Subgroups — C₃⋊(#13094088⋊C₇) #44539787

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	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₂₉⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊(D₂₉⋊C₇)	D₃	1	1	yes	characteristic
5	C₃⋊#13094088	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₃×C₂₉⋊C₇	Dic₃	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	—	3	1	no	Hall
10	C₃×D₂₉⋊C₇	—	13	1	no	—
11	C₃×C₁₃×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₃⋊#261	—	29	1	no	maximal, Hall
13	AGL(1,𝔽₂₉)	—	39	1	no	Hall
14	D₃₇₇	D₃×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	C₇×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₇×#261	—	87	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	—	39	1	no	Hall
27	C₇×C₁₃	—	29	1	no	Hall
28	C₃×C₂₉	C₇×#261	1	1	yes	characteristic, complemented, Hall
29	C₇×Dic₃	—	377	1	no	Hall
30	C₃×D₁₃	—	29	1	no	—
31	D₂₉	—	13	1	no	—
32	#261	—	87	1	no	Hall
33	C₂×C₃×C₇	—	377	1	no	—
34	C₃×C₁₃	AGL(1,𝔽₂₉)	1	1	yes	characteristic, complemented, Hall
35	C₂₉	C₇×C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	1131	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	Dic₃	—	377	1	no	Hall
42	C₇	—	29	1	no	Sylow
43	C₂×C₃	—	377	1	no	—
44	C₄	—	1131	1	no	Sylow
45	C₃	#13094088⋊C₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	377	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₃×C₂₉⋊C₇	C₄	semidirect
5. C₃⋊#13094088	C₇	semidirect
6. C₁₃×C₂₉⋊C₇	Dic₃	semidirect
11. C₃×C₁₃×C₂₉	C₄×C₇	semidirect
15. C₃×C₂₉⋊C₇	#261	semidirect
18. C₁₃×C₂₉	C₇×Dic₃	semidirect
22. C₂₉⋊C₇	C₃⋊#261	semidirect
28. C₃×C₂₉	C₇×#261	semidirect
34. C₃×C₁₃	AGL(1,𝔽₂₉)	semidirect
35. C₂₉	C₇×C₃⋊#261	semidirect
40. C₁₃	C₃⋊AGL(1,𝔽₂₉)	semidirect
45. C₃	#13094088⋊C₇	semidirect

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
C₇×C₃⋊#261	29

Subgroups — C3⋊(#13094088⋊C7) #44539787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#13094088⋊C₇) #44539787