Finite Group DatabasebetaFinite Group Databasebeta← C5×(C2×AGL(1,𝔽5))⋊C8 #13100082
Order 1600.
247 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 100 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×C5×#170 | C4 | semidirect |
| 11. C2×C52×C8 | C4 | semidirect |
| 12. C2×C5×#168 | C4 | semidirect |
| 15. (C2×AGL(1,𝔽5))⋊C8 | C5 | direct (N × H) |
| 20. C2×C5×AGL(1,𝔽5) | C8 | semidirect |
| 50. C2×#170 | C4×C5 | semidirect |
| 62. C2×C5×C8 | C4×C5 | semidirect |
| 63. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 66. C2×#168 | C4×C5 | semidirect |
| 79. C2×AGL(1,𝔽5) | C5×C8 | semidirect |
| 106. C52 | #336 | semidirect |
| 138. C2×C8 | C5×AGL(1,𝔽5) | semidirect |
| 168. C5 | C5×#336 | semidirect |
| 169. C5 | (C2×AGL(1,𝔽5))⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×C5×D5⋊C8 | 2 |
| C2×C5×C8×D5 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 5 |
| C5×#336 | 5 |