Group #23771388 — subgroups

Subgroups — #23771388

Order 10112.

368 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 141 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	#19098502	C₂	1	2	yes	maximal
2	#19098495	C₂	1	4	yes	maximal
3	#19098470	C₂	1	2	yes	maximal
4	#19098461	C₂	1	2	yes	maximal
5	#19098450	C₂	1	4	yes	maximal
6	#391×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
11	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
13	C₇₉⋊#95	C₂²	1	2	yes	—
14	C₇₉⋊#95	C₂²	1	4	yes	—
15	C₇₉⋊#95	C₂²	1	4	yes	—
16	C₇₉⋊#95	C₂²	1	4	yes	—
17	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
20	#95×C₇₉	C₂²	1	4	yes	—
21	C₂²×Dic₇₉	C₂³	1	4	yes	—
22	C₂²×Dic₇₉	C₂³	1	4	yes	—
23	C₄⋊Dic₇₉	—	2	4	no	—
24	C₄⋊Dic₇₉	—	4	2	no	—
25	C₄⋊Dic₇₉	—	4	2	no	—
26	C₄⋊Dic₇₉	—	4	2	no	—
27	Dic₇₉⋊C₄	—	2	8	no	—
28	C₄×Dic₇₉	—	4	2	no	—
29	C₂×Q₈×C₇₉	—	4	1	no	—
30	C₂×Q₈×C₇₉	—	4	1	no	—
31	C₂×Q₈×C₇₉	Q₈	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	2	yes	—
36	C₄⋊C₄×C₇₉	—	4	1	no	—
37	C₄²×C₇₉	—	4	1	no	—
38	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
39	Q₈×C₇₉	—	4	4	no	—
40	C₂×C₄×C₇₉	—	2	2	no	—
41	C₂×C₄×C₇₉	—	2	2	no	—
42	C₂×C₄×C₇₉	—	2	2	no	—
43	C₂×C₄×C₇₉	—	2	1	no	—
44	C₂×C₄×C₇₉	—	2	1	no	—
45	C₂×C₄×C₇₉	—	2	2	no	—
46	C₂×C₄×C₇₉	—	2	2	no	—
47	C₂×C₄×C₇₉	—	2	4	no	—
48	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
49	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
50	C₂×C₄×C₇₉	#41	1	4	yes	—
51	C₂×Dic₇₉	—	2	4	no	—
52	C₂×Dic₇₉	—	2	4	no	—
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	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
58	C₂²×C₇₉	C₂×#41	1	2	yes	—
59	C₂²×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
60	C₂²×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
61	C₂²×C₇₉	2₋¹⁺⁴	1	2	yes	—
62	C₄×C₇₉	—	2	4	no	—
63	C₄×C₇₉	—	2	4	no	—
64	C₄×C₇₉	—	2	2	no	—
65	C₄×C₇₉	—	4	2	no	—
66	Dic₇₉	—	4	4	no	—
67	Dic₇₉	—	4	4	no	—
68	C₂×C₇₉	#539	1	2	yes	—
69	C₂×C₇₉	#543	1	1	yes	characteristic
70	C₂×C₇₉	#555	1	1	yes	characteristic
71	C₂×C₇₉	#557	1	2	yes	—
72	C₂×C₇₉	#563	1	1	yes	characteristic
73	#2809	—	79	1	no	maximal, Sylow
74	C₇₉	#2809	1	1	yes	characteristic, complemented, Sylow
75	#400	—	79	2	no	—
76	#398	—	79	4	no	—
77	#391	—	79	2	no	—
78	#391	D₇₉	1	1	yes	characteristic
79	#389	—	79	2	no	—
80	#387	—	79	4	no	—
81	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
82	C₂×C₄⋊C₄	—	79	2	no	—
83	C₂×C₄⋊C₄	—	79	2	no	—
84	C₂×C₄⋊C₄	—	79	2	no	—
85	C₂×C₄⋊C₄	—	79	4	no	—
86	C₂×C₄⋊C₄	—	79	2	no	—
87	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
88	C₂×C₄²	—	79	2	no	—
89	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
90	#95	—	79	2	no	—
91	#95	—	79	4	no	—
92	#95	—	79	4	no	—
93	#95	—	79	4	no	—
94	#95	C₂×D₇₉	1	4	yes	—
95	C₂×Q₈	—	4	1	no	—
96	C₂×Q₈	—	4	1	no	—
97	C₂×Q₈	Dic₁₅₈	1	4	yes	—
98	C₂²×C₄	—	79	4	no	—
99	C₂²×C₄	—	79	4	no	—
100	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
101	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
103	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
104	C₄⋊C₄	—	4	1	no	—
105	C₄⋊C₄	—	316	2	no	—
106	C₄⋊C₄	—	316	2	no	—
107	C₄⋊C₄	—	316	2	no	—
108	C₄⋊C₄	—	158	8	no	—
109	C₄⋊C₄	—	158	4	no	—
110	C₄²	—	4	1	no	—
111	C₄²	—	316	2	no	—
112	C₂³	C₂³×D₇₉	1	1	yes	characteristic
113	Q₈	—	4	4	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	158	4	no	—
123	C₂×C₄	—	158	4	no	—
124	C₂×C₄	—	158	4	no	—
125	C₂×C₄	—	158	4	no	—
126	C₂×C₄	—	158	4	no	—
127	C₂×C₄	—	158	4	no	—
128	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
129	C₂×C₄	C₂×Dic₁₅₈	1	4	yes	—
130	C₂×C₄	#11929625	1	4	yes	—
131	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
132	C₂²	C₂×#11929625	1	2	yes	—
133	C₂²	#14579206	1	1	yes	characteristic
134	C₂²	#14579206	1	1	yes	characteristic
135	C₂²	#14579208	1	2	yes	—
136	C₄	—	2	4	no	—
137	C₄	—	2	2	no	—
138	C₄	—	2	4	no	—
139	C₄	—	4	2	no	—
140	C₄	—	316	4	no	—
141	C₄	—	316	4	no	—
142	C₂	#19099162	1	2	yes	—
143	C₂	#19099189	1	1	yes	characteristic
144	C₂	#19099279	1	1	yes	characteristic
145	C₂	#19099292	1	2	yes	—
146	C₂	#19099313	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098502

C₂

yes

maximal

#19098495

C₂

yes

maximal

#19098470

C₂

yes

maximal

#19098461

C₂

yes

maximal

#19098450

C₂

yes

maximal

#391×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#95×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂⁴

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

2₋¹⁺⁴

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#539

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic

#389

—

#387

—

C₂²×Q₈

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

—

C₂×D₇₉

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₁₅₈

yes

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×D₇₉

yes

—

101

C₂²×C₄

C₂²×D₇₉

yes

characteristic

102

C₂²×C₄

C₂²×D₇₉

yes

—

103

C₂²×C₄

C₂²×D₇₉

yes

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

316

—

106

C₄⋊C₄

—

316

—

107

C₄⋊C₄

—

316

—

108

C₄⋊C₄

—

158

—

109

C₄⋊C₄

—

158

—

110

C₄²

—

111

C₄²

—

316

—

112

C₂³

C₂³×D₇₉

yes

characteristic

113

Q₈

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

158

—

123

C₂×C₄

—

158

—

124

C₂×C₄

—

158

—

125

C₂×C₄

—

158

—

126

C₂×C₄

—

158

—

127

C₂×C₄

—

158

—

128

C₂×C₄

C₂×Dic₁₅₈

yes

—

129

C₂×C₄

C₂×Dic₁₅₈

yes

—

130

C₂×C₄

#11929625

yes

—

131

C₂²

C₂²×Dic₁₅₈

yes

characteristic

132

C₂²

C₂×#11929625

yes

—

133

C₂²

#14579206

yes

characteristic

134

C₂²

#14579206

yes

characteristic

135

C₂²

#14579208

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

316

—

141

C₄

—

316

—

142

C₂

#19099162

yes

—

143

C₂

#19099189

yes

characteristic

144

C₂

#19099279

yes

characteristic

145

C₂

#19099292

yes

—

146

C₂

#19099313

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#391×C₇₉	C₂
hypercenter	#391	D₇₉
hypocenter	C₇₉	#2809
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #391

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#391×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #391

N	H ≅ G/N	type
74. C₇₉	#2809	semidirect

H ≅ G/N

type

74. C₇₉

#2809

semidirect

Subgroups — #23771388

Conjugacy classes of subgroups

Complements