Group #21470072 — subgroups

Subgroups — C₃₁×#13313 #21470072

Order 7936.

556 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 118 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	C₂²×C₃₁×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#472	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#361	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1381	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×AGL(1,ℤ/8)	—	2	2	no	—
7	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
8	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
9	C₂×C₃₁×D₁₆	—	2	4	no	—
10	C₂×C₃₁×D₁₆	—	2	2	no	—
11	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
12	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#472	—	2	4	no	—
14	C₃₁×#472	—	2	4	no	—
15	C₂×C₃₁×#108	C₂²	1	2	yes	—
16	C₂×C₃₁×#100	—	2	2	no	—
17	C₃₁×#361	—	2	4	no	—
18	C₃₁×C₂²⋊C₁₆	—	2	2	no	—
19	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
20	C₂²×D₄×C₃₁	—	2	2	no	—
21	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
22	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
23	C₂×SD₁₆×C₃₁	—	4	2	no	—
24	C₂×D₈×C₃₁	—	2	2	no	—
25	C₂×D₈×C₃₁	—	2	2	no	—
26	C₂×D₈×C₃₁	—	2	2	no	—
27	C₂×D₈×C₃₁	—	2	2	no	—
28	C₂×D₈×C₃₁	—	2	2	no	—
29	C₂×D₈×C₃₁	—	4	2	no	—
30	C₂×D₈×C₃₁	D₄	1	4	yes	—
31	C₃₁×#131	—	2	2	no	—
32	C₃₁×#131	—	2	2	no	—
33	C₂×M₁₆×C₃₁	—	2	1	no	—
34	C₂×M₁₆×C₃₁	—	2	2	no	—
35	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₃₁	—	2	1	no	—
37	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
38	C₃₁×D₁₆	—	2	8	no	—
39	C₃₁×M₃₂	—	2	2	no	—
40	C₂×C₁₆×C₃₁	—	2	2	no	—
41	C₂×C₁₆×C₃₁	—	2	1	no	—
42	C₂×C₁₆×C₃₁	D₄	1	2	yes	—
43	C₃₁×#108	—	2	2	no	—
44	C₃₁×#108	D₄	1	4	yes	—
45	C₃₁×#100	—	2	8	no	—
46	C₂⁴×C₃₁	—	4	2	no	—
47	#41×C₃₁	—	2	2	no	—
48	#41×C₃₁	—	2	2	no	—
49	C₂×Q₈×C₃₁	D₈	1	1	yes	characteristic
50	C₂×D₄×C₃₁	—	2	1	no	—
51	C₂×D₄×C₃₁	—	2	4	no	—
52	C₂×D₄×C₃₁	—	4	2	no	—
53	C₂×D₄×C₃₁	—	4	2	no	—
54	C₂×D₄×C₃₁	—	4	2	no	—
55	C₂×D₄×C₃₁	—	4	2	no	—
56	C₂×D₄×C₃₁	—	4	2	no	—
57	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
58	C₂²×C₄×C₃₁	—	2	1	no	—
59	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
60	SD₁₆×C₃₁	—	4	8	no	—
61	D₈×C₃₁	—	2	4	no	—
62	D₈×C₃₁	—	2	4	no	—
63	D₈×C₃₁	—	4	8	no	—
64	D₈×C₃₁	—	4	2	no	—
65	D₈×C₃₁	—	4	2	no	—
66	M₁₆×C₃₁	—	2	2	no	—
67	M₁₆×C₃₁	—	2	4	no	—
68	M₁₆×C₃₁	—	4	2	no	—
69	M₁₆×C₃₁	—	4	2	no	—
70	C₂×C₈×C₃₁	—	2	1	no	—
71	C₂×C₈×C₃₁	—	4	2	no	—
72	C₂×C₈×C₃₁	—	4	1	no	—
73	C₂×C₈×C₃₁	—	4	1	no	—
74	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
78	C₁₆×C₃₁	—	2	2	no	—
79	C₁₆×C₃₁	—	4	1	no	—
80	#13313	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂³×C₃₁	—	2	1	no	—
82	C₂³×C₃₁	—	4	4	no	—
83	C₂³×C₃₁	—	8	2	no	—
84	C₂³×C₃₁	—	8	2	no	—
85	C₂³×C₃₁	—	16	4	no	—
86	C₂³×C₃₁	#135	1	1	yes	characteristic
87	Q₈×C₃₁	—	2	2	no	—
88	D₄×C₃₁	—	2	2	no	—
89	D₄×C₃₁	—	4	2	no	—
90	D₄×C₃₁	—	4	4	no	—
91	D₄×C₃₁	—	4	4	no	—
92	D₄×C₃₁	—	8	2	no	—
93	D₄×C₃₁	—	8	2	no	—
94	C₂×C₄×C₃₁	—	2	1	no	—
95	C₂×C₄×C₃₁	—	4	1	no	—
96	C₂×C₄×C₃₁	—	4	1	no	—
97	C₂×C₄×C₃₁	#120	1	2	yes	—
98	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
99	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
100	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
101	C₈×C₃₁	—	4	1	no	—
102	C₈×C₃₁	—	4	4	no	—
103	C₈×C₃₁	#120	1	1	yes	characteristic
104	C₈×C₃₁	#121	1	2	yes	—
105	C₈×C₃₁	#127	1	1	yes	characteristic
106	C₂²×D₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
107	C₂×#472	C₂×C₃₁	1	2	yes	complemented
108	C₂×#361	C₂×C₃₁	1	2	yes	complemented
109	#2113	C₂×C₃₁	1	1	yes	characteristic, complemented
110	#1381	C₂×C₃₁	1	1	yes	characteristic, complemented
111	C₂²×C₃₁	—	2	2	no	—
112	C₂²×C₃₁	—	4	2	no	—
113	C₂²×C₃₁	—	4	1	no	—
114	C₂²×C₃₁	—	8	4	no	—
115	C₂²×C₃₁	—	16	4	no	—
116	C₂²×C₃₁	—	16	4	no	—
117	C₂²×C₃₁	—	16	4	no	—
118	C₂²×C₃₁	#449	1	2	yes	—
119	C₂²×C₃₁	#466	1	1	yes	characteristic
120	C₄×C₃₁	—	4	1	no	—
121	C₄×C₃₁	#392	1	1	yes	characteristic
122	C₄×C₃₁	#447	1	2	yes	—
123	C₄×C₃₁	#469	1	1	yes	characteristic
124	C₂×AGL(1,ℤ/8)	—	2	2	no	—
125	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
126	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
127	C₂×D₁₆	—	2	4	no	—
128	C₂×D₁₆	—	2	2	no	—
129	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
130	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
131	#472	—	2	4	no	—
132	#472	—	2	4	no	—
133	C₂×#108	C₂²×C₃₁	1	2	yes	—
134	C₂×#100	—	2	2	no	—
135	#361	—	2	4	no	—
136	C₂²⋊C₁₆	—	2	2	no	—
137	C₂×C₃₁	—	2	2	no	—
138	C₂×C₃₁	—	8	1	no	—
139	C₂×C₃₁	—	16	4	no	—
140	C₂×C₃₁	#1999	1	1	yes	characteristic
141	C₂×C₃₁	#2221	1	2	yes	—
142	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
143	C₂²×D₄	—	2	2	no	—
144	AGL(1,ℤ/8)	—	2	8	no	—
145	AGL(1,ℤ/8)	—	4	4	no	—
146	C₂×SD₁₆	—	4	2	no	—
147	C₂×D₈	—	2	2	no	—
148	C₂×D₈	—	2	2	no	—
149	C₂×D₈	—	2	2	no	—
150	C₂×D₈	—	2	2	no	—
151	C₂×D₈	—	2	2	no	—
152	C₂×D₈	—	4	2	no	—
153	C₂×D₈	D₄×C₃₁	1	4	yes	—
154	#131	—	2	2	no	—
155	#131	—	2	2	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
161	D₁₆	—	2	8	no	—
162	M₃₂	—	2	2	no	—
163	C₂×C₁₆	—	2	2	no	—
164	C₂×C₁₆	—	2	1	no	—
165	C₂×C₁₆	D₄×C₃₁	1	2	yes	—
166	#108	—	2	2	no	—
167	#108	D₄×C₃₁	1	4	yes	—
168	#100	—	2	8	no	—
169	C₃₁	#13313	1	1	yes	characteristic, direct product factor, Sylow
170	C₂⁴	—	4	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	D₈×C₃₁	1	1	yes	characteristic
174	C₂×D₄	—	2	1	no	—
175	C₂×D₄	—	2	4	no	—
176	C₂×D₄	—	4	2	no	—
177	C₂×D₄	—	4	2	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	2	no	—
181	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
184	SD₁₆	—	4	8	no	—
185	D₈	—	2	4	no	—
186	D₈	—	2	4	no	—
187	D₈	—	4	8	no	—
188	D₈	—	4	2	no	—
189	D₈	—	4	2	no	—
190	M₁₆	—	2	2	no	—
191	M₁₆	—	2	4	no	—
192	M₁₆	—	4	2	no	—
193	M₁₆	—	4	2	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
199	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
200	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
201	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
202	C₁₆	—	2	2	no	—
203	C₁₆	—	4	1	no	—
204	C₂³	—	2	1	no	—
205	C₂³	—	4	4	no	—
206	C₂³	—	8	2	no	—
207	C₂³	—	8	2	no	—
208	C₂³	—	16	4	no	—
209	C₂³	C₃₁×#135	1	1	yes	characteristic
210	Q₈	—	2	2	no	—
211	D₄	—	2	2	no	—
212	D₄	—	4	2	no	—
213	D₄	—	4	4	no	—
214	D₄	—	4	4	no	—
215	D₄	—	8	2	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	C₃₁×#120	1	2	yes	—
221	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
222	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
223	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
224	C₈	—	4	4	no	—
225	C₈	—	4	1	no	—
226	C₈	C₃₁×#120	1	1	yes	characteristic
227	C₈	C₃₁×#121	1	2	yes	—
228	C₈	C₃₁×#127	1	1	yes	characteristic
229	C₂²	—	2	2	no	—
230	C₂²	—	4	2	no	—
231	C₂²	—	4	1	no	—
232	C₂²	—	8	4	no	—
233	C₂²	—	16	4	no	—
234	C₂²	—	16	4	no	—
235	C₂²	—	16	4	no	—
236	C₂²	C₃₁×#449	1	2	yes	—
237	C₂²	C₃₁×#466	1	1	yes	characteristic
238	C₄	—	4	1	no	—
239	C₄	C₃₁×#392	1	1	yes	characteristic
240	C₄	C₃₁×#447	1	2	yes	—
241	C₄	C₃₁×#469	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	8	1	no	—
244	C₂	—	16	4	no	—
245	C₂	C₃₁×#1999	1	1	yes	characteristic
246	C₂	C₃₁×#2221	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₃₁×D₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₃₁×#472

C₂

yes

maximal, complemented

C₂×C₃₁×#361

C₂

yes

maximal, complemented

C₃₁×#2113

C₂

yes

maximal, characteristic, complemented

C₃₁×#1381

C₂

yes

maximal, characteristic, complemented

C₂×C₃₁×AGL(1,ℤ/8)

—

C₂²×D₈×C₃₁

C₂²

yes

—

C₂×C₃₁×#131

C₂²

yes

characteristic

C₂×C₃₁×D₁₆

—

C₂×C₃₁×D₁₆

—

C₂×C₃₁×M₃₂

C₂²

yes

characteristic

C₂²×C₁₆×C₃₁

C₂²

yes

characteristic

C₃₁×#472

—

C₃₁×#472

—

C₂×C₃₁×#108

C₂²

yes

—

C₂×C₃₁×#100

—

C₃₁×#361

—

C₃₁×C₂²⋊C₁₆

—

C₂×#41×C₃₁

D₄

yes

characteristic

C₂²×D₄×C₃₁

—

C₃₁×AGL(1,ℤ/8)

—

C₃₁×AGL(1,ℤ/8)

—

C₂×SD₁₆×C₃₁

—

C₂×D₈×C₃₁

—

C₂×D₈×C₃₁

—

C₂×D₈×C₃₁

—

C₂×D₈×C₃₁

—

C₂×D₈×C₃₁

—

C₂×D₈×C₃₁

—

C₂×D₈×C₃₁

D₄

yes

—

C₃₁×#131

—

C₃₁×#131

—

C₂×M₁₆×C₃₁

—

C₂×M₁₆×C₃₁

—

C₂×M₁₆×C₃₁

D₄

yes

characteristic

C₂²×C₈×C₃₁

—

C₂²×C₈×C₃₁

C₂³

yes

characteristic

C₃₁×D₁₆

—

C₃₁×M₃₂

—

C₂×C₁₆×C₃₁

—

C₂×C₁₆×C₃₁

—

C₂×C₁₆×C₃₁

D₄

yes

—

C₃₁×#108

—

C₃₁×#108

D₄

yes

—

C₃₁×#100

—

C₂⁴×C₃₁

—

#41×C₃₁

—

#41×C₃₁

—

C₂×Q₈×C₃₁

D₈

yes

characteristic

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

D₈

yes

characteristic

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

C₂×D₄

yes

characteristic

SD₁₆×C₃₁

—

D₈×C₃₁

—

D₈×C₃₁

—

D₈×C₃₁

—

D₈×C₃₁

—

D₈×C₃₁

—

M₁₆×C₃₁

—

M₁₆×C₃₁

—

M₁₆×C₃₁

—

M₁₆×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

C₂×D₄

yes

—

C₂×C₈×C₃₁

C₂×D₄

yes

characteristic

C₂×C₈×C₃₁

C₂×D₄

yes

—

C₂×C₈×C₃₁

#41

yes

characteristic

C₁₆×C₃₁

—

C₁₆×C₃₁

—

#13313

C₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

#135

yes

characteristic

Q₈×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

#120

yes

—

C₂×C₄×C₃₁

#121

yes

characteristic

C₂×C₄×C₃₁

C₂×D₈

yes

characteristic

100

C₂×C₄×C₃₁

AGL(1,ℤ/8)

yes

—

101

C₈×C₃₁

—

102

C₈×C₃₁

—

103

C₈×C₃₁

#120

yes

characteristic

104

C₈×C₃₁

#121

yes

—

105

C₈×C₃₁

#127

yes

characteristic

106

C₂²×D₁₆

C₂×C₃₁

yes

characteristic, complemented

107

C₂×#472

C₂×C₃₁

yes

complemented

108

C₂×#361

C₂×C₃₁

yes

complemented

109

#2113

C₂×C₃₁

yes

characteristic, complemented

110

#1381

C₂×C₃₁

yes

characteristic, complemented

111

C₂²×C₃₁

—

112

C₂²×C₃₁

—

113

C₂²×C₃₁

—

114

C₂²×C₃₁

—

115

C₂²×C₃₁

—

116

C₂²×C₃₁

—

117

C₂²×C₃₁

—

118

C₂²×C₃₁

#449

yes

—

119

C₂²×C₃₁

#466

yes

characteristic

120

C₄×C₃₁

—

121

C₄×C₃₁

#392

yes

characteristic

122

C₄×C₃₁

#447

yes

—

123

C₄×C₃₁

#469

yes

characteristic

124

C₂×AGL(1,ℤ/8)

—

125

C₂²×D₈

C₂²×C₃₁

yes

—

126

C₂×#131

C₂²×C₃₁

yes

characteristic

127

C₂×D₁₆

—

128

C₂×D₁₆

—

129

C₂×M₃₂

C₂²×C₃₁

yes

characteristic

130

C₂²×C₁₆

C₂²×C₃₁

yes

characteristic

131

#472

—

132

#472

—

133

C₂×#108

C₂²×C₃₁

yes

—

134

C₂×#100

—

135

#361

—

136

C₂²⋊C₁₆

—

137

C₂×C₃₁

—

138

C₂×C₃₁

—

139

C₂×C₃₁

—

140

C₂×C₃₁

#1999

yes

characteristic

141

C₂×C₃₁

#2221

yes

—

142

C₂×#41

D₄×C₃₁

yes

characteristic

143

C₂²×D₄

—

144

AGL(1,ℤ/8)

—

145

AGL(1,ℤ/8)

—

146

C₂×SD₁₆

—

147

C₂×D₈

—

148

C₂×D₈

—

149

C₂×D₈

—

150

C₂×D₈

—

151

C₂×D₈

—

152

C₂×D₈

—

153

C₂×D₈

D₄×C₃₁

yes

—

154

#131

—

155

#131

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

C₂×M₁₆

D₄×C₃₁

yes

characteristic

159

C₂²×C₈

—

160

C₂²×C₈

C₂³×C₃₁

yes

characteristic

161

D₁₆

—

162

M₃₂

—

163

C₂×C₁₆

—

164

C₂×C₁₆

—

165

C₂×C₁₆

D₄×C₃₁

yes

—

166

#108

—

167

#108

D₄×C₃₁

yes

—

168

#100

—

169

C₃₁

#13313

yes

characteristic, direct product factor, Sylow

170

C₂⁴

—

171

#41

—

172

#41

—

173

C₂×Q₈

D₈×C₃₁

yes

characteristic

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

D₈×C₃₁

yes

characteristic

182

C₂²×C₄

—

183

C₂²×C₄

C₂×D₄×C₃₁

yes

characteristic

184

SD₁₆

—

185

D₈

—

186

D₈

—

187

D₈

—

188

D₈

—

189

D₈

—

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

C₂×D₄×C₃₁

yes

—

199

C₂×C₈

C₂×D₄×C₃₁

yes

characteristic

200

C₂×C₈

C₂×D₄×C₃₁

yes

—

201

C₂×C₈

#41×C₃₁

yes

characteristic

202

C₁₆

—

203

C₁₆

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

C₃₁×#135

yes

characteristic

210

Q₈

—

211

D₄

—

212

D₄

—

213

D₄

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

C₃₁×#120

yes

—

221

C₂×C₄

C₃₁×#121

yes

characteristic

222

C₂×C₄

C₂×D₈×C₃₁

yes

characteristic

223

C₂×C₄

C₃₁×AGL(1,ℤ/8)

yes

—

224

C₈

—

225

C₈

—

226

C₈

C₃₁×#120

yes

characteristic

227

C₈

C₃₁×#121

yes

—

228

C₈

C₃₁×#127

yes

characteristic

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

C₃₁×#449

yes

—

237

C₂²

C₃₁×#466

yes

characteristic

238

C₄

—

239

C₄

C₃₁×#392

yes

characteristic

240

C₄

C₃₁×#447

yes

—

241

C₄

C₃₁×#469

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

—

245

C₂

C₃₁×#1999

yes

characteristic

246

C₂

C₃₁×#2221

yes

—

	subgroup	G/H
center, socle	C₂²×C₃₁	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₃₁
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ C₂×C₃₁×#131 ◁ G

subgroup

G/H

center, socle

C₂²×C₃₁

#466

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₃₁

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ C₂×C₃₁×#131 ◁ G

N	H ≅ G/N	type
1. C₂²×C₃₁×D₁₆	C₂	semidirect
2. C₂×C₃₁×#472	C₂	semidirect
3. C₂×C₃₁×#361	C₂	semidirect
4. C₃₁×#2113	C₂	semidirect
5. C₃₁×#1381	C₂	semidirect
80. #13313	C₃₁	direct (N × H)
106. C₂²×D₁₆	C₂×C₃₁	semidirect
107. C₂×#472	C₂×C₃₁	semidirect
108. C₂×#361	C₂×C₃₁	semidirect
109. #2113	C₂×C₃₁	semidirect
110. #1381	C₂×C₃₁	semidirect
169. C₃₁	#13313	direct (N × H)

H ≅ G/N

type

1. C₂²×C₃₁×D₁₆

C₂

semidirect

2. C₂×C₃₁×#472

C₂

semidirect

3. C₂×C₃₁×#361

C₂

semidirect

4. C₃₁×#2113

C₂

semidirect

5. C₃₁×#1381

C₂

semidirect

80. #13313

C₃₁

direct (N × H)

106. C₂²×D₁₆

C₂×C₃₁

semidirect

107. C₂×#472

C₂×C₃₁

semidirect

108. C₂×#361

C₂×C₃₁

semidirect

109. #2113

C₂×C₃₁

semidirect

110. #1381

C₂×C₃₁

semidirect

169. C₃₁

#13313

direct (N × H)

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

subgroup	index
C₂²×C₃₁×D₁₆	2
C₂×C₃₁×#472	2
C₂×C₃₁×#361	2
C₃₁×#2113	2
C₃₁×#1381	2
#13313	31

subgroup

index

C₂²×C₃₁×D₁₆

C₂×C₃₁×#472

C₂×C₃₁×#361

C₃₁×#2113

C₃₁×#1381

#13313

Subgroups — C₃₁×#13313 #21470072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C31×#13313 #21470072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#13313 #21470072