Subgroups — C₃×#13094088⋊C₇ #44539779

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊(D₂₉⋊C₇)	C₂	1	1	yes	maximal, characteristic
2	#13094088⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₂₉⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊(D₂₉⋊C₇)	C₂×C₃	1	1	yes	characteristic
5	C₃×#13094088	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₃×C₂₉⋊C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×AGL(1,𝔽₂₉)	—	13	1	no	maximal, Hall
8	C₃×D₃₇₇	C₂×C₇	1	1	yes	characteristic
9	#13094088	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×D₂₉⋊C₇	—	13	1	no	—
11	C₃×C₁₃×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×#261	—	29	1	no	maximal, Hall
13	AGL(1,𝔽₂₉)	—	13	1	no	Hall
14	D₃₇₇	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₂₉⋊C₇	#261	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×D₁₃	—	29	1	no	—
17	D₂₉⋊C₇	—	13	1	no	—
18	C₁₃×C₂₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
19	C₇×#261	—	29	1	no	Hall
20	C₃×#1181	—	13	1	no	Hall
21	C₃×C₇×C₁₃	—	29	1	no	Hall
22	C₂₉⋊C₇	C₃×#261	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	—	29	1	no	—
24	C₃×D₂₉	—	13	1	no	—
25	C₃×#261	—	29	1	no	Hall
26	#1181	—	13	1	no	Hall
27	C₇×C₁₃	—	29	1	no	Hall
28	C₃×C₂₉	C₇×#261	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄×C₇	—	377	1	no	Hall
30	C₃×D₁₃	—	29	1	no	—
31	D₂₉	—	13	1	no	—
32	#261	—	29	1	no	Hall
33	C₂×C₃×C₇	—	377	1	no	—
34	C₃×C₁₃	AGL(1,𝔽₂₉)	1	1	yes	characteristic, complemented, Hall
35	C₂₉	C₃×C₇×#261	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	377	1	no	Hall
37	D₁₃	—	29	1	no	—
38	C₃×C₇	—	29	1	no	Hall
39	C₂×C₇	—	377	1	no	—
40	C₁₃	C₃×AGL(1,𝔽₂₉)	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	377	1	no	Hall
42	C₇	—	29	1	no	Sylow
43	C₂×C₃	—	377	1	no	—
44	C₄	—	377	1	no	Sylow
45	C₃	#13094088⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	377	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#13094088⋊C₇
commutator, hypocenter	C₁₃×C₂₉	C₃×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₂₉	C₄×C₇
prime radical	C₃×C₁₃⋊(D₂₉⋊C₇)	C₂
cosocle	D₃₇₇	C₂×C₃×C₇
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. #13094088⋊C₇	C₃	direct (N × H)
3. C₃×C₁₃×C₂₉⋊C₇	C₄	semidirect
5. C₃×#13094088	C₇	semidirect
6. C₁₃×C₂₉⋊C₇	C₃×C₄	semidirect
9. #13094088	C₃×C₇	semidirect
11. C₃×C₁₃×C₂₉	C₄×C₇	semidirect
15. C₃×C₂₉⋊C₇	#261	semidirect
18. C₁₃×C₂₉	C₃×C₄×C₇	semidirect
22. C₂₉⋊C₇	C₃×#261	semidirect
28. C₃×C₂₉	C₇×#261	semidirect
34. C₃×C₁₃	AGL(1,𝔽₂₉)	semidirect
35. C₂₉	C₃×C₇×#261	semidirect
40. C₁₃	C₃×AGL(1,𝔽₂₉)	semidirect
45. C₃	#13094088⋊C₇	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×C₁₃⋊(D₂₉⋊C₇)	2
#13094088⋊C₇	3
C₃×#13094088	7
C₃×AGL(1,𝔽₂₉)	13
C₃×C₇×#261	29

Subgroups — C3×#13094088⋊C7 #44539779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#13094088⋊C₇ #44539779