Subgroups — C₁₉×#11744709 #30685954

Order 17100.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×#4379	—	5	1	no	maximal
4	C₁₉×#4380	—	5	1	no	maximal
5	C₅×C₁₉×D₁₅	—	6	2	no	—
6	C₁₉×#1042	—	9	1	no	maximal, Hall
7	C₁₉×C₃⋊D₁₅	D₅	1	1	yes	characteristic
8	C₅×C₃⋊D₃×C₁₉	—	5	1	no	—
9	C₃×C₅²×C₁₉	—	2	2	no	—
10	C₅×D₅×C₁₉	—	9	1	no	—
11	#11744709	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃²×C₅×C₁₉	—	4	1	no	—
13	C₃²×C₅×C₁₉	Dic₅	1	1	yes	characteristic, complemented
14	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	C₁₉×#157	—	25	1	no	Hall
16	C₁₉×D₁₅	—	6	2	no	—
17	C₅×D₃×C₁₉	—	30	2	no	—
18	C₅²×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
19	C₅×C₃⋊D₁₅	C₂×C₁₉	1	1	yes	characteristic
20	C₁₉×AGL(1,𝔽₅)	—	45	1	no	—
21	C₁₉×Dic₅	—	45	1	no	—
22	C₃⋊D₃×C₁₉	—	5	1	no	—
23	C₃×C₅×C₁₉	—	2	2	no	—
24	C₃×C₅×C₁₉	—	2	2	no	—
25	C₃×C₅×C₁₉	—	4	4	no	—
26	C₃²×C₅²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₉	—	45	1	no	—
28	D₅×C₁₉	—	9	1	no	—
29	#4380	—	5	1	no	—
30	#4379	—	5	1	no	—
31	C₃²×C₁₉	#1042	1	1	yes	characteristic, complemented, Hall
32	C₅×D₁₅	—	6	2	no	—
33	D₃×C₁₉	—	30	2	no	—
34	#1042	—	9	1	no	Hall
35	C₅×C₁₉	—	4	1	no	—
36	C₅×C₁₉	#4379	1	1	yes	characteristic, complemented
37	C₅×C₁₉	#4380	1	1	yes	characteristic, complemented
38	C₃⋊D₁₅	D₅×C₁₉	1	1	yes	characteristic
39	C₅×C₃⋊D₃	—	5	1	no	—
40	C₄×C₁₉	—	225	1	no	Hall
41	C₃×C₅²	—	2	2	no	—
42	C₃×C₁₉	—	2	2	no	—
43	C₅×D₅	—	9	1	no	—
44	C₃²×C₅	—	4	1	no	—
45	C₃²×C₅	C₁₉×Dic₅	1	1	yes	characteristic, complemented
46	C₃²×C₅	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
47	C₂×C₁₉	—	45	1	no	—
48	#157	—	25	1	no	Hall
49	D₁₅	—	6	2	no	—
50	C₅×D₃	—	30	2	no	—
51	C₅²	C₁₉×#157	1	1	yes	characteristic, complemented, Sylow
52	AGL(1,𝔽₅)	—	45	1	no	—
53	Dic₅	—	45	1	no	—
54	C₁₉	#11744709	1	1	yes	characteristic, direct product factor, Sylow
55	C₃⋊D₃	—	5	1	no	—
56	C₃×C₅	—	2	2	no	—
57	C₃×C₅	—	2	2	no	—
58	C₃×C₅	—	4	4	no	—
59	C₂×C₅	—	45	1	no	—
60	D₅	—	9	1	no	—
61	C₃²	C₁₉×#1042	1	1	yes	characteristic, complemented, Sylow
62	D₃	—	30	2	no	—
63	C₅	—	4	1	no	—
64	C₅	C₁₉×#4380	1	1	yes	characteristic, complemented
65	C₅	C₁₉×#4379	1	1	yes	characteristic, complemented
66	C₄	—	225	1	no	Sylow
67	C₃	—	2	2	no	—
68	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#11744709
commutator, hypocenter	C₃²×C₅²	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₄
prime radical	C₅×C₁₉×C₃⋊D₁₅	C₂
cosocle	C₅×C₃⋊D₁₅	C₂×C₁₉
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₉	C₄	semidirect
11. #11744709	C₁₉	direct (N × H)
13. C₃²×C₅×C₁₉	Dic₅	semidirect
14. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
18. C₅²×C₁₉	#157	semidirect
26. C₃²×C₅²	C₄×C₁₉	semidirect
31. C₃²×C₁₉	#1042	semidirect
36. C₅×C₁₉	#4379	semidirect
37. C₅×C₁₉	#4380	semidirect
45. C₃²×C₅	C₁₉×Dic₅	semidirect
46. C₃²×C₅	C₁₉×AGL(1,𝔽₅)	semidirect
51. C₅²	C₁₉×#157	semidirect
54. C₁₉	#11744709	direct (N × H)
61. C₃²	C₁₉×#1042	semidirect
64. C₅	C₁₉×#4380	semidirect
65. C₅	C₁₉×#4379	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₉×C₃⋊D₁₅	2
C₁₉×#4379	5
C₁₉×#4380	5
C₁₉×#1042	9
#11744709	19

Subgroups — C19×#11744709 #30685954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11744709 #30685954