Group #11931425 — subgroups

Subgroups — C₅×#8705 #11931425

Order 1280.

486 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 142 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×C₅×#383	C₂	1	1	yes	maximal, characteristic
2	C₅×#1817	C₂	1	2	yes	maximal
3	C₅×#1280	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
5	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
6	C₅×#383	—	2	4	no	—
7	C₂×C₅×#95	C₄	1	2	yes	—
8	C₂×C₅×#95	C₄	1	2	yes	—
9	C₂×C₅×#95	C₂²	1	2	yes	—
10	C₅×#336	—	2	4	no	—
11	#8705	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄×C₅	C₂×C₄	1	4	yes	—
14	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
16	C₂²×C₅×C₈	—	2	4	no	—
17	C₂×C₄²×C₅	—	2	4	no	—
18	C₂×C₄²×C₅	D₄	1	4	yes	—
19	C₅×C₂²⋊C₈	—	2	8	no	—
20	C₅×#95	—	2	4	no	—
21	C₅×#95	—	2	4	no	—
22	C₅×#95	—	2	4	no	—
23	C₂×#383	C₂×C₅	1	1	yes	characteristic
24	#1817	C₂×C₅	1	2	yes	—
25	#1280	C₂×C₅	1	4	yes	—
26	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₅	—	2	2	no	—
28	C₂²×C₄×C₅	—	2	2	no	—
29	C₂²×C₄×C₅	—	2	4	no	—
30	C₂²×C₄×C₅	—	2	4	no	—
31	C₂²×C₄×C₅	—	2	8	no	—
32	C₂²×C₄×C₅	—	4	2	no	—
33	C₂²×C₄×C₅	—	4	2	no	—
34	C₂²×C₄×C₅	—	4	4	no	—
35	C₂²×C₄×C₅	—	4	4	no	—
36	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
38	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
39	C₂²×C₄×C₅	#41	1	4	yes	—
40	C₂×C₅×C₈	—	4	8	no	—
41	C₂×C₅×C₈	—	4	4	no	—
42	C₄²×C₅	—	2	8	no	—
43	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
44	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
45	#383	—	2	4	no	—
46	C₂×#95	C₄×C₅	1	2	yes	—
47	C₂×#95	C₄×C₅	1	2	yes	—
48	C₂×#95	C₂²×C₅	1	2	yes	—
49	#336	—	2	4	no	—
50	C₂³×C₅	—	2	2	no	—
51	C₂³×C₅	—	2	2	no	—
52	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂³×C₅	#117	1	2	yes	—
54	C₂³×C₅	#131	1	4	yes	—
55	C₂×C₄×C₅	—	2	4	no	—
56	C₂×C₄×C₅	—	2	2	no	—
57	C₂×C₄×C₅	—	2	2	no	—
58	C₂×C₄×C₅	—	2	4	no	—
59	C₂×C₄×C₅	—	2	4	no	—
60	C₂×C₄×C₅	—	4	4	no	—
61	C₂×C₄×C₅	—	4	4	no	—
62	C₂×C₄×C₅	—	4	4	no	—
63	C₂×C₄×C₅	—	4	4	no	—
64	C₂×C₄×C₅	—	4	4	no	—
65	C₂×C₄×C₅	—	4	4	no	—
66	C₂×C₄×C₅	—	8	8	no	—
67	C₂×C₄×C₅	#123	1	4	yes	—
68	C₅×C₈	—	8	4	no	—
69	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
70	C₂³×C₄	C₂×C₄×C₅	1	4	yes	—
71	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
72	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
73	C₂²×C₈	—	2	4	no	—
74	C₂×C₄²	—	2	4	no	—
75	C₂×C₄²	C₅×D₄	1	4	yes	—
76	C₂²⋊C₈	—	2	8	no	—
77	#95	—	2	4	no	—
78	#95	—	2	4	no	—
79	#95	—	2	4	no	—
80	C₂²×C₅	—	2	2	no	—
81	C₂²×C₅	—	2	2	no	—
82	C₂²×C₅	—	2	8	no	—
83	C₂²×C₅	#381	1	1	yes	characteristic
84	C₂²×C₅	#408	1	2	yes	—
85	C₂²×C₅	#410	1	2	yes	—
86	C₂²×C₅	#413	1	2	yes	—
87	C₂²×C₅	#433	1	4	yes	—
88	C₄×C₅	—	2	4	no	—
89	C₄×C₅	—	4	2	no	—
90	C₄×C₅	—	4	2	no	—
91	C₄×C₅	—	8	4	no	—
92	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
93	C₂²×C₄	—	2	2	no	—
94	C₂²×C₄	—	2	2	no	—
95	C₂²×C₄	—	2	4	no	—
96	C₂²×C₄	—	2	4	no	—
97	C₂²×C₄	—	2	8	no	—
98	C₂²×C₄	—	4	2	no	—
99	C₂²×C₄	—	4	2	no	—
100	C₂²×C₄	—	4	4	no	—
101	C₂²×C₄	—	4	4	no	—
102	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
105	C₂²×C₄	C₅×#41	1	4	yes	—
106	C₂×C₈	—	4	8	no	—
107	C₂×C₈	—	4	4	no	—
108	C₄²	—	2	8	no	—
109	C₂×C₅	—	2	4	no	—
110	C₂×C₅	#1473	1	4	yes	—
111	C₂×C₅	#1818	1	1	yes	characteristic
112	C₂×C₅	#1820	1	1	yes	characteristic
113	C₂×C₅	#1822	1	1	yes	characteristic
114	C₂³	—	2	2	no	—
115	C₂³	—	2	2	no	—
116	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³	C₅×#117	1	2	yes	—
118	C₂³	C₅×#131	1	4	yes	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	4	4	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	8	8	no	—
131	C₂×C₄	C₅×#123	1	4	yes	—
132	C₈	—	8	4	no	—
133	C₅	#8705	1	1	yes	characteristic, direct product factor, Sylow
134	C₂²	—	2	2	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	8	no	—
137	C₂²	C₅×#381	1	1	yes	characteristic
138	C₂²	C₅×#408	1	2	yes	—
139	C₂²	C₅×#410	1	2	yes	—
140	C₂²	C₅×#413	1	2	yes	—
141	C₂²	C₅×#433	1	4	yes	—
142	C₄	—	2	4	no	—
143	C₄	—	4	2	no	—
144	C₄	—	4	2	no	—
145	C₄	—	8	4	no	—
146	C₂	—	2	4	no	—
147	C₂	C₅×#1473	1	4	yes	—
148	C₂	C₅×#1818	1	1	yes	characteristic
149	C₂	C₅×#1820	1	1	yes	characteristic
150	C₂	C₅×#1822	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×#383

C₂

yes

maximal, characteristic

C₅×#1817

C₂

yes

maximal

C₅×#1280

C₂

yes

maximal

C₂²×C₄²×C₅

C₂²

yes

characteristic

C₂×C₅×C₂²⋊C₈

C₂²

yes

—

C₅×#383

—

C₂×C₅×#95

C₄

yes

—

C₂×C₅×#95

C₄

yes

—

C₂×C₅×#95

C₂²

yes

—

C₅×#336

—

#8705

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₄×C₅

C₂×C₄

yes

characteristic

C₂³×C₄×C₅

C₂×C₄

yes

—

C₂³×C₄×C₅

C₂×C₄

yes

characteristic

C₂³×C₄×C₅

C₂³

yes

characteristic

C₂²×C₅×C₈

—

C₂×C₄²×C₅

—

C₂×C₄²×C₅

D₄

yes

—

C₅×C₂²⋊C₈

—

C₅×#95

—

C₅×#95

—

C₅×#95

—

C₂×#383

C₂×C₅

yes

characteristic

#1817

C₂×C₅

yes

—

#1280

C₂×C₅

yes

—

C₂⁴×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

#41

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

—

C₂²×C₄²

C₂²×C₅

yes

characteristic

C₂×C₂²⋊C₈

C₂²×C₅

yes

—

#383

—

C₂×#95

C₄×C₅

yes

—

C₂×#95

C₄×C₅

yes

—

C₂×#95

C₂²×C₅

yes

—

#336

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₅

#117

yes

—

C₂³×C₅

#131

yes

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#123

yes

—

C₅×C₈

—

C₂³×C₄

C₂×C₄×C₅

yes

characteristic

C₂³×C₄

C₂×C₄×C₅

yes

—

C₂³×C₄

C₂×C₄×C₅

yes

characteristic

C₂³×C₄

C₂³×C₅

yes

characteristic

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

C₅×D₄

yes

—

C₂²⋊C₈

—

#95

—

#95

—

#95

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#381

yes

characteristic

C₂²×C₅

#408

yes

—

C₂²×C₅

#410

yes

—

C₂²×C₅

#413

yes

—

C₂²×C₅

#433

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₂⁴

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

103

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

104

C₂²×C₄

C₂×C₅×D₄

yes

—

105

C₂²×C₄

C₅×#41

yes

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₄²

—

109

C₂×C₅

—

110

C₂×C₅

#1473

yes

—

111

C₂×C₅

#1818

yes

characteristic

112

C₂×C₅

#1820

yes

characteristic

113

C₂×C₅

#1822

yes

characteristic

114

C₂³

—

115

C₂³

—

116

C₂³

C₂×C₅×C₂²⋊C₄

yes

characteristic

117

C₂³

C₅×#117

yes

—

118

C₂³

C₅×#131

yes

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₅×#123

yes

—

132

C₈

—

133

C₅

#8705

yes

characteristic, direct product factor, Sylow

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

C₅×#381

yes

characteristic

138

C₂²

C₅×#408

yes

—

139

C₂²

C₅×#410

yes

—

140

C₂²

C₅×#413

yes

—

141

C₂²

C₅×#433

yes

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₂

—

147

C₂

C₅×#1473

yes

—

148

C₂

C₅×#1818

yes

characteristic

149

C₂

C₅×#1820

yes

characteristic

150

C₂

C₅×#1822

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂³×C₅

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₅

Frattini, cosocle

C₂³×C₄

C₂³×C₅

prime radical

C₂⁴×C₅

C₂²×C₄

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

N	H ≅ G/N	type
11. #8705	C₅	direct (N × H)
133. C₅	#8705	direct (N × H)

H ≅ G/N

type

11. #8705

C₅

direct (N × H)

133. C₅

#8705

direct (N × H)

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

subgroup	index
C₂×C₅×#383	2
C₅×#1817	2
C₅×#1280	2
#8705	5

subgroup

index

C₂×C₅×#383

C₅×#1817

C₅×#1280

#8705

Subgroups — C₅×#8705 #11931425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8705 #11931425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8705 #11931425