Finite Group Databasebeta

← D₁₃×C₃₁×C₃₇ #44447296

Subgroups — D₁₃×C₃₁×C₃₇ #44447296

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	C₂×C₃₁×C₃₇	—	13	1	no	maximal, Hall
3	C₃₁×C₃₇	D₁₃	1	1	yes	characteristic, direct product factor, Hall
4	D₁₃×C₃₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₁₃×C₃₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₃₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₃₁	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃₇	—	13	1	no	Hall
9	C₂×C₃₁	—	13	1	no	Hall
10	C₃₇	D₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	D₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₁₃	C₃₁×C₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₁₃	C₂×C₃₁×C₃₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁×C₃₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃₁×C₃₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₃₁×C₃₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃₁×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₁×C₃₇	C₂	semidirect
3. C₃₁×C₃₇	D₁₃	direct (N × H)
4. D₁₃×C₃₇	C₃₁	direct (N × H)
5. D₁₃×C₃₁	C₃₇	direct (N × H)
6. C₁₃×C₃₇	C₂×C₃₁	semidirect
7. C₁₃×C₃₁	C₂×C₃₇	semidirect
10. C₃₇	D₁₃×C₃₁	direct (N × H)
11. C₃₁	D₁₃×C₃₇	direct (N × H)
12. D₁₃	C₃₁×C₃₇	direct (N × H)
13. C₁₃	C₂×C₃₁×C₃₇	semidirect

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
C₂×C₃₁×C₃₇	13
D₁₃×C₃₇	31
D₁₃×C₃₁	37