Group #23769380 — subgroups

Subgroups — #23769380

Order 10112.

360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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	#19098502	C₂	1	4	yes	maximal
2	#19098496	C₂	1	4	yes	maximal
3	#19098462	C₂	1	2	yes	maximal
4	#19098459	C₂	1	2	yes	maximal
5	#19098429	C₂	1	1	yes	maximal, characteristic
6	#19098409	C₂	1	1	yes	maximal, characteristic
7	#384×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	—
10	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₇₉⋊#95	C₂²	1	2	yes	—
14	C₇₉⋊#95	C₂²	1	2	yes	—
15	C₇₉⋊#95	C₂²	1	4	yes	—
16	C₇₉⋊#95	C₂²	1	4	yes	—
17	C₇₉⋊#95	C₂²	1	4	yes	—
18	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
19	C₂×C₄⋊C₄×C₇₉	C₂²	1	4	yes	—
20	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₇₉	C₂³	1	2	yes	—
23	C₂²×Dic₇₉	C₂³	1	4	yes	—
24	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
25	C₄⋊Dic₇₉	—	2	4	no	—
26	C₄⋊Dic₇₉	—	4	4	no	—
27	Dic₇₉⋊C₄	—	4	4	no	—
28	C₄×Dic₇₉	—	2	2	no	—
29	C₄×Dic₇₉	—	2	2	no	—
30	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
31	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
32	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₇₉	—	2	4	no	—
34	C₄⋊C₄×C₇₉	—	4	4	no	—
35	C₄²×C₇₉	Q₈	1	4	yes	—
36	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
41	C₂×C₄×C₇₉	—	2	4	no	—
42	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
43	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
44	C₂×C₄×C₇₉	#41	1	2	yes	—
45	C₂×C₄×C₇₉	#41	1	2	yes	—
46	C₂×Dic₇₉	—	2	1	no	—
47	C₂×Dic₇₉	—	2	1	no	—
48	C₂×Dic₇₉	—	2	2	no	—
49	C₂×Dic₇₉	—	2	4	no	—
50	C₂×Dic₇₉	—	2	2	no	—
51	C₂×Dic₇₉	—	2	4	no	—
52	C₂×Dic₇₉	—	2	2	no	—
53	C₂×Dic₇₉	—	2	2	no	—
54	C₂×Dic₇₉	—	2	2	no	—
55	C₂×Dic₇₉	—	2	4	no	—
56	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
57	C₂²×C₇₉	C₂×#41	1	1	yes	characteristic
58	C₂²×C₇₉	C₂×#41	1	1	yes	characteristic
59	C₂²×C₇₉	H(5,𝔽₂)	1	2	yes	—
60	C₂²×C₇₉	2₋¹⁺⁴	1	2	yes	—
61	C₄×C₇₉	—	2	4	no	—
62	C₄×C₇₉	—	4	4	no	—
63	C₄×C₇₉	#125	1	4	yes	—
64	Dic₇₉	—	4	1	no	—
65	Dic₇₉	—	4	1	no	—
66	Dic₇₉	—	4	2	no	—
67	Dic₇₉	—	4	4	no	—
68	C₂×C₇₉	C₂×#125	1	1	yes	characteristic
69	C₂×C₇₉	#540	1	1	yes	characteristic
70	C₂×C₇₉	#541	1	1	yes	characteristic
71	C₂×C₇₉	#542	1	2	yes	—
72	C₂×C₇₉	#544	1	2	yes	—
73	#2647	—	79	1	no	maximal, Sylow
74	C₇₉	#2647	1	1	yes	characteristic, complemented, Sylow
75	#400	—	79	4	no	—
76	#398	—	79	4	no	—
77	#389	—	79	2	no	—
78	#389	—	79	2	no	—
79	#384	D₇₉	1	1	yes	characteristic
80	#382	—	79	1	no	—
81	#376	—	79	1	no	—
82	C₂×C₄⋊C₄	—	79	4	no	—
83	C₂×C₄⋊C₄	—	79	4	no	—
84	C₂×C₄⋊C₄	—	79	2	no	—
85	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
86	C₂×C₄⋊C₄	C₂×D₇₉	1	4	yes	—
87	C₂×C₄²	—	79	1	no	—
88	C₂×C₄²	—	79	1	no	—
89	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
90	#95	—	79	2	no	—
91	#95	—	79	2	no	—
92	#95	—	79	4	no	—
93	#95	—	79	4	no	—
94	#95	—	79	4	no	—
95	C₂²×C₄	—	79	1	no	—
96	C₂²×C₄	—	79	2	no	—
97	C₂²×C₄	—	79	4	no	—
98	C₂²×C₄	—	79	1	no	—
99	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
100	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
101	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
102	C₄⋊C₄	—	2	4	no	—
103	C₄⋊C₄	—	4	4	no	—
104	C₄⋊C₄	—	316	4	no	—
105	C₄⋊C₄	—	316	4	no	—
106	C₄⋊C₄	—	158	4	no	—
107	C₄²	—	158	2	no	—
108	C₄²	—	158	2	no	—
109	C₄²	Dic₁₅₈	1	4	yes	—
110	C₂³	C₂³×D₇₉	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	158	1	no	—
117	C₂×C₄	—	158	1	no	—
118	C₂×C₄	—	158	2	no	—
119	C₂×C₄	—	158	4	no	—
120	C₂×C₄	—	158	2	no	—
121	C₂×C₄	—	158	4	no	—
122	C₂×C₄	—	158	2	no	—
123	C₂×C₄	—	158	2	no	—
124	C₂×C₄	—	158	2	no	—
125	C₂×C₄	—	158	4	no	—
126	C₂×C₄	C₂×Dic₁₅₈	1	4	yes	—
127	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
128	C₂×C₄	#11929623	1	2	yes	—
129	C₂×C₄	#11929625	1	2	yes	—
130	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
131	C₂²	C₂×#11929623	1	1	yes	characteristic
132	C₂²	C₂×#11929625	1	1	yes	characteristic
133	C₂²	#14579206	1	2	yes	—
134	C₂²	#14579209	1	2	yes	—
135	C₄	—	2	4	no	—
136	C₄	—	4	4	no	—
137	C₄	—	316	1	no	—
138	C₄	—	316	1	no	—
139	C₄	—	316	2	no	—
140	C₄	—	316	4	no	—
141	C₄	#14579152	1	4	yes	—
142	C₂	C₂×#14579152	1	1	yes	characteristic
143	C₂	#19099167	1	1	yes	characteristic
144	C₂	#19099174	1	1	yes	characteristic
145	C₂	#19099187	1	2	yes	—
146	C₂	#19099194	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098502

C₂

yes

maximal

#19098496

C₂

yes

maximal

#19098462

C₂

yes

maximal

#19098459

C₂

yes

maximal

#19098429

C₂

yes

maximal, characteristic

#19098409

C₂

yes

maximal, characteristic

#384×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

Q₈

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

characteristic

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

2₋¹⁺⁴

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#125

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#544

yes

—

#2647

—

maximal, Sylow

C₇₉

#2647

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic

#382

—

#376

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

100

C₂²×C₄

C₂²×D₇₉

yes

—

101

C₂²×C₄

C₂²×D₇₉

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

316

—

105

C₄⋊C₄

—

316

—

106

C₄⋊C₄

—

158

—

107

C₄²

—

158

—

108

C₄²

—

158

—

109

C₄²

Dic₁₅₈

yes

—

110

C₂³

C₂³×D₇₉

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

158

—

117

C₂×C₄

—

158

—

118

C₂×C₄

—

158

—

119

C₂×C₄

—

158

—

120

C₂×C₄

—

158

—

121

C₂×C₄

—

158

—

122

C₂×C₄

—

158

—

123

C₂×C₄

—

158

—

124

C₂×C₄

—

158

—

125

C₂×C₄

—

158

—

126

C₂×C₄

C₂×Dic₁₅₈

yes

—

127

C₂×C₄

C₂×Dic₁₅₈

yes

—

128

C₂×C₄

#11929623

yes

—

129

C₂×C₄

#11929625

yes

—

130

C₂²

C₂²×Dic₁₅₈

yes

characteristic

131

C₂²

C₂×#11929623

yes

characteristic

132

C₂²

C₂×#11929625

yes

characteristic

133

C₂²

#14579206

yes

—

134

C₂²

#14579209

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

316

—

138

C₄

—

316

—

139

C₄

—

316

—

140

C₄

—

316

—

141

C₄

#14579152

yes

—

142

C₂

C₂×#14579152

yes

characteristic

143

C₂

#19099167

yes

characteristic

144

C₂

#19099174

yes

characteristic

145

C₂

#19099187

yes

—

146

C₂

#19099194

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#384×C₇₉	C₂
hypercenter	#384	D₇₉
hypocenter	C₇₉	#2647
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#384×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
74. C₇₉	#2647	semidirect

H ≅ G/N

type

74. C₇₉

#2647

semidirect

Subgroups — #23769380

Conjugacy classes of subgroups

Complements