Subgroups — C₁₉×#876 #14269628

Order 1824.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×(C₂×D₃)⋊C₄	C₂	1	3	yes	maximal
3	C₁₉×Dic₃⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₁₉×#126	—	3	1	no	maximal, Hall
5	C₂²×D₃×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₉	C₂²	1	3	yes	—
7	C₂×Dic₃×C₁₉	C₂²	1	3	yes	—
8	C₄⋊C₄×C₁₉	—	3	3	no	—
9	C₂²⋊C₄×C₁₉	—	3	3	no	—
10	C₄²×C₁₉	D₃	1	1	yes	characteristic, complemented
11	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×D₃×C₁₉	—	2	3	no	—
13	C₃×C₄×C₁₉	—	2	3	no	—
14	Dic₃×C₁₉	—	2	3	no	—
15	C₂³×C₁₉	—	3	1	no	—
16	C₂×C₄×C₁₉	—	3	3	no	—
17	C₂×C₄×C₁₉	C₂×D₃	1	3	yes	—
18	C₂×C₃×C₁₉	#41	1	3	yes	—
19	D₃×C₁₉	—	4	1	no	—
20	#876	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₁₉	—	6	3	no	—
22	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
23	C₄×C₁₉	—	2	3	no	—
24	C₄×C₁₉	—	6	3	no	—
25	C₃×C₁₉	#126	1	1	yes	characteristic, complemented, Hall
26	C₃×C₄²	C₂×C₁₉	1	1	yes	characteristic, complemented
27	(C₂×D₃)⋊C₄	C₂×C₁₉	1	3	yes	—
28	Dic₃⋊C₄	C₂×C₁₉	1	3	yes	complemented
29	C₂×C₁₉	—	12	1	no	—
30	C₂×C₁₉	#235	1	3	yes	—
31	#126	—	3	1	no	Sylow
32	C₂²×D₃	C₂²×C₁₉	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂²×C₁₉	1	3	yes	—
34	C₂×Dic₃	C₂²×C₁₉	1	3	yes	—
35	C₁₉	#876	1	1	yes	characteristic, direct product factor, Sylow
36	C₄⋊C₄	—	3	3	no	—
37	C₂²⋊C₄	—	3	3	no	—
38	C₄²	D₃×C₁₉	1	1	yes	characteristic, complemented
39	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
40	C₂×D₃	—	2	3	no	—
41	C₃×C₄	—	2	3	no	—
42	Dic₃	—	2	3	no	—
43	C₂³	—	3	1	no	—
44	C₂×C₄	—	3	3	no	—
45	C₂×C₄	C₂×D₃×C₁₉	1	3	yes	—
46	C₂×C₃	#41×C₁₉	1	3	yes	—
47	D₃	—	4	1	no	—
48	C₂²	—	6	3	no	—
49	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	6	3	no	—
52	C₃	C₁₉×#126	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	12	1	no	—
54	C₂	C₁₉×#235	1	3	yes	—

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₃×C₄²×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂²×D₃×C₁₉	C₂²
hypercenter	C₄²×C₁₉	D₃
hypocenter	C₃	C₁₉×#126
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²×C₁₉	C₂	semidirect
3. C₁₉×Dic₃⋊C₄	C₂	semidirect
10. C₄²×C₁₉	D₃	semidirect
20. #876	C₁₉	direct (N × H)
25. C₃×C₁₉	#126	semidirect
26. C₃×C₄²	C₂×C₁₉	semidirect
28. Dic₃⋊C₄	C₂×C₁₉	semidirect
35. C₁₉	#876	direct (N × H)
38. C₄²	D₃×C₁₉	semidirect
52. C₃	C₁₉×#126	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₉	2
C₁₉×(C₂×D₃)⋊C₄	2
C₁₉×Dic₃⋊C₄	2
C₁₉×#126	3
#876	19

Subgroups — C19×#876 #14269628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#876 #14269628