Group #23765784 — subgroups

Subgroups — #382×D₇₉ #23765784

Order 10112.

712 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 269 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×C₄⋊C₄×D₇₉	C₂	1	2	yes	maximal
2	C₂×C₄²×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#19098429	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098428	C₂	1	2	yes	maximal, complemented
5	#19098427	C₂	1	4	yes	maximal, complemented
6	#95×D₇₉	C₂	1	4	yes	maximal
7	#382×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₇₉	C₂²	1	4	yes	—
9	C₂²×C₄×D₇₉	C₂²	1	2	yes	—
10	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
12	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
13	C₄⋊C₄×D₇₉	—	2	8	no	—
14	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
15	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
16	C₄²×D₇₉	C₄	1	8	yes	complemented
17	C₇₉⋊#95	C₂²	1	8	yes	—
18	C₇₉⋊#95	C₂²	1	4	yes	—
19	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
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	2	yes	—
25	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
26	C₂×C₄×D₇₉	—	2	8	no	—
27	C₂×C₄×D₇₉	—	2	8	no	—
28	C₂×C₄×D₇₉	—	2	16	no	—
29	C₂×C₄×D₇₉	C₂×C₄	1	8	yes	—
30	C₂×C₄×D₇₉	C₂×C₄	1	4	yes	—
31	C₂×C₄×D₇₉	D₄	1	4	yes	—
32	C₂×C₄×D₇₉	Q₈	1	4	yes	—
33	C₄⋊Dic₇₉	—	2	4	no	—
34	Dic₇₉⋊C₄	—	2	8	no	—
35	C₄×Dic₇₉	C₂×C₄	1	8	yes	complemented
36	C₄×Dic₇₉	C₂×C₄	1	4	yes	complemented
37	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
38	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
40	C₄⋊C₄×C₇₉	—	2	4	no	—
41	C₄²×C₇₉	C₂×C₄	1	4	yes	complemented
42	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
43	C₂²×D₇₉	C₂²×C₄	1	2	yes	—
44	C₂²×D₇₉	C₂×D₄	1	2	yes	—
45	C₂²×D₇₉	C₂×Q₈	1	2	yes	—
46	C₂²×D₇₉	#41	1	8	yes	—
47	C₂×C₄×C₇₉	—	2	4	no	—
48	C₂×C₄×C₇₉	—	2	4	no	—
49	C₂×C₄×C₇₉	—	2	8	no	—
50	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
51	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
52	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
54	C₂×Dic₇₉	—	2	4	no	—
55	C₂×Dic₇₉	—	2	4	no	—
56	C₂×Dic₇₉	—	2	8	no	—
57	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
58	C₂×Dic₇₉	C₂²×C₄	1	2	yes	—
59	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
60	C₂×Dic₇₉	C₂×Q₈	1	2	yes	—
61	C₄×D₇₉	—	2	16	no	—
62	C₄×D₇₉	—	4	16	no	—
63	C₄×D₇₉	C₄⋊C₄	1	16	yes	—
64	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
65	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
66	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
67	C₂²×C₇₉	C₂×#41	1	4	yes	—
68	C₂×D₇₉	C₂×C₄⋊C₄	1	4	yes	—
69	C₂×D₇₉	#117	1	8	yes	—
70	C₂×D₇₉	#124	1	8	yes	—
71	C₂×D₇₉	#125	1	8	yes	—
72	C₄×C₇₉	—	2	4	no	—
73	C₄×C₇₉	—	4	4	no	—
74	C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
75	Dic₇₉	—	2	4	no	—
76	Dic₇₉	—	4	4	no	—
77	Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
78	C₂×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₇₉	C₂×#117	1	2	yes	—
80	C₂×C₇₉	C₂×#124	1	2	yes	—
81	C₂×C₇₉	C₂×#125	1	2	yes	—
82	D₇₉	#382	1	8	yes	direct product factor
83	C₂×#382	—	79	1	no	maximal, Sylow
84	C₇₉	C₂×#382	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₄⋊C₄	—	79	2	no	—
86	C₂²×C₄²	—	79	1	no	—
87	#382	—	79	2	no	—
88	#382	—	79	1	no	—
89	#382	—	79	4	no	—
90	#382	D₇₉	1	1	yes	characteristic, direct product factor
91	C₂×#95	—	79	4	no	—
92	C₂³×C₄	—	79	1	no	—
93	C₂³×C₄	—	79	2	no	—
94	C₂³×C₄	—	79	4	no	—
95	C₂×C₄⋊C₄	—	79	4	no	—
96	C₂×C₄⋊C₄	—	79	2	no	—
97	C₂×C₄⋊C₄	—	158	8	no	—
98	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
99	C₂×C₄²	—	79	2	no	—
100	C₂×C₄²	—	79	1	no	—
101	C₂×C₄²	—	79	8	no	—
102	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
103	#95	—	79	8	no	—
104	#95	—	79	4	no	—
105	#95	C₂×D₇₉	1	4	yes	—
106	C₂⁴	—	79	1	no	—
107	C₂²×C₄	—	79	1	no	—
108	C₂²×C₄	—	79	4	no	—
109	C₂²×C₄	—	79	4	no	—
110	C₂²×C₄	—	79	4	no	—
111	C₂²×C₄	—	79	2	no	—
112	C₂²×C₄	—	79	8	no	—
113	C₂²×C₄	—	79	4	no	—
114	C₂²×C₄	—	158	8	no	—
115	C₂²×C₄	—	158	16	no	—
116	C₂²×C₄	—	158	8	no	—
117	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
118	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
119	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
120	C₄⋊C₄	—	2	4	no	—
121	C₄⋊C₄	—	158	8	no	—
122	C₄⋊C₄	—	158	4	no	—
123	C₄²	—	79	8	no	—
124	C₄²	—	79	4	no	—
125	C₄²	C₄×D₇₉	1	4	yes	complemented
126	C₂³	—	79	2	no	—
127	C₂³	—	79	8	no	—
128	C₂³	—	79	2	no	—
129	C₂³	—	79	2	no	—
130	C₂³	C₂³×D₇₉	1	1	yes	characteristic
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	2	8	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	316	16	no	—
135	C₂×C₄	—	79	2	no	—
136	C₂×C₄	—	79	2	no	—
137	C₂×C₄	—	79	2	no	—
138	C₂×C₄	—	79	16	no	—
139	C₂×C₄	—	79	4	no	—
140	C₂×C₄	—	158	16	no	—
141	C₂×C₄	—	158	8	no	—
142	C₂×C₄	—	158	4	no	—
143	C₂×C₄	—	158	4	no	—
144	C₂×C₄	C₂×C₄×D₇₉	1	4	yes	—
145	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
146	C₂×C₄	D₄×D₇₉	1	2	yes	—
147	C₂×C₄	Q₈×D₇₉	1	2	yes	—
148	C₂²	—	79	4	no	—
149	C₂²	—	79	8	no	—
150	C₂²	—	79	8	no	—
151	C₂²	—	79	8	no	—
152	C₂²	C₂²×C₄×D₇₉	1	1	yes	characteristic
153	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
154	C₂²	C₂×Q₈×D₇₉	1	1	yes	characteristic
155	C₂²	#41×D₇₉	1	4	yes	—
156	C₄	—	2	4	no	—
157	C₄	—	4	4	no	—
158	C₄	—	316	4	no	—
159	C₄	—	79	4	no	—
160	C₄	—	158	4	no	—
161	C₄	C₄⋊C₄×D₇₉	1	4	yes	—
162	C₂	—	79	8	no	—
163	C₂	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
164	C₂	#117×D₇₉	1	2	yes	—
165	C₂	#124×D₇₉	1	2	yes	—
166	C₂	#125×D₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊C₄×D₇₉

C₂

yes

maximal

C₂×C₄²×D₇₉

C₂

yes

maximal, characteristic

#19098429

C₂

yes

maximal, characteristic, complemented

#19098428

C₂

yes

maximal, complemented

#19098427

C₂

yes

maximal, complemented

#95×D₇₉

C₂

yes

maximal

#382×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₂²

yes

—

C₂²×C₄×D₇₉

C₂²

yes

—

C₂²×C₄×D₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₄⋊C₄×D₇₉

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₄²×D₇₉

C₄

yes

complemented

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#95×C₇₉

C₂²

yes

—

C₂³×D₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

Q₈

yes

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

C₂×C₄

yes

complemented

C₄×Dic₇₉

C₂×C₄

yes

complemented

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

C₂²×C₄

yes

—

C₂²×D₇₉

C₂×D₄

yes

—

C₂²×D₇₉

C₂×Q₈

yes

—

C₂²×D₇₉

#41

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂×Q₈

yes

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

C₄⋊C₄

yes

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂×D₇₉

C₂×C₄⋊C₄

yes

—

C₂×D₇₉

#117

yes

—

C₂×D₇₉

#124

yes

—

C₂×D₇₉

#125

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₄⋊C₄

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

C₂×C₄⋊C₄

yes

—

C₂×C₇₉

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₇₉

C₂×#117

yes

—

C₂×C₇₉

C₂×#124

yes

—

C₂×C₇₉

C₂×#125

yes

—

D₇₉

#382

yes

direct product factor

C₂×#382

—

maximal, Sylow

C₇₉

C₂×#382

yes

characteristic, complemented, Sylow

C₂²×C₄⋊C₄

—

C₂²×C₄²

—

—

—

—

D₇₉

yes

characteristic, direct product factor

C₂×#95

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

100

C₂×C₄²

—

101

C₂×C₄²

—

102

C₂×C₄²

C₂×D₇₉

yes

characteristic

103

#95

—

104

#95

—

105

#95

C₂×D₇₉

yes

—

106

C₂⁴

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

158

—

115

C₂²×C₄

—

158

—

116

C₂²×C₄

—

158

—

117

C₂²×C₄

C₂²×D₇₉

yes

—

118

C₂²×C₄

C₂²×D₇₉

yes

—

119

C₂²×C₄

C₂²×D₇₉

yes

characteristic

120

C₄⋊C₄

—

121

C₄⋊C₄

—

158

—

122

C₄⋊C₄

—

158

—

123

C₄²

—

124

C₄²

—

125

C₄²

C₄×D₇₉

yes

complemented

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

C₂³×D₇₉

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

316

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

158

—

141

C₂×C₄

—

158

—

142

C₂×C₄

—

158

—

143

C₂×C₄

—

158

—

144

C₂×C₄

C₂×C₄×D₇₉

yes

—

145

C₂×C₄

C₂×C₄×D₇₉

yes

—

146

C₂×C₄

D₄×D₇₉

yes

—

147

C₂×C₄

Q₈×D₇₉

yes

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

C₂²×C₄×D₇₉

yes

characteristic

153

C₂²

C₂×D₄×D₇₉

yes

characteristic

154

C₂²

C₂×Q₈×D₇₉

yes

characteristic

155

C₂²

#41×D₇₉

yes

—

156

C₄

—

157

C₄

—

158

C₄

—

316

—

159

C₄

—

160

C₄

—

158

—

161

C₄

C₄⋊C₄×D₇₉

yes

—

162

C₂

—

163

C₂

C₂×C₄⋊C₄×D₇₉

yes

characteristic

164

C₂

#117×D₇₉

yes

—

165

C₂

#124×D₇₉

yes

—

166

C₂

#125×D₇₉

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₄
Fitting	#382×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂³×D₇₉	C₂³
hypercenter	#382	D₇₉
hypocenter	C₇₉	C₂×#382
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator

C₂²×C₇₉

C₂³×C₄

Fitting

#382×C₇₉

C₂

socle, cosocle

C₂³×C₇₉

C₂⁴

prime radical

C₂³×D₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
3. #19098429	C₂	semidirect
4. #19098428	C₂	semidirect
5. #19098427	C₂	semidirect
7. #382×C₇₉	C₂	semidirect
16. C₄²×D₇₉	C₄	semidirect
35. C₄×Dic₇₉	C₂×C₄	semidirect
36. C₄×Dic₇₉	C₂×C₄	semidirect
41. C₄²×C₇₉	C₂×C₄	semidirect
82. D₇₉	#382	direct (N × H)
84. C₇₉	C₂×#382	semidirect
90. #382	D₇₉	direct (N × H)
125. C₄²	C₄×D₇₉	semidirect

H ≅ G/N

type

3. #19098429

C₂

semidirect

4. #19098428

C₂

semidirect

5. #19098427

C₂

semidirect

7. #382×C₇₉

C₂

semidirect

16. C₄²×D₇₉

C₄

semidirect

35. C₄×Dic₇₉

C₂×C₄

semidirect

36. C₄×Dic₇₉

C₂×C₄

semidirect

41. C₄²×C₇₉

C₂×C₄

semidirect

82. D₇₉

#382

direct (N × H)

84. C₇₉

C₂×#382

semidirect

90. #382

D₇₉

direct (N × H)

125. C₄²

C₄×D₇₉

semidirect

Subgroups — #382×D₇₉ #23765784

Conjugacy classes of subgroups

Complements

Subgroups — #382×D79 #23765784

Conjugacy classes of subgroups

Complements

Subgroups — #382×D₇₉ #23765784