Subgroups — C₂₉×C₃⋊#1042 #22576476

Order 8700.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1042	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂₉×ΓL(1,𝔽₁₆)	—	5	1	no	maximal
5	C₂₉×Dic₁₅	—	5	1	no	maximal
6	C₅×D₅×C₂₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅×C₂₉	—	5	1	no	—
8	C₃×D₅×C₂₉	D₅	1	1	yes	characteristic
9	C₅²×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
10	AGL(1,𝔽₅)×C₂₉	—	15	1	no	—
11	Dic₅×C₂₉	—	15	1	no	—
12	C₃×C₅×C₂₉	—	4	1	no	—
13	C₃×C₅×C₂₉	Dic₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	Dic₃×C₂₉	—	25	1	no	Hall
16	C₃⋊#1042	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×C₂₉	—	5	1	no	—
18	D₅×C₂₉	D₁₅	1	1	yes	characteristic
19	C₂×C₃×C₂₉	—	5	1	no	—
20	C₃×C₅×D₅	C₂×C₂₉	1	1	yes	characteristic
21	C₅×C₂₉	—	4	1	no	—
22	C₅×C₂₉	Dic₁₅	1	1	yes	characteristic, complemented
23	C₅×C₂₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
24	C₄×C₂₉	—	75	1	no	Hall
25	#1042	—	3	1	no	Hall
26	C₃×C₂₉	#1042	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅²	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
28	ΓL(1,𝔽₁₆)	—	5	1	no	—
29	Dic₁₅	—	5	1	no	—
30	C₂×C₂₉	—	5	1	no	—
31	C₅×D₅	D₃×C₂₉	1	1	yes	characteristic
32	C₂×C₃×C₅	—	5	1	no	—
33	C₃×D₅	D₅×C₂₉	1	1	yes	characteristic
34	C₂₉	C₃⋊#1042	1	1	yes	characteristic, direct product factor, Sylow
35	C₅²	Dic₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	15	1	no	—
37	Dic₅	—	15	1	no	—
38	C₃×C₅	—	4	1	no	—
39	C₃×C₅	Dic₅×C₂₉	1	1	yes	characteristic, complemented
40	C₃×C₅	AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented
41	Dic₃	—	25	1	no	Hall
42	C₂×C₅	—	5	1	no	—
43	D₅	C₂₉×D₁₅	1	1	yes	characteristic
44	C₂×C₃	—	5	1	no	—
45	C₅	—	4	1	no	—
46	C₅	C₂₉×Dic₁₅	1	1	yes	characteristic, complemented
47	C₅	C₂₉×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
48	C₄	—	75	1	no	Sylow
49	C₃	C₂₉×#1042	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	C₃⋊#1042
commutator, hypocenter	C₃×C₅²	C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₄
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₂₉	C₄	semidirect
9. C₅²×C₂₉	Dic₃	semidirect
13. C₃×C₅×C₂₉	Dic₅	semidirect
14. C₃×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
16. C₃⋊#1042	C₂₉	direct (N × H)
22. C₅×C₂₉	Dic₁₅	semidirect
23. C₅×C₂₉	ΓL(1,𝔽₁₆)	semidirect
26. C₃×C₂₉	#1042	semidirect
27. C₃×C₅²	C₄×C₂₉	semidirect
34. C₂₉	C₃⋊#1042	direct (N × H)
35. C₅²	Dic₃×C₂₉	semidirect
39. C₃×C₅	Dic₅×C₂₉	semidirect
40. C₃×C₅	AGL(1,𝔽₅)×C₂₉	semidirect
46. C₅	C₂₉×Dic₁₅	semidirect
47. C₅	C₂₉×ΓL(1,𝔽₁₆)	semidirect
49. C₃	C₂₉×#1042	semidirect

Subgroups — C29×C3⋊#1042 #22576476

Conjugacy classes of subgroups

Complements

Subgroups — C₂₉×C₃⋊#1042 #22576476