Subgroups — AGL(1,𝔽₇)×C₁₀₁⋊C₅ #35234608

Order 21210.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×C₁₀₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₁₀₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	AGL(1,𝔽₇)×C₁₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₀₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₀₁⋊C₅	—	7	1	no	maximal, Hall
6	ΓL(1,𝔽₈)×C₁₀₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₀₁⋊C₅	—	7	1	no	Hall
8	D₇×C₁₀₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₀₁⋊C₅	—	7	1	no	Hall
10	C₇×C₁₀₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₀₁	—	7	1	no	Hall
12	C₁₀₁⋊C₅	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₁₀₁	—	7	1	no	Hall
14	C₅×AGL(1,𝔽₇)	—	101	1	no	maximal, Hall
15	C₂×C₁₀₁	—	7	1	no	Hall
16	C₅×ΓL(1,𝔽₈)	—	101	1	no	Hall
17	C₁₀₁	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
18	C₅×D₇	—	101	1	no	Hall
19	AGL(1,𝔽₇)	C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₇	—	101	1	no	Hall
21	C₂×C₃×C₅	—	707	1	no	Hall
22	ΓL(1,𝔽₈)	C₂×C₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	—	707	1	no	Hall
24	D₇	C₃×C₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅	—	707	1	no	Hall
26	C₇	C₂×C₃×C₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	7	1	no	Hall
28	C₅	—	101	1	no	Sylow
29	C₃	—	7	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₀₁	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₀₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)×C₁₀₁⋊C₅	C₂	semidirect
2. D₇×C₁₀₁⋊C₅	C₃	semidirect
3. AGL(1,𝔽₇)×C₁₀₁	C₅	semidirect
4. C₇×C₁₀₁⋊C₅	C₂×C₃	semidirect
6. ΓL(1,𝔽₈)×C₁₀₁	C₂×C₅	semidirect
8. D₇×C₁₀₁	C₃×C₅	semidirect
10. C₇×C₁₀₁	C₂×C₃×C₅	semidirect
12. C₁₀₁⋊C₅	AGL(1,𝔽₇)	direct (N × H)
17. C₁₀₁	C₅×AGL(1,𝔽₇)	semidirect
19. AGL(1,𝔽₇)	C₁₀₁⋊C₅	direct (N × H)
22. ΓL(1,𝔽₈)	C₂×C₁₀₁⋊C₅	semidirect
24. D₇	C₃×C₁₀₁⋊C₅	semidirect
26. C₇	C₂×C₃×C₁₀₁⋊C₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
ΓL(1,𝔽₈)×C₁₀₁⋊C₅	2
D₇×C₁₀₁⋊C₅	3
AGL(1,𝔽₇)×C₁₀₁	5
C₂×C₃×C₁₀₁⋊C₅	7
C₅×AGL(1,𝔽₇)	101

Subgroups — AGL(1,𝔽7)×C101⋊C5 #35234608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₇)×C₁₀₁⋊C₅ #35234608