Finite Group DatabasebetaFinite Group Databasebeta← C2×C9×D5×ΓL(1,𝔽32) #42124517
Order 27900.
144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|
| C2×C5×C9×ΓL(1,𝔽32) | 2 |
| C9×D5×ΓL(1,𝔽32) | 2 |
| C2×C3×D5×ΓL(1,𝔽32) | 3 |
| C2×C9×D5×C31 | 5 |
| C22×C9×ΓL(1,𝔽32) | 5 |
| C2×C5×C9×D5 | 31 |