Finite Group DatabasebetaFinite Group Databasebeta← (C2×AGL(1,𝔽5))⋊C32 #13014366
Order 1280.
202 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 7. C2×#3928 | C4 | semidirect |
| 12. C2×C5×C32 | C4 | semidirect |
| 13. C2×#3926 | C4 | semidirect |
| 64. C2×C32 | AGL(1,𝔽5) | semidirect |
| 70. C2×AGL(1,𝔽5) | C32 | semidirect |
| 147. C5 | #7465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×AGL(1,𝔽5) | 2 |
| C2×D5⋊C32 | 2 |
| C2×D5×C32 | 2 |
| #7465 | 5 |