Subgroups — C₂₇×C₁₀₃₁ #42123763

Order 27837.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₀₃₁	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₀₃₁	C₉	1	1	yes	characteristic
3	C₁₀₃₁	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
4	C₂₇	C₁₀₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₉	C₃×C₁₀₃₁	1	1	yes	characteristic
6	C₃	C₉×C₁₀₃₁	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₁₀₃₁	C₂₇	direct (N × H)
4. C₂₇	C₁₀₃₁	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×C₁₀₃₁	3
C₂₇	1031