Subgroups — C₁₉⋊#11744708 #30685953

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	—	19	1	no	maximal, 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))	D₁₉	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	Dic₁₉	1	1	yes	characteristic, complemented, Hall
23	D₅×C₁₉	—	45	2	no	—
24	D₅×C₁₉	—	90	2	no	—
25	#4380	—	95	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	—	171	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	Dic₁₉	—	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	—	475	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)	—	855	2	no	—
46	C₁₉	#11744708	1	1	yes	characteristic, complemented, 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	—	4275	1	no	Sylow
57	C₃	—	2	2	no	—
58	C₂	—	225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₉	C₄
prime radical, cosocle	C₁₉×C₃⋊(C₃⋊(C₅⋊D₅))	C₂
LCS	G ▷ C₃²×C₅²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₉	C₄	semidirect
12. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
16. C₅²×C₁₉	#157	semidirect
22. C₃²×C₅²	Dic₁₉	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	semidirect
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 #30685953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#11744708 #30685953