Finite Group DatabasebetaFinite Group Databasebeta← C3×D5⋊(C22⋊AGL(1,𝔽5)) #72231019
Order 2400.
596 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|
| C22×C3×D52 | 2 |
| C2×C3×D5⋊AGL(1,𝔽5) | 2 |
| C3×C22⋊#1044 | 2 |
| C3×C22⋊#1043 | 2 |
| C3×#87831 | 2 |
| D5⋊(C22⋊AGL(1,𝔽5)) | 3 |
| C2×C3×C22⋊AGL(1,𝔽5) | 5 |