Finite Group Databasebeta

← C₁₃×D₁₂₄₇ #44569787

Subgroups — C₁₃×D₁₂₄₇ #44569787

Order 32422.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₂₄₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₄₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₄₃	—	29	1	no	maximal, Hall
5	C₁₃×D₂₉	—	43	1	no	maximal, Hall
6	C₁₃×C₄₃	D₂₉	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₂₉	D₄₃	1	1	yes	characteristic, complemented, Hall
8	D₄₃	—	29	1	no	Hall
9	D₂₉	—	43	1	no	Hall
10	C₄₃	C₁₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
11	C₂₉	C₁₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₁₃	—	1247	1	no	Hall
13	C₁₃	D₁₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	1247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₁₂₄₇
commutator, cosocle, hypocenter	C₂₉×C₄₃	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₂₉×C₄₃	C₂
LCS	G ▷ C₂₉×C₄₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂₉×C₄₃	C₂	semidirect
2. D₁₂₄₇	C₁₃	direct (N × H)
3. C₂₉×C₄₃	C₂×C₁₃	semidirect
6. C₁₃×C₄₃	D₂₉	semidirect
7. C₁₃×C₂₉	D₄₃	semidirect
10. C₄₃	C₁₃×D₂₉	semidirect
11. C₂₉	C₁₃×D₄₃	semidirect
13. C₁₃	D₁₂₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₂₉×C₄₃	2
D₁₂₄₇	13
C₁₃×D₄₃	29
C₁₃×D₂₉	43