Group #23772035 — subgroups

Subgroups — #23772035

Order 10112.

392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14579120	C₂	1	1	yes	maximal, characteristic
2	#19098621	C₂	1	8	yes	maximal, complemented
3	#19098586	C₂	1	2	yes	maximal, complemented
4	#19098527	C₂	1	1	yes	maximal, characteristic
5	M₁₆×Dic₇₉	C₂	1	2	yes	maximal, complemented
6	#407×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂×#11929608	C₂²	1	2	yes	—
8	#14579120	C₄	1	4	yes	—
9	#14579120	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₇₉	C₄	1	2	yes	—
11	C₂×C₂²⋊Dic₇₉	C₄	1	2	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
14	Dic₇₉⋊C₈	C₂²	1	8	yes	complemented
15	C₂²⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
16	#14579071	C₂²	1	4	yes	complemented
17	C₈×Dic₇₉	C₂²	1	4	yes	complemented
18	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
20	C₂²⋊C₈×C₇₉	C₂²	1	4	yes	—
21	C₂²×Dic₇₉	C₂×C₄	1	2	yes	—
22	C₂²×Dic₇₉	C₂×C₄	1	2	yes	—
23	#11929608	—	2	4	no	—
24	C₂×C₇₉⋊C₈	C₂³	1	4	yes	—
25	C₄⋊Dic₇₉	C₂×C₄	1	8	yes	—
26	C₂²⋊Dic₇₉	C₂×C₄	1	8	yes	—
27	C₄×Dic₇₉	C₂×C₄	1	2	yes	—
28	C₄×Dic₇₉	C₂×C₄	1	2	yes	—
29	C₄×Dic₇₉	C₂³	1	2	yes	—
30	C₄×Dic₇₉	C₂³	1	2	yes	—
31	C₂⁴×C₇₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₇₉	—	2	4	no	—
33	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₇₉	C₂×C₄	1	2	yes	—
35	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
37	M₁₆×C₇₉	—	2	4	no	—
38	C₂×C₈×C₇₉	C₂³	1	4	yes	—
39	C₂³×C₇₉	—	2	2	no	—
40	C₂³×C₇₉	—	4	2	no	—
41	C₂³×C₇₉	C₂²×C₄	1	2	yes	—
42	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₇₉	—	2	2	no	—
44	C₂×C₄×C₇₉	—	2	4	no	—
45	C₂×C₄×C₇₉	—	2	4	no	—
46	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₇₉	#41	1	4	yes	—
49	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₇₉	—	4	2	no	—
51	C₂×Dic₇₉	—	4	2	no	—
52	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
53	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
54	C₈×C₇₉	—	2	4	no	—
55	C₇₉⋊C₈	—	2	4	no	—
56	C₂²×C₇₉	—	2	2	no	—
57	C₂²×C₇₉	—	2	2	no	—
58	C₂²×C₇₉	—	2	4	no	—
59	C₂²×C₇₉	—	4	4	no	—
60	C₂²×C₇₉	#117	1	2	yes	—
61	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₇₉	—	2	2	no	—
63	C₄×C₇₉	#117	1	2	yes	—
64	C₄×C₇₉	C₂×#41	1	2	yes	—
65	Dic₇₉	—	2	4	no	—
66	Dic₇₉	—	2	4	no	—
67	C₂×C₇₉	—	2	2	no	—
68	C₂×C₇₉	—	4	2	no	—
69	C₂×C₇₉	C₂×#117	1	1	yes	characteristic
70	C₂×C₇₉	#568	1	2	yes	—
71	#2921	—	79	1	no	maximal, Sylow
72	C₇₉	#2921	1	1	yes	characteristic, complemented, Sylow
73	C₂×#117	—	79	1	no	—
74	#433	—	79	8	no	—
75	#423	—	79	2	no	—
76	#407	—	79	1	no	—
77	#407	D₇₉	1	1	yes	characteristic
78	C₄×M₁₆	—	79	2	no	—
79	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic
80	C₂×M₁₆	—	79	2	no	—
81	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
82	#117	—	79	4	no	—
83	#117	—	79	4	no	—
84	C₂×C₄⋊C₄	—	79	2	no	—
85	C₂×C₂²⋊C₄	—	79	2	no	—
86	C₂×C₄²	—	79	1	no	—
87	C₂×C₄²	—	79	1	no	—
88	C₄⋊C₈	—	79	8	no	—
89	C₂²⋊C₈	—	79	4	no	—
90	C₂²⋊C₈	C₂×D₇₉	1	4	yes	—
91	#97	—	79	4	no	—
92	C₄×C₈	—	79	4	no	—
93	C₂⁴	C₄×D₇₉	1	1	yes	characteristic
94	C₂²×C₄	—	2	4	no	—
95	C₂²×C₄	—	79	2	no	—
96	C₂²×C₄	—	79	2	no	—
97	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
98	C₂²×C₄	C₄×D₇₉	1	2	yes	—
99	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
100	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
101	M₁₆	—	2	4	no	—
102	M₁₆	—	158	4	no	—
103	C₂×C₈	—	79	4	no	—
104	C₂×C₈	C₂²×D₇₉	1	4	yes	—
105	C₄⋊C₄	—	79	8	no	—
106	C₂²⋊C₄	—	79	8	no	—
107	C₄²	—	79	2	no	—
108	C₄²	—	79	2	no	—
109	C₄²	—	79	2	no	—
110	C₄²	—	79	2	no	—
111	C₂³	—	2	2	no	—
112	C₂³	—	4	2	no	—
113	C₂³	C₂×C₄×D₇₉	1	2	yes	—
114	C₂³	C₂×C₄×D₇₉	1	1	yes	characteristic
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	316	2	no	—
119	C₂×C₄	—	316	2	no	—
120	C₂×C₄	—	79	4	no	—
121	C₂×C₄	—	79	4	no	—
122	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
123	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
124	C₂×C₄	#11929623	1	4	yes	—
125	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
126	C₈	—	2	4	no	—
127	C₈	—	158	4	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	2	2	no	—
130	C₂²	—	2	4	no	—
131	C₂²	—	4	4	no	—
132	C₂²	#14579117	1	2	yes	—
133	C₂²	C₂²×C₄×D₇₉	1	1	yes	characteristic
134	C₄	—	2	2	no	—
135	C₄	—	158	4	no	—
136	C₄	—	158	4	no	—
137	C₄	#14579117	1	2	yes	—
138	C₄	C₂×#11929623	1	2	yes	—
139	C₂	—	2	2	no	—
140	C₂	—	4	2	no	—
141	C₂	C₂×#14579117	1	1	yes	characteristic
142	C₂	#19099329	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579120

C₂

yes

maximal, characteristic

#19098621

C₂

yes

maximal, complemented

#19098586

C₂

yes

maximal, complemented

#19098527

C₂

yes

maximal, characteristic

M₁₆×Dic₇₉

C₂

yes

maximal, complemented

#407×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

—

#14579120

C₄

yes

—

#14579120

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₄

yes

—

C₂×C₂²⋊Dic₇₉

C₄

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

Dic₇₉⋊C₈

C₂²

yes

complemented

C₂²⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579071

C₂²

yes

complemented

C₈×Dic₇₉

C₂²

yes

complemented

C₂³×C₄×C₇₉

C₂²

yes

characteristic

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂²⋊C₈×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

C₂×C₄

yes

—

C₂²×Dic₇₉

C₂×C₄

yes

—

#11929608

—

C₂×C₇₉⋊C₈

C₂³

yes

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

C₂²⋊Dic₇₉

C₂×C₄

yes

—

C₄×Dic₇₉

C₂×C₄

yes

—

C₄×Dic₇₉

C₂×C₄

yes

—

C₄×Dic₇₉

C₂³

yes

—

C₄×Dic₇₉

C₂³

yes

—

C₂⁴×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂²×C₄

yes

—

C₂³×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#117

yes

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#117

yes

—

C₄×C₇₉

C₂×#41

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#117

yes

characteristic

C₂×C₇₉

#568

yes

—

#2921

—

maximal, Sylow

C₇₉

#2921

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic

C₄×M₁₆

—

C₂³×C₄

C₂×D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

C₂×D₇₉

yes

—

#97

—

C₄×C₈

—

C₂⁴

C₄×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

100

C₂²×C₄

C₂²×D₇₉

yes

characteristic

101

M₁₆

—

102

M₁₆

—

158

—

103

C₂×C₈

—

104

C₂×C₈

C₂²×D₇₉

yes

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₂³

—

112

C₂³

—

113

C₂³

C₂×C₄×D₇₉

yes

—

114

C₂³

C₂×C₄×D₇₉

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

316

—

119

C₂×C₄

—

316

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₂×C₄×D₇₉

yes

—

123

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

124

C₂×C₄

#11929623

yes

—

125

C₂×C₄

C₂³×D₇₉

yes

characteristic

126

C₈

—

127

C₈

—

158

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

#14579117

yes

—

133

C₂²

C₂²×C₄×D₇₉

yes

characteristic

134

C₄

—

135

C₄

—

158

—

136

C₄

—

158

—

137

C₄

#14579117

yes

—

138

C₄

C₂×#11929623

yes

—

139

C₂

—

140

C₂

—

141

C₂

C₂×#14579117

yes

characteristic

142

C₂

#19099329

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₇₉
commutator, socle	C₂²×C₇₉	C₂³×C₄
Fitting	#407×C₇₉	C₂
prime radical	C₂⁴×C₇₉	C₂×C₄
cosocle	C₂×C₄×C₇₉	C₂⁴
hypercenter	#407	D₇₉
hypocenter	C₇₉	#2921
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ #407

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₇₉

commutator, socle

C₂²×C₇₉

C₂³×C₄

Fitting

#407×C₇₉

C₂

prime radical

C₂⁴×C₇₉

C₂×C₄

cosocle

C₂×C₄×C₇₉

C₂⁴

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₄ ◁ #407

N	H ≅ G/N	type
2. #19098621	C₂	semidirect
3. #19098586	C₂	semidirect
5. M₁₆×Dic₇₉	C₂	semidirect
14. Dic₇₉⋊C₈	C₂²	semidirect
16. #14579071	C₂²	semidirect
17. C₈×Dic₇₉	C₂²	semidirect
72. C₇₉	#2921	semidirect

H ≅ G/N

type

2. #19098621

C₂

semidirect

3. #19098586

C₂

semidirect

5. M₁₆×Dic₇₉

C₂

semidirect

14. Dic₇₉⋊C₈

C₂²

semidirect

16. #14579071

C₂²

semidirect

17. C₈×Dic₇₉

C₂²

semidirect

72. C₇₉

#2921

semidirect

Subgroups — #23772035

Conjugacy classes of subgroups

Complements