Finite Group DatabasebetaFinite Group Databasebeta← C3×C5×C19×ΓL(1,𝔽16) #30685869
Order 17100.
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|
| C32×C5×D5×C19 | 2 |
| C5×C19×ΓL(1,𝔽16) | 3 |
| C3×C5×C19×AGL(1,𝔽5) | 3 |
| C3×C19×ΓL(1,𝔽16) | 5 |
| C3×C5×Dic3×C19 | 5 |
| C3×C5×ΓL(1,𝔽16) | 19 |