Group #15696547 — subgroups

Subgroups — C₁₃×#10208 #15696547

Order 3328.

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

normal subgroups only

This group has 508 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	C₁₃×#3214	C₂	1	3	yes	maximal, complemented
2	C₁₃×#1514	C₂	1	3	yes	maximal, complemented
3	C₁₃×#1308	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#532	C₂²	1	3	yes	—
5	C₁₃×#496	—	2	3	no	—
6	C₁₃×#489	—	2	3	no	—
7	C₁₃×#461	—	2	3	no	—
8	C₁₃×#459	—	2	3	no	—
9	C₁₃×#449	—	2	6	no	—
10	C₁₃×#432	C₂²	1	3	yes	—
11	C₁₃×#383	C₂²	1	1	yes	characteristic
12	C₁₃×#327	—	2	6	no	—
13	C₂×C₁₃×#41	—	2	3	no	—
14	C₂×C₁₃×SD₁₆	—	2	6	no	—
15	C₂×C₁₃×D₈	—	2	6	no	—
16	C₁₃×C₄⋊Q₈	D₄	1	3	yes	—
17	C₁₃×#127	D₄	1	3	yes	—
18	C₁₃×#124	—	2	3	no	—
19	C₁₃×#121	—	2	3	no	—
20	C₁₃×#121	—	2	3	no	—
21	C₄×D₄×C₁₃	—	2	3	no	—
22	C₄×D₄×C₁₃	—	2	3	no	—
23	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×C₄⋊C₈	—	2	3	no	—
25	C₁₃×#103	—	2	6	no	—
26	C₁₃×#102	—	2	6	no	—
27	C₁₃×C₂²⋊C₈	D₄	1	6	yes	—
28	C₁₃×#97	—	2	3	no	—
29	C₁₃×#95	—	2	3	no	—
30	#10208	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₁₃×#41	—	8	6	no	—
32	C₂×Q₈×C₁₃	—	2	3	no	—
33	C₂×D₄×C₁₃	—	2	3	no	—
34	C₂×D₄×C₁₃	—	2	3	no	—
35	C₂×D₄×C₁₃	—	2	3	no	—
36	C₂×D₄×C₁₃	—	4	3	no	—
37	C₂²×C₄×C₁₃	—	4	3	no	—
38	C₂²×C₄×C₁₃	—	4	1	no	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
40	C₁₃×SD₁₆	—	8	6	no	—
41	C₁₃×D₈	—	8	6	no	—
42	C₂×C₈×C₁₃	—	2	6	no	—
43	C₁₃×C₄⋊C₄	—	2	3	no	—
44	C₁₃×C₄⋊C₄	—	2	3	no	—
45	C₁₃×C₂²⋊C₄	—	4	3	no	—
46	C₁₃×C₂²⋊C₄	—	4	3	no	—
47	C₄²×C₁₃	C₂×D₄	1	3	yes	—
48	C₄²×C₁₃	#41	1	1	yes	characteristic
49	#3214	C₂×C₁₃	1	3	yes	complemented
50	#1514	C₂×C₁₃	1	3	yes	complemented
51	#1308	C₂×C₁₃	1	1	yes	characteristic, complemented
52	C₂³×C₁₃	—	4	3	no	—
53	C₂³×C₁₃	#127	1	1	yes	characteristic
54	Q₈×C₁₃	—	4	6	no	—
55	D₄×C₁₃	—	4	3	no	—
56	D₄×C₁₃	—	4	6	no	—
57	D₄×C₁₃	—	4	3	no	—
58	D₄×C₁₃	—	8	3	no	—
59	D₄×C₁₃	—	8	6	no	—
60	C₂×C₄×C₁₃	—	4	3	no	—
61	C₂×C₄×C₁₃	—	4	3	no	—
62	C₂×C₄×C₁₃	—	8	6	no	—
63	C₂×C₄×C₁₃	—	8	3	no	—
64	C₂×C₄×C₁₃	#120	1	3	yes	—
65	C₂×C₄×C₁₃	#121	1	3	yes	—
66	C₈×C₁₃	—	4	6	no	—
67	#532	C₂²×C₁₃	1	3	yes	—
68	#496	—	2	3	no	—
69	#489	—	2	3	no	—
70	#461	—	2	3	no	—
71	#459	—	2	3	no	—
72	#449	—	2	6	no	—
73	#432	C₂²×C₁₃	1	3	yes	—
74	#383	C₂²×C₁₃	1	1	yes	characteristic
75	#327	—	2	6	no	—
76	C₂²×C₁₃	—	2	3	no	—
77	C₂²×C₁₃	—	8	3	no	—
78	C₂²×C₁₃	—	8	3	no	—
79	C₂²×C₁₃	—	8	3	no	—
80	C₂²×C₁₃	#392	1	1	yes	characteristic
81	C₄×C₁₃	—	2	3	no	—
82	C₄×C₁₃	—	2	3	no	—
83	C₄×C₁₃	—	8	3	no	—
84	C₄×C₁₃	—	16	1	no	—
85	C₂×#41	—	2	3	no	—
86	C₂×SD₁₆	—	2	6	no	—
87	C₂×D₈	—	2	6	no	—
88	C₄⋊Q₈	D₄×C₁₃	1	3	yes	—
89	#127	D₄×C₁₃	1	3	yes	—
90	#124	—	2	3	no	—
91	#121	—	2	3	no	—
92	#121	—	2	3	no	—
93	C₄×D₄	—	2	3	no	—
94	C₄×D₄	—	2	3	no	—
95	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
96	C₄⋊C₈	—	2	3	no	—
97	#103	—	2	6	no	—
98	#102	—	2	6	no	—
99	C₂²⋊C₈	D₄×C₁₃	1	6	yes	—
100	#97	—	2	3	no	—
101	#95	—	2	3	no	—
102	C₂×C₁₃	—	4	1	no	—
103	C₂×C₁₃	—	16	3	no	—
104	C₂×C₁₃	#2008	1	3	yes	—
105	#41	—	8	6	no	—
106	C₂×Q₈	—	2	3	no	—
107	C₂×D₄	—	2	3	no	—
108	C₂×D₄	—	2	3	no	—
109	C₂×D₄	—	2	3	no	—
110	C₂×D₄	—	4	3	no	—
111	C₂²×C₄	—	4	3	no	—
112	C₂²×C₄	—	4	1	no	—
113	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
114	SD₁₆	—	8	6	no	—
115	D₈	—	8	6	no	—
116	C₂×C₈	—	2	6	no	—
117	C₄⋊C₄	—	2	3	no	—
118	C₄⋊C₄	—	2	3	no	—
119	C₂²⋊C₄	—	4	3	no	—
120	C₂²⋊C₄	—	4	3	no	—
121	C₄²	C₂×D₄×C₁₃	1	3	yes	—
122	C₄²	C₁₃×#41	1	1	yes	characteristic
123	C₁₃	#10208	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³	—	4	3	no	—
125	C₂³	C₁₃×#127	1	1	yes	characteristic
126	Q₈	—	4	6	no	—
127	D₄	—	4	3	no	—
128	D₄	—	4	6	no	—
129	D₄	—	4	3	no	—
130	D₄	—	8	3	no	—
131	D₄	—	8	6	no	—
132	C₂×C₄	—	4	3	no	—
133	C₂×C₄	—	4	3	no	—
134	C₂×C₄	—	8	6	no	—
135	C₂×C₄	—	8	3	no	—
136	C₂×C₄	C₁₃×#120	1	3	yes	—
137	C₂×C₄	C₁₃×#121	1	3	yes	—
138	C₈	—	4	6	no	—
139	C₂²	—	2	3	no	—
140	C₂²	—	8	3	no	—
141	C₂²	—	8	3	no	—
142	C₂²	—	8	3	no	—
143	C₂²	C₁₃×#392	1	1	yes	characteristic
144	C₄	—	2	3	no	—
145	C₄	—	2	3	no	—
146	C₄	—	8	3	no	—
147	C₄	—	16	1	no	—
148	C₂	—	4	1	no	—
149	C₂	—	16	3	no	—
150	C₂	C₁₃×#2008	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#3214

C₂

yes

maximal, complemented

C₁₃×#1514

C₂

yes

maximal, complemented

C₁₃×#1308

C₂

yes

maximal, characteristic, complemented

C₁₃×#532

C₂²

yes

—

C₁₃×#496

—

C₁₃×#489

—

C₁₃×#461

—

C₁₃×#459

—

C₁₃×#449

—

C₁₃×#432

C₂²

yes

—

C₁₃×#383

C₂²

yes

characteristic

C₁₃×#327

—

C₂×C₁₃×#41

—

C₂×C₁₃×SD₁₆

—

C₂×C₁₃×D₈

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₁₃×#127

D₄

yes

—

C₁₃×#124

—

C₁₃×#121

—

C₁₃×#121

—

C₄×D₄×C₁₃

—

C₄×D₄×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×#103

—

C₁₃×#102

—

C₁₃×C₂²⋊C₈

D₄

yes

—

C₁₃×#97

—

C₁₃×#95

—

#10208

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₁₃×#41

—

C₂×Q₈×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

—

C₁₃×SD₁₆

—

C₁₃×D₈

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

#3214

C₂×C₁₃

yes

complemented

#1514

C₂×C₁₃

yes

complemented

#1308

C₂×C₁₃

yes

characteristic, complemented

C₂³×C₁₃

—

C₂³×C₁₃

#127

yes

characteristic

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₈×C₁₃

—

#532

C₂²×C₁₃

yes

—

—

—

—

—

—

C₂²×C₁₃

yes

—

#383

C₂²×C₁₃

yes

characteristic

#327

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#392

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₂×#41

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

D₄×C₁₃

yes

—

#127

D₄×C₁₃

yes

—

#124

—

#121

—

#121

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

C₂³×C₁₃

yes

characteristic

C₄⋊C₈

—

#103

—

#102

—

C₂²⋊C₈

D₄×C₁₃

yes

—

100

#97

—

101

#95

—

102

C₂×C₁₃

—

103

C₂×C₁₃

—

104

C₂×C₁₃

#2008

yes

—

105

#41

—

106

C₂×Q₈

—

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

SD₁₆

—

115

D₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

C₂×D₄×C₁₃

yes

—

122

C₄²

C₁₃×#41

yes

characteristic

123

C₁₃

#10208

yes

characteristic, direct product factor, Sylow

124

C₂³

—

125

C₂³

C₁₃×#127

yes

characteristic

126

Q₈

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₁₃×#120

yes

—

137

C₂×C₄

C₁₃×#121

yes

—

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₁₃×#392

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₂

—

149

C₂

—

150

C₂

C₁₃×#2008

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#3214	C₂	semidirect
2. C₁₃×#1514	C₂	semidirect
3. C₁₃×#1308	C₂	semidirect
30. #10208	C₁₃	direct (N × H)
49. #3214	C₂×C₁₃	semidirect
50. #1514	C₂×C₁₃	semidirect
51. #1308	C₂×C₁₃	semidirect
123. C₁₃	#10208	direct (N × H)

H ≅ G/N

type

1. C₁₃×#3214

C₂

semidirect

2. C₁₃×#1514

C₂

semidirect

3. C₁₃×#1308

C₂

semidirect

30. #10208

C₁₃

direct (N × H)

49. #3214

C₂×C₁₃

semidirect

50. #1514

C₂×C₁₃

semidirect

51. #1308

C₂×C₁₃

semidirect

123. C₁₃

#10208

direct (N × H)

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

subgroup	index
C₁₃×#3214	2
C₁₃×#1514	2
C₁₃×#1308	2
#10208	13

subgroup

index

C₁₃×#3214

C₁₃×#1514

C₁₃×#1308

#10208

Subgroups — C₁₃×#10208 #15696547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10208 #15696547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10208 #15696547