Subgroups — C₂₉×(C₁₉⋊C₃)⋊AGL(1,𝔽₅) #45683265

Order 33060.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₂₉×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₁₉⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₂₉×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂₉×(C₁₉⋊C₃)⋊C₄	—	5	1	no	maximal, Hall
5	D₅×C₁₉×C₂₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂₉×C₁₉⋊C₃	—	5	1	no	—
7	C₅×C₁₉×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂₉×Dic₁₉	—	5	1	no	Hall
9	C₃×AGL(1,𝔽₅)×C₂₉	—	19	1	no	maximal, Hall
10	C₂₉×C₁₉⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₁₉×C₂₉	—	5	1	no	—
13	C₃×D₅×C₂₉	—	19	1	no	—
14	AGL(1,𝔽₅)×C₂₉	—	19	1	no	Hall
15	D₅×C₁₉⋊C₃	C₂×C₂₉	1	1	yes	characteristic
16	C₁₉×C₂₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₂₉	—	19	1	no	Hall
18	C₁₉⋊AGL(1,𝔽₅)	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄×C₂₉	—	95	1	no	Hall
20	D₅×C₂₉	D₁₉⋊C₃	1	1	yes	characteristic
21	C₅×C₁₉⋊C₃	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
22	(C₁₉⋊C₃)⋊C₄	—	5	1	no	Hall
23	D₅×C₁₉	C₂×C₃×C₂₉	1	1	yes	characteristic
24	C₂×C₃×C₂₉	—	95	1	no	—
25	C₅×C₂₉	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
26	C₄×C₂₉	—	95	1	no	Hall
27	C₂×C₁₉⋊C₃	—	5	1	no	—
28	C₅×C₁₉	C₃×C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₂₉	—	19	1	no	Hall
30	Dic₁₉	—	5	1	no	Hall
31	C₃×AGL(1,𝔽₅)	—	19	1	no	Hall
32	C₂×C₂₉	—	5	1	no	—
33	C₁₉⋊C₃	AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₉	—	5	1	no	—
35	C₃×D₅	—	19	1	no	—
36	C₂₉	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
37	AGL(1,𝔽₅)	—	19	1	no	Hall
38	C₁₉	C₃×AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	19	1	no	Hall
40	C₃×C₄	—	95	1	no	Hall
41	D₅	C₂₉×D₁₉⋊C₃	1	1	yes	characteristic
42	C₂×C₃	—	95	1	no	—
43	C₅	C₂₉×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	95	1	no	Sylow
45	C₃	—	19	1	no	Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₉	C₃×C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₂₉	C₃×C₄
prime radical	D₅×C₂₉×C₁₉⋊C₃	C₂
cosocle	D₅×C₁₉	C₂×C₃×C₂₉
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
2. C₂₉×C₁₉⋊AGL(1,𝔽₅)	C₃	semidirect
3. C₅×C₂₉×C₁₉⋊C₃	C₄	semidirect
7. C₅×C₁₉×C₂₉	C₃×C₄	semidirect
10. C₂₉×C₁₉⋊C₃	AGL(1,𝔽₅)	semidirect
11. (C₁₉⋊C₃)⋊AGL(1,𝔽₅)	C₂₉	direct (N × H)
16. C₁₉×C₂₉	C₃×AGL(1,𝔽₅)	semidirect
18. C₁₉⋊AGL(1,𝔽₅)	C₃×C₂₉	semidirect
21. C₅×C₁₉⋊C₃	C₄×C₂₉	semidirect
25. C₅×C₂₉	(C₁₉⋊C₃)⋊C₄	semidirect
28. C₅×C₁₉	C₃×C₄×C₂₉	semidirect
33. C₁₉⋊C₃	AGL(1,𝔽₅)×C₂₉	semidirect
36. C₂₉	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	direct (N × H)
38. C₁₉	C₃×AGL(1,𝔽₅)×C₂₉	semidirect
43. C₅	C₂₉×(C₁₉⋊C₃)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₂₉×C₁₉⋊C₃	2
C₂₉×C₁₉⋊AGL(1,𝔽₅)	3
C₂₉×(C₁₉⋊C₃)⋊C₄	5
C₃×AGL(1,𝔽₅)×C₂₉	19
(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	29

Subgroups — C29×(C19⋊C3)⋊AGL(1,𝔽5) #45683265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×(C₁₉⋊C₃)⋊AGL(1,𝔽₅) #45683265