Finite Group DatabasebetaFinite Group Databasebeta← C7×C13×AGL(1,𝔽5)×ΓL(1,𝔽8) #50303836
Order 38220.
120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|
| C7×D5×C13×ΓL(1,𝔽8) | 2 |
| C72×C13×AGL(1,𝔽5) | 3 |
| C4×C7×C13×ΓL(1,𝔽8) | 5 |
| C3×C7×C13×AGL(1,𝔽5) | 7 |
| C13×AGL(1,𝔽5)×ΓL(1,𝔽8) | 7 |
| C7×AGL(1,𝔽5)×ΓL(1,𝔽8) | 13 |