Group #23764825 — subgroups

Subgroups — #23764825

Order 10112.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14579095	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×(C₂×D₇₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#19098420	C₂	1	2	yes	maximal
4	#19098325	C₂	1	2	yes	maximal, complemented
5	#340×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
7	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
10	#14579095	—	2	2	no	—
11	(C₂×D₇₉)⋊C₈	—	2	2	no	—
12	C₇₉⋊#95	—	2	2	no	—
13	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
15	C₂³×D₇₉	D₄	1	1	yes	characteristic
16	C₂²×Dic₇₉	—	2	2	no	—
17	C₂²×Dic₇₉	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₉	—	2	1	no	—
19	C₂×C₄×D₇₉	—	2	2	no	—
20	C₂×C₄×D₇₉	—	2	2	no	—
21	C₂×C₄×D₇₉	—	2	1	no	—
22	C₂×C₇₉⋊C₈	—	2	1	no	—
23	C₂×C₇₉⋊C₈	—	2	2	no	—
24	C₄⋊Dic₇₉	—	2	2	no	—
25	C₄⋊Dic₇₉	—	2	2	no	—
26	(C₂×D₇₉)⋊C₄	—	4	4	no	—
27	C₂²×C₄×C₇₉	—	2	2	no	—
28	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
29	C₂×C₈×C₇₉	—	2	2	no	—
30	C₂×C₈×C₇₉	D₄	1	2	yes	—
31	C₄⋊C₄×C₇₉	—	2	2	no	—
32	C₄⋊C₄×C₇₉	—	2	2	no	—
33	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×D₇₉	—	2	1	no	—
35	C₂²×D₇₉	—	2	2	no	—
36	C₂²×D₇₉	—	2	1	no	—
37	C₂²×D₇₉	—	2	2	no	—
38	C₂²×D₇₉	D₈	1	2	yes	—
39	C₂×C₄×C₇₉	—	4	2	no	—
40	C₂×C₄×C₇₉	—	4	2	no	—
41	C₂×C₄×C₇₉	—	4	2	no	—
42	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₇₉	#41	1	2	yes	—
44	C₂×C₄×C₇₉	#41	1	2	yes	—
45	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
46	C₂×Dic₇₉	—	2	1	no	—
47	C₂×Dic₇₉	—	2	2	no	—
48	C₂×Dic₇₉	—	4	2	no	—
49	C₂×Dic₇₉	—	4	2	no	—
50	C₂×Dic₇₉	—	4	2	no	—
51	C₄×D₇₉	—	4	1	no	—
52	C₄×D₇₉	—	4	1	no	—
53	C₄×D₇₉	—	4	2	no	—
54	C₈×C₇₉	—	2	2	no	—
55	C₇₉⋊C₈	—	4	1	no	—
56	C₂²×C₇₉	#121	1	1	yes	characteristic
57	C₂²×C₇₉	#123	1	2	yes	—
58	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
59	C₂²×C₇₉	#135	1	1	yes	characteristic
60	C₂²×C₇₉	#137	1	2	yes	—
61	C₂×D₇₉	—	2	2	no	—
62	C₂×D₇₉	—	2	4	no	—
63	C₂×D₇₉	—	4	1	no	—
64	C₂×D₇₉	—	4	1	no	—
65	C₂×D₇₉	—	4	2	no	—
66	C₄×C₇₉	—	8	2	no	—
67	C₄×C₇₉	#123	1	1	yes	characteristic
68	C₄×C₇₉	#124	1	1	yes	characteristic
69	C₄×C₇₉	#126	1	2	yes	—
70	Dic₇₉	—	4	1	no	—
71	Dic₇₉	—	8	2	no	—
72	C₂×C₇₉	#397	1	1	yes	characteristic
73	C₂×C₇₉	#466	1	1	yes	characteristic
74	C₂×C₇₉	#470	1	1	yes	characteristic
75	C₂×C₇₉	#480	1	2	yes	—
76	C₂×C₇₉	#485	1	2	yes	—
77	D₇₉	—	4	2	no	—
78	#2075	—	79	1	no	maximal, Sylow
79	C₇₉	#2075	1	1	yes	characteristic, complemented, Sylow
80	C₂×#107	—	79	1	no	—
81	C₂×C₂²⋊C₈	—	79	1	no	—
82	#380	—	79	2	no	—
83	#340	—	79	2	no	—
84	#340	D₇₉	1	1	yes	characteristic, complemented
85	C₂³×C₄	—	79	1	no	—
86	C₂²×C₈	—	79	1	no	—
87	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
88	C₂×C₄⋊C₄	—	79	2	no	—
89	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
90	C₂×C₂²⋊C₄	—	158	2	no	—
91	#107	—	158	2	no	—
92	C₂²⋊C₈	—	158	2	no	—
93	#95	—	158	2	no	—
94	C₂⁴	—	79	1	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	79	1	no	—
97	C₂²×C₄	—	158	2	no	—
98	C₂²×C₄	—	158	1	no	—
99	C₂²×C₄	—	158	2	no	—
100	C₂²×C₄	—	158	2	no	—
101	C₂²×C₄	—	158	1	no	—
102	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	158	1	no	—
105	C₂×C₈	—	158	2	no	—
106	C₂×C₈	D₃₁₆	1	2	yes	—
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	158	2	no	—
110	C₄⋊C₄	—	158	2	no	—
111	C₂²⋊C₄	—	316	4	no	—
112	C₂³	—	79	2	no	—
113	C₂³	—	158	1	no	—
114	C₂³	—	158	2	no	—
115	C₂³	—	158	1	no	—
116	C₂³	—	158	2	no	—
117	C₂³	D₄×D₇₉	1	1	yes	characteristic
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	316	1	no	—
122	C₂×C₄	—	316	1	no	—
123	C₂×C₄	—	316	2	no	—
124	C₂×C₄	—	316	2	no	—
125	C₂×C₄	—	316	2	no	—
126	C₂×C₄	—	316	2	no	—
127	C₂×C₄	—	158	1	no	—
128	C₂×C₄	—	158	2	no	—
129	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
130	C₂×C₄	#11929623	1	2	yes	—
131	C₂×C₄	#11929624	1	2	yes	—
132	C₂×C₄	#11929625	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	316	1	no	—
135	C₂²	—	316	2	no	—
136	C₂²	—	316	1	no	—
137	C₂²	—	316	1	no	—
138	C₂²	—	158	2	no	—
139	C₂²	—	158	4	no	—
140	C₂²	#14579136	1	1	yes	characteristic
141	C₂²	#14579143	1	2	yes	—
142	C₂²	D₈×D₇₉	1	1	yes	characteristic
143	C₂²	#14579184	1	1	yes	characteristic
144	C₂²	#14579190	1	2	yes	—
145	C₄	—	8	2	no	—
146	C₄	—	316	1	no	—
147	C₄	—	632	2	no	—
148	C₄	#14579145	1	1	yes	characteristic
149	C₄	#14579149	1	1	yes	characteristic
150	C₄	#14579156	1	2	yes	—
151	C₂	—	316	2	no	—
152	C₂	#19098490	1	1	yes	characteristic
153	C₂	#19098800	1	1	yes	characteristic
154	C₂	#19098822	1	1	yes	characteristic
155	C₂	#19098875	1	2	yes	—
156	C₂	#19098903	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579095

C₂

yes

maximal, characteristic, complemented

C₂×(C₂×D₇₉)⋊C₈

C₂

yes

maximal, characteristic

#19098420

C₂

yes

maximal

#19098325

C₂

yes

maximal, complemented

#340×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₂²

yes

characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

—

#14579095

—

(C₂×D₇₉)⋊C₈

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂³×D₇₉

D₄

yes

characteristic

C₂²×Dic₇₉

—

C₂²×Dic₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

D₈

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₂²×C₇₉

#123

yes

—

C₂²×C₇₉

C₂×D₈

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#485

yes

—

D₇₉

—

#2075

—

maximal, Sylow

C₇₉

#2075

yes

characteristic, complemented, Sylow

C₂×#107

—

C₂×C₂²⋊C₈

—

#380

—

#340

—

#340

D₇₉

yes

characteristic, complemented

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

—

158

—

#107

—

158

—

C₂²⋊C₈

—

158

—

#95

—

158

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

100

C₂²×C₄

—

158

—

101

C₂²×C₄

—

158

—

102

C₂²×C₄

C₂²×D₇₉

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

158

—

105

C₂×C₈

—

158

—

106

C₂×C₈

D₃₁₆

yes

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

158

—

110

C₄⋊C₄

—

158

—

111

C₂²⋊C₄

—

316

—

112

C₂³

—

113

C₂³

—

158

—

114

C₂³

—

158

—

115

C₂³

—

158

—

116

C₂³

—

158

—

117

C₂³

D₄×D₇₉

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

316

—

122

C₂×C₄

—

316

—

123

C₂×C₄

—

316

—

124

C₂×C₄

—

316

—

125

C₂×C₄

—

316

—

126

C₂×C₄

—

316

—

127

C₂×C₄

—

158

—

128

C₂×C₄

—

158

—

129

C₂×C₄

C₂×D₃₁₆

yes

characteristic

130

C₂×C₄

#11929623

yes

—

131

C₂×C₄

#11929624

yes

—

132

C₂×C₄

#11929625

yes

characteristic

133

C₈

—

134

C₈

—

316

—

135

C₂²

—

316

—

136

C₂²

—

316

—

137

C₂²

—

316

—

138

C₂²

—

158

—

139

C₂²

—

158

—

140

C₂²

#14579136

yes

characteristic

141

C₂²

#14579143

yes

—

142

C₂²

D₈×D₇₉

yes

characteristic

143

C₂²

#14579184

yes

characteristic

144

C₂²

#14579190

yes

—

145

C₄

—

146

C₄

—

316

—

147

C₄

—

632

—

148

C₄

#14579145

yes

characteristic

149

C₄

#14579149

yes

characteristic

150

C₄

#14579156

yes

—

151

C₂

—

316

—

152

C₂

#19098490

yes

characteristic

153

C₂

#19098800

yes

characteristic

154

C₂

#19098822

yes

characteristic

155

C₂

#19098875

yes

—

156

C₂

#19098903

yes

—

	subgroup	G/H
center	C₂³	D₄×D₇₉
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#340×C₇₉	C₂
socle	C₂³×C₇₉	C₂×D₄
prime radical	C₂³×D₇₉	D₄
hypercenter	#340	D₇₉
hypocenter	C₇₉	#2075
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₇₉

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#340×C₇₉

C₂

socle

C₂³×C₇₉

C₂×D₄

prime radical

C₂³×D₇₉

D₄

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
1. C₂×#14579095	C₂	semidirect
4. #19098325	C₂	semidirect
5. #340×C₇₉	C₂	semidirect
79. C₇₉	#2075	semidirect
84. #340	D₇₉	semidirect

H ≅ G/N

type

1. C₂×#14579095

C₂

semidirect

4. #19098325

C₂

semidirect

5. #340×C₇₉

C₂

semidirect

79. C₇₉

#2075

semidirect

84. #340

D₇₉

semidirect

Subgroups — #23764825

Conjugacy classes of subgroups

Complements