Subgroups — C₅×C₃⋊Dic₅₀₁ #44473602

Order 30060.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₆₇	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅₀₁	—	3	4	no	maximal
3	C₃²×C₅×C₁₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₅₀₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₆₇	D₃	1	4	yes	—
6	C₅×Dic₁₆₇	—	9	1	no	Hall
7	C₂×C₃²×C₁₆₇	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₁₆₇	Dic₃	1	4	yes	complemented
9	Dic₅₀₁	—	3	4	no	—
10	C₂×C₅×C₁₆₇	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₁₆₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₆₇	C₅×D₃	1	4	yes	—
13	C₅×C₁₆₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	Dic₁₆₇	—	9	1	no	Hall
15	C₃×C₁₆₇	C₅×Dic₃	1	4	yes	complemented
16	C₂×C₁₆₇	C₅×C₃⋊D₃	1	1	yes	characteristic
17	C₅×C₃⋊Dic₃	—	167	1	no	maximal, Hall
18	C₁₆₇	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₅	D₁₆₇	1	1	yes	characteristic
20	C₅×Dic₃	—	501	4	no	—
21	C₃²×C₅	Dic₁₆₇	1	1	yes	characteristic, complemented, Hall
22	C₃⋊Dic₃	—	167	1	no	Hall
23	C₂×C₃×C₅	D₅₀₁	1	4	yes	—
24	C₄×C₅	—	1503	1	no	Hall
25	C₂×C₃²	C₅×D₁₆₇	1	1	yes	characteristic
26	C₃×C₅	Dic₅₀₁	1	4	yes	complemented
27	Dic₃	—	501	4	no	—
28	C₂×C₅	C₃⋊D₅₀₁	1	1	yes	characteristic
29	C₃²	C₅×Dic₁₆₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	C₅×D₅₀₁	1	4	yes	—
31	C₅	C₃⋊Dic₅₀₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	—	1503	1	no	Sylow
33	C₃	C₅×Dic₅₀₁	1	4	yes	complemented
34	C₂	C₅×C₃⋊D₅₀₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₅₀₁
commutator, hypocenter	C₃²×C₁₆₇	C₄×C₅
Frattini	C₂	C₅×C₃⋊D₅₀₁
Fitting, socle, prime radical	C₂×C₃²×C₅×C₁₆₇	C₂
cosocle	C₂×C₃²×C₁₆₇	C₂×C₅
LCS	G ▷ C₃²×C₁₆₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅×C₁₆₇	C₄	semidirect
4. C₃⋊Dic₅₀₁	C₅	direct (N × H)
8. C₃×C₅×C₁₆₇	Dic₃	semidirect
11. C₃²×C₁₆₇	C₄×C₅	semidirect
13. C₅×C₁₆₇	C₃⋊Dic₃	semidirect
15. C₃×C₁₆₇	C₅×Dic₃	semidirect
18. C₁₆₇	C₅×C₃⋊Dic₃	semidirect
21. C₃²×C₅	Dic₁₆₇	semidirect
26. C₃×C₅	Dic₅₀₁	semidirect
29. C₃²	C₅×Dic₁₆₇	semidirect
31. C₅	C₃⋊Dic₅₀₁	direct (N × H)
33. C₃	C₅×Dic₅₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅×C₁₆₇	2
C₅×Dic₅₀₁	3
C₃⋊Dic₅₀₁	5
C₅×C₃⋊Dic₃	167

Subgroups — C5×C3⋊Dic501 #44473602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊Dic₅₀₁ #44473602