Group #14300378 — subgroups

Subgroups — #14300378

Order 1920.

520 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 148 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	C₃×#66153	C₂	1	1	yes	maximal, characteristic
2	#11751341	C₂	1	1	yes	maximal, characteristic
3	C₅×#5234	C₂	1	1	yes	maximal, characteristic
4	#11748436	C₂	1	2	yes	maximal, complemented
5	#11745991	C₂	1	2	yes	maximal, complemented
6	#10600795	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	#91815	C₂²	1	2	yes	—
9	C₂×C₅×#208	C₂²	1	1	yes	characteristic
10	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₃×#4094	—	2	4	no	—
12	C₂×C₃×#681	—	2	2	no	—
13	C₂×C₃×#681	C₂²	1	2	yes	—
14	#91118	C₄	1	4	yes	—
15	C₅×#830	—	2	2	no	—
16	#90983	—	2	4	no	—
17	#72026	—	5	1	no	maximal, Hall
18	#66153	D₃	1	1	yes	characteristic
19	C₅×#408	—	3	1	no	—
20	#65529	—	3	1	no	—
21	#65391	—	3	2	no	—
22	#64779	—	3	2	no	—
23	C₃×C₅×#41	—	2	2	no	—
24	C₃×C₅×#41	—	2	2	no	—
25	C₂×C₃×C₅×Q₈	Q₈	1	1	yes	characteristic
26	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
27	C₂×C₃×C₅×D₄	Q₈	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	#6719	C₂×C₄	1	4	yes	—
31	C₄⋊Dic₁₅	—	2	2	no	—
32	C₄×Dic₁₅	—	2	2	no	—
33	C₅×#208	—	2	2	no	—
34	C₂×C₅×C₃⋊C₈	—	2	2	no	—
35	C₂×C₅×C₃⋊C₈	—	2	1	no	—
36	C₂×C₅×C₃⋊C₈	—	2	1	no	—
37	C₃×#681	—	2	4	no	—
38	C₃×#681	—	2	2	no	—
39	C₃×#681	—	2	2	no	—
40	C₂×C₃×#168	—	2	4	no	—
41	C₂×C₃×#168	D₄	1	4	yes	—
42	C₃×#568	—	5	1	no	—
43	#5240	—	5	1	no	—
44	#5234	D₅	1	1	yes	characteristic
45	#5119	—	5	2	no	—
46	#4556	—	5	2	no	—
47	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
48	C₂×C₅×M₁₆	—	3	1	no	—
49	C₂²×C₅×C₈	—	3	1	no	—
50	#4094	—	2	4	no	—
51	#4072	—	3	2	no	—
52	C₂×#681	—	2	2	no	—
53	C₂×#681	C₂×D₃	1	2	yes	—
54	C₅×C₂²⋊C₈	—	6	2	no	—
55	#3966	—	3	4	no	—
56	#3946	—	6	4	no	—
57	#1868	—	15	1	no	Sylow
58	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
59	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
60	C₃×C₅×Q₈	—	2	2	no	—
61	C₃×C₅×D₄	—	2	4	no	—
62	C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₄×C₅	—	2	2	no	—
64	C₂×C₃×C₄×C₅	—	2	2	no	—
65	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
66	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
67	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
68	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	#41	1	2	yes	—
70	C₂×Dic₁₅	—	2	4	no	—
71	C₃×#168	—	2	4	no	—
72	C₅×C₃⋊C₈	—	4	1	no	—
73	C₅×C₃⋊C₈	—	4	1	no	—
74	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
75	C₃×#131	—	10	4	no	—
76	C₂×C₃×M₁₆	—	5	2	no	—
77	C₂×C₃×M₁₆	—	10	2	no	—
78	#926	—	5	2	no	—
79	C₂×#208	C₂×D₅	1	1	yes	characteristic
80	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
81	#834	—	5	4	no	—
82	#830	—	2	2	no	—
83	Dic₃⋊C₈	—	10	4	no	—
84	C₅×#41	—	2	2	no	—
85	C₅×#41	—	2	2	no	—
86	C₂×C₅×Q₈	Dic₆	1	1	yes	characteristic
87	C₂×C₅×D₄	Dic₆	1	1	yes	characteristic
88	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
89	C₂²×C₄×C₅	#67	1	2	yes	—
90	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
91	C₅×M₁₆	—	6	2	no	—
92	C₂×C₅×C₈	—	6	2	no	—
93	C₂×C₅×C₈	—	6	1	no	—
94	C₂×C₅×C₈	—	6	1	no	—
95	C₂²⋊Dic₅	—	3	4	no	—
96	C₄⋊Dic₅	—	6	2	no	—
97	C₄×Dic₅	—	6	2	no	—
98	#681	—	2	4	no	—
99	#681	—	2	2	no	—
100	#681	—	2	2	no	—
101	C₂×#168	—	2	4	no	—
102	C₂×#168	#67	1	4	yes	—
103	#568	—	5	1	no	—
104	#424	—	15	2	no	—
105	#410	—	15	1	no	—
106	#408	—	3	1	no	—
107	#344	—	15	2	no	—
108	C₂²×C₃×C₅	—	2	2	no	—
109	C₂²×C₃×C₅	—	4	1	no	—
110	C₂²×C₃×C₅	—	4	2	no	—
111	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
113	C₃×C₄×C₅	—	2	2	no	—
114	C₃×C₄×C₅	#120	1	1	yes	characteristic
115	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
116	C₃×C₄×C₅	#123	1	1	yes	characteristic
117	Dic₁₅	—	4	4	no	—
118	C₃×#41	—	2	2	no	—
119	C₃×#41	—	2	2	no	—
120	C₂×C₃×Q₈	Dic₁₀	1	1	yes	characteristic
121	C₂×C₃×D₄	Dic₁₀	1	1	yes	characteristic
122	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
123	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
124	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
125	C₃×M₁₆	—	10	4	no	—
126	C₃×M₁₆	—	10	2	no	—
127	C₃×M₁₆	—	10	2	no	—
128	C₂×C₃×C₈	—	5	4	no	—
129	C₂×C₃×C₈	—	10	4	no	—
130	#217	—	5	4	no	—
131	C₄⋊Dic₃	—	10	2	no	—
132	C₄×Dic₃	—	10	2	no	—
133	#208	—	2	2	no	—
134	C₂×C₃⋊C₈	—	2	2	no	—
135	C₂×C₃⋊C₈	—	2	1	no	—
136	C₂×C₃⋊C₈	—	2	1	no	—
137	C₂³×C₅	Dic₃⋊C₄	1	2	yes	—
138	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
139	C₅×Q₈	—	2	2	no	—
140	C₅×D₄	—	2	4	no	—
141	C₅×D₄	—	2	2	no	—
142	C₂×C₄×C₅	—	2	2	no	—
143	C₂×C₄×C₅	—	2	2	no	—
144	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
145	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
146	C₂×C₄×C₅	#235	1	2	yes	—
147	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
148	C₂×C₄×C₅	C₂×#67	1	2	yes	—
149	C₂×Dic₅	—	6	4	no	—
150	C₅×C₈	—	12	1	no	—
151	C₅×C₈	—	12	1	no	—
152	#168	—	2	4	no	—
153	C₂×#41	D₃×D₅	1	1	yes	characteristic
154	#131	—	10	4	no	—
155	C₂×M₁₆	—	3	1	no	—
156	C₂×M₁₆	—	5	2	no	—
157	C₂×M₁₆	—	10	2	no	—
158	C₂²×C₈	—	3	1	no	—
159	#117	—	15	2	no	—
160	C₄⋊C₈	—	30	4	no	—
161	#99	—	15	4	no	—
162	C₂²⋊C₈	—	6	2	no	—
163	C₂×C₃×C₅	—	2	2	no	—
164	C₂×C₃×C₅	—	2	1	no	—
165	C₂×C₃×C₅	—	4	2	no	—
166	C₂×C₃×C₅	#385	1	1	yes	characteristic
167	C₂³×C₃	#683	1	2	yes	—
168	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
169	C₃×Q₈	—	2	2	no	—
170	C₃×D₄	—	2	4	no	—
171	C₃×D₄	—	2	2	no	—
172	C₂×C₃×C₄	—	2	2	no	—
173	C₂×C₃×C₄	—	2	2	no	—
174	C₂×C₃×C₄	#683	1	2	yes	—
175	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
176	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
177	C₂×C₃×C₄	#711	1	2	yes	—
178	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
179	C₂×Dic₃	—	10	4	no	—
180	C₃×C₈	—	10	4	no	—
181	C₃⋊C₈	—	4	1	no	—
182	C₃⋊C₈	—	4	1	no	—
183	C₂²×C₅	—	2	2	no	—
184	C₂²×C₅	—	4	1	no	—
185	C₂²×C₅	—	4	2	no	—
186	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
187	C₂²×C₅	C₄×#67	1	2	yes	—
188	C₄×C₅	—	2	2	no	—
189	C₄×C₅	#924	1	2	yes	—
190	C₄×C₅	#929	1	1	yes	characteristic
191	C₄×C₅	#953	1	1	yes	characteristic
192	Dic₅	—	12	4	no	—
193	#41	—	2	2	no	—
194	#41	—	2	2	no	—
195	C₂×Q₈	#1204	1	1	yes	characteristic
196	C₂×D₄	#1200	1	2	yes	—
197	C₂×D₄	#1204	1	1	yes	characteristic
198	C₂²×C₄	#1201	1	2	yes	—
199	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
200	M₁₆	—	6	2	no	—
201	M₁₆	—	10	4	no	—
202	M₁₆	—	10	2	no	—
203	M₁₆	—	10	2	no	—
204	C₂×C₈	—	5	4	no	—
205	C₂×C₈	—	6	1	no	—
206	C₂×C₈	—	6	1	no	—
207	C₂×C₈	—	6	2	no	—
208	C₂×C₈	—	10	4	no	—
209	C₄⋊C₄	—	30	2	no	—
210	C₂²⋊C₄	—	15	4	no	—
211	C₄²	—	30	2	no	—
212	C₃×C₅	#1868	1	1	yes	characteristic, complemented, Hall
213	C₂²×C₃	—	2	2	no	—
214	C₂²×C₃	—	4	1	no	—
215	C₂²×C₃	—	4	2	no	—
216	C₂²×C₃	#4027	1	2	yes	—
217	C₂²×C₃	C₂×#683	1	1	yes	characteristic
218	C₃×C₄	—	2	2	no	—
219	C₃×C₄	#4024	1	2	yes	—
220	C₃×C₄	#4081	1	1	yes	characteristic
221	C₃×C₄	#4083	1	1	yes	characteristic
222	Dic₃	—	20	4	no	—
223	C₂×C₅	—	2	2	no	—
224	C₂×C₅	—	2	1	no	—
225	C₂×C₅	—	4	2	no	—
226	C₂×C₅	#5210	1	1	yes	characteristic
227	C₂³	#6669	1	2	yes	—
228	C₂³	C₂×#1200	1	1	yes	characteristic
229	Q₈	—	2	2	no	—
230	D₄	—	2	4	no	—
231	D₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	30	4	no	—
235	C₂×C₄	#6669	1	2	yes	—
236	C₂×C₄	#6782	1	2	yes	—
237	C₂×C₄	C₂×#1201	1	1	yes	characteristic
238	C₂×C₄	C₂×#1204	1	1	yes	characteristic
239	C₂×C₄	D₅×#67	1	2	yes	—
240	C₈	—	10	4	no	—
241	C₈	—	12	1	no	—
242	C₈	—	12	1	no	—
243	C₂×C₃	—	2	2	no	—
244	C₂×C₃	—	2	1	no	—
245	C₂×C₃	—	4	2	no	—
246	C₂×C₃	#65235	1	1	yes	characteristic
247	C₅	#72026	1	1	yes	characteristic, complemented, Sylow
248	C₂²	—	2	2	no	—
249	C₂²	—	4	1	no	—
250	C₂²	—	4	2	no	—
251	C₂²	C₂×#6669	1	1	yes	characteristic
252	C₂²	#91552	1	2	yes	—
253	C₄	—	2	2	no	—
254	C₄	—	60	4	no	—
255	C₄	#91539	1	1	yes	characteristic
256	C₄	#91563	1	1	yes	characteristic
257	C₄	#91574	1	2	yes	—
258	C₃	#10600795	1	1	yes	characteristic, complemented, Sylow
259	C₂	—	2	2	no	—
260	C₂	—	2	1	no	—
261	C₂	—	4	2	no	—
262	C₂	#11749508	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#66153

C₂

yes

maximal, characteristic

#11751341

C₂

yes

maximal, characteristic

C₅×#5234

C₂

yes

maximal, characteristic

#11748436

C₂

yes

maximal, complemented

#11745991

C₂

yes

maximal, complemented

#10600795

—

maximal, Hall

C₂×C₃×C₅×#41

C₂²

yes

characteristic

#91815

C₂²

yes

—

C₂×C₅×#208

C₂²

yes

characteristic

C₂²×C₅×C₃⋊C₈

C₂²

yes

characteristic

C₃×#4094

—

C₂×C₃×#681

—

C₂×C₃×#681

C₂²

yes

—

#91118

C₄

yes

—

—

—

—

D₃

yes

—

—

—

—

C₃×C₅×#41

—

C₃×C₅×#41

—

C₂×C₃×C₅×Q₈

Q₈

yes

characteristic

C₂×C₃×C₅×D₄

C₂×C₄

yes

—

C₂×C₃×C₅×D₄

Q₈

yes

characteristic

C₂²×C₃×C₄×C₅

D₄

yes

—

C₂²×C₃×C₄×C₅

C₂³

yes

characteristic

#6719

C₂×C₄

yes

—

C₄⋊Dic₁₅

—

C₄×Dic₁₅

—

C₅×#208

—

C₂×C₅×C₃⋊C₈

—

C₂×C₅×C₃⋊C₈

—

C₂×C₅×C₃⋊C₈

—

C₃×#681

—

C₃×#681

—

C₃×#681

—

C₂×C₃×#168

—

C₂×C₃×#168

D₄

yes

—

C₃×#568

—

#5240

—

#5234

D₅

yes

characteristic

#5119

—

#4556

—

C₂×C₅×#41

C₂×D₃

yes

characteristic

C₂×C₅×M₁₆

—

C₂²×C₅×C₈

—

—

—

—

C₂×D₃

yes

—

C₅×C₂²⋊C₈

—

—

—

—

C₂³×C₃×C₅

C₄⋊C₄

yes

—

C₂³×C₃×C₅

C₂²×C₄

yes

characteristic

C₃×C₅×Q₈

—

C₃×C₅×D₄

—

C₃×C₅×D₄

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₄⋊C₄

yes

—

C₂×C₃×C₄×C₅

C₂×D₄

yes

—

C₂×C₃×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×Q₈

yes

characteristic

C₂×C₃×C₄×C₅

#41

yes

—

C₂×Dic₁₅

—

C₃×#168

—

C₅×C₃⋊C₈

—

C₅×C₃⋊C₈

—

C₂×C₃×#41

C₂×D₅

yes

characteristic

C₃×#131

—

C₂×C₃×M₁₆

—

C₂×C₃×M₁₆

—

#926

—

C₂×#208

C₂×D₅

yes

characteristic

C₂²×C₃⋊C₈

C₂×D₅

yes

characteristic

#834

—

#830

—

Dic₃⋊C₈

—

C₅×#41

—

C₅×#41

—

C₂×C₅×Q₈

Dic₆

yes

characteristic

C₂×C₅×D₄

Dic₆

yes

characteristic

C₂×C₅×D₄

C₄×D₃

yes

—

C₂²×C₄×C₅

#67

yes

—

C₂²×C₄×C₅

C₂²×D₃

yes

characteristic

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂²⋊Dic₅

—

C₄⋊Dic₅

—

C₄×Dic₅

—

#681

—

#681

—

100

#681

—

101

C₂×#168

—

102

C₂×#168

#67

yes

—

103

#568

—

104

#424

—

105

#410

—

106

#408

—

107

#344

—

108

C₂²×C₃×C₅

—

109

C₂²×C₃×C₅

—

110

C₂²×C₃×C₅

—

111

C₂²×C₃×C₅

C₂×C₄⋊C₄

yes

characteristic

112

C₂²×C₃×C₅

C₄×D₄

yes

—

113

C₃×C₄×C₅

—

114

C₃×C₄×C₅

#120

yes

characteristic

115

C₃×C₄×C₅

C₂²⋊Q₈

yes

—

116

C₃×C₄×C₅

#123

yes

characteristic

117

Dic₁₅

—

118

C₃×#41

—

119

C₃×#41

—

120

C₂×C₃×Q₈

Dic₁₀

yes

characteristic

121

C₂×C₃×D₄

Dic₁₀

yes

characteristic

122

C₂×C₃×D₄

C₄×D₅

yes

—

123

C₂²×C₃×C₄

C₂²⋊D₅

yes

—

124

C₂²×C₃×C₄

C₂²×D₅

yes

characteristic

125

C₃×M₁₆

—

126

C₃×M₁₆

—

127

C₃×M₁₆

—

128

C₂×C₃×C₈

—

129

C₂×C₃×C₈

—

130

#217

—

131

C₄⋊Dic₃

—

132

C₄×Dic₃

—

133

#208

—

134

C₂×C₃⋊C₈

—

135

C₂×C₃⋊C₈

—

136

C₂×C₃⋊C₈

—

137

C₂³×C₅

Dic₃⋊C₄

yes

—

138

C₂³×C₅

C₂×C₄×D₃

yes

characteristic

139

C₅×Q₈

—

140

C₅×D₄

—

141

C₅×D₄

—

142

C₂×C₄×C₅

—

143

C₂×C₄×C₅

—

144

C₂×C₄×C₅

Dic₃⋊C₄

yes

—

145

C₂×C₄×C₅

C₂×Dic₆

yes

characteristic

146

C₂×C₄×C₅

#235

yes

—

147

C₂×C₄×C₅

C₂×#67

yes

characteristic

148

C₂×C₄×C₅

C₂×#67

yes

—

149

C₂×Dic₅

—

150

C₅×C₈

—

151

C₅×C₈

—

152

#168

—

153

C₂×#41

D₃×D₅

yes

characteristic

154

#131

—

155

C₂×M₁₆

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

C₂²×C₈

—

159

#117

—

160

C₄⋊C₈

—

161

#99

—

162

C₂²⋊C₈

—

163

C₂×C₃×C₅

—

164

C₂×C₃×C₅

—

165

C₂×C₃×C₅

—

166

C₂×C₃×C₅

#385

yes

characteristic

167

C₂³×C₃

#683

yes

—

168

C₂³×C₃

C₂×C₄×D₅

yes

characteristic

169

C₃×Q₈

—

170

C₃×D₄

—

171

C₃×D₄

—

172

C₂×C₃×C₄

—

173

C₂×C₃×C₄

—

174

C₂×C₃×C₄

#683

yes

—

175

C₂×C₃×C₄

C₂×Dic₁₀

yes

characteristic

176

C₂×C₃×C₄

D₄×D₅

yes

—

177

C₂×C₃×C₄

#711

yes

—

178

C₂×C₃×C₄

C₂×C₂²⋊D₅

yes

characteristic

179

C₂×Dic₃

—

180

C₃×C₈

—

181

C₃⋊C₈

—

182

C₃⋊C₈

—

183

C₂²×C₅

—

184

C₂²×C₅

—

185

C₂²×C₅

—

186

C₂²×C₅

C₂×Dic₃⋊C₄

yes

characteristic

187

C₂²×C₅

C₄×#67

yes

—

188

C₄×C₅

—

189

C₄×C₅

#924

yes

—

190

C₄×C₅

#929

yes

characteristic

191

C₄×C₅

#953

yes

characteristic

192

Dic₅

—

193

#41

—

194

#41

—

195

C₂×Q₈

#1204

yes

characteristic

196

C₂×D₄

#1200

yes

—

197

C₂×D₄

#1204

yes

characteristic

198

C₂²×C₄

#1201

yes

—

199

C₂²×C₄

C₂×D₃×D₅

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₃×C₅

#1868

yes

characteristic, complemented, Hall

213

C₂²×C₃

—

214

C₂²×C₃

—

215

C₂²×C₃

—

216

C₂²×C₃

#4027

yes

—

217

C₂²×C₃

C₂×#683

yes

characteristic

218

C₃×C₄

—

219

C₃×C₄

#4024

yes

—

220

C₃×C₄

#4081

yes

characteristic

221

C₃×C₄

#4083

yes

characteristic

222

Dic₃

—

223

C₂×C₅

—

224

C₂×C₅

—

225

C₂×C₅

—

226

C₂×C₅

#5210

yes

characteristic

227

C₂³

#6669

yes

—

228

C₂³

C₂×#1200

yes

characteristic

229

Q₈

—

230

D₄

—

231

D₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

#6669

yes

—

236

C₂×C₄

#6782

yes

—

237

C₂×C₄

C₂×#1201

yes

characteristic

238

C₂×C₄

C₂×#1204

yes

characteristic

239

C₂×C₄

D₅×#67

yes

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₂×C₃

—

244

C₂×C₃

—

245

C₂×C₃

—

246

C₂×C₃

#65235

yes

characteristic

247

C₅

#72026

yes

characteristic, complemented, Sylow

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

C₂×#6669

yes

characteristic

252

C₂²

#91552

yes

—

253

C₄

—

254

C₄

—

255

C₄

#91539

yes

characteristic

256

C₄

#91563

yes

characteristic

257

C₄

#91574

yes

—

258

C₃

#10600795

yes

characteristic, complemented, Sylow

259

C₂

—

260

C₂

—

261

C₂

—

262

C₂

#11749508

yes

characteristic

	subgroup	G/H
center	C₄	#91563
commutator	C₂³×C₃×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting, prime radical	C₂×C₃×C₅×#41	C₂²
socle	C₂×C₃×C₅	#385
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×#41	D₃×D₅
hypocenter	C₃×C₅	#1868
LCS	G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

subgroup

G/H

center

C₄

#91563

commutator

C₂³×C₃×C₅

C₂²×C₄

Frattini

C₂²×C₄

C₂×D₃×D₅

Fitting, prime radical

C₂×C₃×C₅×#41

C₂²

socle

C₂×C₃×C₅

#385

cosocle

C₂²×C₃×C₄×C₅

C₂³

hypercenter

C₂×#41

D₃×D₅

hypocenter

C₃×C₅

#1868

LCS

G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

N	H ≅ G/N	type
4. #11748436	C₂	semidirect
5. #11745991	C₂	semidirect
212. C₃×C₅	#1868	semidirect
247. C₅	#72026	semidirect
258. C₃	#10600795	semidirect

H ≅ G/N

type

4. #11748436

C₂

semidirect

5. #11745991

C₂

semidirect

212. C₃×C₅

#1868

semidirect

247. C₅

#72026

semidirect

258. C₃

#10600795

semidirect

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

subgroup	index
C₃×#66153	2
#11751341	2
C₅×#5234	2
#11748436	2
#11745991	2
#10600795	3
#72026	5

subgroup

index

Subgroups — #14300378

Conjugacy classes of subgroups

Complements

Maximal subgroups