Group #14285339 — subgroups

Subgroups — C₅×#71777 #14285339

Order 1920.

456 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 170 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×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#4926	C₂	1	2	yes	maximal
3	C₅×#4546	C₂	1	4	yes	maximal, complemented
4	C₅×#1558	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅×Q₈	C₄	1	2	yes	—
6	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
7	C₃×C₅×C₄⋊Q₈	C₄	1	2	yes	—
8	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₅×#830	—	2	2	no	—
12	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	—
13	C₅×#803	—	2	2	no	—
14	#71777	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic
16	C₅×#432	—	3	2	no	—
17	C₅×#333	—	3	4	no	—
18	C₂×C₃×C₅×Q₈	—	2	2	no	—
19	C₂×C₃×C₅×Q₈	—	4	4	no	—
20	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
21	C₂²×C₃×C₄×C₅	—	2	2	no	—
22	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
24	C₃×C₅×C₄⋊C₄	—	2	4	no	—
25	C₃×C₅×C₄⋊C₄	—	2	4	no	—
26	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
27	C₃×C₄²×C₅	D₄	1	2	yes	—
28	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₅×C₃⋊C₈	—	2	4	no	—
30	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
31	#4926	C₂×C₅	1	2	yes	—
32	#4546	C₂×C₅	1	4	yes	complemented
33	C₂²×C₅×Q₈	Dic₃	1	2	yes	—
34	C₅×C₄⋊Q₈	—	2	2	no	—
35	C₅×C₄⋊Q₈	Dic₃	1	2	yes	—
36	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	—
37	C₂×C₅×C₄⋊C₄	—	2	2	no	—
38	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
39	C₅×C₄⋊C₈	—	3	4	no	—
40	C₅×C₂²⋊C₈	—	6	2	no	—
41	C₅×#97	—	6	2	no	—
42	#1558	—	3	1	no	Sylow
43	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
44	C₃×C₅×Q₈	—	4	4	no	—
45	C₃×C₅×Q₈	—	4	4	no	—
46	C₂×C₃×C₄×C₅	—	2	2	no	—
47	C₂×C₃×C₄×C₅	—	2	4	no	—
48	C₂×C₃×C₄×C₅	—	2	4	no	—
49	C₂×C₃×C₄×C₅	—	4	4	no	—
50	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
51	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
54	C₅×C₃⋊C₈	—	4	4	no	—
55	C₂²×C₃×Q₈	C₄×C₅	1	2	yes	—
56	C₃×C₄⋊Q₈	—	2	2	no	—
57	C₃×C₄⋊Q₈	C₄×C₅	1	2	yes	—
58	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
59	C₂×C₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
61	#830	—	2	2	no	—
62	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	—
63	#803	—	2	2	no	—
64	C₂×C₅×Q₈	—	2	2	no	—
65	C₂×C₅×Q₈	—	4	4	no	—
66	C₂×C₅×Q₈	C₂×Dic₃	1	4	yes	—
67	C₂²×C₄×C₅	—	2	2	no	—
68	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
69	C₂²×C₄×C₅	#67	1	2	yes	—
70	C₂×C₅×C₈	—	6	4	no	—
71	C₅×C₄⋊C₄	—	2	4	no	—
72	C₅×C₄⋊C₄	—	2	4	no	—
73	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
74	C₄²×C₅	#67	1	2	yes	—
75	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
76	C₂×C₄⋊Q₈	C₅×D₃	1	1	yes	characteristic
77	#432	—	3	2	no	—
78	#333	—	3	4	no	—
79	C₂²×C₃×C₅	—	2	2	no	—
80	C₂²×C₃×C₅	#100	1	2	yes	—
81	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₃×C₄×C₅	—	2	1	no	—
83	C₃×C₄×C₅	—	2	1	no	—
84	C₃×C₄×C₅	—	2	2	no	—
85	C₃×C₄×C₅	—	4	4	no	—
86	C₃×C₄×C₅	#137	1	4	yes	—
87	C₂×C₃×Q₈	—	2	2	no	—
88	C₂×C₃×Q₈	—	4	4	no	—
89	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	—
90	C₂²×C₃×C₄	—	2	2	no	—
91	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
92	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
93	C₃×C₄⋊C₄	—	2	4	no	—
94	C₃×C₄⋊C₄	—	2	4	no	—
95	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
96	C₃×C₄²	C₅×D₄	1	2	yes	—
97	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
98	C₂×C₃⋊C₈	—	2	4	no	—
99	C₂³×C₅	#217	1	1	yes	characteristic
100	C₅×Q₈	—	4	4	no	—
101	C₅×Q₈	—	4	4	no	—
102	C₂×C₄×C₅	—	2	2	no	—
103	C₂×C₄×C₅	—	2	4	no	—
104	C₂×C₄×C₅	—	2	4	no	—
105	C₂×C₄×C₅	—	4	4	no	—
106	C₂×C₄×C₅	#217	1	2	yes	—
107	C₂×C₄×C₅	#217	1	1	yes	characteristic
108	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
109	C₂×C₄×C₅	C₂×#67	1	2	yes	—
110	C₅×C₈	—	12	4	no	—
111	C₂²×Q₈	C₅×Dic₃	1	2	yes	—
112	C₄⋊Q₈	—	2	2	no	—
113	C₄⋊Q₈	C₅×Dic₃	1	2	yes	—
114	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	—
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
117	C₄⋊C₈	—	3	4	no	—
118	C₂²⋊C₈	—	6	2	no	—
119	#97	—	6	2	no	—
120	C₂×C₃×C₅	—	2	2	no	—
121	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
122	C₂×C₃×C₅	#419	1	2	yes	—
123	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
124	C₃×Q₈	—	4	4	no	—
125	C₃×Q₈	—	4	4	no	—
126	C₂×C₃×C₄	—	2	2	no	—
127	C₂×C₃×C₄	—	2	4	no	—
128	C₂×C₃×C₄	—	2	4	no	—
129	C₂×C₃×C₄	—	4	4	no	—
130	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
131	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
133	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
134	C₃⋊C₈	—	4	4	no	—
135	C₂²×C₅	—	2	2	no	—
136	C₂²×C₅	#833	1	2	yes	—
137	C₂²×C₅	C₂×#217	1	1	yes	characteristic
138	C₄×C₅	—	2	1	no	—
139	C₄×C₅	—	2	1	no	—
140	C₄×C₅	—	2	2	no	—
141	C₄×C₅	—	4	4	no	—
142	C₄×C₅	#942	1	4	yes	—
143	C₂×Q₈	—	2	2	no	—
144	C₂×Q₈	—	4	4	no	—
145	C₂×Q₈	C₂×C₅×Dic₃	1	4	yes	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
148	C₂²×C₄	C₅×#67	1	2	yes	—
149	C₂×C₈	—	6	4	no	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
153	C₄²	C₅×#67	1	2	yes	—
154	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
155	C₃×C₅	#1558	1	1	yes	characteristic, complemented, Hall
156	C₂²×C₃	—	2	2	no	—
157	C₂²×C₃	C₅×#100	1	2	yes	—
158	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
159	C₃×C₄	—	2	1	no	—
160	C₃×C₄	—	2	1	no	—
161	C₃×C₄	—	2	2	no	—
162	C₃×C₄	—	4	4	no	—
163	C₃×C₄	C₅×#137	1	4	yes	—
164	C₂×C₅	—	2	2	no	—
165	C₂×C₅	C₂×#833	1	1	yes	characteristic
166	C₂×C₅	#5225	1	2	yes	—
167	C₂³	C₅×#217	1	1	yes	characteristic
168	Q₈	—	4	4	no	—
169	Q₈	—	4	4	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	C₅×#217	1	2	yes	—
175	C₂×C₄	C₅×#217	1	1	yes	characteristic
176	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
177	C₂×C₄	C₂×C₅×#67	1	2	yes	—
178	C₈	—	12	4	no	—
179	C₂×C₃	—	2	2	no	—
180	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
181	C₂×C₃	C₅×#419	1	2	yes	—
182	C₅	#71777	1	1	yes	characteristic, direct product factor, Sylow
183	C₂²	—	2	2	no	—
184	C₂²	C₅×#833	1	2	yes	—
185	C₂²	C₂×C₅×#217	1	1	yes	characteristic
186	C₄	—	2	1	no	—
187	C₄	—	2	1	no	—
188	C₄	—	2	2	no	—
189	C₄	—	4	4	no	—
190	C₄	C₅×#942	1	4	yes	—
191	C₃	C₅×#1558	1	1	yes	characteristic, complemented, Sylow
192	C₂	—	2	2	no	—
193	C₂	C₂×C₅×#833	1	1	yes	characteristic
194	C₂	C₅×#5225	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₅×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₅×#4926

C₂

yes

maximal

C₅×#4546

C₂

yes

maximal, complemented

C₅×#1558

—

maximal, Hall

C₂²×C₃×C₅×Q₈

C₄

yes

—

C₃×C₅×C₄⋊Q₈

—

C₃×C₅×C₄⋊Q₈

C₄

yes

—

C₃×C₅×C₄⋊Q₈

C₂²

yes

—

C₂×C₃×C₅×C₄⋊C₄

—

C₂×C₃×C₄²×C₅

C₂²

yes

characteristic

C₅×#830

—

C₅×C₄⋊(C₃⋊C₈)

C₂²

yes

—

C₅×#803

—

#71777

C₅

yes

maximal, characteristic, direct product factor, Hall

C₂×C₅×C₄⋊Q₈

D₃

yes

characteristic

C₅×#432

—

C₅×#333

—

C₂×C₃×C₅×Q₈

—

C₂×C₃×C₅×Q₈

—

C₂×C₃×C₅×Q₈

C₂×C₄

yes

—

C₂²×C₃×C₄×C₅

—

C₂²×C₃×C₄×C₅

C₂×C₄

yes

characteristic

C₂²×C₃×C₄×C₅

D₄

yes

—

C₃×C₅×C₄⋊C₄

—

C₃×C₅×C₄⋊C₄

—

C₃×C₄²×C₅

C₂×C₄

yes

characteristic

C₃×C₄²×C₅

D₄

yes

—

C₃×C₄²×C₅

C₂³

yes

characteristic

C₂×C₅×C₃⋊C₈

—

C₂×C₃×C₄⋊Q₈

C₂×C₅

yes

characteristic

#4926

C₂×C₅

yes

—

#4546

C₂×C₅

yes

complemented

C₂²×C₅×Q₈

Dic₃

yes

—

C₅×C₄⋊Q₈

—

C₅×C₄⋊Q₈

Dic₃

yes

—

C₅×C₄⋊Q₈

C₂×D₃

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

C₂×D₃

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#97

—

#1558

—

Sylow

C₂³×C₃×C₅

C₂²⋊C₄

yes

characteristic

C₃×C₅×Q₈

—

C₃×C₅×Q₈

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₂²⋊C₄

yes

—

C₂×C₃×C₄×C₅

C₂²⋊C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

—

C₅×C₃⋊C₈

—

C₂²×C₃×Q₈

C₄×C₅

yes

—

C₃×C₄⋊Q₈

—

C₃×C₄⋊Q₈

C₄×C₅

yes

—

C₃×C₄⋊Q₈

C₂²×C₅

yes

—

C₂×C₃×C₄⋊C₄

—

C₂×C₃×C₄²

C₂²×C₅

yes

characteristic

#830

—

C₄⋊(C₃⋊C₈)

C₂²×C₅

yes

—

#803

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

C₂×Dic₃

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×Dic₃

yes

characteristic

C₂²×C₄×C₅

#67

yes

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×Dic₃

yes

characteristic

C₄²×C₅

#67

yes

—

C₄²×C₅

C₂²×D₃

yes

characteristic

C₂×C₄⋊Q₈

C₅×D₃

yes

characteristic

#432

—

#333

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

#100

yes

—

C₂²×C₃×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

#137

yes

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

C₂×C₄×C₅

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂×C₄×C₅

yes

characteristic

C₂²×C₃×C₄

C₅×D₄

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂×C₄×C₅

yes

characteristic

C₃×C₄²

C₅×D₄

yes

—

C₃×C₄²

C₂³×C₅

yes

characteristic

C₂×C₃⋊C₈

—

C₂³×C₅

#217

yes

characteristic

100

C₅×Q₈

—

101

C₅×Q₈

—

102

C₂×C₄×C₅

—

103

C₂×C₄×C₅

—

104

C₂×C₄×C₅

—

105

C₂×C₄×C₅

—

106

C₂×C₄×C₅

#217

yes

—

107

C₂×C₄×C₅

#217

yes

characteristic

108

C₂×C₄×C₅

C₂²×Dic₃

yes

characteristic

109

C₂×C₄×C₅

C₂×#67

yes

—

110

C₅×C₈

—

111

C₂²×Q₈

C₅×Dic₃

yes

—

112

C₄⋊Q₈

—

113

C₄⋊Q₈

C₅×Dic₃

yes

—

114

C₄⋊Q₈

C₂×C₅×D₃

yes

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄²

C₂×C₅×D₃

yes

characteristic

117

C₄⋊C₈

—

118

C₂²⋊C₈

—

119

#97

—

120

C₂×C₃×C₅

—

121

C₂×C₃×C₅

C₂×#100

yes

characteristic

122

C₂×C₃×C₅

#419

yes

—

123

C₂³×C₃

C₅×C₂²⋊C₄

yes

characteristic

124

C₃×Q₈

—

125

C₃×Q₈

—

126

C₂×C₃×C₄

—

127

C₂×C₃×C₄

—

128

C₂×C₃×C₄

—

129

C₂×C₃×C₄

—

130

C₂×C₃×C₄

C₅×C₂²⋊C₄

yes

—

131

C₂×C₃×C₄

C₅×C₂²⋊C₄

yes

characteristic

132

C₂×C₃×C₄

C₂²×C₄×C₅

yes

characteristic

133

C₂×C₃×C₄

C₂×C₅×D₄

yes

—

134

C₃⋊C₈

—

135

C₂²×C₅

—

136

C₂²×C₅

#833

yes

—

137

C₂²×C₅

C₂×#217

yes

characteristic

138

C₄×C₅

—

139

C₄×C₅

—

140

C₄×C₅

—

141

C₄×C₅

—

142

C₄×C₅

#942

yes

—

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂×Q₈

C₂×C₅×Dic₃

yes

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂×C₅×Dic₃

yes

characteristic

148

C₂²×C₄

C₅×#67

yes

—

149

C₂×C₈

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

C₂×C₅×Dic₃

yes

characteristic

153

C₄²

C₅×#67

yes

—

154

C₄²

C₂²×C₅×D₃

yes

characteristic

155

C₃×C₅

#1558

yes

characteristic, complemented, Hall

156

C₂²×C₃

—

157

C₂²×C₃

C₅×#100

yes

—

158

C₂²×C₃

C₂×C₅×C₂²⋊C₄

yes

characteristic

159

C₃×C₄

—

160

C₃×C₄

—

161

C₃×C₄

—

162

C₃×C₄

—

163

C₃×C₄

C₅×#137

yes

—

164

C₂×C₅

—

165

C₂×C₅

C₂×#833

yes

characteristic

166

C₂×C₅

#5225

yes

—

167

C₂³

C₅×#217

yes

characteristic

168

Q₈

—

169

Q₈

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

C₅×#217

yes

—

175

C₂×C₄

C₅×#217

yes

characteristic

176

C₂×C₄

C₂²×C₅×Dic₃

yes

characteristic

177

C₂×C₄

C₂×C₅×#67

yes

—

178

C₈

—

179

C₂×C₃

—

180

C₂×C₃

C₂×C₅×#100

yes

characteristic

181

C₂×C₃

C₅×#419

yes

—

182

C₅

#71777

yes

characteristic, direct product factor, Sylow

183

C₂²

—

184

C₂²

C₅×#833

yes

—

185

C₂²

C₂×C₅×#217

yes

characteristic

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

C₅×#942

yes

—

191

C₃

C₅×#1558

yes

characteristic, complemented, Sylow

192

C₂

—

193

C₂

C₂×C₅×#833

yes

characteristic

194

C₂

C₅×#5225

yes

—

	subgroup	G/H
center	C₂²×C₅	C₂×#217
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₃×C₅	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₂×C₅×C₄⋊Q₈	D₃
hypocenter	C₃	C₅×#1558
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×C₄⋊Q₈

subgroup

G/H

center

C₂²×C₅

C₂×#217

commutator

C₂×C₃×C₄

C₂²×C₄×C₅

Frattini

C₄²

C₂²×C₅×D₃

Fitting

C₂×C₃×C₅×C₄⋊Q₈

C₂

socle

C₂²×C₃×C₅

C₂×C₂²⋊C₄

prime radical

C₂³×C₃×C₅

C₂²⋊C₄

cosocle

C₃×C₄²

C₂³×C₅

hypercenter

C₂×C₅×C₄⋊Q₈

D₃

hypocenter

C₃

C₅×#1558

LCS

G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃

UCS

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×C₄⋊Q₈

N	H ≅ G/N	type
3. C₅×#4546	C₂	semidirect
14. #71777	C₅	direct (N × H)
32. #4546	C₂×C₅	semidirect
155. C₃×C₅	#1558	semidirect
182. C₅	#71777	direct (N × H)
191. C₃	C₅×#1558	semidirect

H ≅ G/N

type

3. C₅×#4546

C₂

semidirect

14. #71777

C₅

direct (N × H)

32. #4546

C₂×C₅

semidirect

155. C₃×C₅

#1558

semidirect

182. C₅

#71777

direct (N × H)

191. C₃

C₅×#1558

semidirect

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

subgroup	index
C₂×C₃×C₅×C₄⋊Q₈	2
C₅×#4926	2
C₅×#4546	2
C₅×#1558	3
#71777	5

subgroup

index

C₂×C₃×C₅×C₄⋊Q₈

Subgroups — C₅×#71777 #14285339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#71777 #14285339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71777 #14285339