Subgroups — C₁₃×C₃⋊Dic₂₀₁ #44535680

Order 31356.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₂₀₁	—	3	4	no	maximal
3	C₃²×C₁₃×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₆₇	D₃	1	4	yes	—
5	C₁₃×Dic₆₇	—	9	1	no	Hall
6	C₃×C₁₃×C₆₇	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₂₀₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₆₇	C₃⋊D₃	1	1	yes	characteristic
9	C₂×C₃²×C₆₇	C₂×C₁₃	1	1	yes	characteristic
10	C₁₃×C₆₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	Dic₂₀₁	—	3	4	no	—
12	C₃²×C₆₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×C₃⋊Dic₃	—	67	1	no	maximal, Hall
14	C₂×C₃×C₆₇	D₃×C₁₃	1	4	yes	—
15	Dic₆₇	—	9	1	no	Hall
16	C₂×C₃²×C₁₃	D₆₇	1	1	yes	characteristic
17	C₃×C₆₇	Dic₃×C₁₃	1	4	yes	complemented
18	Dic₃×C₁₃	—	201	4	no	—
19	C₂×C₆₇	C₁₃×C₃⋊D₃	1	1	yes	characteristic
20	C₃²×C₁₃	Dic₆₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃	D₂₀₁	1	4	yes	—
22	C₆₇	C₁₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₁₃	—	603	1	no	Hall
24	C₃×C₁₃	Dic₂₀₁	1	4	yes	complemented
25	C₃⋊Dic₃	—	67	1	no	Hall
26	C₂×C₁₃	C₃⋊D₂₀₁	1	1	yes	characteristic
27	C₂×C₃²	C₁₃×D₆₇	1	1	yes	characteristic
28	C₁₃	C₃⋊Dic₂₀₁	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	201	4	no	—
30	C₃²	C₁₃×Dic₆₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₁₃×D₂₀₁	1	4	yes	—
32	C₄	—	603	1	no	Sylow
33	C₃	C₁₃×Dic₂₀₁	1	4	yes	complemented
34	C₂	C₁₃×C₃⋊D₂₀₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₂₀₁
commutator, hypocenter	C₃²×C₆₇	C₄×C₁₃
Frattini	C₂	C₁₃×C₃⋊D₂₀₁
Fitting, socle, prime radical	C₂×C₃²×C₁₃×C₆₇	C₂
cosocle	C₂×C₃²×C₆₇	C₂×C₁₃
LCS	G ▷ C₃²×C₆₇
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃²×C₁₃×C₆₇	C₄	semidirect
6. C₃×C₁₃×C₆₇	Dic₃	semidirect
7. C₃⋊Dic₂₀₁	C₁₃	direct (N × H)
10. C₁₃×C₆₇	C₃⋊Dic₃	semidirect
12. C₃²×C₆₇	C₄×C₁₃	semidirect
17. C₃×C₆₇	Dic₃×C₁₃	semidirect
20. C₃²×C₁₃	Dic₆₇	semidirect
22. C₆₇	C₁₃×C₃⋊Dic₃	semidirect
24. C₃×C₁₃	Dic₂₀₁	semidirect
28. C₁₃	C₃⋊Dic₂₀₁	direct (N × H)
30. C₃²	C₁₃×Dic₆₇	semidirect
33. C₃	C₁₃×Dic₂₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₃×C₆₇	2
C₁₃×Dic₂₀₁	3
C₃⋊Dic₂₀₁	13
C₁₃×C₃⋊Dic₃	67

Subgroups — C13×C3⋊Dic201 #44535680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊Dic₂₀₁ #44535680