Group #15779338 — subgroups

Subgroups — #15779338

Order 3328.

342 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 159 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×#11718103	C₂	1	4	yes	maximal
2	#13116592	C₂	1	1	yes	maximal, characteristic
3	#13114522	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88055	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
9	C₂×#88052	C₂²	1	2	yes	—
10	#11718593	C₄	1	1	yes	characteristic
11	C₂×#88043	C₄	1	1	yes	characteristic
12	C₁₃×C₄⋊C₁₆	—	2	2	no	—
13	#11718103	—	2	8	no	—
14	C₄⋊#6090	—	2	2	no	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
19	C₂²×#1055	C₂×C₄	1	2	yes	—
20	C₁₃×M₃₂	—	2	4	no	—
21	C₂×C₁₃×C₁₆	—	2	2	no	—
22	C₄×C₈×C₁₃	D₄	1	2	yes	—
23	C₄×C₈×C₁₃	Q₈	1	2	yes	—
24	#88071	—	2	2	no	—
25	#88055	—	2	4	no	—
26	C₈×Dic₁₃	D₄	1	4	yes	—
27	C₈×Dic₁₃	Q₈	1	4	yes	—
28	#88052	—	2	4	no	—
29	C₂×#6090	—	2	2	no	—
30	#88043	C₈	1	4	yes	—
31	#12901	—	13	1	no	maximal, Sylow
32	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂²×Dic₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	—	2	2	no	—
36	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
37	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
38	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
41	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
42	C₄²×C₁₃	C₂×C₈	1	2	yes	—
43	C₄×Dic₁₃	—	2	2	no	—
44	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
45	C₂×#1055	C₄⋊C₄	1	4	yes	—
46	C₂×#1055	C₂×C₈	1	4	yes	—
47	C₂×#1055	M₁₆	1	4	yes	—
48	C₁₃×C₁₆	—	4	2	no	—
49	#6090	—	4	2	no	—
50	C₂×#364	—	13	4	no	—
51	#2150	—	13	1	no	—
52	#2150	D₁₃	1	1	yes	characteristic
53	#1726	—	13	1	no	—
54	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
55	C₂×C₄×C₁₃	—	4	2	no	—
56	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
57	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
58	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
61	C₂×Dic₁₃	—	2	4	no	—
62	C₂×Dic₁₃	—	4	4	no	—
63	C₈×C₁₃	—	2	2	no	—
64	C₈×C₁₃	#127	1	1	yes	characteristic
65	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
66	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
67	#1055	C₄⋊C₈	1	8	yes	—
68	C₂×M₃₂	—	13	2	no	—
69	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
70	C₂×#97	—	13	1	no	—
71	C₂×#97	—	13	2	no	—
72	C₂×C₄×C₈	—	13	2	no	—
73	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
74	#376	—	13	1	no	—
75	#364	—	26	8	no	—
76	C₄⋊C₁₆	—	2	2	no	—
77	C₄⋊C₁₆	—	26	2	no	—
78	C₂²×C₁₃	—	2	2	no	—
79	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
80	C₂²×C₁₃	#423	1	2	yes	—
81	C₄×C₁₃	—	2	4	no	—
82	C₄×C₁₃	#384	1	1	yes	characteristic
83	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
84	C₄×C₁₃	#423	1	1	yes	characteristic
85	Dic₁₃	—	4	4	no	—
86	C₂²×C₈	—	13	2	no	—
87	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
88	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
89	C₂×C₄²	—	13	2	no	—
90	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
91	M₃₂	—	2	4	no	—
92	M₃₂	—	26	4	no	—
93	C₂×C₁₆	—	2	2	no	—
94	C₂×C₁₆	—	26	2	no	—
95	#97	—	13	4	no	—
96	#97	—	26	4	no	—
97	C₄×C₈	—	13	4	no	—
98	C₄×C₈	—	13	4	no	—
99	C₄×C₈	Dic₂₆	1	2	yes	—
100	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
101	#95	—	26	2	no	—
102	C₂×C₁₃	—	2	2	no	—
103	C₂×C₁₃	#1842	1	1	yes	characteristic
104	C₂×C₁₃	#2153	1	2	yes	—
105	C₂²×C₄	—	26	2	no	—
106	C₂²×C₄	#6094	1	2	yes	—
107	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	13	4	no	—
110	C₂×C₈	—	13	4	no	—
111	C₂×C₈	—	13	4	no	—
112	C₂×C₈	#6101	1	2	yes	—
113	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
114	C₂×C₈	D₄×D₁₃	1	2	yes	—
115	C₂×C₈	Q₈×D₁₃	1	2	yes	—
116	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
117	C₄²	—	13	4	no	—
118	C₄²	—	26	2	no	—
119	C₄²	C₈×D₁₃	1	2	yes	—
120	C₄²	#6101	1	2	yes	—
121	C₁₆	—	4	2	no	—
122	C₁₆	—	52	2	no	—
123	C₁₃	#12901	1	1	yes	characteristic, complemented, Sylow
124	C₂³	C₂×#6094	1	1	yes	characteristic
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	—	26	4	no	—
127	C₂×C₄	—	52	4	no	—
128	C₂×C₄	#88054	1	4	yes	—
129	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
130	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
131	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
132	C₂×C₄	C₂×#6101	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	13	8	no	—
135	C₈	#88142	1	2	yes	—
136	C₈	#88194	1	1	yes	characteristic
137	C₈	#88198	1	1	yes	characteristic
138	C₂²	—	2	2	no	—
139	C₂²	#11718498	1	2	yes	—
140	C₂²	C₂×#88054	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	52	4	no	—
143	C₄	D₁₃×C₄⋊C₈	1	2	yes	—
144	C₄	#11718637	1	1	yes	characteristic
145	C₄	#11718779	1	1	yes	characteristic
146	C₂	—	2	2	no	—
147	C₂	#13114987	1	1	yes	characteristic
148	C₂	#13116601	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718103

C₂

yes

maximal

#13116592

C₂

yes

maximal, characteristic

#13114522

C₂

yes

maximal, characteristic

C₁₃×#2150

C₂

yes

maximal, characteristic

C₂×C₁₃×M₃₂

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88055

C₄

yes

—

C₂×C₈×Dic₁₃

C₂²

yes

—

C₂×#88052

C₂²

yes

—

#11718593

C₄

yes

characteristic

C₂×#88043

C₄

yes

characteristic

C₁₃×C₄⋊C₁₆

—

#11718103

—

C₄⋊#6090

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#88071

—

#88055

—

C₈×Dic₁₃

D₄

yes

—

C₈×Dic₁₃

Q₈

yes

—

#88052

—

C₂×#6090

—

#88043

C₈

yes

—

#12901

—

maximal, Sylow

C₂²×C₄×C₁₃

M₁₆

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

C₂×C₈

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₄⋊C₄

yes

—

C₂×#1055

C₄⋊C₄

yes

—

C₂×#1055

C₂×C₈

yes

—

C₂×#1055

M₁₆

yes

—

C₁₃×C₁₆

—

—

—

—

D₁₃

yes

characteristic

#1726

—

C₂³×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#127

yes

characteristic

C₈×C₁₃

C₄⋊Q₈

yes

—

C₈×C₁₃

C₄⋊Q₈

yes

characteristic

#1055

C₄⋊C₈

yes

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₁₃

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

#376

—

#364

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₃

#423

yes

—

C₄×C₁₃

—

C₄×C₁₃

#384

yes

characteristic

C₄×C₁₃

C₂×C₄⋊C₈

yes

—

C₄×C₁₃

#423

yes

characteristic

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₃

yes

characteristic

C₂²×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₁₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₂₆

yes

—

100

C₄×C₈

C₂²⋊D₁₃

yes

—

101

#95

—

102

C₂×C₁₃

—

103

C₂×C₁₃

#1842

yes

characteristic

104

C₂×C₁₃

#2153

yes

—

105

C₂²×C₄

—

106

C₂²×C₄

#6094

yes

—

107

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

#6101

yes

—

113

C₂×C₈

C₂×Dic₂₆

yes

characteristic

114

C₂×C₈

D₄×D₁₃

yes

—

115

C₂×C₈

Q₈×D₁₃

yes

—

116

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

117

C₄²

—

118

C₄²

—

119

C₄²

C₈×D₁₃

yes

—

120

C₄²

#6101

yes

—

121

C₁₆

—

122

C₁₆

—

123

C₁₃

#12901

yes

characteristic, complemented, Sylow

124

C₂³

C₂×#6094

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

#88054

yes

—

129

C₂×C₄

C₄⋊C₄×D₁₃

yes

—

130

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

131

C₂×C₄

M₁₆×D₁₃

yes

—

132

C₂×C₄

C₂×#6101

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

#88142

yes

—

136

C₈

#88194

yes

characteristic

137

C₈

#88198

yes

characteristic

138

C₂²

—

139

C₂²

#11718498

yes

—

140

C₂²

C₂×#88054

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

D₁₃×C₄⋊C₈

yes

—

144

C₄

#11718637

yes

characteristic

145

C₄

#11718779

yes

characteristic

146

C₂

—

147

C₂

#13114987

yes

characteristic

148

C₂

#13116601

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#2150	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#2150	D₁₃
hypocenter	C₁₃	#12901
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#2150

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₈

prime radical

C₂³×C₁₃

C₂×M₁₆

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
123. C₁₃	#12901	semidirect

H ≅ G/N

type

123. C₁₃

#12901

semidirect

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

subgroup	index
C₂×#11718103	2
#13116592	2
#13114522	2
C₁₃×#2150	2
#12901	13

subgroup

index

C₁₃×#2150

Subgroups — #15779338

Conjugacy classes of subgroups

Complements

Maximal subgroups