Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#87853 | C2 | semidirect |
| 2. C2×#87829 | C2 | semidirect |
| 4. C5×C22⋊#170 | C2 | semidirect |
| 5. #11716760 | C2 | semidirect |
| 6. #11716754 | C2 | semidirect |
| 7. Dic5×#170 | C2 | semidirect |
| 36. #6032 | D4 | semidirect |
| 45. C22⋊#170 | D5 | semidirect |
| 60. #1039 | M16 | semidirect |
| 142. C52 | #436 | semidirect |
| 222. C5 | #65018 | semidirect |
| 223. C5 | #65695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87853 | 2 |
| C2×#87829 | 2 |
| #11717070 | 2 |
| C5×C22⋊#170 | 2 |
| #11716760 | 2 |
| #11716754 | 2 |
| Dic5×#170 | 2 |
| #65695 | 5 |
| #65018 | 5 |