Group #11933342 — subgroups

Subgroups — C₅×#10622 #11933342

Order 1280.

402 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 134 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×#1954	C₂	1	1	yes	maximal, characteristic
2	C₅×#1834	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1802	C₂	1	2	yes	maximal
4	C₅×#1296	C₂	1	2	yes	maximal, complemented
5	C₅×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
7	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×#102	—	2	2	no	—
10	C₂×C₅×C₂²⋊C₈	—	2	2	no	—
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×#384	C₂²	1	2	yes	—
13	C₅×#340	—	2	2	no	—
14	C₅×#340	—	2	2	no	—
15	#10622	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
17	C₂³×C₄×C₅	—	2	1	no	—
18	C₂²×C₅×C₈	—	2	1	no	—
19	C₂²×C₅×C₈	—	2	2	no	—
20	C₂²×C₅×C₈	D₄	1	2	yes	—
21	C₄×C₅×D₄	—	2	2	no	—
22	C₄×C₅×D₄	—	2	2	no	—
23	C₂×C₅×C₄⋊C₄	—	2	2	no	—
24	C₂×C₅×C₄⋊C₄	—	2	2	no	—
25	C₂×C₅×C₄⋊C₄	—	2	2	no	—
26	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
27	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
28	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
29	C₅×C₄⋊C₈	—	2	2	no	—
30	C₅×C₄⋊C₈	—	2	2	no	—
31	C₅×C₄⋊C₈	—	2	2	no	—
32	C₅×#102	—	4	4	no	—
33	C₅×C₂²⋊C₈	—	4	4	no	—
34	C₄×C₅×C₈	—	2	2	no	—
35	#1954	C₂×C₅	1	1	yes	characteristic
36	#1834	C₂×C₅	1	1	yes	characteristic, complemented
37	#1802	C₂×C₅	1	2	yes	—
38	#1296	C₂×C₅	1	2	yes	complemented
39	#1277	C₂×C₅	1	1	yes	characteristic, complemented
40	C₂⁴×C₅	—	2	1	no	—
41	C₂×C₅×D₄	—	2	2	no	—
42	C₂×C₅×D₄	—	2	1	no	—
43	C₂×C₅×D₄	—	2	2	no	—
44	C₂×C₅×D₄	Q₁₆	1	2	yes	—
45	C₂²×C₄×C₅	—	2	1	no	—
46	C₂²×C₄×C₅	—	4	1	no	—
47	C₂²×C₄×C₅	—	4	1	no	—
48	C₂²×C₄×C₅	—	4	2	no	—
49	C₂²×C₄×C₅	—	4	2	no	—
50	C₂²×C₄×C₅	—	4	2	no	—
51	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₅	#41	1	1	yes	characteristic
54	C₂×C₅×C₈	—	2	2	no	—
55	C₂×C₅×C₈	—	2	2	no	—
56	C₂×C₅×C₈	—	2	2	no	—
57	C₂×C₅×C₈	—	4	2	no	—
58	C₂×C₅×C₈	—	4	1	no	—
59	C₂×C₅×C₈	—	4	2	no	—
60	C₂×C₅×C₈	—	4	2	no	—
61	C₂×C₅×C₈	—	4	2	no	—
62	C₅×C₄⋊C₄	—	2	2	no	—
63	C₅×C₄⋊C₄	—	4	2	no	—
64	C₅×C₄⋊C₄	—	4	2	no	—
65	C₅×C₄⋊C₄	—	4	2	no	—
66	C₅×C₄⋊C₄	—	4	2	no	—
67	C₅×C₄⋊C₄	—	8	2	no	—
68	C₅×C₂²⋊C₄	—	4	2	no	—
69	C₄²×C₅	#41	1	2	yes	—
70	C₄²×C₅	#41	1	2	yes	—
71	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
72	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
73	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
74	C₂×#102	—	2	2	no	—
75	C₂×C₂²⋊C₈	—	2	2	no	—
76	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
77	#384	C₂²×C₅	1	2	yes	—
78	#340	—	2	2	no	—
79	#340	—	2	2	no	—
80	C₂³×C₅	—	2	2	no	—
81	C₂³×C₅	—	4	1	no	—
82	C₂³×C₅	—	4	2	no	—
83	C₂³×C₅	—	4	1	no	—
84	C₂³×C₅	—	4	2	no	—
85	C₂³×C₅	#121	1	1	yes	characteristic
86	C₅×D₄	—	2	4	no	—
87	C₅×D₄	—	4	2	no	—
88	C₂×C₄×C₅	—	2	2	no	—
89	C₂×C₄×C₅	—	4	1	no	—
90	C₂×C₄×C₅	—	4	2	no	—
91	C₂×C₄×C₅	—	8	2	no	—
92	C₂×C₄×C₅	—	8	1	no	—
93	C₂×C₄×C₅	—	8	1	no	—
94	C₂×C₄×C₅	—	8	2	no	—
95	C₂×C₄×C₅	—	8	2	no	—
96	C₂×C₄×C₅	—	8	2	no	—
97	C₂×C₄×C₅	#123	1	1	yes	characteristic
98	C₂×C₄×C₅	#123	1	2	yes	—
99	C₂×C₄×C₅	#124	1	1	yes	characteristic
100	C₂×C₄×C₅	#126	1	2	yes	—
101	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
102	C₂×C₄×C₅	#135	1	1	yes	characteristic
103	C₂×C₄×C₅	#135	1	2	yes	—
104	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
105	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
106	C₅×C₈	—	4	2	no	—
107	C₅×C₈	—	8	2	no	—
108	C₅×C₈	—	8	1	no	—
109	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
110	C₂³×C₄	—	2	1	no	—
111	C₂²×C₈	—	2	2	no	—
112	C₂²×C₈	—	2	1	no	—
113	C₂²×C₈	C₅×D₄	1	2	yes	—
114	C₄×D₄	—	2	2	no	—
115	C₄×D₄	—	2	2	no	—
116	C₂×C₄⋊C₄	—	2	2	no	—
117	C₂×C₄⋊C₄	—	2	2	no	—
118	C₂×C₄⋊C₄	—	2	2	no	—
119	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
122	C₄⋊C₈	—	2	2	no	—
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	—	2	2	no	—
125	#102	—	4	4	no	—
126	C₂²⋊C₈	—	4	4	no	—
127	C₄×C₈	—	2	2	no	—
128	C₂²×C₅	—	4	2	no	—
129	C₂²×C₅	—	4	4	no	—
130	C₂²×C₅	—	8	1	no	—
131	C₂²×C₅	—	8	1	no	—
132	C₂²×C₅	—	8	2	no	—
133	C₂²×C₅	#397	1	1	yes	characteristic
134	C₂²×C₅	#463	1	2	yes	—
135	C₂²×C₅	#467	1	1	yes	characteristic
136	C₂²×C₅	#469	1	1	yes	characteristic
137	C₂²×C₅	#471	1	2	yes	—
138	C₄×C₅	—	2	2	no	—
139	C₄×C₅	—	8	1	no	—
140	C₄×C₅	—	16	2	no	—
141	C₄×C₅	#482	1	2	yes	—
142	C₄×C₅	#482	1	2	yes	—
143	C₄×C₅	#484	1	2	yes	—
144	C₄×C₅	#488	1	1	yes	characteristic
145	C₄×C₅	#490	1	1	yes	characteristic
146	C₂⁴	—	2	1	no	—
147	C₂×D₄	—	2	2	no	—
148	C₂×D₄	—	2	1	no	—
149	C₂×D₄	—	2	2	no	—
150	C₂×D₄	C₅×Q₁₆	1	2	yes	—
151	C₂²×C₄	—	2	1	no	—
152	C₂²×C₄	—	4	1	no	—
153	C₂²×C₄	—	4	1	no	—
154	C₂²×C₄	—	4	2	no	—
155	C₂²×C₄	—	4	2	no	—
156	C₂²×C₄	—	4	2	no	—
157	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
158	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
159	C₂²×C₄	C₅×#41	1	1	yes	characteristic
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	2	2	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	—	4	2	no	—
164	C₂×C₈	—	4	1	no	—
165	C₂×C₈	—	4	2	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	4	2	no	—
168	C₄⋊C₄	—	2	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	8	2	no	—
174	C₂²⋊C₄	—	4	2	no	—
175	C₄²	C₅×#41	1	2	yes	—
176	C₄²	C₅×#41	1	2	yes	—
177	C₂×C₅	—	8	2	no	—
178	C₂×C₅	#1683	1	2	yes	—
179	C₂×C₅	#1701	1	2	yes	—
180	C₂×C₅	#2073	1	1	yes	characteristic
181	C₂×C₅	#2076	1	1	yes	characteristic
182	C₂×C₅	#2079	1	1	yes	characteristic
183	C₂³	—	2	2	no	—
184	C₂³	—	4	1	no	—
185	C₂³	—	4	2	no	—
186	C₂³	—	4	1	no	—
187	C₂³	—	4	2	no	—
188	C₂³	C₅×#121	1	1	yes	characteristic
189	D₄	—	2	4	no	—
190	D₄	—	4	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	8	2	no	—
195	C₂×C₄	—	8	1	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	8	2	no	—
199	C₂×C₄	—	8	2	no	—
200	C₂×C₄	C₅×#123	1	1	yes	characteristic
201	C₂×C₄	C₅×#123	1	2	yes	—
202	C₂×C₄	C₅×#124	1	1	yes	characteristic
203	C₂×C₄	C₅×#126	1	2	yes	—
204	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
205	C₂×C₄	C₅×#135	1	1	yes	characteristic
206	C₂×C₄	C₅×#135	1	2	yes	—
207	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
208	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
209	C₈	—	4	2	no	—
210	C₈	—	8	2	no	—
211	C₈	—	8	1	no	—
212	C₅	#10622	1	1	yes	characteristic, direct product factor, Sylow
213	C₂²	—	4	2	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	8	1	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	2	no	—
218	C₂²	C₅×#397	1	1	yes	characteristic
219	C₂²	C₅×#463	1	2	yes	—
220	C₂²	C₅×#467	1	1	yes	characteristic
221	C₂²	C₅×#469	1	1	yes	characteristic
222	C₂²	C₅×#471	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	16	2	no	—
226	C₄	C₅×#482	1	2	yes	—
227	C₄	C₅×#482	1	2	yes	—
228	C₄	C₅×#484	1	2	yes	—
229	C₄	C₅×#488	1	1	yes	characteristic
230	C₄	C₅×#490	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	C₅×#1683	1	2	yes	—
233	C₂	C₅×#1701	1	2	yes	—
234	C₂	C₅×#2073	1	1	yes	characteristic
235	C₂	C₅×#2076	1	1	yes	characteristic
236	C₂	C₅×#2079	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1954

C₂

yes

maximal, characteristic

C₅×#1834

C₂

yes

maximal, characteristic, complemented

C₅×#1802

C₂

yes

maximal

C₅×#1296

C₂

yes

maximal, complemented

C₅×#1277

C₂

yes

maximal, characteristic, complemented

C₂×C₄×C₅×D₄

C₂²

yes

characteristic

C₂×C₅×C₄⋊C₈

C₂²

yes

—

C₂×C₅×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₅×#102

—

C₂×C₅×C₂²⋊C₈

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×#384

C₂²

yes

—

C₅×#340

—

C₅×#340

—

#10622

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×D₄

D₄

yes

characteristic

C₂³×C₄×C₅

—

C₂²×C₅×C₈

—

C₂²×C₅×C₈

—

C₂²×C₅×C₈

D₄

yes

—

C₄×C₅×D₄

—

C₄×C₅×D₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

D₄

yes

characteristic

C₂×C₅×C₂²⋊C₄

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×#102

—

C₅×C₂²⋊C₈

—

C₄×C₅×C₈

—

#1954

C₂×C₅

yes

characteristic

#1834

C₂×C₅

yes

characteristic, complemented

#1802

C₂×C₅

yes

—

#1296

C₂×C₅

yes

complemented

#1277

C₂×C₅

yes

characteristic, complemented

C₂⁴×C₅

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

Q₁₆

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

#41

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

#41

yes

—

C₄²×C₅

#41

yes

—

C₂×C₄×D₄

C₂²×C₅

yes

characteristic

C₂×C₄⋊C₈

C₂²×C₅

yes

—

C₂×C₄⋊C₈

C₂²×C₅

yes

characteristic

C₂×#102

—

C₂×C₂²⋊C₈

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

#384

C₂²×C₅

yes

—

#340

—

#340

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#121

yes

characteristic

C₅×D₄

—

C₅×D₄

—

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

characteristic

C₂×C₄×C₅

#123

yes

—

C₂×C₄×C₅

#124

yes

characteristic

100

C₂×C₄×C₅

#126

yes

—

101

C₂×C₄×C₅

C₂×Q₁₆

yes

characteristic

102

C₂×C₄×C₅

#135

yes

characteristic

103

C₂×C₄×C₅

#135

yes

—

104

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

105

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

106

C₅×C₈

—

107

C₅×C₈

—

108

C₅×C₈

—

109

C₂²×D₄

C₅×D₄

yes

characteristic

110

C₂³×C₄

—

111

C₂²×C₈

—

112

C₂²×C₈

—

113

C₂²×C₈

C₅×D₄

yes

—

114

C₄×D₄

—

115

C₄×D₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

C₅×D₄

yes

characteristic

120

C₂×C₂²⋊C₄

—

121

C₂×C₄²

C₂³×C₅

yes

characteristic

122

C₄⋊C₈

—

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

#102

—

126

C₂²⋊C₈

—

127

C₄×C₈

—

128

C₂²×C₅

—

129

C₂²×C₅

—

130

C₂²×C₅

—

131

C₂²×C₅

—

132

C₂²×C₅

—

133

C₂²×C₅

#397

yes

characteristic

134

C₂²×C₅

#463

yes

—

135

C₂²×C₅

#467

yes

characteristic

136

C₂²×C₅

#469

yes

characteristic

137

C₂²×C₅

#471

yes

—

138

C₄×C₅

—

139

C₄×C₅

—

140

C₄×C₅

—

141

C₄×C₅

#482

yes

—

142

C₄×C₅

#482

yes

—

143

C₄×C₅

#484

yes

—

144

C₄×C₅

#488

yes

characteristic

145

C₄×C₅

#490

yes

characteristic

146

C₂⁴

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

C₅×Q₁₆

yes

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

158

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

159

C₂²×C₄

C₅×#41

yes

characteristic

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

C₅×#41

yes

—

176

C₄²

C₅×#41

yes

—

177

C₂×C₅

—

178

C₂×C₅

#1683

yes

—

179

C₂×C₅

#1701

yes

—

180

C₂×C₅

#2073

yes

characteristic

181

C₂×C₅

#2076

yes

characteristic

182

C₂×C₅

#2079

yes

characteristic

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

C₅×#121

yes

characteristic

189

D₄

—

190

D₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

C₅×#123

yes

characteristic

201

C₂×C₄

C₅×#123

yes

—

202

C₂×C₄

C₅×#124

yes

characteristic

203

C₂×C₄

C₅×#126

yes

—

204

C₂×C₄

C₂×C₅×Q₁₆

yes

characteristic

205

C₂×C₄

C₅×#135

yes

characteristic

206

C₂×C₄

C₅×#135

yes

—

207

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

208

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

209

C₈

—

210

C₈

—

211

C₈

—

212

C₅

#10622

yes

characteristic, direct product factor, Sylow

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

C₅×#397

yes

characteristic

219

C₂²

C₅×#463

yes

—

220

C₂²

C₅×#467

yes

characteristic

221

C₂²

C₅×#469

yes

characteristic

222

C₂²

C₅×#471

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

C₅×#482

yes

—

227

C₄

C₅×#482

yes

—

228

C₄

C₅×#484

yes

—

229

C₄

C₅×#488

yes

characteristic

230

C₄

C₅×#490

yes

characteristic

231

C₂

—

232

C₂

C₅×#1683

yes

—

233

C₂

C₅×#1701

yes

—

234

C₂

C₅×#2073

yes

characteristic

235

C₂

C₅×#2076

yes

characteristic

236

C₂

C₅×#2079

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₅	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂²×C₅×D₄	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂³×C₅

#121

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂²×C₅×D₄

D₄

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
2. C₅×#1834	C₂	semidirect
4. C₅×#1296	C₂	semidirect
5. C₅×#1277	C₂	semidirect
15. #10622	C₅	direct (N × H)
36. #1834	C₂×C₅	semidirect
38. #1296	C₂×C₅	semidirect
39. #1277	C₂×C₅	semidirect
212. C₅	#10622	direct (N × H)

H ≅ G/N

type

2. C₅×#1834

C₂

semidirect

4. C₅×#1296

C₂

semidirect

5. C₅×#1277

C₂

semidirect

15. #10622

C₅

direct (N × H)

36. #1834

C₂×C₅

semidirect

38. #1296

C₂×C₅

semidirect

39. #1277

C₂×C₅

semidirect

212. C₅

#10622

direct (N × H)

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

subgroup	index
C₅×#1954	2
C₅×#1834	2
C₅×#1802	2
C₅×#1296	2
C₅×#1277	2
#10622	5

subgroup

index

Subgroups — C₅×#10622 #11933342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10622 #11933342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10622 #11933342