Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
431 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×D5×#170 | C2 | semidirect |
| 3. C22⋊#6032 | C2 | semidirect |
| 4. C5×C22⋊#170 | C2 | semidirect |
| 5. #11716753 | C2 | semidirect |
| 14. C2×#6032 | C22 | semidirect |
| 15. C2×C5×#170 | C22 | semidirect |
| 22. C22×C5×D5 | C8 | semidirect |
| 43. C22⋊#170 | D5 | direct (N × H) |
| 49. C22×C52 | C2×C8 | semidirect |
| 56. C2×C5×D5 | C2×C8 | semidirect |
| 81. C2×#170 | C2×D5 | semidirect |
| 91. C5×D5 | C22⋊C8 | semidirect |
| 102. C22×D5 | #170 | semidirect |
| 137. C52 | C2×C22⋊C8 | semidirect |
| 153. C22×C5 | C8×D5 | semidirect |
| 154. C22×C5 | C2×#170 | semidirect |
| 161. C2×D5 | C2×#170 | semidirect |
| 200. D5 | C22⋊#170 | direct (N × H) |
| 220. C5 | D5×C22⋊C8 | semidirect |
| 221. C5 | C2×C22⋊#170 | semidirect |
| 231. C22 | D5×#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×Dic5 | 2 |
| C2×D5×#170 | 2 |
| C22⋊#6032 | 2 |
| C5×C22⋊#170 | 2 |
| #11716753 | 2 |
| C2×C22⋊#170 | 5 |
| D5×C22⋊C8 | 5 |