Group #15784039 — subgroups

Subgroups — #15784039

Order 3328.

1598 conjugacy classes of subgroups; only the 635 normal subgroups are shown.

normal subgroups only

This group has 1598 conjugacy classes of subgroups — too many to draw. Only its 635 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×#11718593	C₂	1	2	yes	maximal
2	#13113063	C₂	1	8	yes	maximal
3	C₄×#88071	C₂	1	4	yes	maximal
4	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₁₃	C₂²	1	4	yes	—
9	C₄³×C₁₃	C₄	1	8	yes	complemented
10	C₂×#88071	C₂²	1	16	yes	—
11	C₂×#88071	C₂²	1	8	yes	—
12	#11718593	C₄	1	16	yes	complemented
13	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
14	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂³×Dic₁₃	C₂³	1	8	yes	—
17	C₂×C₄²×C₁₃	—	2	16	no	—
18	C₂×C₄²×C₁₃	—	2	8	no	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	16	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
23	C₂×C₄×Dic₁₃	—	2	16	no	—
24	C₂×C₄×Dic₁₃	C₂×C₄	1	16	yes	—
25	#88071	—	2	32	no	—
26	#88071	C₂×C₄	1	32	yes	—
27	#13757	—	13	1	no	maximal, Sylow
28	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	—	2	8	no	—
30	C₂²×C₄×C₁₃	—	2	8	no	—
31	C₂²×C₄×C₁₃	—	2	8	no	—
32	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
34	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
37	C₂²×C₄×C₁₃	#41	1	16	yes	—
38	C₂²×C₄×C₁₃	#41	1	8	yes	—
39	C₂²×Dic₁₃	—	2	32	no	—
40	C₂²×Dic₁₃	—	2	16	no	—
41	C₂²×Dic₁₃	C₂²×C₄	1	16	yes	—
42	C₄²×C₁₃	—	2	32	no	—
43	C₄²×C₁₃	—	2	16	no	—
44	C₄²×C₁₃	C₄²	1	16	yes	—
45	C₄×Dic₁₃	—	2	32	no	—
46	C₂×#376	—	13	2	no	—
47	C₂×C₄³	D₁₃	1	1	yes	characteristic
48	#1434	—	13	8	no	—
49	C₄×#95	—	13	4	no	—
50	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
51	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
52	C₂³×C₁₃	C₂×#41	1	4	yes	—
53	C₂³×C₁₃	C₂×#41	1	8	yes	—
54	C₂×C₄×C₁₃	—	2	8	no	—
55	C₂×C₄×C₁₃	—	2	8	no	—
56	C₂×C₄×C₁₃	—	2	8	no	—
57	C₂×C₄×C₁₃	—	2	16	no	—
58	C₂×C₄×C₁₃	—	2	32	no	—
59	C₂×C₄×C₁₃	C₂×C₄²	1	8	yes	—
60	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
61	C₂×C₄×C₁₃	#117	1	16	yes	—
62	C₂×C₄×C₁₃	#117	1	16	yes	—
63	C₂×C₄×C₁₃	#117	1	8	yes	—
64	C₂×Dic₁₃	—	2	16	no	—
65	C₂×Dic₁₃	—	2	32	no	—
66	C₂×Dic₁₃	—	4	32	no	—
67	C₂²×C₄²	—	13	4	no	—
68	C₂²×C₄²	C₂×D₁₃	1	4	yes	—
69	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
70	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
71	#376	—	13	16	no	—
72	C₂×#95	—	13	8	no	—
73	C₂×#95	—	13	16	no	—
74	C₄³	Dic₁₃	1	8	yes	complemented
75	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
76	C₂²×C₁₃	C₂×#117	1	4	yes	—
77	C₂²×C₁₃	C₂×#117	1	2	yes	—
78	C₂²×C₁₃	C₂×#117	1	4	yes	—
79	C₂²×C₁₃	C₄×#41	1	8	yes	—
80	C₂²×C₁₃	#529	1	16	yes	—
81	C₄×C₁₃	—	2	8	no	—
82	C₄×C₁₃	—	2	16	no	—
83	C₄×C₁₃	#376	1	8	yes	—
84	Dic₁₃	—	4	16	no	—
85	C₂³×C₄	—	13	8	no	—
86	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
87	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
88	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
89	C₂×C₄²	—	2	16	no	—
90	C₂×C₄²	—	2	8	no	—
91	C₂×C₄²	—	13	16	no	—
92	C₂×C₄²	—	26	16	no	—
93	C₂×C₄²	C₄×D₁₃	1	8	yes	—
94	C₂×C₄²	C₂×Dic₁₃	1	16	yes	—
95	C₂×C₄²	C₂×Dic₁₃	1	8	yes	—
96	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
97	#95	—	13	32	no	—
98	#95	—	26	32	no	—
99	C₂×C₁₃	C₂×#376	1	1	yes	characteristic
100	C₂×C₁₃	C₄×#117	1	2	yes	—
101	C₂×C₁₃	#2283	1	4	yes	—
102	C₂×C₁₃	#2298	1	8	yes	—
103	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
104	C₂²×C₄	—	2	8	no	—
105	C₂²×C₄	—	2	8	no	—
106	C₂²×C₄	—	2	8	no	—
107	C₂²×C₄	—	13	16	no	—
108	C₂²×C₄	—	26	32	no	—
109	C₂²×C₄	—	26	16	no	—
110	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
111	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
112	C₂²×C₄	#6127	1	16	yes	—
113	C₂²×C₄	#6127	1	8	yes	—
114	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
115	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
116	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
117	C₄²	—	2	32	no	—
118	C₄²	—	2	16	no	—
119	C₄²	—	26	32	no	—
120	C₄²	C₄×Dic₁₃	1	16	yes	—
121	C₁₃	#13757	1	1	yes	characteristic, complemented, Sylow
122	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
123	C₂³	C₂×#6127	1	4	yes	—
124	C₂³	C₂×#6127	1	8	yes	—
125	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
126	C₂×C₄	—	2	16	no	—
127	C₂×C₄	—	2	32	no	—
128	C₂×C₄	—	2	8	no	—
129	C₂×C₄	—	2	8	no	—
130	C₂×C₄	—	2	8	no	—
131	C₂×C₄	—	26	16	no	—
132	C₂×C₄	—	26	32	no	—
133	C₂×C₄	—	52	32	no	—
134	C₂×C₄	#88126	1	16	yes	—
135	C₂×C₄	C₂×C₄×Dic₁₃	1	8	yes	—
136	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
137	C₂×C₄	#88180	1	16	yes	—
138	C₂×C₄	#88180	1	8	yes	—
139	C₂²	C₂×#88126	1	4	yes	—
140	C₂²	C₄×#6127	1	8	yes	—
141	C₂²	#11719184	1	16	yes	—
142	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
143	C₂²	C₂×#88180	1	2	yes	—
144	C₂²	C₂×#88180	1	4	yes	—
145	C₄	—	2	16	no	—
146	C₄	—	2	8	no	—
147	C₄	—	52	16	no	—
148	C₄	#11718593	1	8	yes	—
149	C₂	C₂×#11718593	1	1	yes	characteristic
150	C₂	C₄×#88180	1	2	yes	—
151	C₂	#13117234	1	4	yes	—
152	C₂	#13117333	1	8	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718593

C₂

yes

maximal

#13113063

C₂

yes

maximal

C₄×#88071

C₂

yes

maximal

C₂×C₄³×C₁₃

C₂

yes

maximal, characteristic

C₂²×C₄²×C₁₃

C₂²

yes

—

C₂²×C₄²×C₁₃

C₂²

yes

—

C₂²×C₄²×C₁₃

C₂²

yes

characteristic

C₂²×C₄×Dic₁₃

C₂²

yes

—

C₄³×C₁₃

C₄

yes

complemented

C₂×#88071

C₂²

yes

—

C₂×#88071

C₂²

yes

—

#11718593

C₄

yes

complemented

C₂³×C₄×C₁₃

C₂³

yes

—

C₂³×C₄×C₁₃

C₂³

yes

—

C₂³×C₄×C₁₃

C₂³

yes

characteristic

C₂³×Dic₁₃

C₂³

yes

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

#88071

—

#88071

C₂×C₄

yes

—

#13757

—

maximal, Sylow

C₂⁴×C₁₃

C₂⁴

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

#41

yes

—

C₂²×C₄×C₁₃

#41

yes

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₄²

yes

—

C₄×Dic₁₃

—

C₂×#376

—

C₂×C₄³

D₁₃

yes

characteristic

#1434

—

C₄×#95

—

C₂³×C₁₃

C₂³×C₄

yes

characteristic

C₂³×C₁₃

C₂³×C₄

yes

—

C₂³×C₁₃

C₂×#41

yes

—

C₂³×C₁₃

C₂×#41

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄²

yes

—

C₂×C₄×C₁₃

C₂×C₄²

yes

—

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

#117

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂²×C₄²

—

C₂²×C₄²

C₂×D₁₃

yes

—

C₂²×C₄²

C₂×D₁₃

yes

—

C₂²×C₄²

C₂×D₁₃

yes

characteristic

#376

—

C₂×#95

—

C₂×#95

—

C₄³

Dic₁₃

yes

complemented

C₂²×C₁₃

C₂²×C₄²

yes

characteristic

C₂²×C₁₃

C₂×#117

yes

—

C₂²×C₁₃

C₂×#117

yes

—

C₂²×C₁₃

C₂×#117

yes

—

C₂²×C₁₃

C₄×#41

yes

—

C₂²×C₁₃

#529

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#376

yes

—

Dic₁₃

—

C₂³×C₄

—

C₂³×C₄

C₂²×D₁₃

yes

—

C₂³×C₄

C₂²×D₁₃

yes

—

C₂³×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₄×D₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

—

#95

—

#95

—

C₂×C₁₃

C₂×#376

yes

characteristic

100

C₂×C₁₃

C₄×#117

yes

—

101

C₂×C₁₃

#2283

yes

—

102

C₂×C₁₃

#2298

yes

—

103

C₂⁴

C₂³×D₁₃

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂×C₄×D₁₃

yes

—

111

C₂²×C₄

C₂×C₄×D₁₃

yes

—

112

C₂²×C₄

#6127

yes

—

113

C₂²×C₄

#6127

yes

—

114

C₂²×C₄

C₂²×Dic₁₃

yes

—

115

C₂²×C₄

C₂²×Dic₁₃

yes

—

116

C₂²×C₄

C₂²×Dic₁₃

yes

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₄×Dic₁₃

yes

—

121

C₁₃

#13757

yes

characteristic, complemented, Sylow

122

C₂³

C₂²×C₄×D₁₃

yes

—

123

C₂³

C₂×#6127

yes

—

124

C₂³

C₂×#6127

yes

—

125

C₂³

C₂³×Dic₁₃

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

#88126

yes

—

135

C₂×C₄

C₂×C₄×Dic₁₃

yes

—

136

C₂×C₄

C₂×C₄×Dic₁₃

yes

—

137

C₂×C₄

#88180

yes

—

138

C₂×C₄

#88180

yes

—

139

C₂²

C₂×#88126

yes

—

140

C₂²

C₄×#6127

yes

—

141

C₂²

#11719184

yes

—

142

C₂²

C₂²×C₄×Dic₁₃

yes

characteristic

143

C₂²

C₂×#88180

yes

—

144

C₂²

C₂×#88180

yes

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

#11718593

yes

—

149

C₂

C₂×#11718593

yes

characteristic

150

C₂

C₄×#88180

yes

—

151

C₂

#13117234

yes

—

152

C₂

#13117333

yes

—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂⁴	C₂³×D₁₃
Fitting	C₂×C₄³×C₁₃	C₂
socle, prime radical, cosocle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂×C₄³	D₁₃
hypocenter	C₁₃	#13757
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄³

subgroup

G/H

center

C₂³×C₄

C₂²×D₁₃

commutator

C₂²×C₁₃

C₂²×C₄²

Frattini

C₂⁴

C₂³×D₁₃

Fitting

C₂×C₄³×C₁₃

C₂

socle, prime radical, cosocle

C₂⁴×C₁₃

C₂⁴

hypercenter

C₂×C₄³

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂³×C₄ ◁ C₂×C₄³

N	H ≅ G/N	type
9. C₄³×C₁₃	C₄	semidirect
12. #11718593	C₄	semidirect
74. C₄³	Dic₁₃	semidirect
121. C₁₃	#13757	semidirect

H ≅ G/N

type

9. C₄³×C₁₃

C₄

semidirect

12. #11718593

C₄

semidirect

74. C₄³

Dic₁₃

semidirect

121. C₁₃

#13757

semidirect

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

subgroup	index
C₂×#11718593	2
#13113063	2
C₄×#88071	2
C₂×C₄³×C₁₃	2
#13757	13

subgroup

index

C₂×C₄³×C₁₃

Subgroups — #15784039

Conjugacy classes of subgroups

Complements

Maximal subgroups