Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
281 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 281 conjugacy classes of subgroups — too many to draw. Only its 88 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×D5×#170 | C2 | semidirect |
| 3. C4×#6032 | C2 | semidirect |
| 4. C5×C4⋊#170 | C2 | semidirect |
| 5. #11716753 | C2 | semidirect |
| 22. C5×D20 | C8 | semidirect |
| 26. #6032 | D4 | semidirect |
| 33. C4⋊#170 | D5 | semidirect |
| 41. C2×C5×D5 | C2×C8 | semidirect |
| 42. C4×C52 | C2×C8 | semidirect |
| 86. D20 | #170 | semidirect |
| 100. C52 | C8×D4 | semidirect |
| 109. C2×D5 | C2×#170 | semidirect |
| 114. C4×C5 | C8×D5 | semidirect |
| 115. C4×C5 | C2×#170 | semidirect |
| 154. C5 | #65123 | semidirect |
| 155. C5 | D4×#170 | semidirect |
| 164. C4 | D5×#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#170 | 2 |
| Dic5×D20 | 2 |
| C4×#6032 | 2 |
| C5×C4⋊#170 | 2 |
| #11716753 | 2 |
| D4×#170 | 5 |
| #65123 | 5 |