Finite Group DatabasebetaFinite Group Databasebeta← C3×C5×(C19⋊C3)⋊AGL(1,𝔽5) #30685734
Order 17100.
156 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|
| C3×C5×D5×C19⋊C3 | 2 |
| C3×C5×C19⋊AGL(1,𝔽5) | 3 |
| C5×(C19⋊C3)⋊AGL(1,𝔽5) | 3 |
| C3×(C19⋊C3)⋊AGL(1,𝔽5) | 5 |
| C3×C5×(C19⋊C3)⋊C4 | 5 |
| C32×C5×AGL(1,𝔽5) | 19 |