#170 | semidirect |
| 167. C2×D5 | C2×#170 | semidirect |
| 182. Dic5 | C2×#170 | semidirect |
| 227. C5 | #65692 | semidirect |
| 228. C5 | D4×#170 | semidirect |
| 234. C22 | D5⋊#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6033 | 2 |
| C2×D5⋊#170 | 2 |
| #11717091 | 2 |
| C22⋊#6034 | 2 |
| #11716783 | 2 |
| #11716779 | 2 |
| #11716777 | 2 |
| D4×#170 | 5 |
| #65692 | 5 |