Group #19099178 — subgroups

Subgroups — #19099178

Order 5056.

216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14579160	C₂	1	1	yes	maximal, characteristic, complemented
2	#14579154	C₂	1	2	yes	maximal, complemented
3	#14579148	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579147	C₂	1	2	yes	maximal, complemented
5	#14579144	C₂	1	2	yes	maximal, complemented
6	#14579141	C₂	1	1	yes	maximal, characteristic, complemented
7	#14579140	C₂	1	2	yes	maximal, complemented
8	#14579132	C₂	1	1	yes	maximal, characteristic
9	C₄×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#14579118	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Dic₁₅₈	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₅₈	C₂²	1	2	yes	—
14	C₂×C₂²⋊D₇₉	C₂²	1	2	yes	—
15	C₂×C₄×D₇₉	C₂²	1	1	yes	characteristic
16	C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₇₉	C₂²	1	2	yes	—
18	Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
19	Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
20	Dic₇₉⋊C₄	C₂²	1	2	yes	—
21	Dic₇₉⋊C₄	C₂²	1	2	yes	—
22	C₂²⋊Dic₇₉	C₂²	1	2	yes	—
23	C₂²⋊Dic₇₉	C₂²	1	2	yes	—
24	C₂²⋊Dic₇₉	C₂²	1	2	yes	—
25	(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
26	(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
27	(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
28	C₄×Dic₇₉	C₂²	1	1	yes	characteristic
29	C₄×Dic₇₉	C₂²	1	2	yes	—
30	C₂×D₄×C₇₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄×C₇₉	C₂²	1	2	yes	—
32	C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
34	C₄²×C₇₉	C₂²	1	1	yes	characteristic
35	C₂³×C₇₉	C₂³	1	2	yes	—
36	C₂²×D₇₉	C₂³	1	1	yes	characteristic
37	D₄×C₇₉	—	2	2	no	—
38	C₂×C₄×C₇₉	—	4	2	no	—
39	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
40	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂³	1	2	yes	—
42	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
43	C₂²⋊D₇₉	—	4	2	no	—
44	C₂×Dic₇₉	C₂³	1	1	yes	characteristic
45	C₂×Dic₇₉	C₂³	1	2	yes	—
46	C₂×Dic₇₉	C₂³	1	1	yes	characteristic
47	C₂×Dic₇₉	C₂³	1	2	yes	—
48	C₂×Dic₇₉	C₂³	1	1	yes	characteristic
49	C₄×D₇₉	—	2	2	no	—
50	Dic₁₅₈	—	2	2	no	—
51	Dic₁₅₈	—	4	2	no	—
52	C₂²×C₇₉	—	2	2	no	—
53	C₂²×C₇₉	—	2	2	no	—
54	C₂²×C₇₉	—	2	2	no	—
55	C₂²×C₇₉	C₂⁴	1	1	yes	characteristic
56	C₂×D₇₉	—	2	1	no	—
57	C₂×D₇₉	—	2	1	no	—
58	C₂×D₇₉	—	2	1	no	—
59	C₄×C₇₉	—	2	1	no	—
60	C₄×C₇₉	—	2	2	no	—
61	C₄×C₇₉	—	2	1	no	—
62	C₄×C₇₉	#41	1	2	yes	—
63	Dic₇₉	—	2	2	no	—
64	Dic₇₉	—	2	1	no	—
65	Dic₇₉	—	2	2	no	—
66	Dic₇₉	—	2	1	no	—
67	Dic₇₉	—	2	1	no	—
68	C₂×C₇₉	—	4	2	no	—
69	C₂×C₇₉	C₂×#41	1	1	yes	characteristic
70	C₂×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
71	C₂×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
72	D₇₉	—	4	1	no	—
73	C₇₉	#542	1	1	yes	characteristic, complemented, Sylow
74	#542	—	79	1	no	maximal, Sylow
75	C₄⋊Q₈	—	79	1	no	—
76	#126	—	79	2	no	—
77	#124	—	79	1	no	—
78	#124	—	79	2	no	—
79	#123	—	79	2	no	—
80	C₂²⋊Q₈	—	79	2	no	—
81	C₂²⋊Q₈	—	79	1	no	—
82	#121	—	79	1	no	—
83	C₄×Q₈	—	79	1	no	—
84	C₄×D₄	D₇₉	1	1	yes	characteristic, complemented
85	#117	—	79	1	no	—
86	C₂×Q₈	—	79	2	no	—
87	C₂×Q₈	—	79	1	no	—
88	C₂×D₄	—	79	2	no	—
89	C₂×D₄	C₂×D₇₉	1	1	yes	characteristic
90	C₂²×C₄	—	79	1	no	—
91	C₂²×C₄	C₂×D₇₉	1	2	yes	—
92	C₄⋊C₄	—	79	1	no	—
93	C₄⋊C₄	—	79	1	no	—
94	C₄⋊C₄	—	79	2	no	—
95	C₄⋊C₄	—	79	2	no	—
96	C₄⋊C₄	—	79	1	no	—
97	C₄⋊C₄	—	79	2	no	—
98	C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
99	C₂²⋊C₄	—	79	2	no	—
100	C₂²⋊C₄	—	79	2	no	—
101	C₂²⋊C₄	—	79	2	no	—
102	C₂²⋊C₄	—	79	1	no	—
103	C₂²⋊C₄	—	79	1	no	—
104	C₂²⋊C₄	—	79	2	no	—
105	C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
106	C₄²	—	79	1	no	—
107	C₄²	—	79	2	no	—
108	C₄²	C₂×D₇₉	1	1	yes	characteristic
109	C₂³	—	79	1	no	—
110	C₂³	C₂²×D₇₉	1	2	yes	—
111	Q₈	—	316	2	no	—
112	Q₈	—	158	2	no	—
113	D₄	—	2	2	no	—
114	D₄	—	316	2	no	—
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	79	1	no	—
117	C₂×C₄	—	79	2	no	—
118	C₂×C₄	—	79	1	no	—
119	C₂×C₄	—	79	2	no	—
120	C₂×C₄	—	79	1	no	—
121	C₂×C₄	—	158	2	no	—
122	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
123	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
124	C₂×C₄	C₂²×D₇₉	1	2	yes	—
125	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	—	2	2	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	158	1	no	—
130	C₂²	—	158	1	no	—
131	C₂²	—	158	1	no	—
132	C₂²	C₂³×D₇₉	1	1	yes	characteristic
133	C₄	—	2	1	no	—
134	C₄	—	2	2	no	—
135	C₄	—	2	1	no	—
136	C₄	—	158	1	no	—
137	C₄	—	158	2	no	—
138	C₄	—	158	2	no	—
139	C₄	—	158	1	no	—
140	C₄	—	158	1	no	—
141	C₄	#11929624	1	2	yes	—
142	C₂	—	4	2	no	—
143	C₂	—	316	1	no	—
144	C₂	C₂×#11929624	1	1	yes	characteristic
145	C₂	#14579206	1	1	yes	characteristic
146	C₂	#14579208	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14579160

C₂

yes

maximal, characteristic, complemented

#14579154

C₂

yes

maximal, complemented

#14579148

C₂

yes

maximal, characteristic, complemented

#14579147

C₂

yes

maximal, complemented

#14579144

C₂

yes

maximal, complemented

#14579141

C₂

yes

maximal, characteristic, complemented

#14579140

C₂

yes

maximal, complemented

#14579132

C₂

yes

maximal, characteristic

C₄×Dic₁₅₈

C₂

yes

maximal, characteristic, complemented

#14579118

C₂

yes

maximal, characteristic, complemented

C₄×D₄×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₅₈

C₂²

yes

characteristic

C₂×Dic₁₅₈

C₂²

yes

—

C₂×C₂²⋊D₇₉

C₂²

yes

—

C₂×C₄×D₇₉

C₂²

yes

characteristic

C₄⋊Dic₇₉

C₂²

yes

characteristic

C₄⋊Dic₇₉

C₂²

yes

—

Dic₇₉⋊C₄

C₂²

yes

characteristic

Dic₇₉⋊C₄

C₂²

yes

characteristic

Dic₇₉⋊C₄

C₂²

yes

—

Dic₇₉⋊C₄

C₂²

yes

—

C₂²⋊Dic₇₉

C₂²

yes

—

C₂²⋊Dic₇₉

C₂²

yes

—

C₂²⋊Dic₇₉

C₂²

yes

—

(C₂×D₇₉)⋊C₄

C₂²

yes

characteristic

(C₂×D₇₉)⋊C₄

C₂²

yes

characteristic

(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₄×Dic₇₉

C₂²

yes

characteristic

C₄×Dic₇₉

C₂²

yes

—

C₂×D₄×C₇₉

C₂²

yes

characteristic

C₂²×C₄×C₇₉

C₂²

yes

—

C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂²⋊C₄×C₇₉

C₂²

yes

—

C₄²×C₇₉

C₂²

yes

characteristic

C₂³×C₇₉

C₂³

yes

—

C₂²×D₇₉

C₂³

yes

characteristic

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂³

yes

—

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

C₂³

yes

characteristic

C₂×Dic₇₉

C₂³

yes

—

C₂×Dic₇₉

C₂³

yes

characteristic

C₂×Dic₇₉

C₂³

yes

—

C₂×Dic₇₉

C₂³

yes

characteristic

C₄×D₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂⁴

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#41

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#41

yes

characteristic

C₂×C₇₉

H(5,𝔽₂)

yes

characteristic

C₂×C₇₉

2₋¹⁺⁴

yes

characteristic

D₇₉

—

C₇₉

#542

yes

characteristic, complemented, Sylow

#542

—

maximal, Sylow

C₄⋊Q₈

—

—

—

—

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

D₇₉

yes

characteristic, complemented

#117

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

C₂×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₇₉

yes

characteristic

C₂²⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

C₂×D₇₉

yes

—

106

C₄²

—

107

C₄²

—

108

C₄²

C₂×D₇₉

yes

characteristic

109

C₂³

—

110

C₂³

C₂²×D₇₉

yes

—

111

Q₈

—

316

—

112

Q₈

—

158

—

113

D₄

—

114

D₄

—

316

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

158

—

122

C₂×C₄

C₂²×D₇₉

yes

characteristic

123

C₂×C₄

C₂²×D₇₉

yes

characteristic

124

C₂×C₄

C₂²×D₇₉

yes

—

125

C₂×C₄

C₂²×D₇₉

yes

characteristic

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

158

—

130

C₂²

—

158

—

131

C₂²

—

158

—

132

C₂²

C₂³×D₇₉

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

158

—

137

C₄

—

158

—

138

C₄

—

158

—

139

C₄

—

158

—

140

C₄

—

158

—

141

C₄

#11929624

yes

—

142

C₂

—

143

C₂

—

316

—

144

C₂

C₂×#11929624

yes

characteristic

145

C₂

#14579206

yes

characteristic

146

C₂

#14579208

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴
Fitting	C₄×D₄×C₇₉	C₂
hypercenter	C₄×D₄	D₇₉
hypocenter	C₇₉	#542
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄

subgroup

G/H

center, Frattini

C₂²

C₂³×D₇₉

commutator, socle

C₂²×C₇₉

C₂⁴

Fitting

C₄×D₄×C₇₉

C₂

hypercenter

C₄×D₄

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂² ◁ C₄×D₄

N	H ≅ G/N	type
1. #14579160	C₂	semidirect
2. #14579154	C₂	semidirect
3. #14579148	C₂	semidirect
4. #14579147	C₂	semidirect
5. #14579144	C₂	semidirect
6. #14579141	C₂	semidirect
7. #14579140	C₂	semidirect
9. C₄×Dic₁₅₈	C₂	semidirect
10. #14579118	C₂	semidirect
11. C₄×D₄×C₇₉	C₂	semidirect
73. C₇₉	#542	semidirect
84. C₄×D₄	D₇₉	semidirect

H ≅ G/N

type

1. #14579160

C₂

semidirect

2. #14579154

C₂

semidirect

3. #14579148

C₂

semidirect

4. #14579147

C₂

semidirect

5. #14579144

C₂

semidirect

6. #14579141

C₂

semidirect

7. #14579140

C₂

semidirect

9. C₄×Dic₁₅₈

C₂

semidirect

10. #14579118

C₂

semidirect

11. C₄×D₄×C₇₉

C₂

semidirect

73. C₇₉

#542

semidirect

84. C₄×D₄

D₇₉

semidirect

Subgroups — #19099178

Conjugacy classes of subgroups

Complements