Finite Group Databasebeta

← C₂×C₃₇⋊C₃×C₁₃₉ #44524813

Subgroups — C₂×C₃₇⋊C₃×C₁₃₉ #44524813

Order 30858.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊C₃×C₁₃₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃₇×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₇×C₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃₉	—	37	1	no	maximal, Hall
5	C₃×C₁₃₉	—	37	1	no	Hall
6	C₂×C₁₃₉	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃₇⋊C₃	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃₉	C₂×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₃₇⋊C₃	C₂×C₁₃₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₇	C₃×C₁₃₉	1	1	yes	characteristic, complemented, Hall
11	C₃₇	C₂×C₃×C₁₃₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	37	1	no	Hall
13	C₃	—	37	1	no	Sylow
14	C₂	C₃₇⋊C₃×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₃₉	C₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₂×C₃×C₁₃₉
Frattini	C₁	G
Fitting, socle	C₂×C₃₇×C₁₃₉	C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₁₃₉

Complements

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

N	H ≅ G/N	type
1. C₃₇⋊C₃×C₁₃₉	C₂	direct (N × H)
2. C₂×C₃₇×C₁₃₉	C₃	semidirect
3. C₃₇×C₁₃₉	C₂×C₃	semidirect
6. C₂×C₁₃₉	C₃₇⋊C₃	direct (N × H)
7. C₂×C₃₇⋊C₃	C₁₃₉	direct (N × H)
8. C₁₃₉	C₂×C₃₇⋊C₃	direct (N × H)
9. C₃₇⋊C₃	C₂×C₁₃₉	direct (N × H)
10. C₂×C₃₇	C₃×C₁₃₉	semidirect
11. C₃₇	C₂×C₃×C₁₃₉	semidirect
14. C₂	C₃₇⋊C₃×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇⋊C₃×C₁₃₉	2
C₂×C₃₇×C₁₃₉	3
C₂×C₃×C₁₃₉	37
C₂×C₃₇⋊C₃	139