Subgroups — C₁₉×#11744708 #30685952

Order 17100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊(C₃⋊(C₅⋊D₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×#4380	—	5	2	no	maximal
4	C₁₉×C₃⋊(C₅⋊D₅)	—	6	2	no	—
5	C₁₉×#1044	—	9	1	no	maximal, Hall
6	C₁₉×C₃⋊D₁₅	—	5	2	no	—
7	C₁₉×C₃⋊D₁₅	—	10	2	no	—
8	C₃×C₅²×C₁₉	—	2	2	no	—
9	C₁₉×C₅⋊D₅	—	9	1	no	—
10	#11744708	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₅×C₁₉	—	2	2	no	—
12	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	2	yes	complemented
13	C₁₉×#157	—	25	1	no	Hall
14	C₁₉×D₁₅	—	30	4	no	—
15	C₁₉×D₁₅	—	30	8	no	—
16	C₅²×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
17	C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₁₉	1	1	yes	characteristic
18	C₁₉×AGL(1,𝔽₅)	—	45	2	no	—
19	C₃⋊D₃×C₁₉	—	25	1	no	—
20	C₃×C₅×C₁₉	—	2	8	no	—
21	C₃×C₅×C₁₉	—	2	4	no	—
22	C₃²×C₅²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
23	D₅×C₁₉	—	45	2	no	—
24	D₅×C₁₉	—	90	2	no	—
25	#4380	—	5	2	no	—
26	C₃²×C₁₉	#1044	1	1	yes	characteristic, complemented, Hall
27	C₃⋊(C₅⋊D₅)	—	6	2	no	—
28	D₃×C₁₉	—	150	2	no	—
29	#1044	—	9	1	no	Hall
30	C₅×C₁₉	—	2	2	no	—
31	C₅×C₁₉	#4380	1	2	yes	complemented
32	C₃⋊D₁₅	—	5	2	no	—
33	C₃⋊D₁₅	—	10	2	no	—
34	C₄×C₁₉	—	225	1	no	Hall
35	C₃×C₅²	—	2	2	no	—
36	C₃×C₁₉	—	2	2	no	—
37	C₅⋊D₅	—	9	1	no	—
38	C₃²×C₅	—	2	2	no	—
39	C₃²×C₅	C₁₉×AGL(1,𝔽₅)	1	2	yes	complemented
40	C₂×C₁₉	—	225	1	no	—
41	#157	—	25	1	no	Hall
42	D₁₅	—	30	4	no	—
43	D₁₅	—	30	8	no	—
44	C₅²	C₁₉×#157	1	1	yes	characteristic, complemented, Sylow
45	AGL(1,𝔽₅)	—	45	2	no	—
46	C₁₉	#11744708	1	1	yes	characteristic, direct product factor, Sylow
47	C₃⋊D₃	—	25	1	no	—
48	C₃×C₅	—	2	8	no	—
49	C₃×C₅	—	2	4	no	—
50	D₅	—	45	2	no	—
51	D₅	—	90	2	no	—
52	C₃²	C₁₉×#1044	1	1	yes	characteristic, complemented, Sylow
53	D₃	—	150	2	no	—
54	C₅	—	2	2	no	—
55	C₅	C₁₉×#4380	1	2	yes	complemented
56	C₄	—	225	1	no	Sylow
57	C₃	—	2	2	no	—
58	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#11744708
commutator, hypocenter	C₃²×C₅²	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₄
prime radical	C₁₉×C₃⋊(C₃⋊(C₅⋊D₅))	C₂
cosocle	C₃⋊(C₃⋊(C₅⋊D₅))	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
10. #11744708	C₁₉	direct (N × H)
12. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
16. C₅²×C₁₉	#157	semidirect
22. C₃²×C₅²	C₄×C₁₉	semidirect
26. C₃²×C₁₉	#1044	semidirect
31. C₅×C₁₉	#4380	semidirect
39. C₃²×C₅	C₁₉×AGL(1,𝔽₅)	semidirect
44. C₅²	C₁₉×#157	semidirect
46. C₁₉	#11744708	direct (N × H)
52. C₃²	C₁₉×#1044	semidirect
55. C₅	C₁₉×#4380	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₃⋊(C₃⋊(C₅⋊D₅))	2
C₁₉×#4380	5
C₁₉×#1044	9
#11744708	19

Subgroups — C19×#11744708 #30685952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11744708 #30685952