Finite Group Databasebeta

← C₂²×C₄₁×C₁₂₇ #35209727

Subgroups — C₂²×C₄₁×C₁₂₇ #35209727

Order 20828.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×C₁₂₇	C₂	1	3	yes	maximal, direct product factor
2	C₄₁×C₁₂₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₂₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₂₇	C₂×C₄₁	1	3	yes	direct product factor
5	C₂²×C₄₁	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₂₇	C₂²×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
7	C₂×C₄₁	C₂×C₁₂₇	1	3	yes	direct product factor
8	C₄₁	C₂²×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²	C₄₁×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₂×C₄₁×C₁₂₇	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×C₁₂₇	C₂	direct (N × H)
2. C₄₁×C₁₂₇	C₂²	direct (N × H)
3. C₂²×C₁₂₇	C₄₁	direct (N × H)
4. C₂×C₁₂₇	C₂×C₄₁	direct (N × H)
5. C₂²×C₄₁	C₁₂₇	direct (N × H)
6. C₁₂₇	C₂²×C₄₁	direct (N × H)
7. C₂×C₄₁	C₂×C₁₂₇	direct (N × H)
8. C₄₁	C₂²×C₁₂₇	direct (N × H)
9. C₂²	C₄₁×C₁₂₇	direct (N × H)
10. C₂	C₂×C₄₁×C₁₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×C₁₂₇	2
C₂²×C₁₂₇	41
C₂²×C₄₁	127