Subgroups — C₁₉×#890 #14269643

Order 1824.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₁₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₁₉×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₄×Dic₃×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#125	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
12	C₄⋊C₄×C₁₉	—	3	2	no	—
13	C₄⋊C₄×C₁₉	—	3	2	no	—
14	C₄⋊C₄×C₁₉	—	3	1	no	—
15	C₄⋊C₄×C₁₉	D₃	1	1	yes	characteristic
16	C₄²×C₁₉	—	3	1	no	—
17	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₁₉	—	2	2	no	—
19	C₃×C₄×C₁₉	Q₈	1	2	yes	—
20	Dic₃×C₁₉	—	2	1	no	—
21	Dic₃×C₁₉	—	2	1	no	—
22	Dic₃×C₁₉	—	2	2	no	—
23	C₂×C₄×C₁₉	—	3	1	no	—
24	C₂×C₄×C₁₉	—	3	1	no	—
25	C₂×C₄×C₁₉	—	3	2	no	—
26	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
27	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₃×C₁₉	#41	1	1	yes	characteristic
30	C₂×C₃×C₁₉	#41	1	1	yes	characteristic
31	#890	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₉	—	2	2	no	—
34	C₄×C₁₉	—	6	1	no	—
35	C₄×C₁₉	—	6	1	no	—
36	C₄×C₁₉	—	6	2	no	—
37	C₄×C₁₉	Dic₆	1	2	yes	—
38	C₃×C₁₉	#125	1	1	yes	characteristic, complemented, Hall
39	C₃×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
40	C₄⋊Dic₃	C₂×C₁₉	1	2	yes	—
41	C₄⋊Dic₃	C₂×C₁₉	1	1	yes	characteristic
42	Dic₃⋊C₄	C₂×C₁₉	1	2	yes	—
43	C₄×Dic₃	C₂×C₁₉	1	1	yes	characteristic
44	C₂×C₁₉	C₂×Dic₆	1	1	yes	characteristic
45	C₂×C₁₉	#237	1	1	yes	characteristic
46	C₂×C₁₉	#239	1	1	yes	characteristic
47	#125	—	3	1	no	Sylow
48	C₂×C₃×C₄	C₂²×C₁₉	1	2	yes	—
49	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
50	C₂×Dic₃	C₂²×C₁₉	1	1	yes	characteristic
51	C₂×Dic₃	C₂²×C₁₉	1	1	yes	characteristic
52	C₂×Dic₃	C₂²×C₁₉	1	2	yes	—
53	C₁₉	#890	1	1	yes	characteristic, direct product factor, Sylow
54	C₄⋊C₄	—	3	2	no	—
55	C₄⋊C₄	—	3	2	no	—
56	C₄⋊C₄	—	3	1	no	—
57	C₄⋊C₄	D₃×C₁₉	1	1	yes	characteristic
58	C₄²	—	3	1	no	—
59	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
60	C₃×C₄	—	2	2	no	—
61	C₃×C₄	Q₈×C₁₉	1	2	yes	—
62	Dic₃	—	2	1	no	—
63	Dic₃	—	2	1	no	—
64	Dic₃	—	2	2	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	3	1	no	—
67	C₂×C₄	—	3	2	no	—
68	C₂×C₄	C₂×D₃×C₁₉	1	2	yes	—
69	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
70	C₂×C₃	C₂×Q₈×C₁₉	1	1	yes	characteristic
71	C₂×C₃	#41×C₁₉	1	1	yes	characteristic
72	C₂×C₃	#41×C₁₉	1	1	yes	characteristic
73	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	6	1	no	—
76	C₄	—	6	1	no	—
77	C₄	—	6	2	no	—
78	C₄	C₁₉×Dic₆	1	2	yes	—
79	C₃	C₁₉×#125	1	1	yes	characteristic, complemented, Sylow
80	C₂	C₂×C₁₉×Dic₆	1	1	yes	characteristic
81	C₂	C₁₉×#237	1	1	yes	characteristic
82	C₂	C₁₉×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₃×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂²×C₃×C₁₉	C₂³
hypercenter	C₄⋊C₄×C₁₉	D₃
hypocenter	C₃	C₁₉×#125
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄⋊C₄×C₁₉

Complements

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

N	H ≅ G/N	type
31. #890	C₁₉	direct (N × H)
38. C₃×C₁₉	#125	semidirect
53. C₁₉	#890	direct (N × H)
79. C₃	C₁₉×#125	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄⋊C₄×C₁₉	2
C₁₉×C₄⋊Dic₃	2
C₁₉×Dic₃⋊C₄	2
C₄×Dic₃×C₁₉	2
C₁₉×#125	3
#890	19

Subgroups — C19×#890 #14269643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#890 #14269643