Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
256 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 52 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×D5×C132 | 2 |
| C13×C3⋊#63120 | 3 |
| C3×C13×#63120 | 3 |
| C3×C13×Dic39 | 5 |
| C3×C3⋊#63120 | 13 |
| C3×C13×ΓL(1,𝔽16) | 13 |