Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
431 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 152 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. C22×C5×#170 | C2 | semidirect |
| 3. C5×#4003 | C2 | direct (N × H) |
| 11. C2×C5×#170 | C22 | semidirect |
| 12. C2×#4003 | C5 | direct (N × H) |
| 17. C22×C5×D5 | C8 | semidirect |
| 29. C22×#170 | C2×C5 | semidirect |
| 31. #4003 | C2×C5 | direct (N × H) |
| 40. C2×C5×D5 | C2×C8 | semidirect |
| 58. C2×#170 | C22×C5 | semidirect |
| 62. C2×C52 | C22⋊C8 | semidirect |
| 76. C22×D5 | C5×C8 | semidirect |
| 99. C52 | C2×C22⋊C8 | semidirect |
| 119. C2×D5 | C2×C5×C8 | semidirect |
| 140. C2×C5 | C5×C22⋊C8 | semidirect |
| 141. C2×C5 | #4003 | direct (N × H) |
| 163. C5 | C2×C5×C22⋊C8 | semidirect |
| 164. C5 | C2×#4003 | direct (N × H) |
| 177. C2 | C5×#4003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C22×C5×#170 | 2 |
| C5×#4003 | 2 |
| C2×#4003 | 5 |
| C2×C5×C22⋊C8 | 5 |