Group #20302055 — subgroups

Subgroups — C₂₉×#7155 #20302055

Order 7424.

222 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 134 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×C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1564	C₂	1	2	yes	maximal
3	C₂²×C₁₆×C₂₉	C₄	1	2	yes	—
4	C₂₉×#431	—	2	2	no	—
5	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₂₉	—	2	2	no	—
7	C₂₉×#335	C₄	1	4	yes	—
8	C₂₉×#334	—	2	2	no	—
9	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₂₉	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
12	C₂×C₁₆×C₂₉	—	2	2	no	—
13	C₂×C₁₆×C₂₉	—	2	2	no	—
14	C₂×C₁₆×C₂₉	C₈	1	4	yes	complemented
15	C₂₉×C₄⋊C₈	—	2	4	no	—
16	C₂₉×C₂²⋊C₈	—	4	2	no	—
17	C₄×C₈×C₂₉	—	4	2	no	—
18	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₂₉	D₄	1	2	yes	—
20	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	SD₁₆	1	2	yes	—
22	C₂×C₈×C₂₉	—	2	2	no	—
23	C₂×C₈×C₂₉	—	4	4	no	—
24	C₂×C₈×C₂₉	C₄²	1	1	yes	characteristic
25	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₈×C₂₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₂₉	C₂×C₈	1	2	yes	—
28	C₂×C₈×C₂₉	M₁₆	1	2	yes	—
29	C₄²×C₂₉	C₂²⋊C₄	1	2	yes	—
30	C₄²×C₂₉	D₈	1	1	yes	characteristic
31	C₄²×C₂₉	Q₁₆	1	1	yes	characteristic
32	C₁₆×C₂₉	—	2	4	no	—
33	#7155	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₂₉	#106	1	1	yes	characteristic
35	C₂×C₄×C₂₉	—	2	4	no	—
36	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
37	C₂×C₄×C₂₉	#102	1	2	yes	—
38	C₂×C₄×C₂₉	#103	1	2	yes	—
39	C₂×C₄×C₂₉	C₄⋊C₈	1	2	yes	—
40	C₂×C₄×C₂₉	#107	1	1	yes	characteristic
41	C₂×C₄×C₂₉	#108	1	2	yes	—
42	C₈×C₂₉	—	2	2	no	—
43	C₈×C₂₉	—	8	4	no	—
44	C₈×C₂₉	C₄×C₈	1	1	yes	characteristic
45	C₈×C₂₉	#97	1	1	yes	characteristic
46	C₈×C₂₉	C₂²⋊C₈	1	2	yes	—
47	C₂×C₄×C₁₆	C₂×C₂₉	1	1	yes	characteristic
48	#1564	C₂×C₂₉	1	2	yes	—
49	C₂²×C₂₉	—	2	2	no	—
50	C₂²×C₂₉	#334	1	2	yes	—
51	C₂²×C₂₉	#340	1	1	yes	characteristic
52	C₄×C₂₉	—	2	2	no	—
53	C₄×C₂₉	#335	1	2	yes	—
54	C₄×C₂₉	#336	1	1	yes	characteristic
55	C₄×C₂₉	#341	1	1	yes	characteristic
56	C₄×C₂₉	#359	1	4	yes	—
57	C₂²×C₁₆	C₄×C₂₉	1	2	yes	—
58	#431	—	2	2	no	—
59	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
60	C₄×C₁₆	—	2	2	no	—
61	#335	C₄×C₂₉	1	4	yes	—
62	#334	—	2	2	no	—
63	C₂×C₂₉	—	2	2	no	—
64	C₂×C₂₉	#1277	1	1	yes	characteristic
65	C₂×C₂₉	#1382	1	2	yes	—
66	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
67	C₂²×C₈	Q₈×C₂₉	1	1	yes	characteristic
68	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
69	C₂×C₁₆	—	2	2	no	—
70	C₂×C₁₆	—	2	2	no	—
71	C₂×C₁₆	C₈×C₂₉	1	4	yes	complemented
72	C₄⋊C₈	—	2	4	no	—
73	C₂²⋊C₈	—	4	2	no	—
74	C₄×C₈	—	4	2	no	—
75	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
76	C₄×C₈	D₄×C₂₉	1	2	yes	—
77	C₂₉	#7155	1	1	yes	characteristic, direct product factor, Sylow
78	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
79	C₂²×C₄	SD₁₆×C₂₉	1	2	yes	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	4	4	no	—
82	C₂×C₈	C₄²×C₂₉	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
84	C₂×C₈	C₄⋊C₄×C₂₉	1	2	yes	—
85	C₂×C₈	C₂×C₈×C₂₉	1	2	yes	—
86	C₂×C₈	M₁₆×C₂₉	1	2	yes	—
87	C₄²	C₂²⋊C₄×C₂₉	1	2	yes	—
88	C₄²	D₈×C₂₉	1	1	yes	characteristic
89	C₄²	Q₁₆×C₂₉	1	1	yes	characteristic
90	C₁₆	—	2	4	no	—
91	C₂³	C₂₉×#106	1	1	yes	characteristic
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
94	C₂×C₄	C₂₉×#102	1	2	yes	—
95	C₂×C₄	C₂₉×#103	1	2	yes	—
96	C₂×C₄	C₂₉×C₄⋊C₈	1	2	yes	—
97	C₂×C₄	C₂₉×#107	1	1	yes	characteristic
98	C₂×C₄	C₂₉×#108	1	2	yes	—
99	C₈	—	2	2	no	—
100	C₈	—	8	4	no	—
101	C₈	C₄×C₈×C₂₉	1	1	yes	characteristic
102	C₈	C₂₉×#97	1	1	yes	characteristic
103	C₈	C₂₉×C₂²⋊C₈	1	2	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	C₂₉×#334	1	2	yes	—
106	C₂²	C₂₉×#340	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	C₂₉×#335	1	2	yes	—
109	C₄	C₂₉×#336	1	1	yes	characteristic
110	C₄	C₂₉×#341	1	1	yes	characteristic
111	C₄	C₂₉×#359	1	4	yes	—
112	C₂	—	2	2	no	—
113	C₂	C₂₉×#1277	1	1	yes	characteristic
114	C₂	C₂₉×#1382	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₁₆×C₂₉

C₂

yes

maximal, characteristic

C₂₉×#1564

C₂

yes

maximal

C₂²×C₁₆×C₂₉

C₄

yes

—

C₂₉×#431

—

C₂×C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₁₆×C₂₉

—

C₂₉×#335

C₄

yes

—

C₂₉×#334

—

C₂²×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₂₉

Q₈

yes

characteristic

C₂×C₄²×C₂₉

D₄

yes

characteristic

C₂×C₁₆×C₂₉

—

C₂×C₁₆×C₂₉

—

C₂×C₁₆×C₂₉

C₈

yes

complemented

C₂₉×C₄⋊C₈

—

C₂₉×C₂²⋊C₈

—

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

C₂×C₄

yes

—

C₄×C₈×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₂₉

SD₁₆

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₄²

yes

characteristic

C₂×C₈×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₂₉

C₄⋊C₄

yes

—

C₂×C₈×C₂₉

C₂×C₈

yes

—

C₂×C₈×C₂₉

M₁₆

yes

—

C₄²×C₂₉

C₂²⋊C₄

yes

—

C₄²×C₂₉

D₈

yes

characteristic

C₄²×C₂₉

Q₁₆

yes

characteristic

C₁₆×C₂₉

—

#7155

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

#106

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

#95

yes

characteristic

C₂×C₄×C₂₉

#102

yes

—

C₂×C₄×C₂₉

#103

yes

—

C₂×C₄×C₂₉

C₄⋊C₈

yes

—

C₂×C₄×C₂₉

#107

yes

characteristic

C₂×C₄×C₂₉

#108

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

C₄×C₈

yes

characteristic

C₈×C₂₉

#97

yes

characteristic

C₈×C₂₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₆

C₂×C₂₉

yes

characteristic

#1564

C₂×C₂₉

yes

—

C₂²×C₂₉

—

C₂²×C₂₉

#334

yes

—

C₂²×C₂₉

#340

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

#335

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

C₂²×C₁₆

C₄×C₂₉

yes

—

#431

—

C₂×C₄×C₈

C₂²×C₂₉

yes

characteristic

C₄×C₁₆

—

#335

C₄×C₂₉

yes

—

#334

—

C₂×C₂₉

—

C₂×C₂₉

#1277

yes

characteristic

C₂×C₂₉

#1382

yes

—

C₂²×C₈

C₂×C₄×C₂₉

yes

characteristic

C₂²×C₈

Q₈×C₂₉

yes

characteristic

C₂×C₄²

D₄×C₂₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₈×C₂₉

yes

complemented

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

C₂×C₄×C₂₉

yes

—

C₄×C₈

D₄×C₂₉

yes

—

C₂₉

#7155

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₄⋊C₄×C₂₉

yes

characteristic

C₂²×C₄

SD₁₆×C₂₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₂₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₂₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₂₉

yes

—

C₂×C₈

C₂×C₈×C₂₉

yes

—

C₂×C₈

M₁₆×C₂₉

yes

—

C₄²

C₂²⋊C₄×C₂₉

yes

—

C₄²

D₈×C₂₉

yes

characteristic

C₄²

Q₁₆×C₂₉

yes

characteristic

C₁₆

—

C₂³

C₂₉×#106

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂₉×#95

yes

characteristic

C₂×C₄

C₂₉×#102

yes

—

C₂×C₄

C₂₉×#103

yes

—

C₂×C₄

C₂₉×C₄⋊C₈

yes

—

C₂×C₄

C₂₉×#107

yes

characteristic

C₂×C₄

C₂₉×#108

yes

—

C₈

—

100

C₈

—

101

C₈

C₄×C₈×C₂₉

yes

characteristic

102

C₈

C₂₉×#97

yes

characteristic

103

C₈

C₂₉×C₂²⋊C₈

yes

—

104

C₂²

—

105

C₂²

C₂₉×#334

yes

—

106

C₂²

C₂₉×#340

yes

characteristic

107

C₄

—

108

C₄

C₂₉×#335

yes

—

109

C₄

C₂₉×#336

yes

characteristic

110

C₄

C₂₉×#341

yes

characteristic

111

C₄

C₂₉×#359

yes

—

112

C₂

—

113

C₂

C₂₉×#1277

yes

characteristic

114

C₂

C₂₉×#1382

yes

—

	subgroup	G/H
center	C₄²×C₂₉	D₈
commutator	C₈	C₄×C₈×C₂₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₂₉
socle	C₂²×C₂₉	#340
prime radical	C₂³×C₂₉	#106
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

subgroup

G/H

center

C₄²×C₂₉

D₈

commutator

C₈

C₄×C₈×C₂₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₂₉

C₂²×C₂₉

C₂³×C₂₉

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

N	H ≅ G/N	type
14. C₂×C₁₆×C₂₉	C₈	semidirect
33. #7155	C₂₉	direct (N × H)
71. C₂×C₁₆	C₈×C₂₉	semidirect
77. C₂₉	#7155	direct (N × H)

H ≅ G/N

type

14. C₂×C₁₆×C₂₉

C₈

semidirect

33. #7155

C₂₉

direct (N × H)

71. C₂×C₁₆

C₈×C₂₉

semidirect

77. C₂₉

#7155

direct (N × H)

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

subgroup	index
C₂×C₄×C₁₆×C₂₉	2
C₂₉×#1564	2
#7155	29

subgroup

index

C₂×C₄×C₁₆×C₂₉

C₂₉×#1564

#7155

Subgroups — C₂₉×#7155 #20302055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#7155 #20302055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7155 #20302055