Group #23763423 — subgroups

Subgroups — #23763423

Order 10112.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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	C₂³×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579092	C₂	1	2	yes	maximal, complemented
3	#19098423	C₂	1	1	yes	maximal, characteristic
4	#19098325	C₂	1	2	yes	maximal, complemented
5	#380×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₉⋊C₈	—	2	4	no	—
7	C₂²×C₇₉⋊C₈	C₄	1	4	yes	complemented
8	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
11	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
12	#14579092	—	2	4	no	—
13	C₇₉⋊#95	—	2	1	no	—
14	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
17	#95×C₇₉	—	2	1	no	—
18	C₂²×Dic₇₉	—	2	2	no	—
19	C₂×C₇₉⋊C₈	—	2	8	no	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
22	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
23	C₂×C₇₉⋊C₈	D₄	1	4	yes	—
24	C₄⋊Dic₇₉	—	2	2	no	—
25	C₄⋊Dic₇₉	—	2	2	no	—
26	C₂²⋊Dic₇₉	—	4	2	no	—
27	C₂⁴×C₇₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₇₉	—	2	2	no	—
29	C₂²×C₄×C₇₉	—	2	2	no	—
30	C₂²×C₄×C₇₉	—	2	2	no	—
31	C₂²×C₄×C₇₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₇₉	Q₈	1	2	yes	—
34	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
35	C₄⋊C₄×C₇₉	—	2	2	no	—
36	C₄⋊C₄×C₇₉	—	2	2	no	—
37	C₂²⋊C₄×C₇₉	—	4	2	no	—
38	C₂³×C₇₉	—	2	2	no	—
39	C₂³×C₇₉	—	2	2	no	—
40	C₂³×C₇₉	C₄⋊C₄	1	2	yes	—
41	C₂³×C₇₉	SD₁₆	1	2	yes	—
42	C₂³×C₇₉	SD₁₆	1	2	yes	—
43	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₇₉	—	2	2	no	—
45	C₂×C₄×C₇₉	—	2	2	no	—
46	C₂×C₄×C₇₉	—	2	2	no	—
47	C₂×C₄×C₇₉	—	2	4	no	—
48	C₂×C₄×C₇₉	—	4	2	no	—
49	C₂×C₄×C₇₉	—	4	2	no	—
50	C₂×C₄×C₇₉	—	4	2	no	—
51	C₂×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
52	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₄×C₇₉	#41	1	2	yes	—
56	C₂×Dic₇₉	—	4	2	no	—
57	C₂×Dic₇₉	—	4	2	no	—
58	C₂×Dic₇₉	—	4	2	no	—
59	C₇₉⋊C₈	—	2	2	no	—
60	C₇₉⋊C₈	C₂²⋊C₄	1	4	yes	complemented
61	C₂²×C₇₉	—	2	2	no	—
62	C₂²×C₇₉	—	2	2	no	—
63	C₂²×C₇₉	—	2	4	no	—
64	C₂²×C₇₉	—	2	4	no	—
65	C₂²×C₇₉	#106	1	4	yes	complemented
66	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₇₉	#121	1	2	yes	—
68	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
69	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
70	C₂²×C₇₉	#135	1	2	yes	—
71	C₄×C₇₉	—	2	2	no	—
72	C₄×C₇₉	—	8	2	no	—
73	C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₄×C₇₉	#117	1	1	yes	characteristic
75	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
76	Dic₇₉	—	8	2	no	—
77	C₂×C₇₉	—	2	4	no	—
78	C₂×C₇₉	#380	1	1	yes	characteristic
79	C₂×C₇₉	C₂×#106	1	1	yes	characteristic
80	C₂×C₇₉	#427	1	1	yes	characteristic
81	C₂×C₇₉	#465	1	2	yes	—
82	C₂×C₇₉	#465	1	2	yes	—
83	#1807	—	79	1	no	maximal, Sylow
84	C₇₉	#1807	1	1	yes	characteristic, complemented, Sylow
85	C₂³×C₈	—	79	1	no	—
86	C₂×#106	—	79	2	no	—
87	#380	—	79	1	no	—
88	#380	D₇₉	1	1	yes	characteristic
89	#340	—	79	2	no	—
90	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic
91	C₂²×C₈	—	79	1	no	—
92	C₂²×C₈	—	79	1	no	—
93	C₂²×C₈	—	79	4	no	—
94	C₂²×C₈	—	158	4	no	—
95	C₂×C₄⋊C₄	—	79	2	no	—
96	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
97	C₂×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₂²⋊C₄	—	158	1	no	—
99	#106	—	158	4	no	—
100	#95	—	2	1	no	—
101	#95	—	158	1	no	—
102	C₂⁴	C₂²⋊D₇₉	1	1	yes	characteristic
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	158	2	no	—
107	C₂²×C₄	Dic₁₅₈	1	2	yes	—
108	C₂²×C₄	C₄×D₇₉	1	2	yes	—
109	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
110	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
111	C₂×C₈	—	79	2	no	—
112	C₂×C₈	—	79	4	no	—
113	C₂×C₈	—	79	2	no	—
114	C₂×C₈	—	158	8	no	—
115	C₂×C₈	—	158	2	no	—
116	C₄⋊C₄	—	2	2	no	—
117	C₄⋊C₄	—	2	2	no	—
118	C₄⋊C₄	—	158	2	no	—
119	C₄⋊C₄	—	158	2	no	—
120	C₂²⋊C₄	—	4	2	no	—
121	C₂²⋊C₄	—	316	2	no	—
122	C₂³	—	2	2	no	—
123	C₂³	—	2	2	no	—
124	C₂³	Dic₇₉⋊C₄	1	2	yes	—
125	C₂³	#11929611	1	2	yes	—
126	C₂³	#11929612	1	2	yes	—
127	C₂³	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	4	2	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	316	2	no	—
136	C₂×C₄	—	316	2	no	—
137	C₂×C₄	—	316	2	no	—
138	C₂×C₄	Dic₇₉⋊C₄	1	2	yes	—
139	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
140	C₂×C₄	D₄×D₇₉	1	2	yes	—
141	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
142	C₂×C₄	#11929623	1	2	yes	—
143	C₈	—	79	4	no	—
144	C₈	—	158	2	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	2	4	no	—
147	C₂²	—	2	4	no	—
148	C₂²	—	2	2	no	—
149	C₂²	#14579092	1	4	yes	complemented
150	C₂²	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
151	C₂²	#14579133	1	2	yes	—
152	C₂²	C₂×#11929611	1	1	yes	characteristic
153	C₂²	C₂×#11929612	1	1	yes	characteristic
154	C₂²	#14579181	1	2	yes	—
155	C₄	—	2	2	no	—
156	C₄	—	8	2	no	—
157	C₄	—	632	2	no	—
158	C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
159	C₄	#14579117	1	1	yes	characteristic
160	C₄	#14579138	1	2	yes	—
161	C₂	—	2	4	no	—
162	C₂	#19098421	1	1	yes	characteristic
163	C₂	C₂×#14579092	1	1	yes	characteristic
164	C₂	#19098599	1	1	yes	characteristic
165	C₂	#19098790	1	2	yes	—
166	C₂	#19098794	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₇₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#14579092

C₂

yes

maximal, complemented

#19098423

C₂

yes

maximal, characteristic

#19098325

C₂

yes

maximal, complemented

#380×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

C₄

yes

complemented

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₂²⋊Dic₇₉

—

#14579092

—

C₇₉⋊#95

—

C₂³×C₄×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₇₉

—

#95×C₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂⁴×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₄⋊C₄

yes

—

C₂³×C₇₉

SD₁₆

yes

—

C₂³×C₇₉

SD₁₆

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

C₂²⋊C₄

yes

complemented

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#106

yes

complemented

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₉

#121

yes

—

C₂²×C₇₉

C₂×SD₁₆

yes

characteristic

C₂²×C₇₉

C₂×SD₁₆

yes

characteristic

C₂²×C₇₉

#135

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₉

#117

yes

characteristic

C₄×C₇₉

C₂²⋊Q₈

yes

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#465

yes

—

#1807

—

maximal, Sylow

C₇₉

#1807

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂×#106

—

#380

—

#380

D₇₉

yes

characteristic

#340

—

C₂³×C₄

C₂×D₇₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

158

—

#106

—

158

—

100

#95

—

101

#95

—

158

—

102

C₂⁴

C₂²⋊D₇₉

yes

characteristic

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

158

—

107

C₂²×C₄

Dic₁₅₈

yes

—

108

C₂²×C₄

C₄×D₇₉

yes

—

109

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

110

C₂²×C₄

C₂²×D₇₉

yes

characteristic

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

158

—

115

C₂×C₈

—

158

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

158

—

119

C₄⋊C₄

—

158

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

316

—

122

C₂³

—

123

C₂³

—

124

C₂³

Dic₇₉⋊C₄

yes

—

125

C₂³

#11929611

yes

—

126

C₂³

#11929612

yes

—

127

C₂³

C₂×C₂²⋊D₇₉

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

316

—

136

C₂×C₄

—

316

—

137

C₂×C₄

—

316

—

138

C₂×C₄

Dic₇₉⋊C₄

yes

—

139

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

140

C₂×C₄

D₄×D₇₉

yes

—

141

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

142

C₂×C₄

#11929623

yes

—

143

C₈

—

144

C₈

—

158

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

#14579092

yes

complemented

150

C₂²

C₂×Dic₇₉⋊C₄

yes

characteristic

151

C₂²

#14579133

yes

—

152

C₂²

C₂×#11929611

yes

characteristic

153

C₂²

C₂×#11929612

yes

characteristic

154

C₂²

#14579181

yes

—

155

C₄

—

156

C₄

—

157

C₄

—

632

—

158

C₄

C₂²⋊C₄×D₇₉

yes

characteristic

159

C₄

#14579117

yes

characteristic

160

C₄

#14579138

yes

—

161

C₂

—

162

C₂

#19098421

yes

characteristic

163

C₂

C₂×#14579092

yes

characteristic

164

C₂

#19098599

yes

characteristic

165

C₂

#19098790

yes

—

166

C₂

#19098794

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#380×C₇₉	C₂
socle	C₂³×C₇₉	C₂×D₄
prime radical	C₂⁴×C₇₉	D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#380	D₇₉
hypocenter	C₇₉	#1807
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#380×C₇₉

C₂

socle

C₂³×C₇₉

C₂×D₄

prime radical

C₂⁴×C₇₉

D₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

N	H ≅ G/N	type
2. C₂×#14579092	C₂	semidirect
4. #19098325	C₂	semidirect
7. C₂²×C₇₉⋊C₈	C₄	semidirect
60. C₇₉⋊C₈	C₂²⋊C₄	semidirect
65. C₂²×C₇₉	#106	semidirect
84. C₇₉	#1807	semidirect
149. C₂²	#14579092	semidirect

H ≅ G/N

type

2. C₂×#14579092

C₂

semidirect

4. #19098325

C₂

semidirect

7. C₂²×C₇₉⋊C₈

C₄

semidirect

60. C₇₉⋊C₈

C₂²⋊C₄

semidirect

65. C₂²×C₇₉

#106

semidirect

84. C₇₉

#1807

semidirect

149. C₂²

#14579092

semidirect

Subgroups — #23763423

Conjugacy classes of subgroups

Complements