Group #23763445 — subgroups

Subgroups — #23763445

Order 10112.

260 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14579169	C₂	1	1	yes	maximal, characteristic
2	#19098599	C₂	1	2	yes	maximal, complemented
3	#19098536	C₂	1	2	yes	maximal
4	#19098320	C₂	1	1	yes	maximal, characteristic, complemented
5	H(3,ℤ/4)×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929624	C₂²	1	1	yes	characteristic
7	#14579169	—	2	2	no	—
8	#14579169	—	2	2	no	—
9	C₂×#11929607	C₄	1	2	yes	complemented
10	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₇₉	C₄	1	2	yes	complemented
12	#14579120	C₂²	1	2	yes	—
13	#14579094	—	2	2	no	—
14	#14579092	—	2	2	no	—
15	#14579075	—	2	4	no	—
16	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	#117×C₇₉	C₂²	1	2	yes	—
18	#11929624	—	2	2	no	—
19	#11929624	—	2	2	no	—
20	C₂×Dic₁₅₈	Q₈	1	1	yes	characteristic
21	C₂×D₃₁₆	Q₈	1	1	yes	characteristic
22	C₂×C₂²⋊D₇₉	D₄	1	2	yes	—
23	C₂×C₄×D₇₉	C₂×C₄	1	2	yes	—
24	#11929607	—	2	4	no	—
25	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
28	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
29	C₈×D₇₉	—	2	2	no	—
30	C₈×D₇₉	—	2	2	no	—
31	C₄⋊Dic₇₉	—	2	2	no	—
32	C₂²⋊Dic₇₉	—	2	2	no	—
33	C₄×Dic₇₉	—	2	2	no	—
34	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
35	M₁₆×C₇₉	—	2	2	no	—
36	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
37	C₄⋊C₄×C₇₉	—	2	2	no	—
38	C₂²⋊C₄×C₇₉	—	2	2	no	—
39	C₄²×C₇₉	—	2	2	no	—
40	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×D₇₉	C₄⋊C₄	1	2	yes	—
42	C₂×C₄×C₇₉	—	4	2	no	—
43	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₇₉	#41	1	2	yes	—
47	C₂²⋊D₇₉	—	2	4	no	—
48	C₂×Dic₇₉	—	4	2	no	—
49	C₂×Dic₇₉	C₄⋊C₄	1	2	yes	—
50	D₃₁₆	—	2	2	no	—
51	C₄×D₇₉	—	2	2	no	—
52	C₄×D₇₉	—	2	2	no	—
53	Dic₁₅₈	—	2	2	no	—
54	C₈×C₇₉	—	2	2	no	—
55	C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
56	C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
57	C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₇₉	—	4	1	no	—
59	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₇₉	#121	1	2	yes	—
61	C₂×D₇₉	—	2	2	no	—
62	C₂×D₇₉	—	4	2	no	—
63	C₄×C₇₉	—	8	2	no	—
64	C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₄×C₇₉	#117	1	1	yes	characteristic
66	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
67	Dic₇₉	—	2	2	no	—
68	Dic₇₉	—	8	2	no	—
69	C₂×C₇₉	—	2	2	no	—
70	C₂×C₇₉	—	2	1	no	—
71	C₂×C₇₉	#380	1	1	yes	characteristic
72	D₇₉	—	4	2	no	—
73	#1812	—	79	1	no	maximal, Sylow
74	C₇₉	#1812	1	1	yes	characteristic, complemented, Sylow
75	C₂×#131	—	79	1	no	—
76	#427	—	79	2	no	—
77	#410	—	79	2	no	—
78	H(3,ℤ/4)	—	79	1	no	—
79	H(3,ℤ/4)	D₇₉	1	1	yes	characteristic, complemented
80	C₂×#41	—	79	1	no	—
81	#131	—	158	2	no	—
82	#131	—	158	2	no	—
83	C₂×M₁₆	—	79	2	no	—
84	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
85	C₂²×C₈	—	79	1	no	—
86	C₂²×C₈	—	79	2	no	—
87	#117	—	79	2	no	—
88	#117	C₂×D₇₉	1	2	yes	—
89	#107	—	158	2	no	—
90	#106	—	158	2	no	—
91	#99	—	158	4	no	—
92	#41	—	158	2	no	—
93	#41	—	158	2	no	—
94	C₂×Q₈	—	79	1	no	—
95	C₂×D₄	—	79	2	no	—
96	C₂×D₄	—	79	1	no	—
97	C₂²×C₄	—	79	2	no	—
98	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
99	M₁₆	—	2	2	no	—
100	M₁₆	—	158	4	no	—
101	C₂×C₈	—	79	1	no	—
102	C₂×C₈	—	79	1	no	—
103	C₂×C₈	—	79	2	no	—
104	C₂×C₈	—	79	2	no	—
105	C₂×C₈	—	158	2	no	—
106	C₂×C₈	—	158	2	no	—
107	C₂×C₈	C₄×D₇₉	1	2	yes	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	158	2	no	—
110	C₂²⋊C₄	—	2	2	no	—
111	C₂²⋊C₄	—	158	2	no	—
112	C₄²	—	2	2	no	—
113	C₄²	—	158	2	no	—
114	C₂³	—	79	2	no	—
115	C₂³	D₄×D₇₉	1	1	yes	characteristic
116	Q₈	—	158	2	no	—
117	D₄	—	158	4	no	—
118	D₄	—	158	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	316	2	no	—
121	C₂×C₄	—	79	2	no	—
122	C₂×C₄	—	158	2	no	—
123	C₂×C₄	—	158	2	no	—
124	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
125	C₂×C₄	D₄×D₇₉	1	2	yes	—
126	C₂×C₄	Q₈×D₇₉	1	1	yes	characteristic
127	C₂×C₄	#11929624	1	2	yes	—
128	C₈	—	2	2	no	—
129	C₈	—	79	1	no	—
130	C₈	—	79	1	no	—
131	C₈	—	79	2	no	—
132	C₂²	—	4	1	no	—
133	C₂²	—	316	2	no	—
134	C₂²	—	158	2	no	—
135	C₂²	C₄⋊C₄×D₇₉	1	1	yes	characteristic
136	C₂²	#14579134	1	2	yes	—
137	C₄	—	8	2	no	—
138	C₄	—	632	2	no	—
139	C₄	—	158	2	no	—
140	C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
141	C₄	#14579118	1	1	yes	characteristic
142	C₄	#14579139	1	2	yes	—
143	C₂	—	2	2	no	—
144	C₂	—	2	1	no	—
145	C₂	—	316	2	no	—
146	C₂	#19098422	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579169

C₂

yes

maximal, characteristic

#19098599

C₂

yes

maximal, complemented

#19098536

C₂

yes

maximal

#19098320

C₂

yes

maximal, characteristic, complemented

H(3,ℤ/4)×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929624

C₂²

yes

—

—

C₄

yes

complemented

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₇₉

C₄

yes

complemented

#14579120

C₂²

yes

—

#14579094

—

#14579092

—

#14579075

—

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

#117×C₇₉

C₂²

yes

—

#11929624

—

#11929624

—

C₂×Dic₁₅₈

Q₈

yes

characteristic

C₂×D₃₁₆

Q₈

yes

characteristic

C₂×C₂²⋊D₇₉

D₄

yes

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

#11929607

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₉⋊C₈

D₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₈×D₇₉

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂²×D₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₇₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₇₉⋊C₈

C₂²⋊C₄

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₉

#121

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₉

#117

yes

characteristic

C₄×C₇₉

C₂²⋊Q₈

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#380

yes

characteristic

D₇₉

—

#1812

—

maximal, Sylow

C₇₉

#1812

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic, complemented

C₂×#41

—

#131

—

158

—

#131

—

158

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#117

—

#117

C₂×D₇₉

yes

—

#107

—

158

—

#106

—

158

—

#99

—

158

—

#41

—

158

—

#41

—

158

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

100

M₁₆

—

158

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

158

—

106

C₂×C₈

—

158

—

107

C₂×C₈

C₄×D₇₉

yes

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

158

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

—

158

—

112

C₄²

—

113

C₄²

—

158

—

114

C₂³

—

115

C₂³

D₄×D₇₉

yes

characteristic

116

Q₈

—

158

—

117

D₄

—

158

—

118

D₄

—

158

—

119

C₂×C₄

—

120

C₂×C₄

—

316

—

121

C₂×C₄

—

122

C₂×C₄

—

158

—

123

C₂×C₄

—

158

—

124

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

125

C₂×C₄

D₄×D₇₉

yes

—

126

C₂×C₄

Q₈×D₇₉

yes

characteristic

127

C₂×C₄

#11929624

yes

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₂²

—

133

C₂²

—

316

—

134

C₂²

—

158

—

135

C₂²

C₄⋊C₄×D₇₉

yes

characteristic

136

C₂²

#14579134

yes

—

137

C₄

—

138

C₄

—

632

—

139

C₄

—

158

—

140

C₄

C₂²⋊C₄×D₇₉

yes

characteristic

141

C₄

#14579118

yes

characteristic

142

C₄

#14579139

yes

—

143

C₂

—

144

C₂

—

145

C₂

—

316

—

146

C₂

#19098422

yes

characteristic

	subgroup	G/H
center	C₄	#14579118
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	H(3,ℤ/4)×C₇₉	C₂
socle	C₂×C₇₉	#380
prime radical	C₂×#11929624	C₂²
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	H(3,ℤ/4)	D₇₉
hypocenter	C₇₉	#1812
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#14579118

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

H(3,ℤ/4)×C₇₉

C₂

C₂×C₇₉

C₂²

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
2. #19098599	C₂	semidirect
4. #19098320	C₂	semidirect
5. H(3,ℤ/4)×C₇₉	C₂	semidirect
9. C₂×#11929607	C₄	semidirect
11. C₂×C₈×D₇₉	C₄	semidirect
74. C₇₉	#1812	semidirect
79. H(3,ℤ/4)	D₇₉	semidirect

H ≅ G/N

type

2. #19098599

C₂

semidirect

4. #19098320

C₂

semidirect

5. H(3,ℤ/4)×C₇₉

C₂

semidirect

9. C₂×#11929607

C₄

semidirect

11. C₂×C₈×D₇₉

C₄

semidirect

74. C₇₉

#1812

semidirect

79. H(3,ℤ/4)

D₇₉

semidirect

Subgroups — #23763445

Conjugacy classes of subgroups

Complements