Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
335 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 4. AGL(1,𝔽5)×#168 | C2 | direct (N × H) |
| 7. C2×#6032 | C4 | semidirect |
| 8. D5⋊#168 | C4 | semidirect |
| 12. C2×#6029 | C4 | semidirect |
| 13. C2×C5×#168 | C4 | semidirect |
| 14. D5×#168 | C4 | semidirect |
| 19. C2×C5×AGL(1,𝔽5) | C8 | semidirect |
| 27. #6032 | C2×C4 | semidirect |
| 28. #6029 | C2×C4 | semidirect |
| 29. C5×#168 | C2×C4 | semidirect |
| 42. C5×AGL(1,𝔽5) | C2×C8 | semidirect |
| 67. C2×#168 | AGL(1,𝔽5) | direct (N × H) |
| 71. C2×C52 | C4×C8 | semidirect |
| 73. C5×D5 | C4×C8 | semidirect |
| 77. C2×AGL(1,𝔽5) | #168 | direct (N × H) |
| 100. #168 | C2×AGL(1,𝔽5) | direct (N × H) |
| 105. C52 | C2×C4×C8 | semidirect |
| 115. AGL(1,𝔽5) | C2×#168 | direct (N × H) |
| 142. C2×C5 | C4×#168 | semidirect |
| 143. C2×C5 | C8×AGL(1,𝔽5) | semidirect |
| 146. D5 | C4×#168 | semidirect |
| 161. C5 | C2×C4×#168 | semidirect |
| 162. C5 | C2×C8×AGL(1,𝔽5) | semidirect |
| 174. C2 | AGL(1,𝔽5)×#168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊#168 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×D5×#168 | 2 |
| AGL(1,𝔽5)×#168 | 2 |
| C2×C8×AGL(1,𝔽5) | 5 |
| C2×C4×#168 | 5 |