Group #18016275 — subgroups

Subgroups — C₁₉×#10316 #18016275

Order 4864.

586 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#498	C₂	1	3	yes	maximal
2	C₁₉×#1956	C₂	1	3	yes	maximal
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
5	C₁₉×#498	—	2	12	no	—
6	C₂×C₁₉×#106	—	2	6	no	—
7	C₂×C₁₉×#103	—	2	6	no	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₁₉×#384	C₂²	1	1	yes	characteristic
10	C₂²×Q₈×C₁₉	—	2	3	no	—
11	C₂²×C₈×C₁₉	D₄	1	6	yes	—
12	C₁₉×C₄⋊Q₈	—	2	6	no	—
13	C₁₉×C₄⋊Q₈	—	2	3	no	—
14	C₁₉×C₄⋊Q₈	D₄	1	6	yes	—
15	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
16	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₁₉×#106	—	2	24	no	—
19	C₁₉×#103	—	4	12	no	—
20	C₄×C₈×C₁₉	—	2	6	no	—
21	C₂×Q₈×C₁₉	—	2	6	no	—
22	C₂×Q₈×C₁₉	—	4	3	no	—
23	C₂×Q₈×C₁₉	—	4	6	no	—
24	C₂×Q₈×C₁₉	—	4	6	no	—
25	C₂²×C₄×C₁₉	—	4	3	no	—
26	C₂²×C₄×C₁₉	—	4	1	no	—
27	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
28	C₂×C₈×C₁₉	—	2	6	no	—
29	C₂×C₈×C₁₉	—	2	6	no	—
30	C₂×C₈×C₁₉	SD₁₆	1	12	yes	—
31	C₄⋊C₄×C₁₉	—	2	12	no	—
32	C₄⋊C₄×C₁₉	—	4	6	no	—
33	C₄⋊C₄×C₁₉	—	4	6	no	—
34	C₄²×C₁₉	C₂×D₄	1	3	yes	—
35	C₄²×C₁₉	#41	1	1	yes	characteristic
36	#10316	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂³×C₁₉	#127	1	1	yes	characteristic
38	Q₈×C₁₉	—	4	12	no	—
39	Q₈×C₁₉	—	8	6	no	—
40	C₂×C₄×C₁₉	—	4	6	no	—
41	C₂×C₄×C₁₉	—	8	3	no	—
42	C₂×C₄×C₁₉	—	8	3	no	—
43	C₂×C₄×C₁₉	—	8	3	no	—
44	C₂×C₄×C₁₉	#120	1	3	yes	—
45	C₂×C₄×C₁₉	#121	1	3	yes	—
46	C₂×C₄×C₁₉	C₂×SD₁₆	1	6	yes	—
47	C₂×C₄×C₁₉	#137	1	6	yes	—
48	C₈×C₁₉	—	2	12	no	—
49	C₂×#498	C₂×C₁₉	1	3	yes	—
50	#1956	C₂×C₁₉	1	3	yes	—
51	#1273	C₂×C₁₉	1	1	yes	characteristic
52	C₂²×C₁₉	#392	1	1	yes	characteristic
53	C₂²×C₁₉	#492	1	3	yes	—
54	C₂²×C₁₉	#497	1	3	yes	—
55	C₄×C₁₉	—	8	6	no	—
56	C₄×C₁₉	—	16	1	no	—
57	C₄×C₁₉	#448	1	6	yes	—
58	C₄×C₁₉	#461	1	6	yes	—
59	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
60	#498	—	2	12	no	—
61	C₂×#106	—	2	6	no	—
62	C₂×#103	—	2	6	no	—
63	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
64	#384	C₂²×C₁₉	1	1	yes	characteristic
65	C₂×C₁₉	#1705	1	1	yes	characteristic
66	C₂×C₁₉	#1716	1	3	yes	—
67	C₂×C₁₉	#2013	1	3	yes	—
68	C₂²×Q₈	—	2	3	no	—
69	C₂²×C₈	D₄×C₁₉	1	6	yes	—
70	C₄⋊Q₈	—	2	6	no	—
71	C₄⋊Q₈	—	2	3	no	—
72	C₄⋊Q₈	D₄×C₁₉	1	6	yes	—
73	C₂×C₄⋊C₄	—	2	6	no	—
74	C₂×C₄⋊C₄	—	2	3	no	—
75	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
76	#106	—	2	24	no	—
77	#103	—	4	12	no	—
78	C₄×C₈	—	2	6	no	—
79	C₁₉	#10316	1	1	yes	characteristic, direct product factor, Sylow
80	C₂×Q₈	—	2	6	no	—
81	C₂×Q₈	—	4	3	no	—
82	C₂×Q₈	—	4	6	no	—
83	C₂×Q₈	—	4	6	no	—
84	C₂²×C₄	—	4	3	no	—
85	C₂²×C₄	—	4	1	no	—
86	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
87	C₂×C₈	—	2	6	no	—
88	C₂×C₈	—	2	6	no	—
89	C₂×C₈	SD₁₆×C₁₉	1	12	yes	—
90	C₄⋊C₄	—	2	12	no	—
91	C₄⋊C₄	—	4	6	no	—
92	C₄⋊C₄	—	4	6	no	—
93	C₄²	C₂×D₄×C₁₉	1	3	yes	—
94	C₄²	#41×C₁₉	1	1	yes	characteristic
95	C₂³	C₁₉×#127	1	1	yes	characteristic
96	Q₈	—	4	12	no	—
97	Q₈	—	8	6	no	—
98	C₂×C₄	—	4	6	no	—
99	C₂×C₄	—	8	3	no	—
100	C₂×C₄	—	8	3	no	—
101	C₂×C₄	—	8	3	no	—
102	C₂×C₄	C₁₉×#120	1	3	yes	—
103	C₂×C₄	C₁₉×#121	1	3	yes	—
104	C₂×C₄	C₂×SD₁₆×C₁₉	1	6	yes	—
105	C₂×C₄	C₁₉×#137	1	6	yes	—
106	C₈	—	2	12	no	—
107	C₂²	C₁₉×#392	1	1	yes	characteristic
108	C₂²	C₁₉×#492	1	3	yes	—
109	C₂²	C₁₉×#497	1	3	yes	—
110	C₄	—	8	6	no	—
111	C₄	—	16	1	no	—
112	C₄	C₁₉×#448	1	6	yes	—
113	C₄	C₁₉×#461	1	6	yes	—
114	C₂	C₁₉×#1705	1	1	yes	characteristic
115	C₂	C₁₉×#1716	1	3	yes	—
116	C₂	C₁₉×#2013	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#498

C₂

yes

maximal

C₁₉×#1956

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#498

—

C₂×C₁₉×#106

—

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#106

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

#10316

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#127

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

C₂×#498

C₂×C₁₉

yes

—

#1956

C₂×C₁₉

yes

—

#1273

C₂×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#448

yes

—

C₄×C₁₉

#461

yes

—

C₂×C₄⋊Q₈

C₂²×C₁₉

yes

—

#498

—

C₂×#106

—

C₂×#103

—

C₂×C₄×C₈

C₂²×C₁₉

yes

—

#384

C₂²×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#2013

yes

—

C₂²×Q₈

—

C₂²×C₈

D₄×C₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

D₄×C₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₁₉

yes

characteristic

#106

—

#103

—

C₄×C₈

—

C₁₉

#10316

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

SD₁₆×C₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×D₄×C₁₉

yes

—

C₄²

#41×C₁₉

yes

characteristic

C₂³

C₁₉×#127

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₁₉×#120

yes

—

103

C₂×C₄

C₁₉×#121

yes

—

104

C₂×C₄

C₂×SD₁₆×C₁₉

yes

—

105

C₂×C₄

C₁₉×#137

yes

—

106

C₈

—

107

C₂²

C₁₉×#392

yes

characteristic

108

C₂²

C₁₉×#492

yes

—

109

C₂²

C₁₉×#497

yes

—

110

C₄

—

111

C₄

—

112

C₄

C₁₉×#448

yes

—

113

C₄

C₁₉×#461

yes

—

114

C₂

C₁₉×#1705

yes

characteristic

115

C₂

C₁₉×#1716

yes

—

116

C₂

C₁₉×#2013

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₉

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
36. #10316	C₁₉	direct (N × H)
79. C₁₉	#10316	direct (N × H)

H ≅ G/N

type

36. #10316

C₁₉

direct (N × H)

79. C₁₉

#10316

direct (N × H)

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

subgroup	index
C₂×C₁₉×#498	2
C₁₉×#1956	2
C₁₉×#1273	2
#10316	19

subgroup

index

C₂×C₁₉×#498

C₁₉×#1956

C₁₉×#1273

#10316

Subgroups — C₁₉×#10316 #18016275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10316 #18016275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10316 #18016275