Group #23769370 — subgroups

Subgroups — #23769370

Order 10112.

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

normal subgroups only

This group has 436 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	#19098505	C₂	1	4	yes	maximal, complemented
2	#19098497	C₂	1	4	yes	maximal, complemented
3	#19098436	C₂	1	4	yes	maximal
4	#19098423	C₂	1	2	yes	maximal
5	C₂×#95×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
9	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
10	C₂×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
11	C₇₉⋊#95	C₂²	1	4	yes	—
12	C₇₉⋊#95	C₂²	1	4	yes	—
13	C₇₉⋊#95	C₂²	1	4	yes	—
14	C₂³×C₄×C₇₉	C₂²	1	2	yes	—
15	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
16	#95×C₇₉	C₂²	1	4	yes	—
17	C₂²×Dic₇₉	C₂³	1	4	yes	—
18	C₂²×Dic₇₉	C₂³	1	4	yes	—
19	C₄⋊Dic₇₉	—	4	2	no	—
20	C₄⋊Dic₇₉	—	4	2	no	—
21	Dic₇₉⋊C₄	—	4	4	no	—
22	Dic₇₉⋊C₄	—	4	4	no	—
23	C₂²⋊Dic₇₉	—	2	8	no	—
24	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₇₉	—	2	4	no	—
26	C₂²×C₄×C₇₉	—	4	2	no	—
27	C₂²×C₄×C₇₉	—	4	2	no	—
28	C₂²×C₄×C₇₉	—	4	2	no	—
29	C₂²×C₄×C₇₉	Q₈	1	4	yes	—
30	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
31	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
32	C₂³×C₇₉	—	2	1	no	—
33	C₂³×C₇₉	—	2	2	no	—
34	C₂³×C₇₉	—	2	1	no	—
35	C₂³×C₇₉	C₂×Q₈	1	2	yes	—
36	C₂³×C₇₉	#41	1	4	yes	—
37	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
38	C₂×C₄×C₇₉	—	2	2	no	—
39	C₂×C₄×C₇₉	—	2	2	no	—
40	C₂×C₄×C₇₉	—	2	4	no	—
41	C₂×C₄×C₇₉	—	2	4	no	—
42	C₂×C₄×C₇₉	—	2	4	no	—
43	C₂×C₄×C₇₉	—	4	4	no	—
44	C₂×C₄×C₇₉	—	4	8	no	—
45	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
46	C₂×Dic₇₉	—	2	4	no	—
47	C₂×Dic₇₉	—	2	4	no	—
48	C₂×Dic₇₉	—	2	4	no	—
49	C₂×Dic₇₉	—	2	4	no	—
50	C₂×Dic₇₉	—	2	4	no	—
51	C₂×Dic₇₉	—	2	4	no	—
52	C₂²×C₇₉	—	2	4	no	—
53	C₂²×C₇₉	—	2	4	no	—
54	C₂²×C₇₉	—	2	2	no	—
55	C₂²×C₇₉	—	2	2	no	—
56	C₂²×C₇₉	#125	1	4	yes	—
57	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
58	C₂²×C₇₉	C₂×#41	1	2	yes	—
59	C₂²×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
60	C₂²×C₇₉	H(5,𝔽₂)	1	2	yes	—
61	C₂²×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
62	C₄×C₇₉	—	2	4	no	—
63	C₄×C₇₉	—	4	4	no	—
64	Dic₇₉	—	4	4	no	—
65	Dic₇₉	—	4	4	no	—
66	C₂×C₇₉	—	2	4	no	—
67	C₂×C₇₉	C₂×#125	1	1	yes	characteristic
68	C₂×C₇₉	#538	1	2	yes	—
69	C₂×C₇₉	#539	1	2	yes	—
70	C₂×C₇₉	#543	1	1	yes	characteristic
71	C₂×C₇₉	#544	1	1	yes	characteristic
72	#2646	—	79	1	no	maximal, Sylow
73	C₇₉	#2646	1	1	yes	characteristic, complemented, Sylow
74	#400	—	79	4	no	—
75	#398	—	79	4	no	—
76	#385	—	79	4	no	—
77	#380	—	79	2	no	—
78	C₂×#95	D₇₉	1	1	yes	characteristic
79	C₂³×C₄	C₂×D₇₉	1	2	yes	—
80	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic
81	C₂×C₄⋊C₄	—	79	2	no	—
82	C₂×C₄⋊C₄	—	79	2	no	—
83	C₂×C₄⋊C₄	—	79	4	no	—
84	C₂×C₄⋊C₄	—	79	4	no	—
85	C₂×C₂²⋊C₄	—	79	4	no	—
86	#95	—	79	4	no	—
87	#95	—	79	4	no	—
88	#95	—	79	4	no	—
89	#95	C₂×D₇₉	1	4	yes	—
90	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
91	C₂²×C₄	—	2	4	no	—
92	C₂²×C₄	—	4	2	no	—
93	C₂²×C₄	—	4	2	no	—
94	C₂²×C₄	—	4	2	no	—
95	C₂²×C₄	—	79	4	no	—
96	C₂²×C₄	—	79	4	no	—
97	C₂²×C₄	Dic₁₅₈	1	4	yes	—
98	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
99	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
100	C₄⋊C₄	—	316	4	no	—
101	C₄⋊C₄	—	316	4	no	—
102	C₄⋊C₄	—	316	2	no	—
103	C₄⋊C₄	—	316	2	no	—
104	C₂²⋊C₄	—	158	8	no	—
105	C₂³	—	2	1	no	—
106	C₂³	—	2	2	no	—
107	C₂³	—	2	1	no	—
108	C₂³	C₂×Dic₁₅₈	1	2	yes	—
109	C₂³	#11929624	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	—	4	4	no	—
117	C₂×C₄	—	4	8	no	—
118	C₂×C₄	—	158	4	no	—
119	C₂×C₄	—	158	4	no	—
120	C₂×C₄	—	158	4	no	—
121	C₂×C₄	—	158	4	no	—
122	C₂×C₄	—	158	4	no	—
123	C₂×C₄	—	158	4	no	—
124	C₂×C₄	C₂×Dic₁₅₈	1	4	yes	—
125	C₂²	—	2	4	no	—
126	C₂²	—	2	4	no	—
127	C₂²	—	2	2	no	—
128	C₂²	—	2	2	no	—
129	C₂²	#14579153	1	4	yes	—
130	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
131	C₂²	C₂×#11929624	1	2	yes	—
132	C₂²	#14579206	1	1	yes	characteristic
133	C₂²	#14579206	1	2	yes	—
134	C₂²	#14579209	1	1	yes	characteristic
135	C₄	—	2	4	no	—
136	C₄	—	4	4	no	—
137	C₄	—	316	4	no	—
138	C₄	—	316	4	no	—
139	C₂	—	2	4	no	—
140	C₂	C₂×#14579153	1	1	yes	characteristic
141	C₂	#19099151	1	2	yes	—
142	C₂	#19099160	1	2	yes	—
143	C₂	#19099189	1	1	yes	characteristic
144	C₂	#19099194	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098505

C₂

yes

maximal, complemented

#19098497

C₂

yes

maximal, complemented

#19098436

C₂

yes

maximal

#19098423

C₂

yes

maximal

C₂×#95×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂³×C₄×C₇₉

C₂²

yes

—

C₂³×C₄×C₇₉

C₂²

yes

characteristic

#95×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂⁴×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂×Q₈

yes

—

C₂³×C₇₉

#41

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×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#125

yes

—

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

2₋¹⁺⁴

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#125

yes

characteristic

C₂×C₇₉

#538

yes

—

C₂×C₇₉

#539

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

C₂×#95

D₇₉

yes

characteristic

C₂³×C₄

C₂×D₇₉

yes

—

C₂³×C₄

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

C₂×D₇₉

yes

—

C₂⁴

C₂²×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₁₅₈

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

100

C₄⋊C₄

—

316

—

101

C₄⋊C₄

—

316

—

102

C₄⋊C₄

—

316

—

103

C₄⋊C₄

—

316

—

104

C₂²⋊C₄

—

158

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂×Dic₁₅₈

yes

—

109

C₂³

#11929624

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

—

117

C₂×C₄

—

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

C₂×Dic₁₅₈

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#14579153

yes

—

130

C₂²

C₂²×Dic₁₅₈

yes

characteristic

131

C₂²

C₂×#11929624

yes

—

132

C₂²

#14579206

yes

characteristic

133

C₂²

#14579206

yes

—

134

C₂²

#14579209

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

316

—

138

C₄

—

316

—

139

C₂

—

140

C₂

C₂×#14579153

yes

characteristic

141

C₂

#19099151

yes

—

142

C₂

#19099160

yes

—

143

C₂

#19099189

yes

characteristic

144

C₂

#19099194

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, cosocle	C₂³×C₇₉	C₂⁴
Fitting	C₂×#95×C₇₉	C₂
prime radical	C₂⁴×C₇₉	C₂³
hypercenter	C₂×#95	D₇₉
hypocenter	C₇₉	#2646
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, cosocle

C₂³×C₇₉

C₂⁴

Fitting

C₂×#95×C₇₉

C₂

prime radical

C₂⁴×C₇₉

C₂³

hypercenter

C₂×#95

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
1. #19098505	C₂	semidirect
2. #19098497	C₂	semidirect
73. C₇₉	#2646	semidirect

H ≅ G/N

type

1. #19098505

C₂

semidirect

2. #19098497

C₂

semidirect

73. C₇₉

#2646

semidirect

Subgroups — #23769370

Conjugacy classes of subgroups

Complements