Group #23766593 — subgroups

Subgroups — #23766593

Order 10112.

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

normal subgroups only

This group has 456 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×#14579155	C₂	1	1	yes	maximal, characteristic
2	#19098458	C₂	1	3	yes	maximal, complemented
3	#19098453	C₂	1	3	yes	maximal
4	#19098444	C₂	1	3	yes	maximal, complemented
5	#19098434	C₂	1	3	yes	maximal
6	#19098431	C₂	1	1	yes	maximal, characteristic, complemented
7	#384×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
9	#14579155	C₄	1	8	yes	complemented
10	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
11	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
12	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	3	yes	—
13	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	3	yes	—
14	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
15	C₇₉⋊#95	C₂²	1	3	yes	—
16	C₇₉⋊#95	C₂²	1	3	yes	—
17	C₇₉⋊#95	C₂²	1	3	yes	—
18	C₇₉⋊#95	C₂²	1	3	yes	—
19	C₂×C₄⋊C₄×C₇₉	C₂²	1	3	yes	—
20	C₂×C₄⋊C₄×C₇₉	C₂²	1	3	yes	—
21	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
22	C₂³×D₇₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₇₉	C₂³	1	3	yes	—
24	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₇₉	C₂³	1	3	yes	—
26	C₂×C₄×D₇₉	—	4	3	no	—
27	Dic₇₉⋊C₄	—	4	3	no	—
28	Dic₇₉⋊C₄	C₂×C₄	1	12	yes	complemented
29	(C₂×D₇₉)⋊C₄	—	4	3	no	—
30	(C₂×D₇₉)⋊C₄	C₂×C₄	1	12	yes	—
31	C₄×Dic₇₉	—	4	3	no	—
32	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
34	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
35	C₄⋊C₄×C₇₉	—	4	3	no	—
36	C₄⋊C₄×C₇₉	—	4	3	no	—
37	C₄²×C₇₉	C₂×C₄	1	4	yes	complemented
38	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
39	C₂²×D₇₉	—	2	3	no	—
40	C₂²×D₇₉	—	2	3	no	—
41	C₂²×D₇₉	C₂²×C₄	1	2	yes	—
42	C₂×C₄×C₇₉	—	2	3	no	—
43	C₂×C₄×C₇₉	—	2	3	no	—
44	C₂×C₄×C₇₉	—	2	3	no	—
45	C₂×C₄×C₇₉	—	2	3	no	—
46	C₂×C₄×C₇₉	—	2	3	no	—
47	C₂×C₄×C₇₉	—	2	3	no	—
48	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
49	C₂×Dic₇₉	—	2	3	no	—
50	C₂×Dic₇₉	—	2	3	no	—
51	C₂×Dic₇₉	—	2	3	no	—
52	C₂×Dic₇₉	—	2	3	no	—
53	C₂×Dic₇₉	—	2	6	no	—
54	C₂×Dic₇₉	C₂²×C₄	1	6	yes	—
55	C₄×D₇₉	—	4	4	no	—
56	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
57	C₂²×C₇₉	H(5,𝔽₂)	1	3	yes	—
58	C₂²×C₇₉	2₋¹⁺⁴	1	3	yes	—
59	C₂×D₇₉	—	2	6	no	—
60	C₂×D₇₉	—	4	1	no	—
61	C₂×D₇₉	—	4	3	no	—
62	C₄×C₇₉	—	2	6	no	—
63	C₄×C₇₉	—	4	3	no	—
64	C₄×C₇₉	—	4	1	no	—
65	Dic₇₉	—	2	6	no	—
66	Dic₇₉	—	4	1	no	—
67	Dic₇₉	—	4	3	no	—
68	C₂×C₇₉	#520	1	3	yes	—
69	C₂×C₇₉	#560	1	1	yes	characteristic
70	C₂×C₇₉	#563	1	3	yes	—
71	D₇₉	—	4	2	no	—
72	#2383	—	79	1	no	maximal, Sylow
73	C₇₉	#2383	1	1	yes	characteristic, complemented, Sylow
74	C₂×#126	—	79	1	no	—
75	#389	—	79	3	no	—
76	#388	—	79	3	no	—
77	#387	—	79	3	no	—
78	#385	—	79	3	no	—
79	#384	D₇₉	1	1	yes	characteristic, complemented
80	#383	—	79	1	no	—
81	C₂³×C₄	—	79	1	no	—
82	#126	—	79	8	no	—
83	C₂×C₄⋊C₄	—	79	3	no	—
84	C₂×C₄⋊C₄	—	79	3	no	—
85	C₂×C₄⋊C₄	C₂×D₇₉	1	3	yes	—
86	C₂×C₄⋊C₄	C₂×D₇₉	1	3	yes	—
87	C₂×C₂²⋊C₄	—	79	3	no	—
88	C₂×C₂²⋊C₄	—	79	3	no	—
89	C₂×C₄²	—	79	3	no	—
90	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
91	#95	—	79	3	no	—
92	#95	—	79	3	no	—
93	#95	—	79	3	no	—
94	#95	—	79	3	no	—
95	C₂⁴	—	79	1	no	—
96	C₂²×C₄	—	316	3	no	—
97	C₂²×C₄	—	79	3	no	—
98	C₂²×C₄	—	79	3	no	—
99	C₂²×C₄	—	79	1	no	—
100	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
101	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
102	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
103	C₄⋊C₄	—	4	3	no	—
104	C₄⋊C₄	—	4	3	no	—
105	C₄⋊C₄	—	316	3	no	—
106	C₄⋊C₄	—	79	12	no	—
107	C₂²⋊C₄	—	316	3	no	—
108	C₂²⋊C₄	—	79	12	no	—
109	C₄²	—	316	3	no	—
110	C₄²	C₄×D₇₉	1	4	yes	complemented
111	C₂³	—	79	2	no	—
112	C₂³	—	158	3	no	—
113	C₂³	—	158	3	no	—
114	C₂³	C₂³×D₇₉	1	1	yes	characteristic
115	C₂×C₄	—	2	3	no	—
116	C₂×C₄	—	2	3	no	—
117	C₂×C₄	—	2	3	no	—
118	C₂×C₄	—	2	3	no	—
119	C₂×C₄	—	2	3	no	—
120	C₂×C₄	—	2	3	no	—
121	C₂×C₄	—	316	4	no	—
122	C₂×C₄	—	79	6	no	—
123	C₂×C₄	—	158	3	no	—
124	C₂×C₄	—	158	3	no	—
125	C₂×C₄	—	158	6	no	—
126	C₂×C₄	—	158	3	no	—
127	C₂×C₄	—	158	3	no	—
128	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
129	C₂²	—	316	1	no	—
130	C₂²	—	316	3	no	—
131	C₂²	—	158	6	no	—
132	C₂²	C₂²×C₄×D₇₉	1	1	yes	characteristic
133	C₂²	#14579206	1	3	yes	—
134	C₂²	#14579209	1	3	yes	—
135	C₄	—	2	6	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	3	no	—
138	C₄	—	316	1	no	—
139	C₄	—	316	3	no	—
140	C₄	—	158	6	no	—
141	C₂	—	316	2	no	—
142	C₂	#19099044	1	3	yes	—
143	C₂	#19099300	1	1	yes	characteristic
144	C₂	#19099312	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579155

C₂

yes

maximal, characteristic

#19098458

C₂

yes

maximal, complemented

#19098453

C₂

yes

maximal

#19098444

C₂

yes

maximal, complemented

#19098434

C₂

yes

maximal

#19098431

C₂

yes

maximal, characteristic, complemented

#384×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₂²

yes

characteristic

#14579155

C₄

yes

complemented

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

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

C₂³×D₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂×C₄×D₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

C₂×C₄

yes

complemented

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

C₂×C₄

yes

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₄×D₇₉

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

2₋¹⁺⁴

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#520

yes

—

C₂×C₇₉

#560

yes

characteristic

C₂×C₇₉

#563

yes

—

D₇₉

—

#2383

—

maximal, Sylow

C₇₉

#2383

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic, complemented

#383

—

C₂³×C₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

—

C₂⁴

—

C₂²×C₄

—

316

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×D₇₉

yes

characteristic

101

C₂²×C₄

C₂²×D₇₉

yes

—

102

C₂²×C₄

C₂²×D₇₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

316

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

316

—

108

C₂²⋊C₄

—

109

C₄²

—

316

—

110

C₄²

C₄×D₇₉

yes

complemented

111

C₂³

—

112

C₂³

—

158

—

113

C₂³

—

158

—

114

C₂³

C₂³×D₇₉

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

316

—

122

C₂×C₄

—

123

C₂×C₄

—

158

—

124

C₂×C₄

—

158

—

125

C₂×C₄

—

158

—

126

C₂×C₄

—

158

—

127

C₂×C₄

—

158

—

128

C₂×C₄

C₂×C₄×D₇₉

yes

—

129

C₂²

—

316

—

130

C₂²

—

316

—

131

C₂²

—

158

—

132

C₂²

C₂²×C₄×D₇₉

yes

characteristic

133

C₂²

#14579206

yes

—

134

C₂²

#14579209

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

316

—

139

C₄

—

316

—

140

C₄

—

158

—

141

C₂

—

316

—

142

C₂

#19099044

yes

—

143

C₂

#19099300

yes

characteristic

144

C₂

#19099312

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₄
Fitting	#384×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂³×D₇₉	C₂³
hypercenter	#384	D₇₉
hypocenter	C₇₉	#2383
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator

C₂²×C₇₉

C₂³×C₄

Fitting

#384×C₇₉

C₂

socle, cosocle

C₂³×C₇₉

C₂⁴

prime radical

C₂³×D₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
2. #19098458	C₂	semidirect
4. #19098444	C₂	semidirect
6. #19098431	C₂	semidirect
7. #384×C₇₉	C₂	semidirect
9. #14579155	C₄	semidirect
28. Dic₇₉⋊C₄	C₂×C₄	semidirect
37. C₄²×C₇₉	C₂×C₄	semidirect
73. C₇₉	#2383	semidirect
79. #384	D₇₉	semidirect
110. C₄²	C₄×D₇₉	semidirect

H ≅ G/N

type

2. #19098458

C₂

semidirect

4. #19098444

C₂

semidirect

6. #19098431

C₂

semidirect

7. #384×C₇₉

C₂

semidirect

9. #14579155

C₄

semidirect

28. Dic₇₉⋊C₄

C₂×C₄

semidirect

37. C₄²×C₇₉

C₂×C₄

semidirect

73. C₇₉

#2383

semidirect

79. #384

D₇₉

semidirect

110. C₄²

C₄×D₇₉

semidirect

Subgroups — #23766593

Conjugacy classes of subgroups

Complements