Group #11932112 — subgroups

Subgroups — C₅×#9392 #11932112

Order 1280.

486 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2982	C₂	1	1	yes	maximal, characteristic
2	C₅×#2567	C₂	1	1	yes	maximal, characteristic
3	C₅×#1801	C₂	1	1	yes	maximal, characteristic
4	C₅×#1548	C₂	1	2	yes	maximal
5	C₅×#1303	C₂	1	2	yes	maximal
6	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₅×C₈×Q₈	—	2	4	no	—
9	C₅×#431	—	2	2	no	—
10	C₅×#431	C₂²	1	2	yes	—
11	C₅×#423	C₂²	1	2	yes	—
12	C₂×C₅×#101	—	2	1	no	—
13	C₅×#395	C₄	1	4	yes	—
14	C₅×#391	—	2	1	no	—
15	C₅×#389	—	2	2	no	—
16	C₅×#384	—	2	1	no	—
17	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₅×#343	—	2	1	no	—
19	C₅×#333	—	2	4	no	—
20	#9392	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
22	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
23	C₂×C₅×M₁₆	—	2	2	no	—
24	C₅×C₄⋊Q₈	—	2	2	no	—
25	C₅×C₄⋊Q₈	—	2	2	no	—
26	C₄×C₅×Q₈	—	2	2	no	—
27	C₄×C₅×Q₈	—	2	2	no	—
28	C₂×C₅×C₄⋊C₄	—	2	1	no	—
29	C₂×C₅×C₄⋊C₄	—	2	1	no	—
30	C₂×C₅×C₄⋊C₄	—	2	1	no	—
31	C₂×C₅×C₄⋊C₄	—	2	4	no	—
32	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
33	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₅	—	2	1	no	—
35	C₂×C₄²×C₅	D₄	1	2	yes	—
36	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
37	C₅×C₄⋊C₈	—	2	4	no	—
38	C₅×C₄⋊C₈	—	2	2	no	—
39	C₅×C₄⋊C₈	—	2	2	no	—
40	C₅×C₄⋊C₈	D₄	1	4	yes	—
41	C₅×#101	—	4	2	no	—
42	C₅×C₂²⋊C₈	—	2	2	no	—
43	C₄×C₅×C₈	—	2	4	no	—
44	C₄×C₅×C₈	—	2	2	no	—
45	C₅×#95	—	2	4	no	—
46	C₅×#95	C₂×C₄	1	2	yes	—
47	#2982	C₂×C₅	1	1	yes	characteristic
48	#2567	C₂×C₅	1	1	yes	characteristic
49	#1801	C₂×C₅	1	1	yes	characteristic
50	#1548	C₂×C₅	1	2	yes	—
51	#1303	C₂×C₅	1	2	yes	—
52	C₂×C₅×Q₈	—	2	2	no	—
53	C₂×C₅×Q₈	—	2	2	no	—
54	C₂×C₅×Q₈	—	2	4	no	—
55	C₂×C₅×Q₈	—	8	2	no	—
56	C₂×C₅×Q₈	SD₁₆	1	2	yes	—
57	C₂×C₅×Q₈	Q₁₆	1	2	yes	—
58	C₂²×C₄×C₅	—	2	2	no	—
59	C₂²×C₄×C₅	—	2	2	no	—
60	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
65	C₅×M₁₆	—	4	2	no	—
66	C₅×M₁₆	—	4	2	no	—
67	C₂×C₅×C₈	—	2	4	no	—
68	C₂×C₅×C₈	—	4	2	no	—
69	C₅×C₄⋊C₄	—	2	4	no	—
70	C₅×C₄⋊C₄	—	2	4	no	—
71	C₅×C₄⋊C₄	—	2	2	no	—
72	C₅×C₄⋊C₄	—	4	1	no	—
73	C₅×C₄⋊C₄	—	4	2	no	—
74	C₅×C₄⋊C₄	—	4	1	no	—
75	C₅×C₄⋊C₄	—	8	4	no	—
76	C₄²×C₅	—	2	2	no	—
77	C₄²×C₅	—	2	2	no	—
78	C₄²×C₅	—	4	2	no	—
79	C₄²×C₅	C₂×D₄	1	2	yes	—
80	C₄²×C₅	#41	1	2	yes	—
81	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
82	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
83	C₈×Q₈	—	2	4	no	—
84	#431	—	2	2	no	—
85	#431	C₂²×C₅	1	2	yes	—
86	#423	C₂²×C₅	1	2	yes	—
87	C₂×#101	—	2	1	no	—
88	#395	C₄×C₅	1	4	yes	—
89	#391	—	2	1	no	—
90	#389	—	2	2	no	—
91	#384	—	2	1	no	—
92	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
93	#343	—	2	1	no	—
94	#333	—	2	4	no	—
95	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₅×Q₈	—	2	4	no	—
97	C₅×Q₈	—	2	4	no	—
98	C₅×Q₈	—	8	4	no	—
99	C₂×C₄×C₅	—	2	2	no	—
100	C₂×C₄×C₅	—	2	2	no	—
101	C₂×C₄×C₅	—	2	2	no	—
102	C₂×C₄×C₅	—	2	4	no	—
103	C₂×C₄×C₅	—	2	2	no	—
104	C₂×C₄×C₅	—	4	1	no	—
105	C₂×C₄×C₅	—	4	2	no	—
106	C₂×C₄×C₅	—	4	2	no	—
107	C₂×C₄×C₅	—	4	2	no	—
108	C₂×C₄×C₅	—	4	4	no	—
109	C₂×C₄×C₅	—	4	2	no	—
110	C₂×C₄×C₅	#103	1	4	yes	—
111	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
112	C₂×C₄×C₅	#120	1	1	yes	characteristic
113	C₂×C₄×C₅	#121	1	2	yes	—
114	C₂×C₄×C₅	#123	1	1	yes	characteristic
115	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
116	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
117	C₂×C₄×C₅	#135	1	2	yes	—
118	C₅×C₈	—	4	4	no	—
119	C₅×C₈	—	8	2	no	—
120	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
121	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
122	C₂×M₁₆	—	2	2	no	—
123	C₄⋊Q₈	—	2	2	no	—
124	C₄⋊Q₈	—	2	2	no	—
125	C₄×Q₈	—	2	2	no	—
126	C₄×Q₈	—	2	2	no	—
127	C₂×C₄⋊C₄	—	2	1	no	—
128	C₂×C₄⋊C₄	—	2	1	no	—
129	C₂×C₄⋊C₄	—	2	1	no	—
130	C₂×C₄⋊C₄	—	2	4	no	—
131	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
132	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
133	C₂×C₄²	—	2	1	no	—
134	C₂×C₄²	C₅×D₄	1	2	yes	—
135	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
136	C₄⋊C₈	—	2	4	no	—
137	C₄⋊C₈	—	2	2	no	—
138	C₄⋊C₈	—	2	2	no	—
139	C₄⋊C₈	C₅×D₄	1	4	yes	—
140	#101	—	4	2	no	—
141	C₂²⋊C₈	—	2	2	no	—
142	C₄×C₈	—	2	4	no	—
143	C₄×C₈	—	2	2	no	—
144	#95	—	2	4	no	—
145	#95	C₂×C₄×C₅	1	2	yes	—
146	C₂²×C₅	—	2	1	no	—
147	C₂²×C₅	—	2	1	no	—
148	C₂²×C₅	#386	1	1	yes	characteristic
149	C₂²×C₅	C₂×#103	1	1	yes	characteristic
150	C₂²×C₅	#416	1	1	yes	characteristic
151	C₄×C₅	—	2	1	no	—
152	C₄×C₅	—	2	4	no	—
153	C₄×C₅	—	2	2	no	—
154	C₄×C₅	—	4	4	no	—
155	C₄×C₅	—	4	2	no	—
156	C₄×C₅	—	8	2	no	—
157	C₄×C₅	#456	1	2	yes	—
158	C₄×C₅	#465	1	2	yes	—
159	C₄×C₅	#467	1	2	yes	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	8	2	no	—
164	C₂×Q₈	C₅×SD₁₆	1	2	yes	—
165	C₂×Q₈	C₅×Q₁₆	1	2	yes	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
169	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
170	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
171	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
173	M₁₆	—	4	2	no	—
174	M₁₆	—	4	2	no	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	4	2	no	—
177	C₄⋊C₄	—	2	4	no	—
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	4	1	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	1	no	—
183	C₄⋊C₄	—	8	4	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	C₂×C₅×D₄	1	2	yes	—
188	C₄²	C₅×#41	1	2	yes	—
189	C₂×C₅	—	2	1	no	—
190	C₂×C₅	—	2	1	no	—
191	C₂×C₅	#1886	1	1	yes	characteristic
192	C₂×C₅	#1892	1	1	yes	characteristic
193	C₂×C₅	#1914	1	1	yes	characteristic
194	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
195	Q₈	—	2	4	no	—
196	Q₈	—	2	4	no	—
197	Q₈	—	8	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	C₅×#103	1	4	yes	—
210	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
211	C₂×C₄	C₅×#120	1	1	yes	characteristic
212	C₂×C₄	C₅×#121	1	2	yes	—
213	C₂×C₄	C₅×#123	1	1	yes	characteristic
214	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
215	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
216	C₂×C₄	C₅×#135	1	2	yes	—
217	C₈	—	4	4	no	—
218	C₈	—	8	2	no	—
219	C₅	#9392	1	1	yes	characteristic, direct product factor, Sylow
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	C₅×#386	1	1	yes	characteristic
223	C₂²	C₂×C₅×#103	1	1	yes	characteristic
224	C₂²	C₅×#416	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	4	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	2	no	—
230	C₄	—	8	2	no	—
231	C₄	C₅×#456	1	2	yes	—
232	C₄	C₅×#465	1	2	yes	—
233	C₄	C₅×#467	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	C₅×#1886	1	1	yes	characteristic
237	C₂	C₅×#1892	1	1	yes	characteristic
238	C₂	C₅×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2982

C₂

yes

maximal, characteristic

C₅×#2567

C₂

yes

maximal, characteristic

C₅×#1801

C₂

yes

maximal, characteristic

C₅×#1548

C₂

yes

maximal

C₅×#1303

C₂

yes

maximal

C₂×C₅×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×C₅×Q₈

C₂²

yes

characteristic

C₅×C₈×Q₈

—

C₅×#431

—

C₅×#431

C₂²

yes

—

C₅×#423

C₂²

yes

—

C₂×C₅×#101

—

C₅×#395

C₄

yes

—

C₅×#391

—

C₅×#389

—

C₅×#384

—

C₄×C₅×C₄⋊C₄

C₂²

yes

—

—

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×Q₈

C₂×C₄

yes

—

C₂²×C₅×Q₈

D₄

yes

characteristic

C₂×C₅×M₁₆

—

C₅×C₄⋊Q₈

—

C₅×C₄⋊Q₈

—

C₄×C₅×Q₈

—

C₄×C₅×Q₈

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₅×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄²×C₅

—

C₂×C₄²×C₅

D₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

D₄

yes

—

C₅×#101

—

C₅×C₂²⋊C₈

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

C₅×#95

—

C₅×#95

C₂×C₄

yes

—

#2982

C₂×C₅

yes

characteristic

#2567

C₂×C₅

yes

characteristic

#1801

C₂×C₅

yes

characteristic

#1548

C₂×C₅

yes

—

#1303

C₂×C₅

yes

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

SD₁₆

yes

—

C₂×C₅×Q₈

Q₁₆

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₅×M₁₆

—

C₅×M₁₆

—

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×C₄⋊C₄

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

#41

yes

—

C₂×C₄⋊Q₈

C₂²×C₅

yes

characteristic

C₂×C₄×Q₈

C₂²×C₅

yes

characteristic

C₈×Q₈

—

#431

—

#431

C₂²×C₅

yes

—

#423

C₂²×C₅

yes

—

C₂×#101

—

#395

C₄×C₅

yes

—

#391

—

#389

—

#384

—

C₄×C₄⋊C₄

C₂²×C₅

yes

characteristic

#343

—

#333

—

C₂³×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₅×Q₈

—

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

#103

yes

—

111

C₂×C₄×C₅

C₄×D₄

yes

—

112

C₂×C₄×C₅

#120

yes

characteristic

113

C₂×C₄×C₅

#121

yes

—

114

C₂×C₄×C₅

#123

yes

characteristic

115

C₂×C₄×C₅

C₂×SD₁₆

yes

characteristic

116

C₂×C₄×C₅

C₂×Q₁₆

yes

characteristic

117

C₂×C₄×C₅

#135

yes

—

118

C₅×C₈

—

119

C₅×C₈

—

120

C₂²×Q₈

C₂×C₄×C₅

yes

—

121

C₂²×Q₈

C₅×D₄

yes

characteristic

122

C₂×M₁₆

—

123

C₄⋊Q₈

—

124

C₄⋊Q₈

—

125

C₄×Q₈

—

126

C₄×Q₈

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

C₂×C₄×C₅

yes

—

132

C₂×C₄⋊C₄

C₅×D₄

yes

characteristic

133

C₂×C₄²

—

134

C₂×C₄²

C₅×D₄

yes

—

135

C₂×C₄²

C₂³×C₅

yes

characteristic

136

C₄⋊C₈

—

137

C₄⋊C₈

—

138

C₄⋊C₈

—

139

C₄⋊C₈

C₅×D₄

yes

—

140

#101

—

141

C₂²⋊C₈

—

142

C₄×C₈

—

143

C₄×C₈

—

144

#95

—

145

#95

C₂×C₄×C₅

yes

—

146

C₂²×C₅

—

147

C₂²×C₅

—

148

C₂²×C₅

#386

yes

characteristic

149

C₂²×C₅

C₂×#103

yes

characteristic

150

C₂²×C₅

#416

yes

characteristic

151

C₄×C₅

—

152

C₄×C₅

—

153

C₄×C₅

—

154

C₄×C₅

—

155

C₄×C₅

—

156

C₄×C₅

—

157

C₄×C₅

#456

yes

—

158

C₄×C₅

#465

yes

—

159

C₄×C₅

#467

yes

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

C₅×SD₁₆

yes

—

165

C₂×Q₈

C₅×Q₁₆

yes

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

169

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

170

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

171

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

172

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

173

M₁₆

—

174

M₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

C₂×C₅×D₄

yes

—

188

C₄²

C₅×#41

yes

—

189

C₂×C₅

—

190

C₂×C₅

—

191

C₂×C₅

#1886

yes

characteristic

192

C₂×C₅

#1892

yes

characteristic

193

C₂×C₅

#1914

yes

characteristic

194

C₂³

C₂×C₅×C₂²⋊C₄

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

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

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₅×#103

yes

—

210

C₂×C₄

C₄×C₅×D₄

yes

—

211

C₂×C₄

C₅×#120

yes

characteristic

212

C₂×C₄

C₅×#121

yes

—

213

C₂×C₄

C₅×#123

yes

characteristic

214

C₂×C₄

C₂×C₅×SD₁₆

yes

characteristic

215

C₂×C₄

C₂×C₅×Q₁₆

yes

characteristic

216

C₂×C₄

C₅×#135

yes

—

217

C₈

—

218

C₈

—

219

C₅

#9392

yes

characteristic, direct product factor, Sylow

220

C₂²

—

221

C₂²

—

222

C₂²

C₅×#386

yes

characteristic

223

C₂²

C₂×C₅×#103

yes

characteristic

224

C₂²

C₅×#416

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

C₅×#456

yes

—

232

C₄

C₅×#465

yes

—

233

C₄

C₅×#467

yes

—

234

C₂

—

235

C₂

—

236

C₂

C₅×#1886

yes

characteristic

237

C₂

C₅×#1892

yes

characteristic

238

C₂

C₅×#1914

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#386
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂³×C₅	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#386

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂³×C₅

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
20. #9392	C₅	direct (N × H)
219. C₅	#9392	direct (N × H)

H ≅ G/N

type

20. #9392

C₅

direct (N × H)

219. C₅

#9392

direct (N × H)

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

subgroup	index
C₅×#2982	2
C₅×#2567	2
C₅×#1801	2
C₅×#1548	2
C₅×#1303	2
#9392	5

subgroup

index

Subgroups — C₅×#9392 #11932112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#9392 #11932112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9392 #11932112