Group #18014755 — subgroups

Subgroups — C₁₉×#8796 #18014755

Order 4864.

228 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 118 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	C₁₉×#1568	C₂	1	2	yes	maximal
2	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1287	C₂	1	4	yes	maximal
4	C₁₉×#432	C₂²	1	4	yes	—
5	C₁₉×#431	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#335	—	2	2	no	—
8	C₁₉×#334	—	2	2	no	—
9	C₁₉×#322	C₄	1	2	yes	—
10	C₈²×C₁₉	C₄	1	2	yes	—
11	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₁₉×C₄⋊C₈	—	2	4	no	—
15	C₁₉×C₄⋊C₈	—	2	2	no	—
16	C₁₉×C₂²⋊C₈	—	2	2	no	—
17	C₁₉×C₂²⋊C₈	—	2	4	no	—
18	C₁₉×#97	—	2	4	no	—
19	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	#41	1	2	yes	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	4	no	—
29	C₂×C₈×C₁₉	—	4	4	no	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₄²×C₁₉	#41	1	2	yes	—
37	#8796	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂³×C₁₉	#125	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#117	1	2	yes	—
44	C₂×C₄×C₁₉	#124	1	2	yes	—
45	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
46	C₈×C₁₉	—	2	1	no	—
47	C₈×C₁₉	—	2	1	no	—
48	C₈×C₁₉	—	4	4	no	—
49	C₈×C₁₉	—	8	4	no	—
50	C₈×C₁₉	#108	1	2	yes	—
51	C₈×C₁₉	#108	1	2	yes	—
52	#1568	C₂×C₁₉	1	2	yes	—
53	#1450	C₂×C₁₉	1	1	yes	characteristic
54	#1287	C₂×C₁₉	1	4	yes	—
55	C₂²×C₁₉	—	2	2	no	—
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	#382	1	1	yes	characteristic
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	C₂×#108	1	1	yes	characteristic
62	C₄×C₁₉	C₂×#108	1	1	yes	characteristic
63	#432	C₂²×C₁₉	1	4	yes	—
64	#431	C₂²×C₁₉	1	2	yes	—
65	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
66	#335	—	2	2	no	—
67	#334	—	2	2	no	—
68	#322	C₄×C₁₉	1	2	yes	—
69	C₈²	C₄×C₁₉	1	2	yes	—
70	C₂×C₁₉	—	4	1	no	—
71	C₂×C₁₉	#1833	1	2	yes	—
72	C₂×C₁₉	#1837	1	1	yes	characteristic
73	C₂²×C₈	Q₈×C₁₉	1	1	yes	characteristic
74	C₂²×C₈	Q₈×C₁₉	1	1	yes	characteristic
75	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
76	C₄⋊C₈	—	2	4	no	—
77	C₄⋊C₈	—	2	2	no	—
78	C₂²⋊C₈	—	2	2	no	—
79	C₂²⋊C₈	—	2	4	no	—
80	#97	—	2	4	no	—
81	C₄×C₈	C₂×C₄×C₁₉	1	4	yes	—
82	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
83	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
84	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
85	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
86	C₁₉	#8796	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
88	C₂²×C₄	#41×C₁₉	1	2	yes	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	—	4	4	no	—
93	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
94	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
95	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
96	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
97	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
98	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
99	C₄²	#41×C₁₉	1	2	yes	—
100	C₂³	C₁₉×#125	1	1	yes	characteristic
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
105	C₂×C₄	C₁₉×#117	1	2	yes	—
106	C₂×C₄	C₁₉×#124	1	2	yes	—
107	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
108	C₈	—	2	1	no	—
109	C₈	—	2	1	no	—
110	C₈	—	4	4	no	—
111	C₈	—	8	4	no	—
112	C₈	C₁₉×#108	1	2	yes	—
113	C₈	C₁₉×#108	1	2	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	1	no	—
116	C₂²	C₁₉×#382	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	—	2	2	no	—
119	C₄	—	2	1	no	—
120	C₄	C₂×C₁₉×#108	1	1	yes	characteristic
121	C₄	C₂×C₁₉×#108	1	1	yes	characteristic
122	C₂	—	4	1	no	—
123	C₂	C₁₉×#1833	1	2	yes	—
124	C₂	C₁₉×#1837	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1568

C₂

yes

maximal

C₁₉×#1450

C₂

yes

maximal, characteristic

C₁₉×#1287

C₂

yes

maximal

C₁₉×#432

C₂²

yes

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₁₉×#322

C₄

yes

—

C₈²×C₁₉

C₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

#8796

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#125

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#125

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#108

yes

—

C₈×C₁₉

#108

yes

—

#1568

C₂×C₁₉

yes

—

#1450

C₂×C₁₉

yes

characteristic

#1287

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×C₁₉

yes

—

#431

C₂²×C₁₉

yes

—

C₂×C₄×C₈

C₂²×C₁₉

yes

—

—

C₄×C₁₉

yes

—

C₈²

C₄×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

#1833

yes

—

C₂×C₁₉

#1837

yes

characteristic

C₂²×C₈

Q₈×C₁₉

yes

characteristic

C₂²×C₈

Q₈×C₁₉

yes

characteristic

C₂×C₄²

C₂³×C₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

C₄×C₈

D₄×C₁₉

yes

characteristic

C₄×C₈

D₄×C₁₉

yes

characteristic

C₁₉

#8796

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₂×Q₈×C₁₉

yes

characteristic

C₂²×C₄

#41×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₉

yes

characteristic

C₄²

C₂²×C₄×C₁₉

yes

characteristic

C₄²

C₂×D₄×C₁₉

yes

characteristic

C₄²

#41×C₁₉

yes

—

100

C₂³

C₁₉×#125

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×C₄⋊C₄×C₁₉

yes

characteristic

105

C₂×C₄

C₁₉×#117

yes

—

106

C₂×C₄

C₁₉×#124

yes

—

107

C₂×C₄

C₁₉×#125

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

C₁₉×#108

yes

—

113

C₈

C₁₉×#108

yes

—

114

C₂²

—

115

C₂²

—

116

C₂²

C₁₉×#382

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

C₂×C₁₉×#108

yes

characteristic

121

C₄

C₂×C₁₉×#108

yes

characteristic

122

C₂

—

123

C₂

C₁₉×#1833

yes

—

124

C₂

C₁₉×#1837

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#382
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#382

commutator

C₄²

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

C₂³×C₁₉

G ▷ C₄² ▷ C₂² ▷ C₁

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
37. #8796	C₁₉	direct (N × H)
86. C₁₉	#8796	direct (N × H)

H ≅ G/N

type

37. #8796

C₁₉

direct (N × H)

86. C₁₉

#8796

direct (N × H)

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

subgroup	index
C₁₉×#1568	2
C₁₉×#1450	2
C₁₉×#1287	2
#8796	19

subgroup

index

C₁₉×#1568

C₁₉×#1450

C₁₉×#1287

#8796

Subgroups — C₁₉×#8796 #18014755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8796 #18014755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8796 #18014755