Finite Group Databasebeta

← C₂×C₄₇×D₃₁ #19154201

Subgroups — C₂×C₄₇×D₃₁ #19154201

Order 5828.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×D₃₁	C₂	1	2	yes	maximal, direct product factor
3	C₃₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₄₇	—	31	1	no	maximal, Hall
5	C₂×D₃₁	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₄₇	—	31	2	no	—
7	C₂×C₄₇	D₃₁	1	1	yes	characteristic, direct product factor
8	C₂×C₃₁	C₂×C₄₇	1	1	yes	characteristic, complemented
9	D₃₁	C₂×C₄₇	1	2	yes	direct product factor
10	C₄₇	C₂×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₂²×C₄₇	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	31	1	no	Sylow
13	C₂	—	31	2	no	—
14	C₂	C₄₇×D₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₃₁
commutator, hypocenter	C₃₁	C₂²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃₁×C₄₇	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×C₄₇	C₂	semidirect
2. C₄₇×D₃₁	C₂	direct (N × H)
3. C₃₁×C₄₇	C₂²	semidirect
5. C₂×D₃₁	C₄₇	direct (N × H)
7. C₂×C₄₇	D₃₁	direct (N × H)
8. C₂×C₃₁	C₂×C₄₇	semidirect
9. D₃₁	C₂×C₄₇	direct (N × H)
10. C₄₇	C₂×D₃₁	direct (N × H)
11. C₃₁	C₂²×C₄₇	semidirect
14. C₂	C₄₇×D₃₁	direct (N × H)