Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11716742 | C2 | direct (N × H) |
| 12. C2×#6029 | C4 | semidirect |
| 13. C2×C5×#168 | C4 | semidirect |
| 14. D5×#168 | C4 | semidirect |
| 29. #6029 | C2×C4 | semidirect |
| 30. C5×#168 | C2×C4 | semidirect |
| 70. C2×#168 | AGL(1,𝔽5) | semidirect |
| 74. C2×C52 | #106 | semidirect |
| 76. C5×D5 | #106 | semidirect |
| 106. #168 | C2×AGL(1,𝔽5) | semidirect |
| 111. C52 | C2×#106 | semidirect |
| 153. C2×C5 | #3940 | semidirect |
| 154. C2×C5 | #3993 | semidirect |
| 157. D5 | #3940 | semidirect |
| 174. C5 | C2×#3940 | semidirect |
| 175. C5 | C2×#3993 | semidirect |
| 190. C2 | #11716742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1042 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×D5×#168 | 2 |
| #11716742 | 2 |
| C2×#3993 | 5 |
| C2×#3940 | 5 |