Group #15696697 — subgroups

Subgroups — C₁₃×#10358 #15696697

Order 3328.

484 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 106 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	C₁₃×#2844	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#1961	C₂	1	3	yes	maximal
3	C₁₃×#1295	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×#102	—	2	3	no	—
6	C₂×C₁₃×#102	—	2	3	no	—
7	C₂×C₁₃×#97	C₂²	1	3	yes	—
8	C₁₃×#400	—	2	3	no	—
9	C₁₃×#395	—	2	3	no	—
10	C₁₃×#382	C₂²	1	3	yes	—
11	C₂²×Q₈×C₁₃	—	2	1	no	—
12	C₂²×D₄×C₁₃	—	2	3	no	—
13	C₂²×C₈×C₁₃	—	2	3	no	—
14	C₁₃×#127	—	2	3	no	—
15	C₁₃×#127	Q₈	1	2	yes	complemented
16	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
17	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
18	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
19	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
20	C₁₃×#102	—	4	6	no	—
21	C₁₃×#102	—	4	6	no	—
22	C₁₃×#97	—	2	6	no	—
23	C₁₃×#95	—	2	3	no	—
24	C₁₃×#95	—	2	1	no	—
25	C₁₃×#95	—	2	6	no	—
26	#10358	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂⁴×C₁₃	—	4	1	no	—
28	C₂×Q₈×C₁₃	—	8	3	no	—
29	C₂×D₄×C₁₃	—	2	6	no	—
30	C₂×D₄×C₁₃	—	4	3	no	—
31	C₂×D₄×C₁₃	—	4	3	no	—
32	C₂×D₄×C₁₃	—	4	3	no	—
33	C₂×D₄×C₁₃	—	4	3	no	—
34	C₂×D₄×C₁₃	—	4	3	no	—
35	C₂²×C₄×C₁₃	—	2	3	no	—
36	C₂²×C₄×C₁₃	—	2	3	no	—
37	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
38	C₂×C₈×C₁₃	—	2	6	no	—
39	C₂×C₈×C₁₃	—	4	3	no	—
40	C₂×C₈×C₁₃	—	4	3	no	—
41	C₁₃×C₄⋊C₄	—	4	3	no	—
42	C₁₃×C₄⋊C₄	—	4	3	no	—
43	C₁₃×C₄⋊C₄	—	8	3	no	—
44	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
45	C₄²×C₁₃	#41	1	3	yes	—
46	#2844	C₂×C₁₃	1	1	yes	characteristic, complemented
47	#1961	C₂×C₁₃	1	3	yes	—
48	#1295	C₂×C₁₃	1	3	yes	complemented
49	C₂³×C₁₃	—	4	2	no	—
50	C₂³×C₁₃	—	8	3	no	—
51	C₂³×C₁₃	—	8	3	no	—
52	C₂³×C₁₃	#120	1	1	yes	characteristic
53	Q₈×C₁₃	—	8	4	no	—
54	D₄×C₁₃	—	4	6	no	—
55	D₄×C₁₃	—	4	6	no	—
56	D₄×C₁₃	—	8	3	no	—
57	D₄×C₁₃	—	8	3	no	—
58	C₂×C₄×C₁₃	—	2	3	no	—
59	C₂×C₄×C₁₃	—	2	3	no	—
60	C₂×C₄×C₁₃	—	4	3	no	—
61	C₂×C₄×C₁₃	—	4	3	no	—
62	C₂×C₄×C₁₃	—	4	6	no	—
63	C₂×C₄×C₁₃	—	4	6	no	—
64	C₂×C₄×C₁₃	C₂²⋊Q₈	1	3	yes	—
65	C₂×C₄×C₁₃	#124	1	3	yes	—
66	C₈×C₁₃	—	4	6	no	—
67	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
68	C₂×#102	—	2	3	no	—
69	C₂×#102	—	2	3	no	—
70	C₂×#97	C₂²×C₁₃	1	3	yes	—
71	#400	—	2	3	no	—
72	#395	—	2	3	no	—
73	#382	C₂²×C₁₃	1	3	yes	—
74	C₂²×C₁₃	—	8	6	no	—
75	C₂²×C₁₃	—	16	1	no	—
76	C₂²×C₁₃	—	16	3	no	—
77	C₂²×C₁₃	#393	1	1	yes	characteristic
78	C₂²×C₁₃	#453	1	3	yes	—
79	C₂²×C₁₃	#454	1	3	yes	—
80	C₄×C₁₃	—	2	3	no	—
81	C₄×C₁₃	—	2	3	no	—
82	C₄×C₁₃	—	8	3	no	—
83	C₄×C₁₃	—	8	3	no	—
84	C₂²×Q₈	—	2	1	no	—
85	C₂²×D₄	—	2	3	no	—
86	C₂²×C₈	—	2	3	no	—
87	#127	—	2	3	no	—
88	#127	Q₈×C₁₃	1	2	yes	complemented
89	C₂×C₄⋊C₄	—	2	3	no	—
90	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
91	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
92	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
93	#102	—	4	6	no	—
94	#102	—	4	6	no	—
95	#97	—	2	6	no	—
96	#95	—	2	3	no	—
97	#95	—	2	1	no	—
98	#95	—	2	6	no	—
99	C₂×C₁₃	—	16	2	no	—
100	C₂×C₁₃	#1655	1	1	yes	characteristic
101	C₂×C₁₃	#1657	1	3	yes	—
102	C₂×C₁₃	#2027	1	3	yes	—
103	C₂⁴	—	4	1	no	—
104	C₂×Q₈	—	8	3	no	—
105	C₂×D₄	—	2	6	no	—
106	C₂×D₄	—	4	3	no	—
107	C₂×D₄	—	4	3	no	—
108	C₂×D₄	—	4	3	no	—
109	C₂×D₄	—	4	3	no	—
110	C₂×D₄	—	4	3	no	—
111	C₂²×C₄	—	2	3	no	—
112	C₂²×C₄	—	2	3	no	—
113	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
114	C₂×C₈	—	2	6	no	—
115	C₂×C₈	—	4	3	no	—
116	C₂×C₈	—	4	3	no	—
117	C₄⋊C₄	—	4	3	no	—
118	C₄⋊C₄	—	4	3	no	—
119	C₄⋊C₄	—	8	3	no	—
120	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
121	C₄²	C₁₃×#41	1	3	yes	—
122	C₁₃	#10358	1	1	yes	characteristic, direct product factor, Sylow
123	C₂³	—	4	2	no	—
124	C₂³	—	8	3	no	—
125	C₂³	—	8	3	no	—
126	C₂³	C₁₃×#120	1	1	yes	characteristic
127	Q₈	—	8	4	no	—
128	D₄	—	4	6	no	—
129	D₄	—	4	6	no	—
130	D₄	—	8	3	no	—
131	D₄	—	8	3	no	—
132	C₂×C₄	—	2	3	no	—
133	C₂×C₄	—	2	3	no	—
134	C₂×C₄	—	4	3	no	—
135	C₂×C₄	—	4	3	no	—
136	C₂×C₄	—	4	6	no	—
137	C₂×C₄	—	4	6	no	—
138	C₂×C₄	C₁₃×C₂²⋊Q₈	1	3	yes	—
139	C₂×C₄	C₁₃×#124	1	3	yes	—
140	C₈	—	4	6	no	—
141	C₂²	—	8	6	no	—
142	C₂²	—	16	1	no	—
143	C₂²	—	16	3	no	—
144	C₂²	C₁₃×#393	1	1	yes	characteristic
145	C₂²	C₁₃×#453	1	3	yes	—
146	C₂²	C₁₃×#454	1	3	yes	—
147	C₄	—	2	3	no	—
148	C₄	—	2	3	no	—
149	C₄	—	8	3	no	—
150	C₄	—	8	3	no	—
151	C₂	—	16	2	no	—
152	C₂	C₁₃×#1655	1	1	yes	characteristic
153	C₂	C₁₃×#1657	1	3	yes	—
154	C₂	C₁₃×#2027	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2844

C₂

yes

maximal, characteristic, complemented

C₁₃×#1961

C₂

yes

maximal

C₁₃×#1295

C₂

yes

maximal, complemented

C₂×C₁₃×#127

C₂²

yes

characteristic

C₂×C₁₃×#102

—

C₂×C₁₃×#102

—

C₂×C₁₃×#97

C₂²

yes

—

C₁₃×#400

—

C₁₃×#395

—

C₁₃×#382

C₂²

yes

—

C₂²×Q₈×C₁₃

—

C₂²×D₄×C₁₃

—

C₂²×C₈×C₁₃

—

C₁₃×#127

—

C₁₃×#127

Q₈

yes

complemented

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#102

—

C₁₃×#102

—

C₁₃×#97

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

#10358

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

#2844

C₂×C₁₃

yes

characteristic, complemented

#1961

C₂×C₁₃

yes

—

#1295

C₂×C₁₃

yes

complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#120

yes

characteristic

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#124

yes

—

C₈×C₁₃

—

C₂×#127

C₂²×C₁₃

yes

characteristic

C₂×#102

—

C₂×#102

—

C₂×#97

C₂²×C₁₃

yes

—

#400

—

#395

—

#382

C₂²×C₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#393

yes

characteristic

C₂²×C₁₃

#453

yes

—

C₂²×C₁₃

#454

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₂²×Q₈

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

Q₈×C₁₃

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

C₂×C₄²

C₂³×C₁₃

yes

—

—

—

—

—

—

C₂×C₁₃

—

100

C₂×C₁₃

#1655

yes

characteristic

101

C₂×C₁₃

#1657

yes

—

102

C₂×C₁₃

#2027

yes

—

103

C₂⁴

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×D₄×C₁₃

yes

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄²

C₂×Q₈×C₁₃

yes

characteristic

121

C₄²

C₁₃×#41

yes

—

122

C₁₃

#10358

yes

characteristic, direct product factor, Sylow

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

C₂³

C₁₃×#120

yes

characteristic

127

Q₈

—

128

D₄

—

129

D₄

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

139

C₂×C₄

C₁₃×#124

yes

—

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

C₁₃×#393

yes

characteristic

145

C₂²

C₁₃×#453

yes

—

146

C₂²

C₁₃×#454

yes

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₂

—

152

C₂

C₁₃×#1655

yes

characteristic

153

C₂

C₁₃×#1657

yes

—

154

C₂

C₁₃×#2027

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₂×C₁₃×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#2844	C₂	semidirect
3. C₁₃×#1295	C₂	semidirect
15. C₁₃×#127	Q₈	semidirect
26. #10358	C₁₃	direct (N × H)
46. #2844	C₂×C₁₃	semidirect
48. #1295	C₂×C₁₃	semidirect
88. #127	Q₈×C₁₃	semidirect
122. C₁₃	#10358	direct (N × H)

H ≅ G/N

type

1. C₁₃×#2844

C₂

semidirect

3. C₁₃×#1295

C₂

semidirect

15. C₁₃×#127

Q₈

semidirect

26. #10358

C₁₃

direct (N × H)

46. #2844

C₂×C₁₃

semidirect

48. #1295

C₂×C₁₃

semidirect

88. #127

Q₈×C₁₃

semidirect

122. C₁₃

#10358

direct (N × H)

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

subgroup	index
C₁₃×#2844	2
C₁₃×#1961	2
C₁₃×#1295	2
#10358	13

subgroup

index

C₁₃×#2844

C₁₃×#1961

C₁₃×#1295

#10358

Subgroups — C₁₃×#10358 #15696697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10358 #15696697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10358 #15696697