Subgroups — C₃×C₅×AGL(1,𝔽₄₇) #44569871

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)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₄₇⋊C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₄₇⋊C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	AGL(1,𝔽₄₇)	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×D₄₇	C₂₃	1	1	yes	maximal, characteristic, complemented, Hall
8	C₄₇⋊C₂₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅×C₂₃	—	47	1	no	maximal, Hall
11	C₅×D₄₇	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₂₃	—	47	1	no	Hall
13	C₃×D₄₇	C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
14	C₅×C₄₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₂₃	—	47	1	no	Hall
16	C₃×C₄₇	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₂₃	—	47	1	no	Hall
18	C₅×C₂₃	—	47	1	no	Hall
19	D₄₇	C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₂₃	—	47	1	no	Hall
21	C₄₇	C₂×C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₂₃	—	47	1	no	Hall
23	C₂×C₃×C₅	—	47	1	no	Hall
24	C₂₃	—	47	1	no	Sylow
25	C₃×C₅	AGL(1,𝔽₄₇)	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅	—	47	1	no	Hall
27	C₂×C₃	—	47	1	no	Hall
28	C₅	C₃×AGL(1,𝔽₄₇)	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×AGL(1,𝔽₄₇)	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	47	1	no	Sylow

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

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)
3. C₃×AGL(1,𝔽₄₇)	C₅	direct (N × H)
4. C₅×C₄₇⋊C₂₃	C₂×C₃	semidirect
5. C₃×C₄₇⋊C₂₃	C₂×C₅	semidirect
6. AGL(1,𝔽₄₇)	C₃×C₅	direct (N × H)
7. C₃×C₅×D₄₇	C₂₃	semidirect
8. C₄₇⋊C₂₃	C₂×C₃×C₅	semidirect
9. C₃×C₅×C₄₇	C₂×C₂₃	semidirect
11. C₅×D₄₇	C₃×C₂₃	semidirect
13. C₃×D₄₇	C₅×C₂₃	semidirect
14. C₅×C₄₇	C₂×C₃×C₂₃	semidirect
16. C₃×C₄₇	C₂×C₅×C₂₃	semidirect
19. D₄₇	C₃×C₅×C₂₃	semidirect
21. C₄₇	C₂×C₃×C₅×C₂₃	semidirect
25. C₃×C₅	AGL(1,𝔽₄₇)	direct (N × H)
28. C₅	C₃×AGL(1,𝔽₄₇)	direct (N × H)
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×C₅×D₄₇	23
C₂×C₃×C₅×C₂₃	47

Subgroups — C3×C5×AGL(1,𝔽47) #44569871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×AGL(1,𝔽₄₇) #44569871