Finite Group Databasebeta

← C₁₃×C₃₁×D₃₇ #44447293

Subgroups — C₁₃×C₃₁×D₃₇ #44447293

Order 29822.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₃₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₃₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₃₁	—	37	1	no	maximal, Hall
6	C₁₃×C₃₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₃₁	D₃₇	1	1	yes	characteristic, direct product factor, Hall
8	D₃₇	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃₁	—	37	1	no	Hall
10	C₃₇	C₂×C₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
11	C₃₁	C₁₃×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₁₃	—	37	1	no	Hall
13	C₁₃	C₃₁×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₃₁	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₃₁×C₃₇	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₁₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₁×C₃₇	C₂	semidirect
2. C₃₁×D₃₇	C₁₃	direct (N × H)
3. C₃₁×C₃₇	C₂×C₁₃	semidirect
4. C₁₃×D₃₇	C₃₁	direct (N × H)
6. C₁₃×C₃₇	C₂×C₃₁	semidirect
7. C₁₃×C₃₁	D₃₇	direct (N × H)
8. D₃₇	C₁₃×C₃₁	direct (N × H)
10. C₃₇	C₂×C₁₃×C₃₁	semidirect
11. C₃₁	C₁₃×D₃₇	direct (N × H)
13. C₁₃	C₃₁×D₃₇	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×C₃₁×C₃₇	2
C₃₁×D₃₇	13
C₁₃×D₃₇	31
C₂×C₁₃×C₃₁	37