Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
261 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 70 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×C5×#700 | C2 | semidirect |
| 2. C2×#87829 | C2 | semidirect |
| 4. #11716846 | C2 | semidirect |
| 5. #11716759 | C2 | semidirect |
| 6. #11716754 | C2 | semidirect |
| 7. Dic5×#170 | C2 | semidirect |
| 38. C5×#170 | D4 | semidirect |
| 40. C2×#700 | D5 | semidirect |
| 63. C5×Dic5 | M16 | semidirect |
| 129. #170 | C22⋊D5 | semidirect |
| 141. C52 | #436 | semidirect |
| 171. Dic5 | #700 | semidirect |
| 218. C5 | #65417 | semidirect |
| 219. C5 | #65705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#700 | 2 |
| C2×#87829 | 2 |
| #11717022 | 2 |
| #11716846 | 2 |
| #11716759 | 2 |
| #11716754 | 2 |
| Dic5×#170 | 2 |
| #65705 | 5 |
| #65417 | 5 |