Subgroups — C₂₉×#11763979 #44539870

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₇⋊#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₂₉×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₂₉×AGL(1,𝔽₁₃)	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×Dic₇×C₂₉	—	13	1	no	maximal, Hall
8	C₂₉×D₁₃⋊C₃	D₇	1	1	yes	characteristic
9	C₂₉×#261	—	7	1	no	Hall
10	C₂×C₃×C₇×C₂₉	—	13	1	no	—
11	C₂₉×C₁₃⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
12	#11763979	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	Dic₇×C₂₉	—	13	1	no	Hall
14	D₁₃×C₂₉	C₃×D₇	1	1	yes	characteristic
15	C₃×C₇×C₂₉	—	13	1	no	Hall
16	C₇×D₁₃⋊C₃	C₂×C₂₉	1	1	yes	characteristic
17	C₂×C₇×C₂₉	—	13	1	no	—
18	C₁₃×C₂₉	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
19	C₇⋊#261	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₄×C₂₉	—	91	1	no	Hall
21	C₇×C₁₃⋊C₃	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
22	C₇×C₂₉	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	C₂×C₃×C₂₉	1	1	yes	characteristic
24	C₂×C₃×C₂₉	—	13	1	no	—
25	AGL(1,𝔽₁₃)	—	7	1	no	Hall
26	C₄×C₂₉	—	91	1	no	Hall
27	C₇×C₁₃	C₃×C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₂₉	—	13	1	no	Hall
29	C₃×Dic₇	—	13	1	no	Hall
30	D₁₃⋊C₃	D₇×C₂₉	1	1	yes	characteristic
31	C₂×C₂₉	—	13	1	no	—
32	#261	—	7	1	no	Hall
33	C₂×C₃×C₇	—	13	1	no	—
34	C₁₃⋊C₃	Dic₇×C₂₉	1	1	yes	characteristic, complemented, Hall
35	C₂₉	#11763979	1	1	yes	characteristic, direct product factor, Sylow
36	Dic₇	—	13	1	no	Hall
37	D₁₃	C₃×D₇×C₂₉	1	1	yes	characteristic
38	C₃×C₇	—	13	1	no	Hall
39	C₂×C₇	—	13	1	no	—
40	C₁₃	C₃×Dic₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	91	1	no	Hall
42	C₇	C₂₉×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	13	1	no	—
44	C₄	—	91	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	#11763979
commutator, hypocenter	C₇×C₁₃	C₃×C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₉	C₃×C₄
prime radical	C₇×C₂₉×D₁₃⋊C₃	C₂
cosocle	C₇×D₁₃	C₂×C₃×C₂₉
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
2. C₂₉×C₇⋊#261	C₃	semidirect
3. C₇×C₂₉×C₁₃⋊C₃	C₄	semidirect
6. C₇×C₁₃×C₂₉	C₃×C₄	semidirect
11. C₂₉×C₁₃⋊C₃	Dic₇	semidirect
12. #11763979	C₂₉	direct (N × H)
18. C₁₃×C₂₉	C₃×Dic₇	semidirect
19. C₇⋊#261	C₃×C₂₉	semidirect
21. C₇×C₁₃⋊C₃	C₄×C₂₉	semidirect
22. C₇×C₂₉	AGL(1,𝔽₁₃)	semidirect
27. C₇×C₁₃	C₃×C₄×C₂₉	semidirect
34. C₁₃⋊C₃	Dic₇×C₂₉	semidirect
35. C₂₉	#11763979	direct (N × H)
40. C₁₃	C₃×Dic₇×C₂₉	semidirect
42. C₇	C₂₉×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
C₇×C₂₉×D₁₃⋊C₃	2
C₂₉×C₇⋊#261	3
C₂₉×AGL(1,𝔽₁₃)	7
C₃×Dic₇×C₂₉	13
#11763979	29

Subgroups — C29×#11763979 #44539870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#11763979 #44539870