Subgroups — C₃×C₅⋊AGL(1,𝔽₄₇) #44569873

Order 32430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄₇⋊C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊AGL(1,𝔽₄₇)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×AGL(1,𝔽₄₇)	—	5	1	no	maximal, Hall
4	C₅×C₄₇⋊C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₄₇⋊C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
6	AGL(1,𝔽₄₇)	—	5	1	no	Hall
7	C₃×D₂₃₅	C₂₃	1	1	yes	maximal, characteristic, complemented, Hall
8	C₄₇⋊C₂₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₅×C₂₃	—	47	1	no	maximal, Hall
11	D₂₃₅	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₂₃	—	47	1	no	Hall
13	C₃×D₄₇	—	5	1	no	Hall
14	C₅×C₄₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
15	D₅×C₂₃	—	47	1	no	Hall
16	C₃×C₄₇	D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₂₃	—	235	1	no	Hall
18	C₅×C₂₃	—	47	1	no	Hall
19	D₄₇	—	5	1	no	Hall
20	C₃×C₂₃	—	47	1	no	Hall
21	C₄₇	C₃×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₂₃	—	235	1	no	Hall
23	C₃×D₅	—	47	1	no	Hall
24	C₂₃	—	47	1	no	Sylow
25	C₃×C₅	AGL(1,𝔽₄₇)	1	1	yes	characteristic, complemented, Hall
26	D₅	—	47	1	no	Hall
27	C₂×C₃	—	235	1	no	Hall
28	C₅	C₃×AGL(1,𝔽₄₇)	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₅⋊AGL(1,𝔽₄₇)	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	235	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊AGL(1,𝔽₄₇)
commutator, cosocle, hypocenter	C₅×C₄₇	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₄₇	C₂×C₂₃
LCS	G ▷ C₅×C₄₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₄₇⋊C₂₃	C₂	semidirect
2. C₅⋊AGL(1,𝔽₄₇)	C₃	direct (N × H)
4. C₅×C₄₇⋊C₂₃	C₂×C₃	semidirect
5. C₃×C₄₇⋊C₂₃	D₅	semidirect
7. C₃×D₂₃₅	C₂₃	semidirect
8. C₄₇⋊C₂₃	C₃×D₅	semidirect
9. C₃×C₅×C₄₇	C₂×C₂₃	semidirect
11. D₂₃₅	C₃×C₂₃	semidirect
14. C₅×C₄₇	C₂×C₃×C₂₃	semidirect
16. C₃×C₄₇	D₅×C₂₃	semidirect
21. C₄₇	C₃×D₅×C₂₃	semidirect
25. C₃×C₅	AGL(1,𝔽₄₇)	semidirect
28. C₅	C₃×AGL(1,𝔽₄₇)	semidirect
29. C₃	C₅⋊AGL(1,𝔽₄₇)	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×C₅×C₄₇⋊C₂₃	2
C₅⋊AGL(1,𝔽₄₇)	3
C₃×AGL(1,𝔽₄₇)	5
C₃×D₂₃₅	23
C₃×D₅×C₂₃	47

Subgroups — C3×C5⋊AGL(1,𝔽47) #44569873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊AGL(1,𝔽₄₇) #44569873