Group #23765739 — subgroups

Subgroups — #23765739

Order 10112.

752 conjugacy classes of subgroups; only the 341 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 341 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×#14579118	C₂	1	2	yes	maximal
2	C₂×C₄²×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#19098414	C₂	1	4	yes	maximal, complemented
4	#19098410	C₂	1	4	yes	maximal
5	#19098409	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄²×Dic₇₉	C₂	1	2	yes	maximal, complemented
7	#376×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₇₉	C₂²	1	2	yes	—
9	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
10	#14579118	C₄	1	16	yes	complemented
11	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
12	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₇₉	C₂²	1	8	yes	—
14	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
16	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
17	C₄²×D₇₉	C₄	1	8	yes	complemented
18	C₇₉⋊#95	C₂²	1	4	yes	—
19	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₇₉	C₂²	1	2	yes	—
21	#95×C₇₉	C₂²	1	4	yes	—
22	C₂³×D₇₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₇₉	C₂³	1	4	yes	—
24	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₇₉	C₂³	1	2	yes	—
26	C₂×C₄×D₇₉	—	2	8	no	—
27	C₂×C₄×D₇₉	C₂×C₄	1	8	yes	—
28	C₂×C₄×D₇₉	C₂×C₄	1	4	yes	—
29	C₂×C₄×D₇₉	C₂×C₄	1	8	yes	—
30	Dic₇₉⋊C₄	C₂×C₄	1	16	yes	complemented
31	(C₂×D₇₉)⋊C₄	C₂×C₄	1	16	yes	—
32	C₄×Dic₇₉	—	2	16	no	—
33	C₄×Dic₇₉	C₂×C₄	1	8	yes	—
34	C₄×Dic₇₉	C₂×C₄	1	4	yes	—
35	C₄×Dic₇₉	C₂×C₄	1	8	yes	complemented
36	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
38	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
39	C₄²×C₇₉	C₂×C₄	1	4	yes	—
40	C₄²×C₇₉	C₂×C₄	1	8	yes	complemented
41	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
42	C₂²×D₇₉	—	2	4	no	—
43	C₂²×D₇₉	C₂²×C₄	1	4	yes	—
44	C₂²×D₇₉	C₂²×C₄	1	2	yes	—
45	C₂×C₄×C₇₉	—	2	8	no	—
46	C₂×C₄×C₇₉	—	2	4	no	—
47	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
48	C₂×C₄×C₇₉	C₂²×C₄	1	8	yes	—
49	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
50	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
51	C₂×Dic₇₉	—	2	8	no	—
52	C₂×Dic₇₉	C₂²×C₄	1	8	yes	—
53	C₂×Dic₇₉	C₂²×C₄	1	2	yes	—
54	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
55	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
56	C₂×Dic₇₉	#41	1	8	yes	—
57	C₄×D₇₉	—	2	16	no	—
58	C₄×D₇₉	C₄²	1	16	yes	complemented
59	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₇₉	C₂³×C₄	1	2	yes	—
61	C₂²×C₇₉	C₂×#41	1	4	yes	—
62	C₂×D₇₉	—	2	4	no	—
63	C₂×D₇₉	—	2	8	no	—
64	C₂×D₇₉	C₂×C₄²	1	4	yes	—
65	C₄×C₇₉	—	2	4	no	—
66	C₄×C₇₉	—	2	8	no	—
67	C₄×C₇₉	C₂×C₄²	1	4	yes	—
68	Dic₇₉	—	2	8	no	—
69	Dic₇₉	C₂×C₄²	1	4	yes	—
70	Dic₇₉	#117	1	8	yes	complemented
71	C₂×C₇₉	C₂²×C₄²	1	1	yes	characteristic
72	C₂×C₇₉	C₂×#117	1	2	yes	—
73	C₂×C₇₉	C₄×#41	1	4	yes	—
74	D₇₉	—	2	4	no	—
75	C₄×#117	—	79	1	no	maximal, Sylow
76	C₇₉	C₄×#117	1	1	yes	characteristic, complemented, Sylow
77	C₂×#117	—	79	2	no	—
78	C₂²×C₄²	—	79	1	no	—
79	C₄×C₄⋊C₄	—	79	4	no	—
80	C₄×C₂²⋊C₄	—	79	4	no	—
81	#376	—	79	1	no	—
82	#376	D₇₉	1	1	yes	characteristic, complemented
83	C₄³	—	79	2	no	—
84	C₂³×C₄	—	79	1	no	—
85	C₂³×C₄	—	79	2	no	—
86	#117	—	79	16	no	—
87	C₂×C₄⋊C₄	—	79	4	no	—
88	C₂×C₂²⋊C₄	—	79	4	no	—
89	C₂×C₄²	—	79	2	no	—
90	C₂×C₄²	—	79	2	no	—
91	C₂×C₄²	—	79	1	no	—
92	C₂×C₄²	—	79	8	no	—
93	C₂×C₄²	—	79	8	no	—
94	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
95	C₂×C₄²	C₂×D₇₉	1	2	yes	—
96	#95	—	79	4	no	—
97	#95	C₂×D₇₉	1	4	yes	—
98	C₂⁴	—	79	1	no	—
99	C₂²×C₄	—	79	2	no	—
100	C₂²×C₄	—	79	1	no	—
101	C₂²×C₄	—	79	4	no	—
102	C₂²×C₄	—	79	8	no	—
103	C₂²×C₄	—	79	4	no	—
104	C₂²×C₄	—	79	8	no	—
105	C₂²×C₄	—	158	8	no	—
106	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
107	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
108	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
109	C₄⋊C₄	—	79	16	no	—
110	C₂²⋊C₄	—	79	16	no	—
111	C₄²	—	79	8	no	—
112	C₄²	—	79	4	no	—
113	C₄²	—	79	8	no	—
114	C₄²	—	158	16	no	—
115	C₄²	C₄×D₇₉	1	4	yes	—
116	C₄²	C₄×D₇₉	1	8	yes	complemented
117	C₂³	—	79	4	no	—
118	C₂³	—	79	2	no	—
119	C₂³	—	158	4	no	—
120	C₂³	C₂³×D₇₉	1	1	yes	characteristic
121	C₂×C₄	—	2	8	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	79	8	no	—
124	C₂×C₄	—	79	2	no	—
125	C₂×C₄	—	79	4	no	—
126	C₂×C₄	—	79	4	no	—
127	C₂×C₄	—	79	16	no	—
128	C₂×C₄	—	79	8	no	—
129	C₂×C₄	—	158	16	no	—
130	C₂×C₄	—	158	8	no	—
131	C₂×C₄	C₂×C₄×D₇₉	1	4	yes	—
132	C₂×C₄	C₂×C₄×D₇₉	1	8	yes	—
133	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
134	C₂×C₄	C₂×C₄×D₇₉	1	4	yes	—
135	C₂²	—	79	4	no	—
136	C₂²	—	158	4	no	—
137	C₂²	—	158	8	no	—
138	C₂²	C₂²×C₄×D₇₉	1	1	yes	characteristic
139	C₂²	C₂²×C₄×D₇₉	1	2	yes	—
140	C₂²	#41×D₇₉	1	4	yes	—
141	C₄	—	2	4	no	—
142	C₄	—	2	8	no	—
143	C₄	—	79	4	no	—
144	C₄	—	79	8	no	—
145	C₄	—	158	8	no	—
146	C₄	C₄²×D₇₉	1	4	yes	—
147	C₂	—	158	4	no	—
148	C₂	C₂×C₄²×D₇₉	1	1	yes	characteristic
149	C₂	#117×D₇₉	1	2	yes	—
150	C₂	#19099031	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579118

C₂

yes

maximal

C₂×C₄²×D₇₉

C₂

yes

maximal, characteristic

#19098414

C₂

yes

maximal, complemented

#19098410

C₂

yes

maximal

#19098409

C₂

yes

maximal, characteristic, complemented

C₄²×Dic₇₉

C₂

yes

maximal, complemented

#376×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₂²

yes

—

C₂²×C₄×D₇₉

C₂²

yes

characteristic

#14579118

C₄

yes

complemented

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₄²×D₇₉

C₄

yes

complemented

C₇₉⋊#95

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

—

C₂³×D₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

Dic₇₉⋊C₄

C₂×C₄

yes

complemented

(C₂×D₇₉)⋊C₄

C₂×C₄

yes

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂×C₄

yes

—

C₄×Dic₇₉

C₂×C₄

yes

—

C₄×Dic₇₉

C₂×C₄

yes

complemented

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

C₂²×C₄

yes

—

C₂²×D₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

#41

yes

—

C₄×D₇₉

—

C₄×D₇₉

C₄²

yes

complemented

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

C₂³×C₄

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

C₂×C₄²

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₄²

yes

—

Dic₇₉

—

Dic₇₉

C₂×C₄²

yes

—

Dic₇₉

#117

yes

complemented

C₂×C₇₉

C₂²×C₄²

yes

characteristic

C₂×C₇₉

C₂×#117

yes

—

C₂×C₇₉

C₄×#41

yes

—

D₇₉

—

C₄×#117

—

maximal, Sylow

C₇₉

C₄×#117

yes

characteristic, complemented, Sylow

C₂×#117

—

C₂²×C₄²

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

—

#376

D₇₉

yes

characteristic, complemented

C₄³

—

C₂³×C₄

—

C₂³×C₄

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₂×C₄²

C₂×D₇₉

yes

—

#95

—

#95

C₂×D₇₉

yes

—

C₂⁴

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

158

—

106

C₂²×C₄

C₂²×D₇₉

yes

—

107

C₂²×C₄

C₂²×D₇₉

yes

—

108

C₂²×C₄

C₂²×D₇₉

yes

characteristic

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

158

—

115

C₄²

C₄×D₇₉

yes

—

116

C₄²

C₄×D₇₉

yes

complemented

117

C₂³

—

118

C₂³

—

119

C₂³

—

158

—

120

C₂³

C₂³×D₇₉

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

158

—

130

C₂×C₄

—

158

—

131

C₂×C₄

C₂×C₄×D₇₉

yes

—

132

C₂×C₄

C₂×C₄×D₇₉

yes

—

133

C₂×C₄

C₂×C₄×D₇₉

yes

—

134

C₂×C₄

C₂×C₄×D₇₉

yes

—

135

C₂²

—

136

C₂²

—

158

—

137

C₂²

—

158

—

138

C₂²

C₂²×C₄×D₇₉

yes

characteristic

139

C₂²

C₂²×C₄×D₇₉

yes

—

140

C₂²

#41×D₇₉

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

158

—

146

C₄

C₄²×D₇₉

yes

—

147

C₂

—

158

—

148

C₂

C₂×C₄²×D₇₉

yes

characteristic

149

C₂

#117×D₇₉

yes

—

150

C₂

#19099031

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇₉
commutator	C₂×C₇₉	C₂²×C₄²
Frattini	C₂³	C₂³×D₇₉
Fitting	#376×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂³×D₇₉	C₂³
hypercenter	#376	D₇₉
hypocenter	C₇₉	C₄×#117
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₇₉

commutator

C₂×C₇₉

C₂²×C₄²

Frattini

C₂³

C₂³×D₇₉

Fitting

#376×C₇₉

C₂

socle, cosocle

C₂³×C₇₉

C₂⁴

prime radical

C₂³×D₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₇₉ ▷ C₇₉

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
3. #19098414	C₂	semidirect
5. #19098409	C₂	semidirect
6. C₄²×Dic₇₉	C₂	semidirect
7. #376×C₇₉	C₂	semidirect
10. #14579118	C₄	semidirect
17. C₄²×D₇₉	C₄	semidirect
30. Dic₇₉⋊C₄	C₂×C₄	semidirect
35. C₄×Dic₇₉	C₂×C₄	semidirect
40. C₄²×C₇₉	C₂×C₄	semidirect
58. C₄×D₇₉	C₄²	semidirect
70. Dic₇₉	#117	semidirect
76. C₇₉	C₄×#117	semidirect
82. #376	D₇₉	semidirect
116. C₄²	C₄×D₇₉	semidirect

H ≅ G/N

type

3. #19098414

C₂

semidirect

5. #19098409

C₂

semidirect

6. C₄²×Dic₇₉

C₂

semidirect

7. #376×C₇₉

C₂

semidirect

10. #14579118

C₄

semidirect

17. C₄²×D₇₉

C₄

semidirect

30. Dic₇₉⋊C₄

C₂×C₄

semidirect

35. C₄×Dic₇₉

C₂×C₄

semidirect

40. C₄²×C₇₉

C₂×C₄

semidirect

58. C₄×D₇₉

C₄²

semidirect

70. Dic₇₉

#117

semidirect

76. C₇₉

C₄×#117

semidirect

82. #376

D₇₉

semidirect

116. C₄²

C₄×D₇₉

semidirect

Subgroups — #23765739

Conjugacy classes of subgroups

Complements