Group #23765898 — subgroups

Subgroups — #23765898

Order 10112.

524 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 237 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	#19098456	C₂	1	4	yes	maximal
2	#19098449	C₂	1	4	yes	maximal, complemented
3	C₄×C₄⋊Dic₇₉	C₂	1	2	yes	maximal, complemented
4	C₄×C₂²⋊Dic₇₉	C₂	1	2	yes	maximal
5	#19098409	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#117×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	—
9	C₂×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
10	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
13	C₇₉⋊#95	C₂²	1	4	yes	—
14	C₇₉⋊#95	C₂²	1	4	yes	—
15	C₇₉⋊#95	C₂²	1	4	yes	—
16	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
17	#117×C₇₉	C₄	1	8	yes	complemented
18	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×Dic₇₉	C₂³	1	4	yes	—
23	C₂²×Dic₇₉	C₂³	1	4	yes	—
24	C₄⋊Dic₇₉	—	2	8	no	—
25	C₂²⋊Dic₇₉	—	2	8	no	—
26	C₄×Dic₇₉	—	2	8	no	—
27	C₄×Dic₇₉	—	2	4	no	—
28	C₄×Dic₇₉	—	2	4	no	—
29	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₇₉	—	2	4	no	—
31	C₂²×C₄×C₇₉	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
33	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
36	C₄⋊C₄×C₇₉	C₂×C₄	1	8	yes	—
37	C₂²⋊C₄×C₇₉	C₂×C₄	1	8	yes	—
38	C₄²×C₇₉	C₂×C₄	1	4	yes	—
39	C₄²×C₇₉	C₂×C₄	1	4	yes	—
40	C₂³×C₇₉	—	2	4	no	—
41	C₂³×C₇₉	—	2	2	no	—
42	C₂³×C₇₉	C₂²×C₄	1	2	yes	—
43	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
44	C₂×C₄×C₇₉	—	2	4	no	—
45	C₂×C₄×C₇₉	—	2	4	no	—
46	C₂×C₄×C₇₉	—	2	2	no	—
47	C₂×C₄×C₇₉	—	2	8	no	—
48	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
49	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
50	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
51	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
52	C₂×C₄×C₇₉	#41	1	4	yes	—
53	C₂×Dic₇₉	—	2	4	no	—
54	C₂×Dic₇₉	—	2	4	no	—
55	C₂×Dic₇₉	—	2	4	no	—
56	C₂×Dic₇₉	—	2	4	no	—
57	C₂×Dic₇₉	—	2	4	no	—
58	C₂×Dic₇₉	#41	1	8	yes	—
59	C₂²×C₇₉	—	2	2	no	—
60	C₂²×C₇₉	—	2	4	no	—
61	C₂²×C₇₉	—	4	4	no	—
62	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
63	C₂²×C₇₉	C₂×#41	1	4	yes	—
64	C₂²×C₇₉	C₂×#41	1	2	yes	—
65	C₄×C₇₉	—	2	2	no	—
66	C₄×C₇₉	—	2	4	no	—
67	C₄×C₇₉	—	2	4	no	—
68	C₄×C₇₉	#117	1	4	yes	—
69	Dic₇₉	—	2	8	no	—
70	Dic₇₉	—	4	4	no	—
71	C₂×C₇₉	—	4	2	no	—
72	C₂×C₇₉	C₂×#117	1	1	yes	characteristic
73	C₂×C₇₉	C₄×#41	1	2	yes	—
74	C₂×C₇₉	#529	1	4	yes	—
75	#2298	—	79	1	no	maximal, Sylow
76	C₇₉	#2298	1	1	yes	characteristic, complemented, Sylow
77	C₂×#117	D₇₉	1	1	yes	characteristic
78	#388	—	79	4	no	—
79	#387	—	79	4	no	—
80	C₄×C₄⋊C₄	—	79	2	no	—
81	C₄×C₂²⋊C₄	—	79	2	no	—
82	#376	—	79	1	no	—
83	C₄³	—	79	1	no	—
84	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic
85	#117	Dic₇₉	1	8	yes	complemented
86	C₂×C₄⋊C₄	—	79	4	no	—
87	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
88	C₂×C₂²⋊C₄	—	79	4	no	—
89	C₂×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
90	C₂×C₄²	—	79	4	no	—
91	C₂×C₄²	—	79	2	no	—
92	C₂×C₄²	—	79	2	no	—
93	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
94	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
95	#95	—	79	4	no	—
96	#95	—	79	4	no	—
97	#95	—	79	4	no	—
98	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
99	C₂²×C₄	—	2	4	no	—
100	C₂²×C₄	—	79	4	no	—
101	C₂²×C₄	—	79	4	no	—
102	C₂²×C₄	C₂×Dic₇₉	1	4	yes	—
103	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
104	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
105	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
106	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
107	C₄⋊C₄	—	158	8	no	—
108	C₄⋊C₄	C₂×Dic₇₉	1	8	yes	—
109	C₂²⋊C₄	—	158	8	no	—
110	C₂²⋊C₄	C₂×Dic₇₉	1	8	yes	—
111	C₄²	—	158	8	no	—
112	C₄²	—	158	4	no	—
113	C₄²	—	158	4	no	—
114	C₄²	C₂×Dic₇₉	1	4	yes	—
115	C₄²	C₂×Dic₇₉	1	4	yes	—
116	C₂³	—	2	4	no	—
117	C₂³	—	2	2	no	—
118	C₂³	C₂²×Dic₇₉	1	2	yes	—
119	C₂³	C₂³×D₇₉	1	1	yes	characteristic
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	8	no	—
124	C₂×C₄	—	79	8	no	—
125	C₂×C₄	—	158	4	no	—
126	C₂×C₄	—	158	4	no	—
127	C₂×C₄	—	158	4	no	—
128	C₂×C₄	—	158	4	no	—
129	C₂×C₄	—	158	4	no	—
130	C₂×C₄	C₂²×Dic₇₉	1	4	yes	—
131	C₂×C₄	C₂²×Dic₇₉	1	4	yes	—
132	C₂×C₄	C₂²×Dic₇₉	1	2	yes	—
133	C₂×C₄	C₂²×Dic₇₉	1	2	yes	—
134	C₂×C₄	#11929624	1	4	yes	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	4	no	—
137	C₂²	—	4	4	no	—
138	C₂²	C₂³×Dic₇₉	1	1	yes	characteristic
139	C₂²	#41×D₇₉	1	4	yes	—
140	C₂²	C₂×#11929624	1	2	yes	—
141	C₄	—	2	2	no	—
142	C₄	—	2	4	no	—
143	C₄	—	2	4	no	—
144	C₄	—	316	4	no	—
145	C₄	—	158	8	no	—
146	C₄	#14579120	1	4	yes	—
147	C₂	—	4	2	no	—
148	C₂	C₂×#14579120	1	1	yes	characteristic
149	C₂	#41×Dic₇₉	1	2	yes	—
150	C₂	#19099091	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098456

C₂

yes

maximal

#19098449

C₂

yes

maximal, complemented

C₄×C₄⋊Dic₇₉

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₇₉

C₂

yes

maximal

#19098409

C₂

yes

maximal, characteristic, complemented

C₄²×Dic₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#117×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂³×C₄×C₇₉

C₂²

yes

characteristic

#117×C₇₉

C₄

yes

complemented

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂⁴×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂²⋊C₄×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂²×C₄

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

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×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

#41

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#117

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#117

yes

characteristic

C₂×C₇₉

C₄×#41

yes

—

C₂×C₇₉

#529

yes

—

#2298

—

maximal, Sylow

C₇₉

#2298

yes

characteristic, complemented, Sylow

C₂×#117

D₇₉

yes

characteristic

#388

—

#387

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

—

C₄³

—

C₂³×C₄

C₂×D₇₉

yes

characteristic

#117

Dic₇₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₂×C₄²

C₂×D₇₉

yes

—

—

—

C₂⁴

C₂²×D₇₉

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂×Dic₇₉

yes

—

103

C₂²×C₄

C₂²×D₇₉

yes

characteristic

104

C₂²×C₄

C₂²×D₇₉

yes

—

105

C₂²×C₄

C₂²×D₇₉

yes

—

106

C₂²×C₄

C₂²×D₇₉

yes

characteristic

107

C₄⋊C₄

—

158

—

108

C₄⋊C₄

C₂×Dic₇₉

yes

—

109

C₂²⋊C₄

—

158

—

110

C₂²⋊C₄

C₂×Dic₇₉

yes

—

111

C₄²

—

158

—

112

C₄²

—

158

—

113

C₄²

—

158

—

114

C₄²

C₂×Dic₇₉

yes

—

115

C₄²

C₂×Dic₇₉

yes

—

116

C₂³

—

117

C₂³

—

118

C₂³

C₂²×Dic₇₉

yes

—

119

C₂³

C₂³×D₇₉

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

158

—

126

C₂×C₄

—

158

—

127

C₂×C₄

—

158

—

128

C₂×C₄

—

158

—

129

C₂×C₄

—

158

—

130

C₂×C₄

C₂²×Dic₇₉

yes

—

131

C₂×C₄

C₂²×Dic₇₉

yes

—

132

C₂×C₄

C₂²×Dic₇₉

yes

—

133

C₂×C₄

C₂²×Dic₇₉

yes

—

134

C₂×C₄

#11929624

yes

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂³×Dic₇₉

yes

characteristic

139

C₂²

#41×D₇₉

yes

—

140

C₂²

C₂×#11929624

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

316

—

145

C₄

—

158

—

146

C₄

#14579120

yes

—

147

C₂

—

148

C₂

C₂×#14579120

yes

characteristic

149

C₂

#41×Dic₇₉

yes

—

150

C₂

#19099091

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇₉
commutator	C₂²×C₇₉	C₂³×C₄
Frattini	C₂³	C₂³×D₇₉
Fitting	C₂×#117×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂⁴×C₇₉	C₂³
hypercenter	C₂×#117	D₇₉
hypocenter	C₇₉	#2298
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

subgroup

G/H

center

C₂²×C₄

C₂²×D₇₉

commutator

C₂²×C₇₉

C₂³×C₄

Frattini

C₂³

C₂³×D₇₉

Fitting

C₂×#117×C₇₉

C₂

socle, cosocle

C₂³×C₇₉

C₂⁴

prime radical

C₂⁴×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂²×C₄ ◁ C₂×#117

N	H ≅ G/N	type
2. #19098449	C₂	semidirect
3. C₄×C₄⋊Dic₇₉	C₂	semidirect
5. #19098409	C₂	semidirect
6. C₄²×Dic₇₉	C₂	semidirect
17. #117×C₇₉	C₄	semidirect
76. C₇₉	#2298	semidirect
85. #117	Dic₇₉	semidirect

H ≅ G/N

type

2. #19098449

C₂

semidirect

3. C₄×C₄⋊Dic₇₉

C₂

semidirect

5. #19098409

C₂

semidirect

6. C₄²×Dic₇₉

C₂

semidirect

17. #117×C₇₉

C₄

semidirect

76. C₇₉

#2298

semidirect

85. #117

Dic₇₉

semidirect

Subgroups — #23765898

Conjugacy classes of subgroups

Complements