Finite Group Databasebeta

← C₃×D₂₉×C₁₃₇ #37558616

Subgroups — C₃×D₂₉×C₁₃₇ #37558616

Order 23838.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₉×C₁₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₁₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃₇	—	29	1	no	maximal, Hall
5	C₃×C₁₃₇	D₂₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₃₇	—	29	1	no	Hall
7	C₃×D₂₉	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃₇	C₃×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₂₉	C₂×C₁₃₇	1	1	yes	characteristic, complemented, Hall
10	D₂₉	C₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂₉	C₂×C₃×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	29	1	no	Hall
13	C₃	D₂₉×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃₇	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₃×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₁₃₇	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃×C₁₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×C₁₃₇	C₂	semidirect
2. D₂₉×C₁₃₇	C₃	direct (N × H)
3. C₂₉×C₁₃₇	C₂×C₃	semidirect
5. C₃×C₁₃₇	D₂₉	direct (N × H)
7. C₃×D₂₉	C₁₃₇	direct (N × H)
8. C₁₃₇	C₃×D₂₉	direct (N × H)
9. C₃×C₂₉	C₂×C₁₃₇	semidirect
10. D₂₉	C₃×C₁₃₇	direct (N × H)
11. C₂₉	C₂×C₃×C₁₃₇	semidirect
13. C₃	D₂₉×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₂₉×C₁₃₇	2
D₂₉×C₁₃₇	3
C₂×C₃×C₁₃₇	29
C₃×D₂₉	137