Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
295 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 295 conjugacy classes of subgroups — too many to draw. Only its 82 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×C5×#170 | C2 | semidirect |
| 2. C2×#87827 | C2 | semidirect |
| 4. C22⋊#6032 | C2 | semidirect |
| 5. #11716760 | C2 | semidirect |
| 6. #11716754 | C2 | semidirect |
| 7. Dic5×#170 | C2 | semidirect |
| 25. C22⋊(C5⋊D5) | C8 | semidirect |
| 38. C5×#170 | D4 | semidirect |
| 39. C22×#170 | D5 | semidirect |
| 55. C22×C52 | C2×C8 | semidirect |
| 59. C2×C5⋊D5 | C2×C8 | semidirect |
| 60. #1039 | C2×C8 | semidirect |
| 130. #170 | C22⋊D5 | semidirect |
| 142. C52 | C8×D4 | semidirect |
| 151. C22×C5 | C8×D5 | semidirect |
| 152. C22×C5 | D5⋊C8 | semidirect |
| 222. C5 | C8×C22⋊D5 | semidirect |
| 223. C5 | #65692 | semidirect |
| 229. C22 | #87827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#170 | 2 |
| C2×#87827 | 2 |
| #11717070 | 2 |
| C22⋊#6032 | 2 |
| #11716760 | 2 |
| #11716754 | 2 |
| Dic5×#170 | 2 |
| #65692 | 5 |
| C8×C22⋊D5 | 5 |