Finite Group DatabasebetaFinite Group DatabasebetaOrder 35700.
192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C17 | C22×C3 |
| LCS | G ▷ C52×C7×C17 | |
| UCS | C1 | |
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 |
|---|---|
| C5⋊(C5⋊(C17⋊AGL(1,𝔽7))) | 2 |
| C5×ΓL(1,𝔽8)×D85 | 2 |
| C5×C17×C5⋊AGL(1,𝔽7) | 2 |
| D35×D85 | 3 |
| AGL(1,𝔽7)×D85 | 5 |
| D17×C5⋊AGL(1,𝔽7) | 5 |
| C3×D5×D85 | 7 |
| D5×C5⋊AGL(1,𝔽7) | 17 |