Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 122 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. #11716732 | 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 |
| 27. #6032 | C2×C4 | semidirect |
| 28. #6029 | C2×C4 | semidirect |
| 29. C5×#168 | C2×C4 | semidirect |
| 67. C2×#168 | AGL(1,𝔽5) | semidirect |
| 71. C2×C52 | #97 | semidirect |
| 73. C5×D5 | #97 | semidirect |
| 100. #168 | C2×AGL(1,𝔽5) | semidirect |
| 105. C52 | C2×#97 | semidirect |
| 142. C2×C5 | #3935 | semidirect |
| 143. C2×C5 | #3992 | semidirect |
| 146. D5 | #3935 | semidirect |
| 161. C5 | C2×#3935 | semidirect |
| 162. C5 | C2×#3992 | semidirect |
| 174. C2 | #11716732 | 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 |
| #11716732 | 2 |
| C2×#3992 | 5 |
| C2×#3935 | 5 |