Finite Group DatabasebetaFinite Group Databasebeta← (C2×AGL(1,𝔽5))⋊#168 #13099778
Order 1600.
247 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 6. C2×#6032 | C4 | semidirect |
| 11. C2×#6029 | C4 | semidirect |
| 12. C2×C5×#168 | C4 | semidirect |
| 20. C2×C5×AGL(1,𝔽5) | C8 | semidirect |
| 66. C2×#168 | AGL(1,𝔽5) | semidirect |
| 79. C2×AGL(1,𝔽5) | #168 | semidirect |
| 106. C52 | #336 | semidirect |
| 168. C5 | #64744 | semidirect |
| 169. C5 | (C2×AGL(1,𝔽5))⋊C8 | semidirect |
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 |
| (C2×AGL(1,𝔽5))⋊C8 | 5 |
| #64744 | 5 |