Subgroups — C₆₇×C₃⋊AGL(1,𝔽₁₃) #44535709

Order 31356.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₆₇×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₆₇×C₃⋊#261	C₃	1	1	yes	maximal, characteristic, complemented
3	C₆₇×AGL(1,𝔽₁₃)	—	3	1	no	maximal
4	C₃×C₁₃⋊C₃×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₆₇×D₁₃⋊C₃	—	2	1	no	—
6	C₆₇×D₁₃⋊C₃	D₃	1	1	yes	characteristic
7	C₃×D₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
8	#261×C₆₇	—	3	1	no	Hall
9	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₃⋊C₃×C₆₇	—	2	1	no	—
11	C₁₃⋊C₃×C₆₇	Dic₃	1	1	yes	characteristic, complemented
12	C₃×Dic₃×C₆₇	—	13	1	no	maximal, Hall
13	D₁₃×C₆₇	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₆₇	—	13	1	no	—
15	C₁₃×C₆₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄×C₆₇	—	39	1	no	—
17	Dic₃×C₆₇	—	13	1	no	—
18	C₃²×C₆₇	—	13	1	no	Hall
19	C₃⋊AGL(1,𝔽₁₃)	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₃×C₆₇	—	13	1	no	—
21	C₂×C₃×C₆₇	—	13	1	no	—
22	C₂×C₃×C₆₇	—	26	1	no	—
23	C₄×C₆₇	—	39	1	no	Hall
24	C₃×D₁₃⋊C₃	C₂×C₆₇	1	1	yes	characteristic
25	C₃×C₆₇	—	13	1	no	—
26	C₃×C₆₇	—	26	1	no	—
27	C₃×C₆₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
28	C₃⋊#261	C₃×C₆₇	1	1	yes	characteristic, complemented
29	AGL(1,𝔽₁₃)	—	3	1	no	—
30	C₂×C₆₇	—	13	1	no	—
31	C₃×C₁₃⋊C₃	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
32	C₃×D₁₃	C₂×C₃×C₆₇	1	1	yes	characteristic
33	D₁₃⋊C₃	—	2	1	no	—
34	D₁₃⋊C₃	D₃×C₆₇	1	1	yes	characteristic
35	C₆₇	C₃⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
36	#261	—	3	1	no	Hall
37	C₃×C₁₃	C₃×C₄×C₆₇	1	1	yes	characteristic, complemented
38	C₁₃⋊C₃	—	2	1	no	—
39	C₁₃⋊C₃	Dic₃×C₆₇	1	1	yes	characteristic, complemented
40	C₃×Dic₃	—	13	1	no	Hall
41	D₁₃	C₃×D₃×C₆₇	1	1	yes	characteristic
42	C₂×C₃²	—	13	1	no	—
43	C₁₃	C₃×Dic₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	39	1	no	—
45	Dic₃	—	13	1	no	—
46	C₃²	—	13	1	no	Sylow
47	C₂×C₃	—	13	1	no	—
48	C₂×C₃	—	13	1	no	—
49	C₂×C₃	—	26	1	no	—
50	C₄	—	39	1	no	Sylow
51	C₃	—	13	1	no	—
52	C₃	—	26	1	no	—
53	C₃	C₆₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
54	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₆₇	C₃⋊AGL(1,𝔽₁₃)
commutator, hypocenter	C₃×C₁₃	C₃×C₄×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₆₇	C₃×C₄
prime radical	C₃×C₆₇×D₁₃⋊C₃	C₂
cosocle	C₃×D₁₃	C₂×C₃×C₆₇
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₆₇

Complements

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

N	H ≅ G/N	type
2. C₆₇×C₃⋊#261	C₃	semidirect
4. C₃×C₁₃⋊C₃×C₆₇	C₄	semidirect
9. C₃×C₁₃×C₆₇	C₃×C₄	semidirect
11. C₁₃⋊C₃×C₆₇	Dic₃	semidirect
15. C₁₃×C₆₇	C₃×Dic₃	semidirect
19. C₃⋊AGL(1,𝔽₁₃)	C₆₇	direct (N × H)
27. C₃×C₆₇	AGL(1,𝔽₁₃)	semidirect
28. C₃⋊#261	C₃×C₆₇	semidirect
31. C₃×C₁₃⋊C₃	C₄×C₆₇	semidirect
35. C₆₇	C₃⋊AGL(1,𝔽₁₃)	direct (N × H)
37. C₃×C₁₃	C₃×C₄×C₆₇	semidirect
39. C₁₃⋊C₃	Dic₃×C₆₇	semidirect
43. C₁₃	C₃×Dic₃×C₆₇	semidirect
53. C₃	C₆₇×AGL(1,𝔽₁₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₆₇×D₁₃⋊C₃	2
C₆₇×C₃⋊#261	3
C₆₇×AGL(1,𝔽₁₃)	3
C₃×Dic₃×C₆₇	13
C₃⋊AGL(1,𝔽₁₃)	67

Subgroups — C67×C3⋊AGL(1,𝔽13) #44535709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×C₃⋊AGL(1,𝔽₁₃) #44535709