Group #16815370 — subgroups

Subgroups — C₂₉×#1656 #16815370

Order 3712.

230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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	C₂₉×#562	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#496	C₂	1	2	yes	maximal, complemented
3	C₂₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#329	C₂	1	2	yes	maximal, complemented
6	C₂×SD₁₆×C₂₉	—	2	2	no	—
7	C₂×D₈×C₂₉	—	2	2	no	—
8	C₂₉×#127	C₂²	1	1	yes	characteristic
9	C₂₉×#125	C₂²	1	1	yes	characteristic
10	C₂₉×#124	C₂²	1	2	yes	—
11	C₂₉×#123	—	2	2	no	—
12	C₂₉×C₂²⋊Q₈	—	2	2	no	—
13	C₂₉×#121	—	2	2	no	—
14	C₂₉×#102	—	2	2	no	—
15	C₂₉×#97	C₂²	1	1	yes	characteristic
16	C₂₉×#97	C₂²	1	2	yes	—
17	C₂×Q₈×C₂₉	D₄	1	2	yes	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	—	2	2	no	—
20	C₂×D₄×C₂₉	—	2	1	no	—
21	C₂×D₄×C₂₉	D₄	1	2	yes	—
22	C₂²×C₄×C₂₉	—	2	2	no	—
23	SD₁₆×C₂₉	—	4	4	no	—
24	D₈×C₂₉	—	4	4	no	—
25	C₂×C₈×C₂₉	—	2	2	no	—
26	C₂×C₈×C₂₉	—	2	1	no	—
27	C₄⋊C₄×C₂₉	—	2	2	no	—
28	C₄⋊C₄×C₂₉	—	2	2	no	—
29	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
30	C₂²⋊C₄×C₂₉	—	2	2	no	—
31	C₂²⋊C₄×C₂₉	—	2	2	no	—
32	C₂²⋊C₄×C₂₉	—	2	2	no	—
33	C₄²×C₂₉	C₂³	1	1	yes	characteristic
34	C₂³×C₂₉	—	2	2	no	—
35	C₂³×C₂₉	—	4	1	no	—
36	Q₈×C₂₉	—	4	2	no	—
37	D₄×C₂₉	—	4	2	no	—
38	D₄×C₂₉	—	4	2	no	—
39	D₄×C₂₉	—	4	2	no	—
40	D₄×C₂₉	—	4	2	no	—
41	D₄×C₂₉	—	8	2	no	—
42	C₂×C₄×C₂₉	—	2	2	no	—
43	C₂×C₄×C₂₉	—	2	2	no	—
44	C₂×C₄×C₂₉	—	8	2	no	—
45	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
47	C₈×C₂₉	—	2	4	no	—
48	C₈×C₂₉	—	4	1	no	—
49	#1656	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₂₉	—	4	2	no	—
51	C₂²×C₂₉	—	4	2	no	—
52	C₂²×C₂₉	—	4	2	no	—
53	C₂²×C₂₉	—	8	2	no	—
54	C₂²×C₂₉	—	8	1	no	—
55	C₂²×C₂₉	#120	1	1	yes	characteristic
56	C₄×C₂₉	—	2	2	no	—
57	C₄×C₂₉	—	2	1	no	—
58	C₄×C₂₉	—	4	2	no	—
59	C₄×C₂₉	—	4	2	no	—
60	#562	C₂×C₂₉	1	1	yes	characteristic, complemented
61	#496	C₂×C₂₉	1	2	yes	complemented
62	#490	C₂×C₂₉	1	1	yes	characteristic, complemented
63	#330	C₂×C₂₉	1	1	yes	characteristic, complemented
64	#329	C₂×C₂₉	1	2	yes	complemented
65	C₂×C₂₉	—	8	2	no	—
66	C₂×C₂₉	—	16	1	no	—
67	C₂×C₂₉	#453	1	2	yes	—
68	C₂×C₂₉	#454	1	1	yes	characteristic
69	C₂×SD₁₆	—	2	2	no	—
70	C₂×D₈	—	2	2	no	—
71	#127	C₂²×C₂₉	1	1	yes	characteristic
72	#125	C₂²×C₂₉	1	1	yes	characteristic
73	#124	C₂²×C₂₉	1	2	yes	—
74	#123	—	2	2	no	—
75	C₂²⋊Q₈	—	2	2	no	—
76	#121	—	2	2	no	—
77	#102	—	2	2	no	—
78	#97	C₂²×C₂₉	1	1	yes	characteristic
79	#97	C₂²×C₂₉	1	2	yes	—
80	C₂₉	#1656	1	1	yes	characteristic, direct product factor, Sylow
81	C₂×Q₈	D₄×C₂₉	1	2	yes	—
82	C₂×D₄	—	2	2	no	—
83	C₂×D₄	—	2	1	no	—
84	C₂×D₄	—	2	2	no	—
85	C₂×D₄	D₄×C₂₉	1	2	yes	—
86	C₂²×C₄	—	2	2	no	—
87	SD₁₆	—	4	4	no	—
88	D₈	—	4	4	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	1	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	2	2	no	—
93	C₄⋊C₄	D₄×C₂₉	1	2	yes	—
94	C₂²⋊C₄	—	2	2	no	—
95	C₂²⋊C₄	—	2	2	no	—
96	C₂²⋊C₄	—	2	2	no	—
97	C₄²	C₂³×C₂₉	1	1	yes	characteristic
98	C₂³	—	2	2	no	—
99	C₂³	—	4	1	no	—
100	Q₈	—	4	2	no	—
101	D₄	—	4	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	8	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	8	2	no	—
109	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
110	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
111	C₈	—	2	4	no	—
112	C₈	—	4	1	no	—
113	C₂²	—	4	2	no	—
114	C₂²	—	4	2	no	—
115	C₂²	—	4	2	no	—
116	C₂²	—	8	2	no	—
117	C₂²	—	8	1	no	—
118	C₂²	C₂₉×#120	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	—	2	1	no	—
121	C₄	—	4	2	no	—
122	C₄	—	4	2	no	—
123	C₂	—	8	2	no	—
124	C₂	—	16	1	no	—
125	C₂	C₂₉×#453	1	2	yes	—
126	C₂	C₂₉×#454	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#562

C₂

yes

maximal, characteristic, complemented

C₂₉×#496

C₂

yes

maximal, complemented

C₂₉×#490

C₂

yes

maximal, characteristic, complemented

C₂₉×#330

C₂

yes

maximal, characteristic, complemented

C₂₉×#329

C₂

yes

maximal, complemented

C₂×SD₁₆×C₂₉

—

C₂×D₈×C₂₉

—

C₂₉×#127

C₂²

yes

characteristic

C₂₉×#125

C₂²

yes

characteristic

C₂₉×#124

C₂²

yes

—

C₂₉×#123

—

C₂₉×C₂²⋊Q₈

—

C₂₉×#121

—

C₂₉×#102

—

C₂₉×#97

C₂²

yes

characteristic

C₂₉×#97

C₂²

yes

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

—

SD₁₆×C₂₉

—

D₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₂²⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

C₂³×C₂₉

—

C₂³×C₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

#1656

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#120

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

#562

C₂×C₂₉

yes

characteristic, complemented

#496

C₂×C₂₉

yes

complemented

#490

C₂×C₂₉

yes

characteristic, complemented

#330

C₂×C₂₉

yes

characteristic, complemented

#329

C₂×C₂₉

yes

complemented

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#453

yes

—

C₂×C₂₉

#454

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

#127

C₂²×C₂₉

yes

characteristic

#125

C₂²×C₂₉

yes

characteristic

#124

C₂²×C₂₉

yes

—

#123

—

C₂²⋊Q₈

—

#121

—

#102

—

#97

C₂²×C₂₉

yes

characteristic

#97

C₂²×C₂₉

yes

—

C₂₉

#1656

yes

characteristic, direct product factor, Sylow

C₂×Q₈

D₄×C₂₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

D₄×C₂₉

yes

—

C₂²×C₄

—

SD₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₂₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂³×C₂₉

yes

characteristic

C₂³

—

C₂³

—

100

Q₈

—

101

D₄

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂×D₄×C₂₉

yes

characteristic

110

C₂×C₄

C₂×D₄×C₂₉

yes

—

111

C₈

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

C₂₉×#120

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₂

—

124

C₂

—

125

C₂

C₂₉×#453

yes

—

126

C₂

C₂₉×#454

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₉

#120

commutator, Frattini, cosocle

C₄²

C₂³×C₂₉

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
1. C₂₉×#562	C₂	semidirect
2. C₂₉×#496	C₂	semidirect
3. C₂₉×#490	C₂	semidirect
4. C₂₉×#330	C₂	semidirect
5. C₂₉×#329	C₂	semidirect
49. #1656	C₂₉	direct (N × H)
60. #562	C₂×C₂₉	semidirect
61. #496	C₂×C₂₉	semidirect
62. #490	C₂×C₂₉	semidirect
63. #330	C₂×C₂₉	semidirect
64. #329	C₂×C₂₉	semidirect
80. C₂₉	#1656	direct (N × H)

H ≅ G/N

type

1. C₂₉×#562

C₂

semidirect

2. C₂₉×#496

C₂

semidirect

3. C₂₉×#490

C₂

semidirect

4. C₂₉×#330

C₂

semidirect

5. C₂₉×#329

C₂

semidirect

49. #1656

C₂₉

direct (N × H)

60. #562

C₂×C₂₉

semidirect

61. #496

C₂×C₂₉

semidirect

62. #490

C₂×C₂₉

semidirect

63. #330

C₂×C₂₉

semidirect

64. #329

C₂×C₂₉

semidirect

80. C₂₉

#1656

direct (N × H)

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

subgroup	index
C₂₉×#562	2
C₂₉×#496	2
C₂₉×#490	2
C₂₉×#330	2
C₂₉×#329	2
#1656	29

subgroup

index

C₂₉×#562

C₂₉×#496

C₂₉×#490

C₂₉×#330

C₂₉×#329

#1656

Subgroups — C₂₉×#1656 #16815370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#1656 #16815370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1656 #16815370