Group #14269679 — subgroups

Subgroups — C₂×C₁₉×(C₂×D₃)⋊C₄ #14269679

Order 1824.

264 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 114 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	C₂³×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₂²⋊C₄×C₁₉	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×D₃×C₁₉	—	2	2	no	—
8	C₂²×D₃×C₁₉	—	2	2	no	—
9	C₂²×D₃×C₁₉	C₄	1	4	yes	complemented
10	C₂²×D₃×C₁₉	C₂²	1	2	yes	—
11	C₂×C₃×C₄×C₁₉	—	2	2	no	—
12	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	complemented
13	C₂×Dic₃×C₁₉	—	2	2	no	—
14	C₂×Dic₃×C₁₉	C₂²	1	2	yes	complemented
15	C₂⁴×C₁₉	—	3	1	no	—
16	C₂²×C₄×C₁₉	—	3	1	no	—
17	C₂²×C₄×C₁₉	D₃	1	1	yes	characteristic, complemented
18	C₂²⋊C₄×C₁₉	—	3	4	no	—
19	C₂²×C₃×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₃×C₁₉	D₄	1	2	yes	—
21	C₂²×C₃×C₁₉	D₄	1	2	yes	—
22	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×D₃×C₁₉	—	2	8	no	—
24	C₂×D₃×C₁₉	—	2	2	no	—
25	C₂×D₃×C₁₉	—	2	2	no	—
26	C₂×D₃×C₁₉	C₂×C₄	1	4	yes	complemented
27	C₃×C₄×C₁₉	—	2	2	no	—
28	Dic₃×C₁₉	—	2	2	no	—
29	C₂³×C₁₉	—	3	4	no	—
30	C₂³×C₁₉	—	3	2	no	—
31	C₂³×C₁₉	—	6	2	no	—
32	C₂³×C₁₉	—	6	2	no	—
33	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	—	3	2	no	—
36	C₂×C₄×C₁₉	—	6	2	no	—
37	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	complemented
38	C₂×C₃×C₁₉	C₂²⋊C₄	1	4	yes	complemented
39	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
42	D₃×C₁₉	—	2	4	no	—
43	C₂×(C₂×D₃)⋊C₄	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂²×C₁₉	—	3	4	no	—
45	C₂²×C₁₉	—	6	8	no	—
46	C₂²×C₁₉	—	6	2	no	—
47	C₂²×C₁₉	—	6	2	no	—
48	C₂²×C₁₉	C₄×D₃	1	2	yes	—
49	C₂²×C₁₉	D₁₂	1	2	yes	—
50	C₂²×C₁₉	#67	1	2	yes	—
51	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
52	C₄×C₁₉	—	2	2	no	—
53	C₄×C₁₉	—	6	2	no	—
54	C₃×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
55	C₂³×D₃	C₂×C₁₉	1	1	yes	characteristic
56	C₂²×C₃×C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
57	C₂²×Dic₃	C₂×C₁₉	1	1	yes	characteristic, complemented
58	(C₂×D₃)⋊C₄	C₂×C₁₉	1	4	yes	direct product factor
59	C₂×C₁₉	—	6	4	no	—
60	C₂×C₁₉	(C₂×D₃)⋊C₄	1	4	yes	direct product factor
61	C₂×C₁₉	C₂×C₄×D₃	1	1	yes	characteristic
62	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
63	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
64	C₂×C₂²⋊C₄	—	3	1	no	Sylow
65	C₂³×C₃	C₂²×C₁₉	1	1	yes	characteristic
66	C₂²×D₃	—	2	2	no	—
67	C₂²×D₃	—	2	2	no	—
68	C₂²×D₃	C₄×C₁₉	1	4	yes	complemented
69	C₂²×D₃	C₂²×C₁₉	1	2	yes	—
70	C₂×C₃×C₄	—	2	2	no	—
71	C₂×C₃×C₄	C₂²×C₁₉	1	2	yes	complemented
72	C₂×Dic₃	—	2	2	no	—
73	C₂×Dic₃	C₂²×C₁₉	1	2	yes	complemented
74	C₁₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
75	C₂⁴	—	3	1	no	—
76	C₂²×C₄	—	3	1	no	—
77	C₂²×C₄	D₃×C₁₉	1	1	yes	characteristic, complemented
78	C₂²⋊C₄	—	3	4	no	—
79	C₂²×C₃	C₂×C₄×C₁₉	1	2	yes	—
80	C₂²×C₃	D₄×C₁₉	1	2	yes	—
81	C₂²×C₃	D₄×C₁₉	1	2	yes	—
82	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
83	C₂×D₃	—	2	8	no	—
84	C₂×D₃	—	2	2	no	—
85	C₂×D₃	—	2	2	no	—
86	C₂×D₃	C₂×C₄×C₁₉	1	4	yes	complemented
87	C₃×C₄	—	2	2	no	—
88	Dic₃	—	2	2	no	—
89	C₂³	—	3	4	no	—
90	C₂³	—	3	2	no	—
91	C₂³	—	6	2	no	—
92	C₂³	—	6	2	no	—
93	C₂³	C₂×D₃×C₁₉	1	1	yes	characteristic
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	3	2	no	—
96	C₂×C₄	—	6	2	no	—
97	C₂×C₄	C₂×D₃×C₁₉	1	2	yes	complemented
98	C₂×C₃	C₂²⋊C₄×C₁₉	1	4	yes	complemented
99	C₂×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
100	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
101	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
102	D₃	—	2	4	no	—
103	C₂²	—	3	4	no	—
104	C₂²	—	6	8	no	—
105	C₂²	—	6	2	no	—
106	C₂²	—	6	2	no	—
107	C₂²	C₄×D₃×C₁₉	1	2	yes	—
108	C₂²	C₁₉×D₁₂	1	2	yes	—
109	C₂²	C₁₉×#67	1	2	yes	—
110	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	6	2	no	—
113	C₃	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
114	C₂	—	6	4	no	—
115	C₂	C₁₉×(C₂×D₃)⋊C₄	1	4	yes	direct product factor
116	C₂	C₂×C₄×D₃×C₁₉	1	1	yes	characteristic
117	C₂	C₂×C₁₉×D₁₂	1	1	yes	characteristic
118	C₂	C₂×C₁₉×#67	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×D₃×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₃×C₄×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₃×C₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×(C₂×D₃)⋊C₄

C₂

yes

maximal, direct product factor

C₂×C₂²⋊C₄×C₁₉

—

maximal, Hall

C₂³×C₃×C₁₉

C₂²

yes

characteristic

C₂²×D₃×C₁₉

—

C₂²×D₃×C₁₉

—

C₂²×D₃×C₁₉

C₄

yes

complemented

C₂²×D₃×C₁₉

C₂²

yes

—

C₂×C₃×C₄×C₁₉

—

C₂×C₃×C₄×C₁₉

C₂²

yes

complemented

C₂×Dic₃×C₁₉

—

C₂×Dic₃×C₁₉

C₂²

yes

complemented

C₂⁴×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₃

yes

characteristic, complemented

C₂²⋊C₄×C₁₉

—

C₂²×C₃×C₁₉

C₂×C₄

yes

—

C₂²×C₃×C₁₉

D₄

yes

—

C₂²×C₃×C₁₉

D₄

yes

—

C₂²×C₃×C₁₉

C₂³

yes

characteristic

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

C₂×C₄

yes

complemented

C₃×C₄×C₁₉

—

Dic₃×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₃

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₃

yes

complemented

C₂×C₃×C₁₉

C₂²⋊C₄

yes

complemented

C₂×C₃×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

D₃×C₁₉

—

C₂×(C₂×D₃)⋊C₄

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₃

yes

—

C₂²×C₁₉

D₁₂

yes

—

C₂²×C₁₉

#67

yes

—

C₂²×C₁₉

C₂²×D₃

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₃×C₁₉

C₂×C₂²⋊C₄

yes

characteristic, complemented, Hall

C₂³×D₃

C₂×C₁₉

yes

characteristic

C₂²×C₃×C₄

C₂×C₁₉

yes

characteristic, complemented

C₂²×Dic₃

C₂×C₁₉

yes

characteristic, complemented

(C₂×D₃)⋊C₄

C₂×C₁₉

yes

direct product factor

C₂×C₁₉

—

C₂×C₁₉

(C₂×D₃)⋊C₄

yes

direct product factor

C₂×C₁₉

C₂×C₄×D₃

yes

characteristic

C₂×C₁₉

C₂×D₁₂

yes

characteristic

C₂×C₁₉

C₂×#67

yes

characteristic

C₂×C₂²⋊C₄

—

Sylow

C₂³×C₃

C₂²×C₁₉

yes

characteristic

C₂²×D₃

—

C₂²×D₃

—

C₂²×D₃

C₄×C₁₉

yes

complemented

C₂²×D₃

C₂²×C₁₉

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×C₁₉

yes

complemented

C₂×Dic₃

—

C₂×Dic₃

C₂²×C₁₉

yes

complemented

C₁₉

C₂×(C₂×D₃)⋊C₄

yes

characteristic, direct product factor, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

D₃×C₁₉

yes

characteristic, complemented

C₂²⋊C₄

—

C₂²×C₃

C₂×C₄×C₁₉

yes

—

C₂²×C₃

D₄×C₁₉

yes

—

C₂²×C₃

D₄×C₁₉

yes

—

C₂²×C₃

C₂³×C₁₉

yes

characteristic

C₂×D₃

—

C₂×D₃

—

C₂×D₃

—

C₂×D₃

C₂×C₄×C₁₉

yes

complemented

C₃×C₄

—

Dic₃

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×D₃×C₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₃×C₁₉

yes

complemented

C₂×C₃

C₂²⋊C₄×C₁₉

yes

complemented

C₂×C₃

C₂²×C₄×C₁₉

yes

characteristic

100

C₂×C₃

C₂×D₄×C₁₉

yes

characteristic

101

C₂×C₃

C₂×D₄×C₁₉

yes

characteristic

102

D₃

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

C₄×D₃×C₁₉

yes

—

108

C₂²

C₁₉×D₁₂

yes

—

109

C₂²

C₁₉×#67

yes

—

110

C₂²

C₂²×D₃×C₁₉

yes

characteristic

111

C₄

—

112

C₄

—

113

C₃

C₂×C₂²⋊C₄×C₁₉

yes

characteristic, complemented, Sylow

114

C₂

—

115

C₂

C₁₉×(C₂×D₃)⋊C₄

yes

direct product factor

116

C₂

C₂×C₄×D₃×C₁₉

yes

characteristic

117

C₂

C₂×C₁₉×D₁₂

yes

characteristic

118

C₂

C₂×C₁₉×#67

yes

characteristic

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

subgroup

G/H

center

C₂³×C₁₉

C₂×D₃

commutator

C₂×C₃

C₂²×C₄×C₁₉

Frattini

C₂²

C₂²×D₃×C₁₉

Fitting

C₂²×C₃×C₄×C₁₉

C₂

socle

C₂³×C₃×C₁₉

C₂²

prime radical

C₂³×D₃×C₁₉

C₂

cosocle

C₂²×C₃

C₂³×C₁₉

hypercenter

C₂²×C₄×C₁₉

D₃

hypocenter

C₃

C₂×C₂²⋊C₄×C₁₉

LCS

G ▷ C₂×C₃ ▷ C₃

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉

N	H ≅ G/N	type
2. C₂²×C₃×C₄×C₁₉	C₂	semidirect
3. C₂²×Dic₃×C₁₉	C₂	semidirect
4. C₁₉×(C₂×D₃)⋊C₄	C₂	direct (N × H)
9. C₂²×D₃×C₁₉	C₄	semidirect
12. C₂×C₃×C₄×C₁₉	C₂²	semidirect
14. C₂×Dic₃×C₁₉	C₂²	semidirect
17. C₂²×C₄×C₁₉	D₃	semidirect
26. C₂×D₃×C₁₉	C₂×C₄	semidirect
37. C₂×C₄×C₁₉	C₂×D₃	semidirect
38. C₂×C₃×C₁₉	C₂²⋊C₄	semidirect
43. C₂×(C₂×D₃)⋊C₄	C₁₉	direct (N × H)
54. C₃×C₁₉	C₂×C₂²⋊C₄	semidirect
56. C₂²×C₃×C₄	C₂×C₁₉	semidirect
57. C₂²×Dic₃	C₂×C₁₉	semidirect
58. (C₂×D₃)⋊C₄	C₂×C₁₉	direct (N × H)
60. C₂×C₁₉	(C₂×D₃)⋊C₄	direct (N × H)
68. C₂²×D₃	C₄×C₁₉	semidirect
71. C₂×C₃×C₄	C₂²×C₁₉	semidirect
73. C₂×Dic₃	C₂²×C₁₉	semidirect
74. C₁₉	C₂×(C₂×D₃)⋊C₄	direct (N × H)
77. C₂²×C₄	D₃×C₁₉	semidirect
86. C₂×D₃	C₂×C₄×C₁₉	semidirect
97. C₂×C₄	C₂×D₃×C₁₉	semidirect
98. C₂×C₃	C₂²⋊C₄×C₁₉	semidirect
113. C₃	C₂×C₂²⋊C₄×C₁₉	semidirect
115. C₂	C₁₉×(C₂×D₃)⋊C₄	direct (N × H)

H ≅ G/N

type

2. C₂²×C₃×C₄×C₁₉

C₂

semidirect

3. C₂²×Dic₃×C₁₉

C₂

semidirect

4. C₁₉×(C₂×D₃)⋊C₄

C₂

direct (N × H)

9. C₂²×D₃×C₁₉

C₄

semidirect

12. C₂×C₃×C₄×C₁₉

C₂²

semidirect

14. C₂×Dic₃×C₁₉

C₂²

semidirect

17. C₂²×C₄×C₁₉

D₃

semidirect

26. C₂×D₃×C₁₉

C₂×C₄

semidirect

37. C₂×C₄×C₁₉

C₂×D₃

semidirect

38. C₂×C₃×C₁₉

C₂²⋊C₄

semidirect

43. C₂×(C₂×D₃)⋊C₄

C₁₉

direct (N × H)

54. C₃×C₁₉

C₂×C₂²⋊C₄

semidirect

56. C₂²×C₃×C₄

C₂×C₁₉

semidirect

57. C₂²×Dic₃

C₂×C₁₉

semidirect

58. (C₂×D₃)⋊C₄

C₂×C₁₉

direct (N × H)

60. C₂×C₁₉

(C₂×D₃)⋊C₄

direct (N × H)

68. C₂²×D₃

C₄×C₁₉

semidirect

71. C₂×C₃×C₄

C₂²×C₁₉

semidirect

73. C₂×Dic₃

C₂²×C₁₉

semidirect

74. C₁₉

C₂×(C₂×D₃)⋊C₄

direct (N × H)

77. C₂²×C₄

D₃×C₁₉

semidirect

86. C₂×D₃

C₂×C₄×C₁₉

semidirect

97. C₂×C₄

C₂×D₃×C₁₉

semidirect

98. C₂×C₃

C₂²⋊C₄×C₁₉

semidirect

113. C₃

C₂×C₂²⋊C₄×C₁₉

semidirect

115. C₂

C₁₉×(C₂×D₃)⋊C₄

direct (N × H)

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

subgroup	index
C₂³×D₃×C₁₉	2
C₂²×C₃×C₄×C₁₉	2
C₂²×Dic₃×C₁₉	2
C₁₉×(C₂×D₃)⋊C₄	2
C₂×C₂²⋊C₄×C₁₉	3
C₂×(C₂×D₃)⋊C₄	19

subgroup

index

C₂³×D₃×C₁₉

C₂²×C₃×C₄×C₁₉

C₂²×Dic₃×C₁₉

C₁₉×(C₂×D₃)⋊C₄

C₂×C₂²⋊C₄×C₁₉

C₂×(C₂×D₃)⋊C₄

Subgroups — C₂×C₁₉×(C₂×D₃)⋊C₄ #14269679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C19×(C2×D3)⋊C4 #14269679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×(C₂×D₃)⋊C₄ #14269679