Subgroups — C₃×C₇⋊(D₁₅₁⋊C₅) #44540259

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊(D₁₅₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₀₅₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₅₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₁₅₁⋊C₅	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₅₁⋊C₅	D₇	1	1	yes	characteristic, complemented, Hall
8	D₁₀₅₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	D₁₅₁⋊C₅	—	7	1	no	Hall
10	C₇×C₁₅₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₅₁	—	7	1	no	Hall
12	C₁₅₁⋊C₅	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
14	D₁₅₁	—	7	1	no	Hall
15	C₃×C₅×D₇	—	151	1	no	maximal, Hall
16	C₁₅₁	C₃×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	—	151	1	no	Hall
18	C₅×D₇	—	151	1	no	Hall
19	C₃×D₇	—	151	1	no	Hall
20	C₅×C₇	—	151	1	no	Hall
21	C₂×C₃×C₅	—	1057	1	no	Hall
22	C₃×C₇	D₁₅₁⋊C₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	—	151	1	no	Hall
24	D₇	—	151	1	no	Hall
25	C₂×C₅	—	1057	1	no	Hall
26	C₇	C₃×D₁₅₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	1057	1	no	Hall
28	C₅	—	151	1	no	Sylow
29	C₃	C₇⋊(D₁₅₁⋊C₅)	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	1057	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₇⋊(D₁₅₁⋊C₅)
commutator, cosocle, hypocenter	C₇×C₁₅₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₅₁	C₂×C₅
LCS	G ▷ C₇×C₁₅₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₅₁⋊C₅	C₂	semidirect
2. C₇⋊(D₁₅₁⋊C₅)	C₃	direct (N × H)
3. C₃×D₁₀₅₇	C₅	semidirect
4. C₇×C₁₅₁⋊C₅	C₂×C₃	semidirect
6. C₃×C₇×C₁₅₁	C₂×C₅	semidirect
7. C₃×C₁₅₁⋊C₅	D₇	semidirect
8. D₁₀₅₇	C₃×C₅	semidirect
10. C₇×C₁₅₁	C₂×C₃×C₅	semidirect
12. C₁₅₁⋊C₅	C₃×D₇	semidirect
13. C₃×C₁₅₁	C₅×D₇	semidirect
16. C₁₅₁	C₃×C₅×D₇	semidirect
22. C₃×C₇	D₁₅₁⋊C₅	semidirect
26. C₇	C₃×D₁₅₁⋊C₅	semidirect
29. C₃	C₇⋊(D₁₅₁⋊C₅)	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×C₇×C₁₅₁⋊C₅	2
C₇⋊(D₁₅₁⋊C₅)	3
C₃×D₁₀₅₇	5
C₃×D₁₅₁⋊C₅	7
C₃×C₅×D₇	151

Subgroups — C3×C7⋊(D151⋊C5) #44540259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇⋊(D₁₅₁⋊C₅) #44540259