Group #14559992 — subgroups

Subgroups — C₁₉×#2135 #14559992

Order 2432.

230 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 84 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×#536	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#413	C₂	1	2	yes	maximal
3	C₁₉×#356	C₂	1	4	yes	maximal, complemented
4	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×Q₈×C₁₉	C₄	1	1	yes	characteristic
6	C₂×M₁₆×C₁₉	—	2	2	no	—
7	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₁₉×#124	C₄	1	2	yes	—
9	C₁₉×#123	—	2	2	no	—
10	C₁₉×C₂²⋊Q₈	—	2	2	no	—
11	C₁₉×#117	C₄	1	1	yes	characteristic
12	C₁₉×#101	C₂²	1	4	yes	—
13	C₁₉×#100	—	2	2	no	—
14	#41×C₁₉	—	4	2	no	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂×Q₈×C₁₉	—	4	2	no	—
17	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×D₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	D₄	1	2	yes	—
24	M₁₆×C₁₉	—	2	4	no	—
25	M₁₆×C₁₉	—	4	2	no	—
26	C₂×C₈×C₁₉	—	4	2	no	—
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₂²⋊C₄×C₁₉	—	2	1	no	—
30	C₂²⋊C₄×C₁₉	—	2	4	no	—
31	C₄²×C₁₉	C₂×C₄	1	2	yes	—
32	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
33	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	Q₈×C₁₉	—	4	1	no	—
35	Q₈×C₁₉	—	4	2	no	—
36	Q₈×C₁₉	—	4	2	no	—
37	D₄×C₁₉	—	4	1	no	—
38	D₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₈×C₁₉	—	4	4	no	—
49	#2135	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₁₉	—	2	1	no	—
51	C₂²×C₁₉	—	2	2	no	—
52	C₂²×C₁₉	—	4	2	no	—
53	C₂²×C₁₉	—	4	1	no	—
54	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₄×C₁₉	—	2	2	no	—
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	—	4	2	no	—
58	C₄×C₁₉	—	4	2	no	—
59	C₄×C₁₉	#99	1	2	yes	—
60	#536	C₂×C₁₉	1	1	yes	characteristic
61	#413	C₂×C₁₉	1	2	yes	—
62	#356	C₂×C₁₉	1	4	yes	complemented
63	C₂×C₁₉	—	2	1	no	—
64	C₂×C₁₉	—	4	1	no	—
65	C₂×C₁₉	—	4	2	no	—
66	C₂×C₁₉	C₂×#99	1	1	yes	characteristic
67	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
68	C₂²×Q₈	C₄×C₁₉	1	1	yes	characteristic
69	C₂×M₁₆	—	2	2	no	—
70	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
71	#124	C₄×C₁₉	1	2	yes	—
72	#123	—	2	2	no	—
73	C₂²⋊Q₈	—	2	2	no	—
74	#117	C₄×C₁₉	1	1	yes	characteristic
75	#101	C₂²×C₁₉	1	4	yes	—
76	#100	—	2	2	no	—
77	C₁₉	#2135	1	1	yes	characteristic, direct product factor, Sylow
78	#41	—	4	2	no	—
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	4	2	no	—
81	C₂×Q₈	C₂×C₄×C₁₉	1	2	yes	—
82	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
83	C₂×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
84	C₂×D₄	D₄×C₁₉	1	2	yes	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
87	C₂²×C₄	D₄×C₁₉	1	2	yes	—
88	M₁₆	—	2	4	no	—
89	M₁₆	—	4	2	no	—
90	C₂×C₈	—	4	2	no	—
91	C₄⋊C₄	—	2	1	no	—
92	C₄⋊C₄	—	2	4	no	—
93	C₂²⋊C₄	—	2	1	no	—
94	C₂²⋊C₄	—	2	4	no	—
95	C₄²	C₂×C₄×C₁₉	1	2	yes	—
96	C₂³	C₂²⋊C₄×C₁₉	1	2	yes	—
97	C₂³	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
98	Q₈	—	4	1	no	—
99	Q₈	—	4	2	no	—
100	Q₈	—	4	2	no	—
101	D₄	—	4	1	no	—
102	D₄	—	4	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
110	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
111	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
112	C₈	—	4	4	no	—
113	C₂²	—	2	1	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	4	2	no	—
116	C₂²	—	4	1	no	—
117	C₂²	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	2	1	no	—
120	C₄	—	4	2	no	—
121	C₄	—	4	2	no	—
122	C₄	C₁₉×#99	1	2	yes	—
123	C₂	—	2	1	no	—
124	C₂	—	4	1	no	—
125	C₂	—	4	2	no	—
126	C₂	C₂×C₁₉×#99	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#536

C₂

yes

maximal, characteristic

C₁₉×#413

C₂

yes

maximal

C₁₉×#356

C₂

yes

maximal, complemented

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#124

C₄

yes

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#117

C₄

yes

characteristic

C₁₉×#101

C₂²

yes

—

C₁₉×#100

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₈×C₁₉

—

#2135

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#99

yes

—

#536

C₂×C₁₉

yes

characteristic

#413

C₂×C₁₉

yes

—

#356

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#99

yes

characteristic

C₂×#41

C₂²×C₁₉

yes

characteristic

C₂²×Q₈

C₄×C₁₉

yes

characteristic

C₂×M₁₆

—

C₄⋊Q₈

C₂²×C₁₉

yes

—

#124

C₄×C₁₉

yes

—

#123

—

C₂²⋊Q₈

—

#117

C₄×C₁₉

yes

characteristic

#101

C₂²×C₁₉

yes

—

#100

—

C₁₉

#2135

yes

characteristic, direct product factor, Sylow

#41

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×C₄×C₁₉

yes

—

C₂×Q₈

C₂³×C₁₉

yes

characteristic

C₂×D₄

C₂×C₄×C₁₉

yes

characteristic

C₂×D₄

D₄×C₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₄

D₄×C₁₉

yes

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂×C₄×C₁₉

yes

—

C₂³

C₂²⋊C₄×C₁₉

yes

—

C₂³

C₂²⋊C₄×C₁₉

yes

characteristic

Q₈

—

Q₈

—

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

110

C₂×C₄

C₂²×C₄×C₁₉

yes

characteristic

111

C₂×C₄

C₂×D₄×C₁₉

yes

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

C₁₉×#99

yes

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

C₂×C₁₉×#99

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#99
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×Q₈	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

C₂×#99

commutator

C₂×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×Q₈

C₂³×C₁₉

prime radical

C₂×#41×C₁₉

C₂²

LCS

G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#356	C₂	semidirect
49. #2135	C₁₉	direct (N × H)
62. #356	C₂×C₁₉	semidirect
77. C₁₉	#2135	direct (N × H)

H ≅ G/N

type

3. C₁₉×#356

C₂

semidirect

49. #2135

C₁₉

direct (N × H)

62. #356

C₂×C₁₉

semidirect

77. C₁₉

#2135

direct (N × H)

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

subgroup	index
C₁₉×#536	2
C₁₉×#413	2
C₁₉×#356	2
#2135	19

subgroup

index

C₁₉×#536

C₁₉×#413

C₁₉×#356

#2135

Subgroups — C₁₉×#2135 #14559992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2135 #14559992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2135 #14559992