Finite Group DatabasebetaFinite Group Databasebeta← C4×C5×C22⋊AGL(1,𝔽5) #13104523
Order 1600.
543 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 172 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.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 5 |
| C4×C5×C22⋊C4 | 5 |