Group #23771770 — subgroups

Subgroups — #23771770

Order 10112.

524 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14579153	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098470	C₂	1	2	yes	maximal, complemented
3	#19098466	C₂	1	2	yes	maximal
4	#19098457	C₂	1	8	yes	maximal, complemented
5	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#124×C₇₉	C₂	1	1	yes	maximal, characteristic
7	#14579153	—	2	4	no	—
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
10	C₂×C₂²⋊Dic₇₉	C₂²	1	8	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
13	C₇₉⋊#95	C₂²	1	8	yes	—
14	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
16	#124×C₇₉	—	2	4	no	—
17	C₂×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	—
18	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₇₉	C₂³	1	4	yes	—
20	C₂²×Dic₇₉	C₂³	1	4	yes	—
21	C₄⋊Dic₇₉	—	2	4	no	—
22	Dic₇₉⋊C₄	—	2	8	no	—
23	C₂²⋊Dic₇₉	—	2	16	no	—
24	C₄×Dic₇₉	—	2	8	no	—
25	C₄×Dic₇₉	—	2	4	no	—
26	C₂⁴×C₇₉	C₂³	1	2	yes	—
27	C₂×Q₈×C₇₉	—	2	2	no	—
28	C₂×Q₈×C₇₉	—	2	4	no	—
29	C₂×D₄×C₇₉	—	2	2	no	—
30	C₂×D₄×C₇₉	—	2	4	no	—
31	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
32	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
33	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
34	C₂²⋊C₄×C₇₉	—	2	8	no	—
35	C₄²×C₇₉	D₄	1	4	yes	—
36	C₂³×C₇₉	—	2	2	no	—
37	C₂³×C₇₉	—	2	8	no	—
38	C₂³×C₇₉	—	2	4	no	—
39	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
40	Q₈×C₇₉	—	4	4	no	—
41	D₄×C₇₉	—	4	4	no	—
42	C₂×C₄×C₇₉	—	2	4	no	—
43	C₂×C₄×C₇₉	—	2	2	no	—
44	C₂×C₄×C₇₉	—	2	4	no	—
45	C₂×C₄×C₇₉	C₂×D₄	1	4	yes	—
46	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₇₉	#41	1	4	yes	—
48	C₂×Dic₇₉	—	2	4	no	—
49	C₂×Dic₇₉	—	2	4	no	—
50	C₂×Dic₇₉	—	2	4	no	—
51	C₂×Dic₇₉	—	2	8	no	—
52	C₂×Dic₇₉	#41	1	8	yes	—
53	C₂²×C₇₉	—	4	2	no	—
54	C₂²×C₇₉	—	4	8	no	—
55	C₂²×C₇₉	—	4	4	no	—
56	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
57	C₂²×C₇₉	C₂×#41	1	4	yes	—
58	C₂²×C₇₉	C₂×#41	1	2	yes	—
59	C₄×C₇₉	—	2	4	no	—
60	C₄×C₇₉	—	4	2	no	—
61	C₄×C₇₉	#124	1	4	yes	—
62	Dic₇₉	—	2	8	no	—
63	Dic₇₉	—	4	4	no	—
64	C₂×C₇₉	—	8	2	no	—
65	C₂×C₇₉	C₂×#124	1	1	yes	characteristic
66	C₂×C₇₉	#529	1	4	yes	—
67	C₂×C₇₉	#532	1	2	yes	—
68	#2861	—	79	1	no	maximal, Sylow
69	C₇₉	#2861	1	1	yes	characteristic, complemented, Sylow
70	C₂×#125	—	79	1	no	—
71	C₂×#124	D₇₉	1	1	yes	characteristic
72	#391	—	79	2	no	—
73	#390	—	79	2	no	—
74	#388	—	79	8	no	—
75	C₄³	—	79	1	no	—
76	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
77	C₂²×D₄	C₂×D₇₉	1	1	yes	characteristic
78	#125	—	158	4	no	—
79	#124	—	2	4	no	—
80	C₂×C₄⋊C₄	—	79	4	no	—
81	C₂×C₄⋊C₄	—	79	2	no	—
82	C₂×C₂²⋊C₄	—	79	8	no	—
83	C₂×C₂²⋊C₄	C₂×D₇₉	1	4	yes	—
84	C₂×C₄²	—	79	4	no	—
85	C₂×C₄²	—	79	2	no	—
86	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
87	#95	—	79	8	no	—
88	C₂⁴	C₂²×D₇₉	1	2	yes	—
89	C₂×Q₈	—	2	2	no	—
90	C₂×Q₈	—	2	4	no	—
91	C₂×D₄	—	2	2	no	—
92	C₂×D₄	—	2	4	no	—
93	C₂²×C₄	—	79	4	no	—
94	C₂²×C₄	—	79	4	no	—
95	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
96	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
97	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
98	C₄⋊C₄	—	158	8	no	—
99	C₄⋊C₄	—	158	4	no	—
100	C₂²⋊C₄	—	2	8	no	—
101	C₂²⋊C₄	—	158	16	no	—
102	C₄²	—	158	8	no	—
103	C₄²	—	158	4	no	—
104	C₄²	C₂²⋊D₇₉	1	4	yes	—
105	C₂³	—	2	8	no	—
106	C₂³	—	2	4	no	—
107	C₂³	—	2	2	no	—
108	C₂³	C₂³×D₇₉	1	1	yes	characteristic
109	Q₈	—	4	4	no	—
110	D₄	—	4	4	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	79	8	no	—
115	C₂×C₄	—	158	8	no	—
116	C₂×C₄	—	158	4	no	—
117	C₂×C₄	—	158	4	no	—
118	C₂×C₄	—	158	4	no	—
119	C₂×C₄	C₂×C₂²⋊D₇₉	1	4	yes	—
120	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
121	C₂×C₄	#11929623	1	4	yes	—
122	C₂²	—	4	2	no	—
123	C₂²	—	4	8	no	—
124	C₂²	—	4	4	no	—
125	C₂²	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
126	C₂²	#41×D₇₉	1	4	yes	—
127	C₂²	C₂×#11929623	1	2	yes	—
128	C₄	—	2	4	no	—
129	C₄	—	4	2	no	—
130	C₄	—	316	4	no	—
131	C₄	—	158	8	no	—
132	C₄	#14579148	1	4	yes	—
133	C₂	—	8	2	no	—
134	C₂	C₂×#14579148	1	1	yes	characteristic
135	C₂	#19099092	1	4	yes	—
136	C₂	#19099109	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579153

C₂

yes

maximal, characteristic, complemented

#19098470

C₂

yes

maximal, complemented

#19098466

C₂

yes

maximal

#19098457

C₂

yes

maximal, complemented

C₄²×Dic₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#124×C₇₉

C₂

yes

maximal, characteristic

#14579153

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂²×D₄×C₇₉

C₂²

yes

characteristic

#124×C₇₉

—

C₂×C₂²⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂⁴×C₇₉

C₂³

yes

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂⁴

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

#41

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#124

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#124

yes

characteristic

C₂×C₇₉

#529

yes

—

C₂×C₇₉

#532

yes

—

#2861

—

maximal, Sylow

C₇₉

#2861

yes

characteristic, complemented, Sylow

C₂×#125

—

C₂×#124

D₇₉

yes

—

—

—

C₄³

—

C₂²×Q₈

C₂×D₇₉

yes

characteristic

C₂²×D₄

C₂×D₇₉

yes

characteristic

#125

—

158

—

#124

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#95

—

C₂⁴

C₂²×D₇₉

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

158

—

102

C₄²

—

158

—

103

C₄²

—

158

—

104

C₄²

C₂²⋊D₇₉

yes

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂³×D₇₉

yes

characteristic

109

Q₈

—

110

D₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

158

—

116

C₂×C₄

—

158

—

117

C₂×C₄

—

158

—

118

C₂×C₄

—

158

—

119

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

120

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

121

C₂×C₄

#11929623

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₂²×C₂²⋊D₇₉

yes

characteristic

126

C₂²

#41×D₇₉

yes

—

127

C₂²

C₂×#11929623

yes

—

128

C₄

—

129

C₄

—

130

C₄

—

316

—

131

C₄

—

158

—

132

C₄

#14579148

yes

—

133

C₂

—

134

C₂

C₂×#14579148

yes

characteristic

135

C₂

#19099092

yes

—

136

C₂

#19099109

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, cosocle	C₂³×C₇₉	C₂⁴
Fitting	C₂×#124×C₇₉	C₂
prime radical	C₂²×D₄×C₇₉	C₂²
hypercenter	C₂×#124	D₇₉
hypocenter	C₇₉	#2861
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#124

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, cosocle

C₂³×C₇₉

C₂⁴

Fitting

C₂×#124×C₇₉

C₂

prime radical

C₂²×D₄×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×#14579153	C₂	semidirect
2. #19098470	C₂	semidirect
4. #19098457	C₂	semidirect
5. C₄²×Dic₇₉	C₂	semidirect
69. C₇₉	#2861	semidirect

H ≅ G/N

type

1. C₂×#14579153

C₂

semidirect

2. #19098470

C₂

semidirect

4. #19098457

C₂

semidirect

5. C₄²×Dic₇₉

C₂

semidirect

69. C₇₉

#2861

semidirect

Subgroups — #23771770

Conjugacy classes of subgroups

Complements