Group #13102238 — subgroups

Subgroups — C₅×#65281 #13102238

Order 1600.

464 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 122 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×C₅²×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#685	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#685	C₂	1	2	yes	maximal
4	C₂×C₅×#683	C₂	1	2	yes	maximal, complemented
5	C₅×#3963	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₅²	C₂²	1	2	yes	—
8	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
9	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
10	C₂²×C₅×Dic₅	C₂²	1	2	yes	—
11	C₅²×C₄⋊C₄	—	2	2	no	—
12	C₅×#685	—	2	2	no	—
13	C₅×#685	—	2	4	no	—
14	C₅×#683	—	2	4	no	—
15	C₅×#399	—	5	1	no	maximal
16	#65281	C₅	1	1	yes	maximal, characteristic, direct product factor
17	C₂³×C₅²	C₂³	1	1	yes	characteristic
18	C₂²×C₅×D₅	—	2	2	no	—
19	C₂²×C₅×D₅	—	2	1	no	—
20	C₂²×C₅×D₅	—	2	2	no	—
21	C₂²×C₅×D₅	—	2	1	no	—
22	C₂²×C₅×D₅	Q₈	1	2	yes	—
23	C₂×C₄×C₅²	—	2	2	no	—
24	C₂×C₄×C₅²	—	2	2	no	—
25	C₂×C₄×C₅²	—	2	2	no	—
26	C₂×C₄×C₅²	—	2	2	no	—
27	C₂×C₄×C₅²	D₄	1	2	yes	—
28	C₂×C₅×Dic₅	—	2	2	no	—
29	C₂×C₅×Dic₅	—	2	2	no	—
30	C₂×C₅×Dic₅	—	2	2	no	—
31	C₂×C₅×Dic₅	—	2	1	no	—
32	C₂×C₅×Dic₅	D₄	1	4	yes	—
33	C₂×C₅×C₄⋊C₄	—	2	2	no	—
34	C₂×C₅×C₄⋊C₄	—	5	2	no	—
35	C₂×C₅×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
36	C₂×C₅×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
37	C₂×C₅×C₂²⋊C₄	—	5	2	no	—
38	C₂×C₅×C₂²⋊C₄	—	5	1	no	—
39	C₂×#685	C₂×C₅	1	1	yes	characteristic
40	C₂×#685	C₂×C₅	1	2	yes	—
41	C₂×#683	C₂×C₅	1	2	yes	complemented
42	C₅×#95	—	5	1	no	—
43	#3963	C₂×C₅	1	1	yes	characteristic, complemented
44	C₂²×C₅²	C₂×D₄	1	2	yes	—
45	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₅²	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₅²	#41	1	2	yes	—
48	C₂²×C₅²	#41	1	1	yes	characteristic
49	C₂×C₅×D₅	—	2	4	no	—
50	C₂×C₅×D₅	—	2	2	no	—
51	C₂×C₅×D₅	—	4	2	no	—
52	C₂×C₅×D₅	—	4	1	no	—
53	C₂×C₅×D₅	—	4	1	no	—
54	C₄×C₅²	—	2	2	no	—
55	C₄×C₅²	—	4	2	no	—
56	C₅×Dic₅	—	2	4	no	—
57	C₅×Dic₅	—	4	1	no	—
58	C₂⁴×C₅	—	5	1	no	—
59	C₂³×D₅	C₂²×C₅	1	1	yes	characteristic
60	C₂²×C₄×C₅	—	2	2	no	—
61	C₂²×C₄×C₅	—	2	4	no	—
62	C₂²×C₄×C₅	—	5	2	no	—
63	C₂²×C₄×C₅	—	5	1	no	—
64	C₂²×C₄×C₅	C₂×D₅	1	2	yes	—
65	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
66	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	—
67	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
68	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
69	C₂²×Dic₅	C₂²×C₅	1	2	yes	—
70	C₅×C₄⋊C₄	—	2	8	no	—
71	C₅×C₄⋊C₄	—	2	2	no	—
72	C₅×C₄⋊C₄	—	2	2	no	—
73	C₅×C₄⋊C₄	—	10	4	no	—
74	C₅×C₂²⋊C₄	—	10	4	no	—
75	C₅×C₂²⋊C₄	—	10	2	no	—
76	#685	—	2	2	no	—
77	#685	—	2	4	no	—
78	#683	—	2	4	no	—
79	#399	—	5	1	no	Sylow
80	C₂×C₅²	C₂²⋊Q₈	1	2	yes	—
81	C₂×C₅²	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₅²	#123	1	2	yes	—
83	C₂×C₅²	#123	1	1	yes	characteristic
84	C₂×C₅²	#127	1	1	yes	characteristic
85	C₅×D₅	—	4	2	no	—
86	C₂³×C₅	—	2	2	no	—
87	C₂³×C₅	—	5	2	no	—
88	C₂³×C₅	—	10	2	no	—
89	C₂³×C₅	—	10	2	no	—
90	C₂³×C₅	—	10	1	no	—
91	C₂³×C₅	—	10	1	no	—
92	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
93	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
94	C₂²×D₅	—	2	2	no	—
95	C₂²×D₅	—	2	1	no	—
96	C₂²×D₅	—	2	2	no	—
97	C₂²×D₅	—	2	1	no	—
98	C₂²×D₅	C₅×Q₈	1	2	yes	—
99	C₂×C₄×C₅	—	2	8	no	—
100	C₂×C₄×C₅	—	2	2	no	—
101	C₂×C₄×C₅	—	2	2	no	—
102	C₂×C₄×C₅	—	2	8	no	—
103	C₂×C₄×C₅	—	2	2	no	—
104	C₂×C₄×C₅	—	2	2	no	—
105	C₂×C₄×C₅	—	2	2	no	—
106	C₂×C₄×C₅	—	2	2	no	—
107	C₂×C₄×C₅	—	2	2	no	—
108	C₂×C₄×C₅	—	2	2	no	—
109	C₂×C₄×C₅	—	2	4	no	—
110	C₂×C₄×C₅	—	4	4	no	—
111	C₂×C₄×C₅	—	4	4	no	—
112	C₂×C₄×C₅	—	5	4	no	—
113	C₂×C₄×C₅	—	10	2	no	—
114	C₂×C₄×C₅	—	10	2	no	—
115	C₂×C₄×C₅	—	10	2	no	—
116	C₂×C₄×C₅	—	10	1	no	—
117	C₂×C₄×C₅	C₂²⋊D₅	1	2	yes	—
118	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
119	C₂×Dic₅	—	2	2	no	—
120	C₂×Dic₅	—	2	2	no	—
121	C₂×Dic₅	—	2	2	no	—
122	C₂×Dic₅	—	2	1	no	—
123	C₂×Dic₅	C₅×D₄	1	4	yes	—
124	C₂×C₄⋊C₄	—	5	2	no	—
125	C₂×C₄⋊C₄	C₅×D₅	1	1	yes	characteristic, complemented
126	C₂×C₂²⋊C₄	—	5	2	no	—
127	C₂×C₂²⋊C₄	—	5	1	no	—
128	#95	—	5	1	no	—
129	C₅²	#399	1	1	yes	characteristic, complemented, Sylow
130	C₂²×C₅	—	2	4	no	—
131	C₂²×C₅	—	2	4	no	—
132	C₂²×C₅	—	2	2	no	—
133	C₂²×C₅	—	2	2	no	—
134	C₂²×C₅	—	2	2	no	—
135	C₂²×C₅	—	10	4	no	—
136	C₂²×C₅	—	10	2	no	—
137	C₂²×C₅	—	20	2	no	—
138	C₂²×C₅	—	20	1	no	—
139	C₂²×C₅	—	20	1	no	—
140	C₂²×C₅	#709	1	2	yes	—
141	C₂²×C₅	D₄×D₅	1	2	yes	—
142	C₂²×C₅	Q₈×D₅	1	1	yes	characteristic
143	C₂²×C₅	#713	1	1	yes	characteristic
144	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
145	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
146	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
147	C₂²×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
148	C₂²×C₅	C₅×#41	1	2	yes	—
149	C₂²×C₅	C₅×#41	1	1	yes	characteristic
150	C₂×D₅	—	2	4	no	—
151	C₂×D₅	—	2	2	no	—
152	C₂×D₅	—	4	2	no	—
153	C₂×D₅	—	4	1	no	—
154	C₂×D₅	—	4	1	no	—
155	C₄×C₅	—	2	8	no	—
156	C₄×C₅	—	2	2	no	—
157	C₄×C₅	—	2	2	no	—
158	C₄×C₅	—	4	8	no	—
159	C₄×C₅	—	4	2	no	—
160	C₄×C₅	—	4	2	no	—
161	C₄×C₅	—	10	4	no	—
162	C₄×C₅	—	20	1	no	—
163	Dic₅	—	2	4	no	—
164	Dic₅	—	4	1	no	—
165	C₂⁴	—	5	1	no	—
166	C₂²×C₄	—	5	2	no	—
167	C₂²×C₄	—	5	1	no	—
168	C₂²×C₄	C₂×C₅×D₅	1	2	yes	—
169	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	10	4	no	—
172	C₂²⋊C₄	—	10	4	no	—
173	C₂²⋊C₄	—	10	2	no	—
174	C₂×C₅	—	2	4	no	—
175	C₂×C₅	—	2	4	no	—
176	C₂×C₅	—	2	2	no	—
177	C₂×C₅	—	2	2	no	—
178	C₂×C₅	—	2	2	no	—
179	C₂×C₅	—	20	2	no	—
180	C₂×C₅	#4040	1	2	yes	—
181	C₂×C₅	#4042	1	2	yes	—
182	C₂×C₅	#4075	1	1	yes	characteristic
183	C₂×C₅	#4086	1	1	yes	characteristic
184	C₂×C₅	#4092	1	1	yes	characteristic
185	C₂×C₅	C₅×C₂²⋊Q₈	1	2	yes	—
186	C₂×C₅	C₅×C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₅	C₅×#123	1	2	yes	—
188	C₂×C₅	C₅×#123	1	1	yes	characteristic
189	C₂×C₅	C₅×#127	1	1	yes	characteristic
190	D₅	—	4	2	no	—
191	C₂³	—	5	2	no	—
192	C₂³	—	10	2	no	—
193	C₂³	—	10	2	no	—
194	C₂³	—	10	1	no	—
195	C₂³	—	10	1	no	—
196	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	5	4	no	—
202	C₂×C₄	—	10	2	no	—
203	C₂×C₄	—	10	2	no	—
204	C₂×C₄	—	10	2	no	—
205	C₂×C₄	—	10	1	no	—
206	C₂×C₄	C₅×C₂²⋊D₅	1	2	yes	—
207	C₅	—	2	2	no	—
208	C₅	#65281	1	1	yes	characteristic, direct product factor
209	C₅	C₅×#399	1	1	yes	characteristic, complemented
210	C₂²	—	10	4	no	—
211	C₂²	—	10	2	no	—
212	C₂²	—	20	2	no	—
213	C₂²	—	20	1	no	—
214	C₂²	—	20	1	no	—
215	C₂²	C₅×#709	1	2	yes	—
216	C₂²	C₅×D₄×D₅	1	2	yes	—
217	C₂²	C₅×Q₈×D₅	1	1	yes	characteristic
218	C₂²	C₅×#713	1	1	yes	characteristic
219	C₂²	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	—	10	4	no	—
223	C₄	—	20	1	no	—
224	C₂	—	20	2	no	—
225	C₂	C₅×#4040	1	2	yes	—
226	C₂	C₅×#4042	1	2	yes	—
227	C₂	C₅×#4075	1	1	yes	characteristic
228	C₂	C₅×#4086	1	1	yes	characteristic
229	C₂	C₅×#4092	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅²×C₄⋊C₄

C₂

yes

maximal, characteristic, complemented

C₂×C₅×#685

C₂

yes

maximal, characteristic

C₂×C₅×#685

C₂

yes

maximal

C₂×C₅×#683

C₂

yes

maximal, complemented

C₅×#3963

C₂

yes

maximal, characteristic, complemented

C₂³×C₅×D₅

C₂²

yes

characteristic

C₂²×C₄×C₅²

C₂²

yes

—

C₂²×C₄×C₅²

C₂²

yes

characteristic

C₂²×C₅×Dic₅

C₂²

yes

characteristic

C₂²×C₅×Dic₅

C₂²

yes

—

C₅²×C₄⋊C₄

—

—

—

—

—

C₅

yes

maximal, characteristic, direct product factor

C₂³×C₅²

C₂³

yes

characteristic

C₂²×C₅×D₅

—

C₂²×C₅×D₅

—

C₂²×C₅×D₅

—

C₂²×C₅×D₅

—

C₂²×C₅×D₅

Q₈

yes

—

C₂×C₄×C₅²

—

C₂×C₄×C₅²

—

C₂×C₄×C₅²

—

C₂×C₄×C₅²

—

C₂×C₄×C₅²

D₄

yes

—

C₂×C₅×Dic₅

—

C₂×C₅×Dic₅

—

C₂×C₅×Dic₅

—

C₂×C₅×Dic₅

—

C₂×C₅×Dic₅

D₄

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

D₅

yes

characteristic, complemented

C₂×C₅×C₄⋊C₄

C₂×C₅

yes

characteristic, complemented

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

—

C₂×#685

C₂×C₅

yes

characteristic

C₂×#685

C₂×C₅

yes

—

C₂×#683

C₂×C₅

yes

complemented

C₅×#95

—

#3963

C₂×C₅

yes

characteristic, complemented

C₂²×C₅²

C₂×D₄

yes

—

C₂²×C₅²

C₂×D₄

yes

characteristic

C₂²×C₅²

C₂×Q₈

yes

characteristic

C₂²×C₅²

#41

yes

—

C₂²×C₅²

#41

yes

characteristic

C₂×C₅×D₅

—

C₂×C₅×D₅

—

C₂×C₅×D₅

—

C₂×C₅×D₅

—

C₂×C₅×D₅

—

C₄×C₅²

—

C₄×C₅²

—

C₅×Dic₅

—

C₅×Dic₅

—

C₂⁴×C₅

—

C₂³×D₅

C₂²×C₅

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₅

yes

—

C₂²×C₄×C₅

C₂×D₅

yes

characteristic

C₂²×C₄×C₅

C₂²×C₅

yes

—

C₂²×C₄×C₅

C₂²×C₅

yes

characteristic

C₂²×Dic₅

C₂²×C₅

yes

characteristic

C₂²×Dic₅

C₂²×C₅

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

—

—

—

—

C₂×C₅²

C₂²⋊Q₈

yes

—

C₂×C₅²

C₂²⋊Q₈

yes

characteristic

C₂×C₅²

#123

yes

—

C₂×C₅²

yes

C₂×C₅²

yes

C₅×D₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

C₂²×D₅

yes

characteristic

C₂³×C₅

yes

characteristic

C₂²×D₅

—

C₂²×D₅

—

C₂²×D₅

—

C₂²×D₅

—

C₂²×D₅

C₅×Q₈

yes

—

C₂×C₄×C₅

—

100

C₂×C₄×C₅

—

101

C₂×C₄×C₅

—

102

C₂×C₄×C₅

—

103

C₂×C₄×C₅

—

104

C₂×C₄×C₅

—

105

C₂×C₄×C₅

—

106

C₂×C₄×C₅

—

107

C₂×C₄×C₅

—

108

C₂×C₄×C₅

—

109

C₂×C₄×C₅

—

110

C₂×C₄×C₅

—

111

C₂×C₄×C₅

—

112

C₂×C₄×C₅

—

113

C₂×C₄×C₅

—

114

C₂×C₄×C₅

—

115

C₂×C₄×C₅

—

116

C₂×C₄×C₅

—

117

C₂×C₄×C₅

C₂²⋊D₅

yes

—

118

C₂×C₄×C₅

C₅×D₄

yes

—

119

C₂×Dic₅

—

120

C₂×Dic₅

—

121

C₂×Dic₅

—

122

C₂×Dic₅

—

123

C₂×Dic₅

C₅×D₄

yes

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

C₅×D₅

yes

characteristic, complemented

126

C₂×C₂²⋊C₄

—

127

C₂×C₂²⋊C₄

—

128

#95

—

129

C₅²

#399

yes

characteristic, complemented, Sylow

130

C₂²×C₅

—

131

C₂²×C₅

—

132

C₂²×C₅

—

133

C₂²×C₅

—

134

C₂²×C₅

—

135

C₂²×C₅

—

136

C₂²×C₅

—

137

C₂²×C₅

—

138

C₂²×C₅

—

139

C₂²×C₅

—

140

C₂²×C₅

#709

yes

—

141

C₂²×C₅

D₄×D₅

yes

—

142

C₂²×C₅

Q₈×D₅

yes

characteristic

143

C₂²×C₅

#713

yes

characteristic

144

C₂²×C₅

C₂×C₂²⋊D₅

yes

characteristic

145

C₂²×C₅

C₂×C₅×D₄

yes

—

146

C₂²×C₅

C₂×C₅×D₄

yes

characteristic

147

C₂²×C₅

C₂×C₅×Q₈

yes

characteristic

148

C₂²×C₅

C₅×#41

yes

—

149

C₂²×C₅

C₅×#41

yes

characteristic

150

C₂×D₅

—

151

C₂×D₅

—

152

C₂×D₅

—

153

C₂×D₅

—

154

C₂×D₅

—

155

C₄×C₅

—

156

C₄×C₅

—

157

C₄×C₅

—

158

C₄×C₅

—

159

C₄×C₅

—

160

C₄×C₅

—

161

C₄×C₅

—

162

C₄×C₅

—

163

Dic₅

—

164

Dic₅

—

165

C₂⁴

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

C₂×C₅×D₅

yes

—

169

C₂²×C₄

C₂×C₅×D₅

yes

characteristic

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂×C₅

—

175

C₂×C₅

—

176

C₂×C₅

—

177

C₂×C₅

—

178

C₂×C₅

—

179

C₂×C₅

—

180

C₂×C₅

#4040

yes

—

181

C₂×C₅

#4042

yes

—

182

C₂×C₅

#4075

yes

characteristic

183

C₂×C₅

#4086

yes

characteristic

184

C₂×C₅

#4092

yes

characteristic

185

C₂×C₅

C₅×C₂²⋊Q₈

yes

—

186

C₂×C₅

C₅×C₂²⋊Q₈

yes

characteristic

187

C₂×C₅

C₅×#123

yes

—

188

C₂×C₅

C₅×#123

yes

characteristic

189

C₂×C₅

C₅×#127

yes

characteristic

190

D₅

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

C₂²×C₅×D₅

yes

characteristic

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₅×C₂²⋊D₅

yes

—

207

C₅

—

208

C₅

#65281

yes

characteristic, direct product factor

209

C₅

C₅×#399

yes

characteristic, complemented

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₅×#709

yes

—

216

C₂²

C₅×D₄×D₅

yes

—

217

C₂²

C₅×Q₈×D₅

yes

characteristic

218

C₂²

C₅×#713

yes

characteristic

219

C₂²

C₂×C₅×C₂²⋊D₅

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₂

—

225

C₂

C₅×#4040

yes

—

226

C₂

C₅×#4042

yes

—

227

C₂

C₅×#4075

yes

characteristic

228

C₂

C₅×#4086

yes

characteristic

229

C₂

C₅×#4092

yes

characteristic

	subgroup	G/H
center	C₂³×C₅	C₂²×D₅
commutator, cosocle	C₂³×C₅	C₂³×C₅
Frattini	C₂³	C₂²×C₅×D₅
Fitting	C₂×C₅²×C₄⋊C₄	C₂
socle	C₂³×C₅²	C₂³
prime radical	C₂³×C₅×D₅	C₂²
hypercenter	C₂×C₅×C₄⋊C₄	D₅
hypocenter	C₅	C₅×#399
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₄⋊C₄

subgroup

G/H

center

C₂³×C₅

C₂²×D₅

commutator, cosocle

C₂³×C₅

Frattini

C₂³

C₂²×C₅×D₅

Fitting

C₂×C₅²×C₄⋊C₄

C₂

socle

C₂³×C₅²

C₂³

prime radical

C₂³×C₅×D₅

C₂²

hypercenter

C₂×C₅×C₄⋊C₄

D₅

C₅

G ▷ C₂³×C₅ ▷ C₅

C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₄⋊C₄

N	H ≅ G/N	type
1. C₂×C₅²×C₄⋊C₄	C₂	semidirect
4. C₂×C₅×#683	C₂	semidirect
5. C₅×#3963	C₂	semidirect
16. #65281	C₅	direct (N × H)
35. C₂×C₅×C₄⋊C₄	D₅	semidirect
36. C₂×C₅×C₄⋊C₄	C₂×C₅	semidirect
41. C₂×#683	C₂×C₅	semidirect
43. #3963	C₂×C₅	semidirect
125. C₂×C₄⋊C₄	C₅×D₅	semidirect
129. C₅²	#399	semidirect
208. C₅	#65281	direct (N × H)
209. C₅	C₅×#399	semidirect

H ≅ G/N

type

1. C₂×C₅²×C₄⋊C₄

C₂

semidirect

4. C₂×C₅×#683

C₂

semidirect

5. C₅×#3963

C₂

semidirect

16. #65281

C₅

direct (N × H)

35. C₂×C₅×C₄⋊C₄

D₅

semidirect

36. C₂×C₅×C₄⋊C₄

C₂×C₅

semidirect

41. C₂×#683

C₂×C₅

semidirect

43. #3963

C₂×C₅

semidirect

125. C₂×C₄⋊C₄

C₅×D₅

semidirect

129. C₅²

#399

semidirect

208. C₅

#65281

direct (N × H)

209. C₅

C₅×#399

semidirect

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

subgroup	index
C₂×C₅²×C₄⋊C₄	2
C₂×C₅×#685	2
C₂×C₅×#683	2
C₅×#3963	2
C₅×#399	5
#65281	5

subgroup

index

C₂×C₅²×C₄⋊C₄

C₂×C₅×#685

C₂×C₅×#683

C₅×#3963

C₅×#399

#65281

Subgroups — C₅×#65281 #13102238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#65281 #13102238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#65281 #13102238