Subgroups — C₁₉×#13133347 #44568115

Order 32300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₅⋊D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₇×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×#66776	—	5	1	no	maximal
4	C₁₉×#66775	—	5	1	no	maximal
5	C₁₉×D₈₅	—	5	1	no	—
6	C₁₉×D₈₅	—	5	1	no	—
7	C₁₉×D₈₅	—	10	2	no	—
8	C₁₉×#1044	—	17	1	no	maximal, Hall
9	#13133347	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₇×C₁₉	—	2	2	no	—
11	C₅×C₁₇×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	C₅×C₁₇×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
13	C₁₉×#595	—	25	1	no	Hall
14	C₁₉×C₅⋊D₅	—	17	1	no	—
15	C₅⋊D₈₅	C₂×C₁₉	1	1	yes	characteristic
16	C₁₉×D₁₇	—	25	1	no	—
17	C₅²×C₁₉	#595	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₁₇	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₁₉×AGL(1,𝔽₅)	—	85	1	no	—
20	C₁₉×AGL(1,𝔽₅)	—	85	1	no	—
21	#66776	—	5	1	no	—
22	#66775	—	5	1	no	—
23	C₁₇×C₁₉	#1044	1	1	yes	characteristic, complemented, Hall
24	D₅×C₁₉	—	85	1	no	—
25	D₅×C₁₉	—	85	1	no	—
26	D₅×C₁₉	—	170	2	no	—
27	D₈₅	—	5	1	no	—
28	D₈₅	—	5	1	no	—
29	D₈₅	—	10	2	no	—
30	#1044	—	17	1	no	Hall
31	C₅×C₁₉	—	2	2	no	—
32	C₅×C₁₉	#66775	1	1	yes	characteristic, complemented
33	C₅×C₁₉	#66776	1	1	yes	characteristic, complemented
34	C₅×C₁₇	—	2	2	no	—
35	C₅×C₁₇	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
36	C₅×C₁₇	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
37	C₄×C₁₉	—	425	1	no	Hall
38	#595	—	25	1	no	Hall
39	C₅⋊D₅	—	17	1	no	—
40	C₂×C₁₉	—	425	1	no	—
41	D₁₇	—	25	1	no	—
42	C₅²	C₁₉×#595	1	1	yes	characteristic, complemented, Sylow
43	AGL(1,𝔽₅)	—	85	1	no	—
44	AGL(1,𝔽₅)	—	85	1	no	—
45	C₁₉	#13133347	1	1	yes	characteristic, direct product factor, Sylow
46	C₁₇	C₁₉×#1044	1	1	yes	characteristic, complemented, Sylow
47	D₅	—	85	1	no	—
48	D₅	—	85	1	no	—
49	D₅	—	170	2	no	—
50	C₅	—	2	2	no	—
51	C₅	C₁₉×#66775	1	1	yes	characteristic, complemented
52	C₅	C₁₉×#66776	1	1	yes	characteristic, complemented
53	C₄	—	425	1	no	Sylow
54	C₂	—	425	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#13133347
commutator, hypocenter	C₅²×C₁₇	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇×C₁₉	C₄
prime radical	C₁₉×C₅⋊D₈₅	C₂
cosocle	C₅⋊D₈₅	C₂×C₁₉
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₇×C₁₉	C₄	semidirect
9. #13133347	C₁₉	direct (N × H)
11. C₅×C₁₇×C₁₉	AGL(1,𝔽₅)	semidirect
12. C₅×C₁₇×C₁₉	AGL(1,𝔽₅)	semidirect
17. C₅²×C₁₉	#595	semidirect
18. C₅²×C₁₇	C₄×C₁₉	semidirect
23. C₁₇×C₁₉	#1044	semidirect
32. C₅×C₁₉	#66775	semidirect
33. C₅×C₁₉	#66776	semidirect
35. C₅×C₁₇	C₁₉×AGL(1,𝔽₅)	semidirect
36. C₅×C₁₇	C₁₉×AGL(1,𝔽₅)	semidirect
42. C₅²	C₁₉×#595	semidirect
45. C₁₉	#13133347	direct (N × H)
46. C₁₇	C₁₉×#1044	semidirect
51. C₅	C₁₉×#66775	semidirect
52. C₅	C₁₉×#66776	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₅⋊D₈₅	2
C₁₉×#66776	5
C₁₉×#66775	5
C₁₉×#1044	17
#13133347	19

Subgroups — C19×#13133347 #44568115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13133347 #44568115