Subgroups — C₃×D₅₁₅₁ #44525593

Order 30906.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₁₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₇₁₇	—	3	1	no	maximal
4	C₃×C₁₇×C₁₀₁	—	2	1	no	—
5	C₃×C₁₇×C₁₀₁	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₇×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₇₁₇	—	3	1	no	Hall
8	C₃×D₃₀₃	—	17	1	no	maximal, Hall
9	C₁₇×C₁₀₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₀₁	D₁₇	1	1	yes	characteristic, complemented, Hall
11	D₃₀₃	—	17	1	no	—
12	C₃×D₁₀₁	—	51	1	no	—
13	C₃×D₅₁	—	101	1	no	maximal, Hall
14	C₃×C₁₀₁	—	2	1	no	—
15	C₃×C₁₀₁	C₃×D₁₇	1	1	yes	characteristic, complemented
16	C₃×C₁₀₁	D₅₁	1	1	yes	characteristic, complemented
17	D₁₀₁	—	51	1	no	Hall
18	C₃²×C₁₇	D₁₀₁	1	1	yes	characteristic, complemented, Hall
19	D₅₁	—	101	1	no	—
20	C₃×D₁₇	—	303	1	no	—
21	C₁₀₁	C₃×D₅₁	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₇	—	2	1	no	—
23	C₃×C₁₇	C₃×D₁₀₁	1	1	yes	characteristic, complemented
24	C₃×C₁₇	D₃₀₃	1	1	yes	characteristic, complemented
25	D₁₇	—	303	1	no	Hall
26	C₃×D₃	—	1717	1	no	Hall
27	C₁₇	C₃×D₃₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₃²	D₁₇₁₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	5151	1	no	—
30	D₃	—	1717	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₇₁₇	1	1	yes	characteristic, complemented
33	C₃	D₅₁₅₁	1	1	yes	characteristic, direct product factor
34	C₂	—	5151	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₁₅₁
commutator, cosocle, hypocenter	C₃×C₁₇×C₁₀₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₁₀₁	C₂
LCS	G ▷ C₃×C₁₇×C₁₀₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×C₁₀₁	C₂	semidirect
2. D₅₁₅₁	C₃	direct (N × H)
5. C₃×C₁₇×C₁₀₁	D₃	semidirect
6. C₃×C₁₇×C₁₀₁	C₂×C₃	semidirect
9. C₁₇×C₁₀₁	C₃×D₃	semidirect
10. C₃²×C₁₀₁	D₁₇	semidirect
15. C₃×C₁₀₁	C₃×D₁₇	semidirect
16. C₃×C₁₀₁	D₅₁	semidirect
18. C₃²×C₁₇	D₁₀₁	semidirect
21. C₁₀₁	C₃×D₅₁	semidirect
23. C₃×C₁₇	C₃×D₁₀₁	semidirect
24. C₃×C₁₇	D₃₀₃	semidirect
27. C₁₇	C₃×D₃₀₃	semidirect
28. C₃²	D₁₇₁₇	semidirect
32. C₃	C₃×D₁₇₁₇	semidirect
33. C₃	D₅₁₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×C₁₀₁	2
D₅₁₅₁	3
C₃×D₁₇₁₇	3
C₃×D₃₀₃	17
C₃×D₅₁	101

Subgroups — C3×D5151 #44525593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₁₅₁ #44525593