Group #23761286 — subgroups

Subgroups — #23761286

Order 10112.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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	#19098527	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929608	C₄	1	2	yes	complemented
5	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
6	C₂×C₄×Dic₇₉	—	2	1	no	—
7	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
8	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
9	C₇₉⋊#95	C₄	1	2	yes	complemented
10	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
12	C₂×C₄²×C₇₉	—	2	1	no	—
13	#95×C₇₉	C₄	1	2	yes	complemented
14	C₂²×Dic₇₉	—	2	2	no	—
15	#11929608	—	4	2	no	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂²⋊Dic₇₉	—	2	4	no	—
18	C₄×Dic₇₉	—	4	2	no	—
19	C₂⁴×C₇₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₇₉	—	2	2	no	—
21	C₂²×C₄×C₇₉	—	4	2	no	—
22	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₇₉	Q₈	1	1	yes	characteristic
28	C₂²⋊C₄×C₇₉	—	2	4	no	—
29	C₄²×C₇₉	—	4	2	no	—
30	C₂³×C₇₉	—	2	2	no	—
31	C₂³×C₇₉	—	2	2	no	—
32	C₂³×C₇₉	—	4	1	no	—
33	C₂³×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂³×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	—	2	2	no	—
37	C₂×C₄×C₇₉	—	2	2	no	—
38	C₂×C₄×C₇₉	—	2	2	no	—
39	C₂×C₄×C₇₉	—	2	4	no	—
40	C₂×C₄×C₇₉	—	4	1	no	—
41	C₂×C₄×C₇₉	—	4	1	no	—
42	C₂×C₄×C₇₉	—	4	1	no	—
43	C₂×C₄×C₇₉	—	4	2	no	—
44	C₂×C₄×C₇₉	—	4	2	no	—
45	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
46	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
49	C₂×Dic₇₉	—	2	4	no	—
50	C₂×Dic₇₉	—	4	2	no	—
51	C₂×Dic₇₉	—	4	2	no	—
52	C₇₉⋊C₈	—	4	2	no	—
53	C₂²×C₇₉	—	2	1	no	—
54	C₂²×C₇₉	—	2	1	no	—
55	C₂²×C₇₉	—	2	1	no	—
56	C₂²×C₇₉	—	2	1	no	—
57	C₂²×C₇₉	—	2	1	no	—
58	C₂²×C₇₉	—	2	1	no	—
59	C₂²×C₇₉	—	2	1	no	—
60	C₂²×C₇₉	—	4	4	no	—
61	C₂²×C₇₉	#95	1	1	yes	characteristic
62	C₂²×C₇₉	#104	1	2	yes	—
63	C₂²×C₇₉	#104	1	2	yes	—
64	C₄×C₇₉	—	2	1	no	—
65	C₄×C₇₉	—	2	1	no	—
66	C₄×C₇₉	—	2	1	no	—
67	C₄×C₇₉	—	4	4	no	—
68	C₄×C₇₉	#99	1	2	yes	—
69	Dic₇₉	—	4	4	no	—
70	C₂×C₇₉	—	2	2	no	—
71	C₂×C₇₉	—	2	2	no	—
72	C₂×C₇₉	—	4	1	no	—
73	C₂×C₇₉	#339	1	1	yes	characteristic
74	C₂×C₇₉	#339	1	1	yes	characteristic
75	C₂×C₇₉	#342	1	1	yes	characteristic
76	#1297	—	79	1	no	maximal, Sylow
77	C₇₉	#1297	1	1	yes	characteristic, complemented, Sylow
78	#407	—	79	1	no	—
79	C₄×C₂²⋊C₄	—	79	1	no	—
80	C₄×C₂²⋊C₄	D₇₉	1	1	yes	characteristic
81	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic
82	C₂×M₁₆	—	79	2	no	—
83	C₂×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₂²⋊C₄	—	158	1	no	—
85	C₂×C₄²	—	2	1	no	—
86	C₂×C₄²	—	158	1	no	—
87	C₂²⋊C₈	—	158	1	no	—
88	C₂²⋊C₈	—	158	1	no	—
89	#95	—	79	2	no	—
90	#95	Dic₇₉	1	2	yes	complemented
91	C₂⁴	C₂²⋊D₇₉	1	1	yes	characteristic
92	C₂²×C₄	—	2	2	no	—
93	C₂²×C₄	—	4	2	no	—
94	C₂²×C₄	—	158	2	no	—
95	C₂²×C₄	Dic₁₅₈	1	1	yes	characteristic
96	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
97	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
98	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
99	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
100	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
101	M₁₆	—	316	2	no	—
102	C₂×C₈	—	158	2	no	—
103	C₂²⋊C₄	—	2	4	no	—
104	C₂²⋊C₄	—	158	4	no	—
105	C₄²	—	4	2	no	—
106	C₄²	—	316	2	no	—
107	C₂³	—	2	2	no	—
108	C₂³	—	2	2	no	—
109	C₂³	—	4	1	no	—
110	C₂³	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
111	C₂³	C₂²⋊Dic₇₉	1	1	yes	characteristic
112	C₂³	Dic₇₉⋊C₄	1	1	yes	characteristic
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	4	2	no	—
122	C₂×C₄	—	316	2	no	—
123	C₂×C₄	—	316	2	no	—
124	C₂×C₄	—	158	4	no	—
125	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
126	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
127	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
128	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
129	C₈	—	316	2	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	4	4	no	—
138	C₂²	C₇₉⋊#95	1	1	yes	characteristic
139	C₂²	#14579088	1	2	yes	—
140	C₂²	#14579089	1	2	yes	—
141	C₄	—	2	1	no	—
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	4	4	no	—
145	C₄	—	316	4	no	—
146	C₄	#14579075	1	2	yes	—
147	C₂	—	2	2	no	—
148	C₂	—	2	2	no	—
149	C₂	—	4	1	no	—
150	C₂	#19098322	1	1	yes	characteristic
151	C₂	#19098323	1	1	yes	characteristic
152	C₂	#19098329	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098527

C₂

yes

maximal, characteristic

C₄×C₂²⋊Dic₇₉

C₂

yes

maximal, characteristic

C₄×C₂²⋊C₄×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₄

yes

complemented

C₂×C₂²⋊Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₇₉⋊#95

C₄

yes

complemented

C₂³×C₄×C₇₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

—

#95×C₇₉

C₄

yes

complemented

C₂²×Dic₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂⁴×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

Q₈

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂²⋊C₄

yes

characteristic

C₂³×C₇₉

C₂²⋊C₄

yes

characteristic

C₂³×C₇₉

C₄⋊C₄

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

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#95

yes

characteristic

C₂²×C₇₉

#104

yes

—

C₂²×C₇₉

#104

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#99

yes

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#407

—

C₄×C₂²⋊C₄

—

C₄×C₂²⋊C₄

D₇₉

yes

characteristic

C₂³×C₄

C₂×D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

158

—

C₂×C₄²

—

C₂×C₄²

—

158

—

C₂²⋊C₈

—

158

—

C₂²⋊C₈

—

158

—

#95

—

#95

Dic₇₉

yes

complemented

C₂⁴

C₂²⋊D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

Dic₁₅₈

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

C₂×Dic₇₉

yes

characteristic

100

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

101

M₁₆

—

316

—

102

C₂×C₈

—

158

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

158

—

105

C₄²

—

106

C₄²

—

316

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

(C₂×D₇₉)⋊C₄

yes

characteristic

111

C₂³

C₂²⋊Dic₇₉

yes

characteristic

112

C₂³

Dic₇₉⋊C₄

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

316

—

123

C₂×C₄

—

316

—

124

C₂×C₄

—

158

—

125

C₂×C₄

C₄×Dic₇₉

yes

characteristic

126

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

127

C₂×C₄

Dic₇₉⋊C₄

yes

characteristic

128

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

129

C₈

—

316

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₇₉⋊#95

yes

characteristic

139

C₂²

#14579088

yes

—

140

C₂²

#14579089

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

316

—

146

C₄

#14579075

yes

—

147

C₂

—

148

C₂

—

149

C₂

—

150

C₂

#19098322

yes

characteristic

151

C₂

#19098323

yes

characteristic

152

C₂

#19098329

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₇₉)⋊C₄
commutator	C₂×C₄×C₇₉	C₄²
Frattini	C₂³×C₄	C₂×D₇₉
Fitting	C₄×C₂²⋊C₄×C₇₉	C₂
socle	C₂²×C₇₉	#95
prime radical	C₂⁴×C₇₉	D₄
cosocle	C₂³×C₄×C₇₉	C₂²
hypercenter	C₄×C₂²⋊C₄	D₇₉
hypocenter	C₇₉	#1297
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₄×C₂²⋊C₄

subgroup

G/H

center

C₂×C₄

(C₂×D₇₉)⋊C₄

commutator

C₂×C₄×C₇₉

C₄²

Frattini

C₂³×C₄

C₂×D₇₉

Fitting

C₄×C₂²⋊C₄×C₇₉

C₂

socle

C₂²×C₇₉

#95

prime radical

C₂⁴×C₇₉

D₄

cosocle

C₂³×C₄×C₇₉

C₂²

hypercenter

C₄×C₂²⋊C₄

D₇₉

hypocenter

C₇₉

#1297

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₄×C₂²⋊C₄

N	H ≅ G/N	type
4. C₂×#11929608	C₄	semidirect
9. C₇₉⋊#95	C₄	semidirect
13. #95×C₇₉	C₄	semidirect
77. C₇₉	#1297	semidirect
90. #95	Dic₇₉	semidirect

H ≅ G/N

type

4. C₂×#11929608

C₄

semidirect

9. C₇₉⋊#95

C₄

semidirect

13. #95×C₇₉

C₄

semidirect

77. C₇₉

#1297

semidirect

90. #95

Dic₇₉

semidirect

Subgroups — #23761286

Conjugacy classes of subgroups

Complements