Group #23773987 — subgroups

Subgroups — #23773987

Order 10112.

368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19099118	C₂	1	2	yes	maximal
2	#19098943	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098915	C₂	1	2	yes	maximal, complemented
4	#19098805	C₂	1	4	yes	maximal
5	#19098657	C₂	1	4	yes	maximal, complemented
6	C₄×C₈×D₇₉	C₂	1	1	yes	maximal, characteristic
7	#500×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₃₁₆	C₂²	1	4	yes	—
9	C₂×C₈×D₇₉	C₂²	1	2	yes	—
10	#14579161	C₂²	1	2	yes	—
11	#14579152	—	2	2	no	—
12	#14579141	C₂²	1	4	yes	—
13	#14579137	—	2	2	no	—
14	Q₈×Dic₇₉	—	2	2	no	—
15	#14579126	C₂²	1	4	yes	—
16	#14579119	—	2	2	no	—
17	C₄²×D₇₉	C₂²	1	1	yes	characteristic
18	#14579084	C₂²	1	8	yes	—
19	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₇₉	C₂²	1	2	yes	—
21	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
22	#107×C₇₉	C₂²	1	4	yes	—
23	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₅₈	C₂³	1	4	yes	—
25	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
26	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
27	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
28	Dic₃₁₆	—	2	8	no	—
29	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
30	C₈×D₇₉	—	2	4	no	—
31	C₄⋊Dic₇₉	—	2	4	no	—
32	C₄⋊Dic₇₉	—	2	2	no	—
33	C₄⋊Dic₇₉	—	2	2	no	—
34	Dic₇₉⋊C₄	—	2	4	no	—
35	(C₂×D₇₉)⋊C₄	—	2	4	no	—
36	C₄×Dic₇₉	—	2	4	no	—
37	C₄×Dic₇₉	D₄	1	1	yes	characteristic
38	C₄×Dic₇₉	D₄	1	1	yes	characteristic
39	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
40	C₂×Q₈×C₇₉	—	2	2	no	—
41	C₂×C₈×C₇₉	C₂³	1	2	yes	—
42	C₄⋊C₄×C₇₉	—	2	2	no	—
43	C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
44	C₄²×C₇₉	C₂³	1	1	yes	characteristic
45	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
46	Q₈×C₇₉	—	4	4	no	—
47	C₂×C₄×C₇₉	—	2	4	no	—
48	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₇₉	—	2	4	no	—
52	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
53	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
55	C₄×D₇₉	—	2	2	no	—
56	C₄×D₇₉	—	2	2	no	—
57	C₄×D₇₉	Q₁₆	1	4	yes	complemented
58	Dic₁₅₈	—	2	8	no	—
59	C₈×C₇₉	#41	1	4	yes	—
60	C₇₉⋊C₈	—	2	2	no	—
61	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
62	C₂×D₇₉	—	2	1	no	—
63	C₂×D₇₉	—	2	1	no	—
64	C₂×D₇₉	C₂×Q₁₆	1	2	yes	—
65	C₄×C₇₉	—	4	4	no	—
66	C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
67	C₄×C₇₉	#135	1	2	yes	—
68	C₄×C₇₉	C₂×#41	1	2	yes	—
69	Dic₇₉	—	2	1	no	—
70	Dic₇₉	—	2	1	no	—
71	Dic₇₉	—	4	4	no	—
72	Dic₇₉	C₂×Q₁₆	1	2	yes	—
73	C₂×C₇₉	#532	1	1	yes	characteristic
74	C₂×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
75	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
76	D₇₉	—	2	2	no	—
77	#3170	—	79	1	no	maximal, Sylow
78	C₇₉	#3170	1	1	yes	characteristic, complemented, Sylow
79	#533	—	79	2	no	—
80	#500	D₇₉	1	1	yes	characteristic, complemented
81	#494	—	79	1	no	—
82	#487	—	79	2	no	—
83	#467	—	79	4	no	—
84	C₄×Q₁₆	—	79	4	no	—
85	C₂×C₄×C₈	—	79	1	no	—
86	C₂×Q₁₆	—	79	4	no	—
87	C₂²×C₈	—	79	2	no	—
88	C₄⋊Q₈	—	79	2	no	—
89	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
90	#125	—	158	2	no	—
91	C₂²⋊Q₈	—	79	4	no	—
92	C₂²⋊Q₈	—	158	2	no	—
93	C₄×Q₈	—	79	4	no	—
94	C₄×Q₈	—	158	2	no	—
95	#117	—	158	2	no	—
96	C₂×C₄²	—	79	1	no	—
97	#107	C₂×D₇₉	1	4	yes	—
98	#103	—	79	8	no	—
99	C₄×C₈	—	79	2	no	—
100	C₄×C₈	—	79	1	no	—
101	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
102	C₂×Q₈	—	2	2	no	—
103	C₂×Q₈	—	79	4	no	—
104	C₂²×C₄	—	79	1	no	—
105	C₂²×C₄	—	79	1	no	—
106	C₂²×C₄	—	79	1	no	—
107	Q₁₆	—	158	8	no	—
108	C₂×C₈	—	79	2	no	—
109	C₂×C₈	—	158	4	no	—
110	C₂×C₈	C₂²×D₇₉	1	2	yes	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	158	4	no	—
113	C₄⋊C₄	—	158	4	no	—
114	C₄⋊C₄	—	158	2	no	—
115	C₄⋊C₄	—	158	2	no	—
116	C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
117	C₂²⋊C₄	—	158	4	no	—
118	C₄²	—	79	1	no	—
119	C₄²	—	79	1	no	—
120	C₄²	—	79	1	no	—
121	C₄²	—	158	4	no	—
122	C₄²	C₂²×D₇₉	1	1	yes	characteristic
123	C₂³	—	79	1	no	—
124	Q₈	—	4	4	no	—
125	Q₈	—	158	8	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	79	1	no	—
128	C₂×C₄	—	79	4	no	—
129	C₂×C₄	—	79	1	no	—
130	C₂×C₄	—	79	1	no	—
131	C₂×C₄	—	158	4	no	—
132	C₂×C₄	—	158	2	no	—
133	C₂×C₄	—	158	2	no	—
134	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
135	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
136	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
137	C₈	—	158	2	no	—
138	C₈	#11929625	1	4	yes	—
139	C₂²	—	79	2	no	—
140	C₂²	—	158	1	no	—
141	C₂²	—	158	1	no	—
142	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
143	C₄	—	4	4	no	—
144	C₄	—	316	4	no	—
145	C₄	—	79	2	no	—
146	C₄	—	158	1	no	—
147	C₄	—	158	1	no	—
148	C₄	Q₁₆×D₇₉	1	2	yes	—
149	C₄	#14579180	1	2	yes	—
150	C₄	C₂×#11929625	1	2	yes	—
151	C₂	—	158	2	no	—
152	C₂	#19099114	1	1	yes	characteristic
153	C₂	C₂×Q₁₆×D₇₉	1	1	yes	characteristic
154	C₂	C₂×#14579180	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099118

C₂

yes

maximal

#19098943

C₂

yes

maximal, characteristic, complemented

#19098915

C₂

yes

maximal, complemented

#19098805

C₂

yes

maximal

#19098657

C₂

yes

maximal, complemented

C₄×C₈×D₇₉

C₂

yes

maximal, characteristic

#500×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₂²

yes

—

C₂×C₈×D₇₉

C₂²

yes

—

#14579161

C₂²

yes

—

#14579152

—

#14579141

C₂²

yes

—

#14579137

—

Q₈×Dic₇₉

—

#14579126

C₂²

yes

—

#14579119

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579084

C₂²

yes

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₈×Dic₇₉

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

—

#107×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

C₂³

yes

—

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

C₂³

yes

characteristic

Dic₃₁₆

—

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

Q₁₆

yes

complemented

Dic₁₅₈

—

C₈×C₇₉

#41

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

C₂×Q₁₆

yes

—

C₄×C₇₉

—

C₄×C₇₉

C₂×Q₁₆

yes

—

C₄×C₇₉

#135

yes

—

C₄×C₇₉

C₂×#41

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

C₂×Q₁₆

yes

—

C₂×C₇₉

#532

yes

characteristic

C₂×C₇₉

C₂²×Q₁₆

yes

characteristic

C₂×C₇₉

C₂×#135

yes

characteristic

D₇₉

—

#3170

—

maximal, Sylow

C₇₉

#3170

yes

characteristic, complemented, Sylow

#533

—

#500

D₇₉

yes

characteristic, complemented

#494

—

#487

—

#467

—

C₄×Q₁₆

—

C₂×C₄×C₈

—

C₂×Q₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

—

#125

—

158

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

158

—

C₄×Q₈

—

C₄×Q₈

—

158

—

#117

—

158

—

C₂×C₄²

—

#107

C₂×D₇₉

yes

—

#103

—

C₄×C₈

—

100

C₄×C₈

—

101

C₄×C₈

C₂×D₇₉

yes

characteristic

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

Q₁₆

—

158

—

108

C₂×C₈

—

109

C₂×C₈

—

158

—

110

C₂×C₈

C₂²×D₇₉

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

158

—

113

C₄⋊C₄

—

158

—

114

C₄⋊C₄

—

158

—

115

C₄⋊C₄

—

158

—

116

C₄⋊C₄

C₂²×D₇₉

yes

—

117

C₂²⋊C₄

—

158

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

158

—

122

C₄²

C₂²×D₇₉

yes

characteristic

123

C₂³

—

124

Q₈

—

125

Q₈

—

158

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

158

—

132

C₂×C₄

—

158

—

133

C₂×C₄

—

158

—

134

C₂×C₄

D₄×D₇₉

yes

characteristic

135

C₂×C₄

D₄×D₇₉

yes

characteristic

136

C₂×C₄

C₂³×D₇₉

yes

characteristic

137

C₈

—

158

—

138

C₈

#11929625

yes

—

139

C₂²

—

140

C₂²

—

158

—

141

C₂²

—

158

—

142

C₂²

C₂×D₄×D₇₉

yes

characteristic

143

C₄

—

144

C₄

—

316

—

145

C₄

—

146

C₄

—

158

—

147

C₄

—

158

—

148

C₄

Q₁₆×D₇₉

yes

—

149

C₄

#14579180

yes

—

150

C₄

C₂×#11929625

yes

—

151

C₂

—

158

—

152

C₂

#19099114

yes

characteristic

153

C₂

C₂×Q₁₆×D₇₉

yes

characteristic

154

C₂

C₂×#14579180

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#500×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂²×D₇₉	C₂×D₄
hypercenter	#500	D₇₉
hypocenter	C₇₉	#3170
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#500×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂²×D₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
2. #19098943	C₂	semidirect
3. #19098915	C₂	semidirect
5. #19098657	C₂	semidirect
7. #500×C₇₉	C₂	semidirect
57. C₄×D₇₉	Q₁₆	semidirect
78. C₇₉	#3170	semidirect
80. #500	D₇₉	semidirect

H ≅ G/N

type

2. #19098943

C₂

semidirect

3. #19098915

C₂

semidirect

5. #19098657

C₂

semidirect

7. #500×C₇₉

C₂

semidirect

57. C₄×D₇₉

Q₁₆

semidirect

78. C₇₉

#3170

semidirect

80. #500

D₇₉

semidirect

Subgroups — #23773987

Conjugacy classes of subgroups

Complements