Subgroups — C₅×#20263627 #44540270

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15691748	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇×C₁₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20263627	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₅₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₁₅₁⋊C₃	—	7	1	no	maximal, Hall
6	#15691748	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₅₁⋊C₃	—	7	1	no	Hall
8	D₇×C₁₅₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₁₅₁	—	7	1	no	Hall
10	C₇×C₁₅₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₅₁⋊C₃	—	7	1	no	Hall
12	C₅×C₁₅₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
13	C₁₅₁⋊C₃	—	7	1	no	Hall
14	C₂×C₁₅₁	—	7	1	no	Hall
15	C₅×AGL(1,𝔽₇)	—	151	1	no	maximal, Hall
16	C₁₅₁	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
17	C₅×ΓL(1,𝔽₈)	—	151	1	no	Hall
18	C₅×D₇	C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Hall
19	AGL(1,𝔽₇)	—	151	1	no	Hall
20	C₅×C₇	C₂×C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅	—	1057	1	no	Hall
22	ΓL(1,𝔽₈)	—	151	1	no	Hall
23	C₃×C₅	—	1057	1	no	Hall
24	D₇	C₅×C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅	—	7	1	no	Hall
26	C₇	C₂×C₅×C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	1057	1	no	Hall
28	C₅	#20263627	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	1057	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#20263627
commutator, cosocle, hypocenter	C₇×C₁₅₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₅₁	C₂×C₃
LCS	G ▷ C₇×C₁₅₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#15691748	C₂	semidirect
2. C₅×D₇×C₁₅₁	C₃	semidirect
3. #20263627	C₅	direct (N × H)
4. C₅×C₇×C₁₅₁	C₂×C₃	semidirect
6. #15691748	C₂×C₅	semidirect
8. D₇×C₁₅₁	C₃×C₅	semidirect
10. C₇×C₁₅₁	C₂×C₃×C₅	semidirect
12. C₅×C₁₅₁	AGL(1,𝔽₇)	semidirect
16. C₁₅₁	C₅×AGL(1,𝔽₇)	semidirect
18. C₅×D₇	C₁₅₁⋊C₃	semidirect
20. C₅×C₇	C₂×C₁₅₁⋊C₃	semidirect
24. D₇	C₅×C₁₅₁⋊C₃	semidirect
26. C₇	C₂×C₅×C₁₅₁⋊C₃	semidirect
28. C₅	#20263627	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#15691748	2
C₅×D₇×C₁₅₁	3
#20263627	5
C₂×C₅×C₁₅₁⋊C₃	7
C₅×AGL(1,𝔽₇)	151

Subgroups — C5×#20263627 #44540270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20263627 #44540270