Subgroups — C₁₉×#11744710 #30685956

Order 17100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×#4379	—	5	6	no	maximal
4	C₅²×D₃×C₁₉	—	6	2	no	—
5	C₁₉×#1039	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₃×C₁₉	D₅	1	6	yes	—
7	C₃×C₅²×C₁₉	—	2	2	no	—
8	C₂×C₅²×C₁₉	—	9	1	no	—
9	#11744710	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₅×C₁₉	Dic₅	1	6	yes	complemented
11	C₁₉×#157	—	25	1	no	Hall
12	C₅×D₃×C₁₉	—	6	12	no	—
13	C₅²×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
14	C₅²×C₃⋊D₃	C₂×C₁₉	1	1	yes	characteristic
15	C₁₉×Dic₅	—	45	6	no	—
16	C₃⋊D₃×C₁₉	C₅⋊D₅	1	1	yes	characteristic
17	C₃×C₅×C₁₉	—	2	12	no	—
18	C₃²×C₅²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₁₉	—	9	6	no	—
20	#4379	—	5	6	no	—
21	C₃²×C₁₉	#1039	1	1	yes	characteristic, complemented, Hall
22	C₅²×D₃	—	6	2	no	—
23	D₃×C₁₉	—	6	2	no	—
24	#1039	—	9	1	no	Hall
25	C₅×C₁₉	#4379	1	6	yes	complemented
26	C₅×C₃⋊D₃	D₅×C₁₉	1	6	yes	—
27	C₄×C₁₉	—	225	1	no	Hall
28	C₃×C₅²	—	2	2	no	—
29	C₃×C₁₉	—	2	2	no	—
30	C₂×C₅²	—	9	1	no	—
31	C₃²×C₅	C₁₉×Dic₅	1	6	yes	complemented
32	C₂×C₁₉	—	9	1	no	—
33	#157	—	25	1	no	Hall
34	C₅×D₃	—	6	12	no	—
35	C₅²	C₁₉×#157	1	1	yes	characteristic, complemented, Sylow
36	Dic₅	—	45	6	no	—
37	C₁₉	#11744710	1	1	yes	characteristic, direct product factor, Sylow
38	C₃⋊D₃	C₁₉×C₅⋊D₅	1	1	yes	characteristic
39	C₃×C₅	—	2	12	no	—
40	C₂×C₅	—	9	6	no	—
41	C₃²	C₁₉×#1039	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	C₁₉×#4379	1	6	yes	complemented
44	C₄	—	225	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#11744710
commutator, hypocenter	C₃²×C₅²	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₄
prime radical	C₅²×C₃⋊D₃×C₁₉	C₂
cosocle	C₅²×C₃⋊D₃	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
9. #11744710	C₁₉	direct (N × H)
10. C₃²×C₅×C₁₉	Dic₅	semidirect
13. C₅²×C₁₉	#157	semidirect
18. C₃²×C₅²	C₄×C₁₉	semidirect
21. C₃²×C₁₉	#1039	semidirect
25. C₅×C₁₉	#4379	semidirect
31. C₃²×C₅	C₁₉×Dic₅	semidirect
35. C₅²	C₁₉×#157	semidirect
37. C₁₉	#11744710	direct (N × H)
41. C₃²	C₁₉×#1039	semidirect
43. 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
C₅²×C₃⋊D₃×C₁₉	2
C₁₉×#4379	5
C₁₉×#1039	9
#11744710	19

Subgroups — C19×#11744710 #30685956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11744710 #30685956