Subgroups — C₂×C₅₃×AGL(1,𝔽₁₉) #49136270

Order 36252.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×AGL(1,𝔽₁₉)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅₃×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₅₃×#4296	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅₃×D₁₉⋊C₃	C₂×C₃	1	2	yes	—
6	C₂×C₅₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₂×D₁₉×C₅₃	C₉	1	1	yes	characteristic, complemented, Hall
8	C₅₃×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₁₉×C₅₃	C₂×C₉	1	1	yes	characteristic, complemented
10	D₁₉×C₅₃	C₂×C₉	1	2	yes	complemented
11	C₂²×C₉×C₅₃	—	19	1	no	maximal, Hall
12	C₁₉×C₅₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₅₃	—	19	2	no	—
14	C₂×C₉×C₅₃	—	19	1	no	—
15	C₂×AGL(1,𝔽₁₉)	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₃×C₅₃	—	19	1	no	—
17	C₉×C₅₃	—	19	1	no	Hall
18	C₂×#4296	C₂×C₅₃	1	1	yes	characteristic, complemented
19	AGL(1,𝔽₁₉)	C₂×C₅₃	1	2	yes	direct product factor
20	C₂×C₃×C₅₃	—	19	2	no	—
21	C₂×C₃×C₅₃	—	19	1	no	—
22	C₂×D₁₉⋊C₃	C₃×C₅₃	1	1	yes	characteristic
23	C₂²×C₅₃	—	19	1	no	Hall
24	#4296	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅₃	—	19	1	no	—
26	C₂×C₁₉⋊C₃	C₂×C₃×C₅₃	1	1	yes	characteristic
27	D₁₉⋊C₃	C₂×C₃×C₅₃	1	2	yes	—
28	C₂×C₅₃	—	19	2	no	—
29	C₂×C₅₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor
30	C₂×D₁₉	C₉×C₅₃	1	1	yes	characteristic, complemented, Hall
31	C₁₉⋊C₃	C₂²×C₃×C₅₃	1	1	yes	characteristic
32	C₅₃	C₂×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₁₉	C₂×C₉×C₅₃	1	1	yes	characteristic, complemented
34	D₁₉	C₂×C₉×C₅₃	1	2	yes	complemented
35	C₂²×C₉	—	19	1	no	Hall
36	C₁₉	C₂²×C₉×C₅₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	—	19	2	no	—
38	C₂×C₉	—	19	1	no	—
39	C₂²×C₃	—	19	1	no	—
40	C₉	—	19	1	no	Sylow
41	C₂×C₃	—	19	2	no	—
42	C₂×C₃	—	19	1	no	—
43	C₂²	—	19	1	no	Sylow
44	C₃	—	19	1	no	—
45	C₂	—	19	2	no	—
46	C₂	C₅₃×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅₃	AGL(1,𝔽₁₉)
commutator, hypocenter	C₁₉	C₂²×C₉×C₅₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₅₃	C₂×C₉
prime radical	C₂×C₅₃×D₁₉⋊C₃	C₃
cosocle	C₁₉⋊C₃	C₂²×C₃×C₅₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#4296	C₂	semidirect
2. C₅₃×AGL(1,𝔽₁₉)	C₂	direct (N × H)
4. C₅₃×#4296	C₂²	semidirect
7. C₂×D₁₉×C₅₃	C₉	semidirect
9. C₂×C₁₉×C₅₃	C₂×C₉	semidirect
10. D₁₉×C₅₃	C₂×C₉	semidirect
12. C₁₉×C₅₃	C₂²×C₉	semidirect
15. C₂×AGL(1,𝔽₁₉)	C₅₃	direct (N × H)
18. C₂×#4296	C₂×C₅₃	semidirect
19. AGL(1,𝔽₁₉)	C₂×C₅₃	direct (N × H)
24. #4296	C₂²×C₅₃	semidirect
29. C₂×C₅₃	AGL(1,𝔽₁₉)	direct (N × H)
30. C₂×D₁₉	C₉×C₅₃	semidirect
32. C₅₃	C₂×AGL(1,𝔽₁₉)	direct (N × H)
33. C₂×C₁₉	C₂×C₉×C₅₃	semidirect
34. D₁₉	C₂×C₉×C₅₃	semidirect
36. C₁₉	C₂²×C₉×C₅₃	semidirect
46. C₂	C₅₃×AGL(1,𝔽₁₉)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#4296	2
C₅₃×AGL(1,𝔽₁₉)	2
C₂×C₅₃×D₁₉⋊C₃	3
C₂²×C₉×C₅₃	19
C₂×AGL(1,𝔽₁₉)	53

Subgroups — C2×C53×AGL(1,𝔽19) #49136270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×AGL(1,𝔽₁₉) #49136270