Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
295 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 295 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
| 3. C5×C22⋊#170 | C2 | semidirect |
| 4. C5×C4⋊#170 | C2 | semidirect |
| 5. C4×C5×#170 | C2 | semidirect |
| 15. D4×#170 | C5 | direct (N × H) |
| 18. C52×D4 | C8 | semidirect |
| 27. C5×#170 | D4 | direct (N × H) |
| 28. C22×#170 | C2×C5 | semidirect |
| 32. C22⋊#170 | C2×C5 | semidirect |
| 33. C4⋊#170 | C2×C5 | semidirect |
| 34. C4×#170 | C2×C5 | semidirect |
| 40. C22×C52 | C2×C8 | semidirect |
| 42. C4×C52 | C2×C8 | semidirect |
| 75. C5×D4 | C5×C8 | semidirect |
| 76. C5×D4 | #170 | direct (N × H) |
| 92. #170 | C5×D4 | direct (N × H) |
| 101. C52 | C8×D4 | semidirect |
| 110. C22×C5 | C2×C5×C8 | semidirect |
| 111. C22×C5 | C2×#170 | semidirect |
| 119. C4×C5 | C2×C5×C8 | semidirect |
| 120. C4×C5 | C2×#170 | semidirect |
| 147. D4 | C5×#170 | direct (N × H) |
| 158. C5 | C5×C8×D4 | semidirect |
| 159. C5 | D4×#170 | direct (N × H) |
| 162. C22 | C2×C5×#170 | semidirect |
| 168. C4 | C2×C5×#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#170 | 2 |
| C5×D4×Dic5 | 2 |
| C5×C22⋊#170 | 2 |
| C5×C4⋊#170 | 2 |
| C4×C5×#170 | 2 |
| D4×#170 | 5 |
| C5×C8×D4 | 5 |