Group #18019608 — subgroups

Subgroups — C₄×C₁₉×D₃₂ #18019608

Order 4864.

214 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 94 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×D₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×D₁₆	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1415	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×D₁₆	C₂²	1	2	yes	—
7	C₄×D₈×C₁₉	—	2	2	no	—
8	C₁₉×D₃₂	C₄	1	4	yes	direct product factor
9	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
11	C₁₉×#366	C₂²	1	2	yes	—
12	C₁₉×#357	—	2	2	no	—
13	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×D₈×C₁₉	—	2	2	no	—
15	C₄×D₄×C₁₉	—	4	2	no	—
16	C₁₉×D₁₆	—	2	2	no	—
17	C₁₉×D₁₆	C₂×C₄	1	4	yes	complemented
18	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
20	C₁₉×#107	—	2	2	no	—
21	C₁₉×#102	—	4	2	no	—
22	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₁₉×C₃₂	—	2	1	no	—
24	C₁₉×C₃₂	C₂×C₄	1	2	yes	complemented
25	C₂×D₄×C₁₉	—	4	2	no	—
26	C₂²×C₄×C₁₉	—	8	2	no	—
27	D₈×C₁₉	—	2	4	no	—
28	D₈×C₁₉	—	4	2	no	—
29	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₄⋊C₄×C₁₉	—	4	2	no	—
32	C₂²⋊C₄×C₁₉	—	8	2	no	—
33	C₄²×C₁₉	D₈	1	1	yes	characteristic
34	C₁₆×C₁₉	—	2	1	no	—
35	C₁₆×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₁₆×C₁₉	#41	1	1	yes	characteristic
37	C₄×D₃₂	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂³×C₁₉	—	8	2	no	—
39	D₄×C₁₉	—	4	4	no	—
40	D₄×C₁₉	—	8	2	no	—
41	C₂×C₄×C₁₉	—	8	2	no	—
42	C₂×C₄×C₁₉	—	16	4	no	—
43	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
44	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
46	C₈×C₁₉	—	2	1	no	—
47	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
48	C₈×C₁₉	#135	1	1	yes	characteristic
49	C₂×D₃₂	C₂×C₁₉	1	1	yes	characteristic
50	C₄×D₁₆	C₂×C₁₉	1	2	yes	complemented
51	#1423	C₂×C₁₉	1	1	yes	characteristic, complemented
52	#1415	C₂×C₁₉	1	2	yes	complemented
53	C₄×C₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
54	C₂²×C₁₉	—	8	4	no	—
55	C₂²×C₁₉	—	16	2	no	—
56	C₂²×C₁₉	—	16	2	no	—
57	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
58	C₄×C₁₉	—	2	1	no	—
59	C₄×C₁₉	—	16	2	no	—
60	C₄×C₁₉	D₃₂	1	2	yes	direct product factor
61	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
62	C₄×C₁₉	#508	1	1	yes	characteristic
63	C₂×D₁₆	C₂²×C₁₉	1	2	yes	—
64	C₄×D₈	—	2	2	no	—
65	D₃₂	C₄×C₁₉	1	4	yes	direct product factor
66	C₂×C₃₂	C₂²×C₁₉	1	1	yes	characteristic
67	C₂×C₃₂	C₂²×C₁₉	1	1	yes	characteristic
68	#366	C₂²×C₁₉	1	2	yes	—
69	#357	—	2	2	no	—
70	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
71	C₂×C₁₉	—	16	4	no	—
72	C₂×C₁₉	C₄×D₁₆	1	1	yes	characteristic
73	C₂×C₁₉	C₂×D₃₂	1	1	yes	characteristic
74	C₂×C₁₉	#2262	1	1	yes	characteristic
75	C₂×D₈	—	2	2	no	—
76	C₄×D₄	—	4	2	no	—
77	D₁₆	—	2	2	no	—
78	D₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
79	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
80	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
81	#107	—	2	2	no	—
82	#102	—	4	2	no	—
83	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
84	C₃₂	—	2	1	no	—
85	C₃₂	C₂×C₄×C₁₉	1	2	yes	complemented
86	C₁₉	C₄×D₃₂	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×D₄	—	4	2	no	—
88	C₂²×C₄	—	8	2	no	—
89	D₈	—	2	4	no	—
90	D₈	—	4	2	no	—
91	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
92	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
93	C₄⋊C₄	—	4	2	no	—
94	C₂²⋊C₄	—	8	2	no	—
95	C₄²	D₈×C₁₉	1	1	yes	characteristic
96	C₁₆	—	2	1	no	—
97	C₁₆	C₂²×C₄×C₁₉	1	1	yes	characteristic
98	C₁₆	#41×C₁₉	1	1	yes	characteristic
99	C₂³	—	8	2	no	—
100	D₄	—	4	4	no	—
101	D₄	—	8	2	no	—
102	C₂×C₄	—	8	2	no	—
103	C₂×C₄	—	16	4	no	—
104	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
105	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
106	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
107	C₈	—	2	1	no	—
108	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
109	C₈	C₁₉×#135	1	1	yes	characteristic
110	C₂²	—	8	4	no	—
111	C₂²	—	16	2	no	—
112	C₂²	—	16	2	no	—
113	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	16	2	no	—
116	C₄	C₁₉×D₃₂	1	2	yes	direct product factor
117	C₄	C₄×D₈×C₁₉	1	1	yes	characteristic
118	C₄	C₁₉×#508	1	1	yes	characteristic
119	C₂	—	16	4	no	—
120	C₂	C₄×C₁₉×D₁₆	1	1	yes	characteristic
121	C₂	C₂×C₁₉×D₃₂	1	1	yes	characteristic
122	C₂	C₁₉×#2262	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×D₃₂

C₂

yes

maximal, characteristic

C₄×C₁₉×D₁₆

C₂

yes

maximal, complemented

C₁₉×#1423

C₂

yes

maximal, characteristic, complemented

C₁₉×#1415

C₂

yes

maximal, complemented

C₄×C₁₉×C₃₂

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₂²

yes

—

C₄×D₈×C₁₉

—

C₁₉×D₃₂

C₄

yes

direct product factor

C₂×C₁₉×C₃₂

C₂²

yes

characteristic

C₂×C₁₉×C₃₂

C₂²

yes

characteristic

C₁₉×#366

C₂²

yes

—

C₁₉×#357

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×D₁₆

—

C₁₉×D₁₆

C₂×C₄

yes

complemented

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#102

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₁₉×C₃₂

C₂×C₄

yes

complemented

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂²×C₄

yes

characteristic

C₁₆×C₁₉

#41

yes

characteristic

C₄×D₃₂

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₄×D₄

yes

characteristic

C₈×C₁₉

#135

yes

characteristic

C₂×D₃₂

C₂×C₁₉

yes

characteristic

C₄×D₁₆

C₂×C₁₉

yes

complemented

#1423

C₂×C₁₉

yes

characteristic, complemented

#1415

C₂×C₁₉

yes

complemented

C₄×C₃₂

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₃₂

yes

direct product factor

C₄×C₁₉

C₄×D₈

yes

characteristic

C₄×C₁₉

#508

yes

characteristic

C₂×D₁₆

C₂²×C₁₉

yes

—

C₄×D₈

—

D₃₂

C₄×C₁₉

yes

direct product factor

C₂×C₃₂

C₂²×C₁₉

yes

characteristic

C₂×C₃₂

C₂²×C₁₉

yes

characteristic

#366

C₂²×C₁₉

yes

—

#357

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

C₄×D₁₆

yes

characteristic

C₂×C₁₉

C₂×D₃₂

yes

characteristic

C₂×C₁₉

#2262

yes

characteristic

C₂×D₈

—

C₄×D₄

—

D₁₆

—

D₁₆

C₂×C₄×C₁₉

yes

complemented

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

#107

—

#102

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₃₂

C₂×C₄×C₁₉

yes

complemented

C₁₉

C₄×D₃₂

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

—

C₂×C₈

D₈×C₁₉

yes

characteristic

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₈×C₁₉

yes

characteristic

C₁₆

—

C₁₆

C₂²×C₄×C₁₉

yes

characteristic

C₁₆

#41×C₁₉

yes

characteristic

C₂³

—

100

D₄

—

101

D₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₁₉×D₁₆

yes

characteristic

105

C₂×C₄

C₁₉×D₁₆

yes

characteristic

106

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

107

C₈

—

108

C₈

C₄×D₄×C₁₉

yes

characteristic

109

C₈

C₁₉×#135

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

C₁₉×D₃₂

yes

direct product factor

117

C₄

C₄×D₈×C₁₉

yes

characteristic

118

C₄

C₁₉×#508

yes

characteristic

119

C₂

—

120

C₂

C₄×C₁₉×D₁₆

yes

characteristic

121

C₂

C₂×C₁₉×D₃₂

yes

characteristic

122

C₂

C₁₉×#2262

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	D₁₆
commutator	C₁₆	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×D₁₆
prime radical	C₂×C₁₉×D₃₂	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

D₁₆

commutator

C₁₆

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

socle

C₂²×C₁₉

C₂×D₁₆

prime radical

C₂×C₁₉×D₃₂

C₂

LCS

G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₄×C₁₉×D₁₆	C₂	semidirect
3. C₁₉×#1423	C₂	semidirect
4. C₁₉×#1415	C₂	semidirect
5. C₄×C₁₉×C₃₂	C₂	semidirect
8. C₁₉×D₃₂	C₄	direct (N × H)
17. C₁₉×D₁₆	C₂×C₄	semidirect
24. C₁₉×C₃₂	C₂×C₄	semidirect
37. C₄×D₃₂	C₁₉	direct (N × H)
50. C₄×D₁₆	C₂×C₁₉	semidirect
51. #1423	C₂×C₁₉	semidirect
52. #1415	C₂×C₁₉	semidirect
53. C₄×C₃₂	C₂×C₁₉	semidirect
60. C₄×C₁₉	D₃₂	direct (N × H)
65. D₃₂	C₄×C₁₉	direct (N × H)
78. D₁₆	C₂×C₄×C₁₉	semidirect
85. C₃₂	C₂×C₄×C₁₉	semidirect
86. C₁₉	C₄×D₃₂	direct (N × H)
116. C₄	C₁₉×D₃₂	direct (N × H)

H ≅ G/N

type

2. C₄×C₁₉×D₁₆

C₂

semidirect

3. C₁₉×#1423

C₂

semidirect

4. C₁₉×#1415

C₂

semidirect

5. C₄×C₁₉×C₃₂

C₂

semidirect

8. C₁₉×D₃₂

C₄

direct (N × H)

17. C₁₉×D₁₆

C₂×C₄

semidirect

24. C₁₉×C₃₂

C₂×C₄

semidirect

37. C₄×D₃₂

C₁₉

direct (N × H)

50. C₄×D₁₆

C₂×C₁₉

semidirect

51. #1423

C₂×C₁₉

semidirect

52. #1415

C₂×C₁₉

semidirect

53. C₄×C₃₂

C₂×C₁₉

semidirect

60. C₄×C₁₉

D₃₂

direct (N × H)

65. D₃₂

C₄×C₁₉

direct (N × H)

78. D₁₆

C₂×C₄×C₁₉

semidirect

85. C₃₂

C₂×C₄×C₁₉

semidirect

86. C₁₉

C₄×D₃₂

direct (N × H)

116. C₄

C₁₉×D₃₂

direct (N × H)

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

subgroup	index
C₂×C₁₉×D₃₂	2
C₄×C₁₉×D₁₆	2
C₁₉×#1423	2
C₁₉×#1415	2
C₄×C₁₉×C₃₂	2
C₄×D₃₂	19

subgroup

index

C₂×C₁₉×D₃₂

C₄×C₁₉×D₁₆

C₁₉×#1423

C₁₉×#1415

C₄×C₁₉×C₃₂

C₄×D₃₂

Subgroups — C₄×C₁₉×D₃₂ #18019608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×C19×D32 #18019608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×D₃₂ #18019608