Group #11993076 — subgroups

Subgroups — #11993076

Order 1280.

422 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 203 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	C₅×#1845	C₂	1	1	yes	maximal, characteristic
2	#10600558	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×#168	C₂	1	1	yes	maximal, characteristic
4	#10600367	C₂	1	4	yes	maximal
5	C₂×C₅×#107	—	2	2	no	—
6	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₅×#384	C₂²	1	2	yes	—
8	C₂×#3950	—	2	2	no	—
9	#65224	C₂²	1	2	yes	—
10	C₂×C₄×#168	C₂²	1	2	yes	—
11	#64749	—	2	8	no	—
12	C₈×#168	C₄	1	4	yes	complemented
13	#8816	—	5	1	no	maximal, Sylow
14	C₂²×C₅×C₈	D₄	1	2	yes	—
15	C₂×C₅×C₄⋊C₄	—	2	2	no	—
16	C₂×C₅×C₄⋊C₄	—	2	4	no	—
17	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
18	C₂×C₄⋊Dic₅	—	2	2	no	—
19	C₂×C₄⋊Dic₅	—	2	4	no	—
20	C₂²×#168	D₄	1	4	yes	—
21	C₅×#107	—	4	4	no	—
22	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
23	C₄×C₅×C₈	Q₈	1	2	yes	—
24	#3950	—	4	4	no	—
25	C₄×#168	C₂×C₄	1	4	yes	—
26	C₄×#168	Q₈	1	4	yes	—
27	#1845	—	5	1	no	—
28	#1845	D₅	1	1	yes	characteristic
29	#1834	—	5	4	no	—
30	C₂×C₈²	—	5	1	no	—
31	C₂²×C₄×C₅	—	4	2	no	—
32	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
33	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
34	C₂²×Dic₅	—	4	2	no	—
35	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
36	C₂×C₅×C₈	D₈	1	4	yes	—
37	C₂×C₅×C₈	Q₁₆	1	4	yes	—
38	C₅×C₄⋊C₄	—	4	4	no	—
39	C₅×C₄⋊C₄	—	4	8	no	—
40	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
42	C₄²×C₅	C₂×Q₈	1	2	yes	—
43	C₄⋊Dic₅	—	4	4	no	—
44	C₄⋊Dic₅	—	4	8	no	—
45	C₂×#168	—	2	4	no	—
46	C₂×#168	—	2	4	no	—
47	C₂×#168	C₄⋊C₄	1	8	yes	—
48	C₂×#107	—	2	2	no	—
49	C₂×#107	—	10	2	no	—
50	C₂×C₄×C₈	—	5	2	no	—
51	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
52	#384	—	5	2	no	—
53	#384	C₂×D₅	1	2	yes	—
54	#340	—	10	8	no	—
55	C₈²	—	5	4	no	—
56	C₂³×C₅	#127	1	1	yes	characteristic
57	C₂×C₄×C₅	—	8	2	no	—
58	C₂×C₄×C₅	—	8	4	no	—
59	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
60	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
62	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
63	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
64	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
65	C₂×C₄×C₅	#135	1	4	yes	—
66	C₂×C₄×C₅	#135	1	4	yes	—
67	C₂×Dic₅	—	8	2	no	—
68	C₂×Dic₅	—	8	4	no	—
69	C₅×C₈	#107	1	8	yes	—
70	#168	—	2	8	no	—
71	C₂²×C₈	—	5	4	no	—
72	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
73	C₂×C₄⋊C₄	—	2	4	no	—
74	C₂×C₄⋊C₄	—	2	2	no	—
75	C₂×C₄⋊C₄	—	10	4	no	—
76	C₂×C₄⋊C₄	—	10	2	no	—
77	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
78	#107	—	4	4	no	—
79	#107	—	20	4	no	—
80	C₄×C₈	—	5	4	no	—
81	C₄×C₈	—	5	4	no	—
82	C₄×C₈	Dic₁₀	1	2	yes	—
83	C₄×C₈	C₄×D₅	1	2	yes	—
84	C₂²×C₅	#384	1	1	yes	characteristic
85	C₂²×C₅	#493	1	1	yes	characteristic
86	C₂²×C₅	#494	1	1	yes	characteristic
87	C₂²×C₅	#495	1	2	yes	—
88	C₂²×C₅	#495	1	2	yes	—
89	C₄×C₅	—	16	2	no	—
90	C₄×C₅	C₂×#107	1	2	yes	—
91	C₄×C₅	#427	1	4	yes	—
92	C₄×C₅	#499	1	4	yes	—
93	C₄×C₅	#500	1	2	yes	—
94	Dic₅	—	16	2	no	—
95	C₂²×C₄	—	4	2	no	—
96	C₂²×C₄	—	20	2	no	—
97	C₂²×C₄	D₄×D₅	1	2	yes	—
98	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
99	C₂×C₈	—	5	8	no	—
100	C₂×C₈	—	10	4	no	—
101	C₂×C₈	—	10	4	no	—
102	C₂×C₈	#683	1	4	yes	—
103	C₂×C₈	#686	1	4	yes	—
104	C₂×C₈	#689	1	4	yes	—
105	C₄⋊C₄	—	4	8	no	—
106	C₄⋊C₄	—	4	4	no	—
107	C₄⋊C₄	—	20	8	no	—
108	C₄⋊C₄	—	20	4	no	—
109	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
110	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
111	C₄²	Q₈×D₅	1	2	yes	—
112	C₂×C₅	#1709	1	1	yes	characteristic
113	C₂×C₅	#1709	1	1	yes	characteristic
114	C₂×C₅	#1710	1	2	yes	—
115	C₂×C₅	#1845	1	1	yes	characteristic
116	C₂×C₅	#1846	1	2	yes	—
117	C₂³	#4086	1	1	yes	characteristic
118	C₂×C₄	—	8	2	no	—
119	C₂×C₄	—	8	4	no	—
120	C₂×C₄	—	40	2	no	—
121	C₂×C₄	—	40	4	no	—
122	C₂×C₄	#4034	1	2	yes	—
123	C₂×C₄	D₅×C₄⋊C₄	1	2	yes	—
124	C₂×C₄	#4058	1	4	yes	—
125	C₂×C₄	#4065	1	4	yes	—
126	C₂×C₄	C₂×#683	1	1	yes	characteristic
127	C₂×C₄	C₂×#686	1	2	yes	—
128	C₂×C₄	C₂×#689	1	2	yes	—
129	C₂×C₄	#4090	1	1	yes	characteristic
130	C₈	—	10	8	no	—
131	C₈	#3939	1	8	yes	—
132	C₅	#8816	1	1	yes	characteristic, complemented, Sylow
133	C₂²	#65265	1	1	yes	characteristic
134	C₂²	#65362	1	1	yes	characteristic
135	C₂²	#65381	1	1	yes	characteristic
136	C₂²	#65444	1	2	yes	—
137	C₂²	#65480	1	2	yes	—
138	C₄	—	16	2	no	—
139	C₄	—	80	2	no	—
140	C₄	#65167	1	4	yes	—
141	C₄	#65169	1	4	yes	—
142	C₄	C₂×#3939	1	2	yes	—
143	C₄	#65367	1	2	yes	—
144	C₂	#10600370	1	1	yes	characteristic
145	C₂	#10601400	1	2	yes	—
146	C₂	#10602068	1	1	yes	characteristic
147	C₂	#10602090	1	1	yes	characteristic
148	C₂	#10602154	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1845

C₂

yes

maximal, characteristic

#10600558

C₂

yes

maximal, characteristic

C₂×C₈×#168

C₂

yes

maximal, characteristic

#10600367

C₂

yes

maximal

C₂×C₅×#107

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×#384

C₂²

yes

—

C₂×#3950

—

#65224

C₂²

yes

—

C₂×C₄×#168

C₂²

yes

—

#64749

—

C₈×#168

C₄

yes

complemented

#8816

—

maximal, Sylow

C₂²×C₅×C₈

D₄

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₂×C₄⋊Dic₅

—

C₂×C₄⋊Dic₅

—

C₂²×#168

D₄

yes

—

C₅×#107

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

#3950

—

C₄×#168

C₂×C₄

yes

—

C₄×#168

Q₈

yes

—

#1845

—

#1845

D₅

yes

characteristic

#1834

—

C₂×C₈²

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×Dic₅

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

D₈

yes

—

C₂×C₅×C₈

Q₁₆

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₂×#168

—

C₂×#168

—

C₂×#168

C₄⋊C₄

yes

—

C₂×#107

—

C₂×#107

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₅

yes

characteristic

#384

—

#384

C₂×D₅

yes

—

#340

—

C₈²

—

C₂³×C₅

#127

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₂×C₄×C₅

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₅

C₂×D₈

yes

—

C₂×C₄×C₅

C₂×Q₁₆

yes

—

C₂×C₄×C₅

#135

yes

—

C₂×C₄×C₅

#135

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₅×C₈

#107

yes

—

#168

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₅

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₅

yes

characteristic

#107

—

#107

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₁₀

yes

—

C₄×C₈

C₄×D₅

yes

—

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

—

C₂²×C₅

#495

yes

—

C₄×C₅

—

C₄×C₅

C₂×#107

yes

—

C₄×C₅

#427

yes

—

C₄×C₅

#499

yes

—

C₄×C₅

#500

yes

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄×D₅

yes

—

C₂²×C₄

C₂×C₂²⋊D₅

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

#683

yes

—

103

C₂×C₈

#686

yes

—

104

C₂×C₈

#689

yes

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

C₂×Dic₁₀

yes

characteristic

110

C₄²

C₂×C₄×D₅

yes

characteristic

111

C₄²

Q₈×D₅

yes

—

112

C₂×C₅

#1709

yes

characteristic

113

C₂×C₅

#1709

yes

characteristic

114

C₂×C₅

#1710

yes

—

115

C₂×C₅

#1845

yes

characteristic

116

C₂×C₅

#1846

yes

—

117

C₂³

#4086

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

#4034

yes

—

123

C₂×C₄

D₅×C₄⋊C₄

yes

—

124

C₂×C₄

#4058

yes

—

125

C₂×C₄

#4065

yes

—

126

C₂×C₄

C₂×#683

yes

characteristic

127

C₂×C₄

C₂×#686

yes

—

128

C₂×C₄

C₂×#689

yes

—

129

C₂×C₄

#4090

yes

characteristic

130

C₈

—

131

C₈

#3939

yes

—

132

C₅

#8816

yes

characteristic, complemented, Sylow

133

C₂²

#65265

yes

characteristic

134

C₂²

#65362

yes

characteristic

135

C₂²

#65381

yes

characteristic

136

C₂²

#65444

yes

—

137

C₂²

#65480

yes

—

138

C₄

—

139

C₄

—

140

C₄

#65167

yes

—

141

C₄

#65169

yes

—

142

C₄

C₂×#3939

yes

—

143

C₄

#65367

yes

—

144

C₂

#10600370

yes

characteristic

145

C₂

#10601400

yes

—

146

C₂

#10602068

yes

characteristic

147

C₂

#10602090

yes

characteristic

148

C₂

#10602154

yes

—

	subgroup	G/H
center	C₂³	#4086
commutator	C₄²×C₅	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₅×#1845	C₂
socle, prime radical	C₂³×C₅	#127
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	#1845	D₅
hypocenter	C₅	#8816
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#4086

commutator

C₄²×C₅

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅

C₂

C₂³×C₅

C₂×C₄²×C₅

C₂³

D₅

C₅

G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
12. C₈×#168	C₄	semidirect
132. C₅	#8816	semidirect

H ≅ G/N

type

12. C₈×#168

C₄

semidirect

132. C₅

#8816

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#1845	2
#10600558	2
C₂×C₈×#168	2
#10600367	2
#8816	5

subgroup

index

C₂×C₈×#168

Subgroups — #11993076

Conjugacy classes of subgroups

Complements

Maximal subgroups