Group #21467068 — subgroups

Subgroups — C₃₁×#10309 #21467068

Order 7936.

618 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 186 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×C₃₁×#500	C₂	1	2	yes	maximal
2	C₂×C₃₁×#494	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1990	C₂	1	2	yes	maximal
4	C₃₁×#1956	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₃₁	—	2	2	no	—
7	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₃₁×#500	—	2	4	no	—
10	C₃₁×#500	—	2	4	no	—
11	C₃₁×#494	—	2	4	no	—
12	C₂×C₃₁×#107	—	2	4	no	—
13	C₂×C₃₁×#103	—	2	2	no	—
14	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
16	C₃₁×#384	C₂²	1	1	yes	characteristic
17	C₃₁×#340	—	2	4	no	—
18	C₂²×Q₈×C₃₁	—	2	1	no	—
19	C₂²×Q₈×C₃₁	—	2	2	no	—
20	C₂×Q₁₆×C₃₁	—	2	8	no	—
21	C₂×Q₁₆×C₃₁	—	4	4	no	—
22	C₂×Q₁₆×C₃₁	—	4	4	no	—
23	C₂²×C₈×C₃₁	D₄	1	2	yes	—
24	C₂²×C₈×C₃₁	D₄	1	4	yes	—
25	C₃₁×C₄⋊Q₈	—	2	2	no	—
26	C₃₁×C₄⋊Q₈	—	2	2	no	—
27	C₃₁×C₄⋊Q₈	—	2	2	no	—
28	C₃₁×C₄⋊Q₈	—	2	2	no	—
29	C₃₁×C₄⋊Q₈	—	2	1	no	—
30	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
31	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
36	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
37	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
38	C₃₁×#107	—	2	16	no	—
39	C₃₁×#103	—	4	4	no	—
40	C₄×C₈×C₃₁	—	2	2	no	—
41	C₄×C₈×C₃₁	—	2	2	no	—
42	C₄×C₈×C₃₁	—	2	2	no	—
43	C₂×Q₈×C₃₁	—	2	4	no	—
44	C₂×Q₈×C₃₁	—	2	2	no	—
45	C₂×Q₈×C₃₁	—	4	1	no	—
46	C₂×Q₈×C₃₁	—	4	2	no	—
47	C₂×Q₈×C₃₁	—	4	2	no	—
48	C₂×Q₈×C₃₁	—	4	4	no	—
49	C₂×Q₈×C₃₁	—	4	4	no	—
50	C₂×Q₈×C₃₁	—	4	2	no	—
51	C₂²×C₄×C₃₁	—	4	1	no	—
52	C₂²×C₄×C₃₁	—	4	2	no	—
53	C₂²×C₄×C₃₁	—	4	1	no	—
54	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
56	Q₁₆×C₃₁	—	4	16	no	—
57	C₂×C₈×C₃₁	—	2	4	no	—
58	C₂×C₈×C₃₁	—	2	2	no	—
59	C₂×C₈×C₃₁	—	2	2	no	—
60	C₂×C₈×C₃₁	—	2	4	no	—
61	C₂×C₈×C₃₁	D₈	1	4	yes	—
62	C₂×C₈×C₃₁	Q₁₆	1	8	yes	complemented
63	C₄⋊C₄×C₃₁	—	2	4	no	—
64	C₄⋊C₄×C₃₁	—	2	4	no	—
65	C₄⋊C₄×C₃₁	—	2	4	no	—
66	C₄⋊C₄×C₃₁	—	4	2	no	—
67	C₄⋊C₄×C₃₁	—	4	2	no	—
68	C₄⋊C₄×C₃₁	—	4	2	no	—
69	C₄⋊C₄×C₃₁	—	4	2	no	—
70	C₄⋊C₄×C₃₁	—	4	4	no	—
71	C₄²×C₃₁	C₂×D₄	1	2	yes	—
72	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₃₁	#41	1	1	yes	characteristic
74	#10309	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂³×C₃₁	#127	1	1	yes	characteristic
76	Q₈×C₃₁	—	4	8	no	—
77	Q₈×C₃₁	—	4	4	no	—
78	Q₈×C₃₁	—	8	2	no	—
79	Q₈×C₃₁	—	8	4	no	—
80	C₂×C₄×C₃₁	—	4	2	no	—
81	C₂×C₄×C₃₁	—	4	4	no	—
82	C₂×C₄×C₃₁	—	8	1	no	—
83	C₂×C₄×C₃₁	—	8	2	no	—
84	C₂×C₄×C₃₁	—	8	2	no	—
85	C₂×C₄×C₃₁	—	8	1	no	—
86	C₂×C₄×C₃₁	—	8	1	no	—
87	C₂×C₄×C₃₁	—	8	2	no	—
88	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
89	C₂×C₄×C₃₁	#120	1	2	yes	—
90	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
91	C₂×C₄×C₃₁	#121	1	2	yes	—
92	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
94	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
95	C₂×C₄×C₃₁	#137	1	4	yes	—
96	C₈×C₃₁	—	2	4	no	—
97	C₈×C₃₁	—	2	8	no	—
98	C₂×#500	C₂×C₃₁	1	2	yes	—
99	C₂×#494	C₂×C₃₁	1	1	yes	characteristic
100	#1990	C₂×C₃₁	1	2	yes	—
101	#1956	C₂×C₃₁	1	1	yes	characteristic
102	#1273	C₂×C₃₁	1	1	yes	characteristic
103	C₂²×C₃₁	#392	1	1	yes	characteristic
104	C₂²×C₃₁	#493	1	1	yes	characteristic
105	C₂²×C₃₁	#494	1	2	yes	—
106	C₂²×C₃₁	#496	1	1	yes	characteristic
107	C₂²×C₃₁	#497	1	2	yes	—
108	C₄×C₃₁	—	8	4	no	—
109	C₄×C₃₁	—	8	2	no	—
110	C₄×C₃₁	—	16	1	no	—
111	C₄×C₃₁	#447	1	2	yes	—
112	C₄×C₃₁	#451	1	4	yes	—
113	C₄×C₃₁	#459	1	2	yes	—
114	C₄×C₃₁	#462	1	4	yes	—
115	C₂²×Q₁₆	—	2	2	no	—
116	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
117	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
118	#500	—	2	4	no	—
119	#500	—	2	4	no	—
120	#494	—	2	4	no	—
121	C₂×#107	—	2	4	no	—
122	C₂×#103	—	2	2	no	—
123	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
125	#384	C₂²×C₃₁	1	1	yes	characteristic
126	#340	—	2	4	no	—
127	C₂×C₃₁	#1713	1	1	yes	characteristic
128	C₂×C₃₁	#1722	1	1	yes	characteristic
129	C₂×C₃₁	#1723	1	2	yes	—
130	C₂×C₃₁	#2011	1	1	yes	characteristic
131	C₂×C₃₁	#2016	1	2	yes	—
132	C₂²×Q₈	—	2	2	no	—
133	C₂²×Q₈	—	2	1	no	—
134	C₂×Q₁₆	—	2	8	no	—
135	C₂×Q₁₆	—	4	4	no	—
136	C₂×Q₁₆	—	4	4	no	—
137	C₂²×C₈	D₄×C₃₁	1	2	yes	—
138	C₂²×C₈	D₄×C₃₁	1	4	yes	—
139	C₄⋊Q₈	—	2	2	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
145	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
146	C₂×C₄⋊C₄	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
152	#107	—	2	16	no	—
153	#103	—	4	4	no	—
154	C₄×C₈	—	2	2	no	—
155	C₄×C₈	—	2	2	no	—
156	C₄×C₈	—	2	2	no	—
157	C₃₁	#10309	1	1	yes	characteristic, direct product factor, Sylow
158	C₂×Q₈	—	2	4	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	1	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	—	4	1	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
170	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
171	Q₁₆	—	4	16	no	—
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	D₈×C₃₁	1	4	yes	—
177	C₂×C₈	Q₁₆×C₃₁	1	8	yes	complemented
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	4	no	—
186	C₄²	C₂×D₄×C₃₁	1	2	yes	—
187	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
188	C₄²	#41×C₃₁	1	1	yes	characteristic
189	C₂³	C₃₁×#127	1	1	yes	characteristic
190	Q₈	—	4	8	no	—
191	Q₈	—	4	4	no	—
192	Q₈	—	8	2	no	—
193	Q₈	—	8	4	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	8	2	no	—
199	C₂×C₄	—	8	1	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	—	8	2	no	—
202	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
203	C₂×C₄	C₃₁×#120	1	2	yes	—
204	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
205	C₂×C₄	C₃₁×#121	1	2	yes	—
206	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
207	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
208	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
209	C₂×C₄	C₃₁×#137	1	4	yes	—
210	C₈	—	2	4	no	—
211	C₈	—	2	8	no	—
212	C₂²	C₃₁×#392	1	1	yes	characteristic
213	C₂²	C₃₁×#493	1	1	yes	characteristic
214	C₂²	C₃₁×#494	1	2	yes	—
215	C₂²	C₃₁×#496	1	1	yes	characteristic
216	C₂²	C₃₁×#497	1	2	yes	—
217	C₄	—	8	4	no	—
218	C₄	—	8	2	no	—
219	C₄	—	16	1	no	—
220	C₄	C₃₁×#447	1	2	yes	—
221	C₄	C₃₁×#451	1	4	yes	—
222	C₄	C₃₁×#459	1	2	yes	—
223	C₄	C₃₁×#462	1	4	yes	—
224	C₂	C₃₁×#1713	1	1	yes	characteristic
225	C₂	C₃₁×#1722	1	1	yes	characteristic
226	C₂	C₃₁×#1723	1	2	yes	—
227	C₂	C₃₁×#2011	1	1	yes	characteristic
228	C₂	C₃₁×#2016	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃₁×#500

C₂

yes

maximal

C₂×C₃₁×#494

C₂

yes

maximal, characteristic

C₃₁×#1990

C₂

yes

maximal

C₃₁×#1956

C₂

yes

maximal, characteristic

C₃₁×#1273

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₃₁

—

C₂×C₃₁×C₄⋊Q₈

C₂²

yes

—

C₂×C₃₁×C₄⋊Q₈

C₂²

yes

characteristic

C₃₁×#500

—

C₃₁×#500

—

C₃₁×#494

—

C₂×C₃₁×#107

—

C₂×C₃₁×#103

—

C₂×C₄×C₈×C₃₁

C₂²

yes

characteristic

C₂×C₄×C₈×C₃₁

C₂²

yes

—

C₃₁×#384

C₂²

yes

characteristic

C₃₁×#340

—

C₂²×Q₈×C₃₁

—

C₂²×Q₈×C₃₁

—

C₂×Q₁₆×C₃₁

—

C₂×Q₁₆×C₃₁

—

C₂×Q₁₆×C₃₁

—

C₂²×C₈×C₃₁

D₄

yes

—

C₂²×C₈×C₃₁

D₄

yes

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

D₄

yes

—

C₃₁×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄²×C₃₁

C₂³

yes

characteristic

C₃₁×#107

—

C₃₁×#103

—

C₄×C₈×C₃₁

—

C₄×C₈×C₃₁

—

C₄×C₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₃₁

C₂×D₄

yes

—

Q₁₆×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

D₈

yes

—

C₂×C₈×C₃₁

Q₁₆

yes

complemented

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

C₂×D₄

yes

—

C₄²×C₃₁

C₂×D₄

yes

C₄²×C₃₁

yes

C₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₃₁

#127

yes

characteristic

Q₈×C₃₁

—

Q₈×C₃₁

—

Q₈×C₃₁

—

Q₈×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

#120

yes

characteristic

C₂×C₄×C₃₁

#120

yes

—

C₂×C₄×C₃₁

#121

yes

characteristic

C₂×C₄×C₃₁

#121

yes

—

C₂×C₄×C₃₁

C₂×D₈

yes

—

C₂×C₄×C₃₁

C₂×Q₁₆

yes

—

C₂×C₄×C₃₁

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₃₁

#137

yes

—

C₈×C₃₁

—

C₈×C₃₁

—

C₂×#500

C₂×C₃₁

yes

—

C₂×#494

C₂×C₃₁

yes

characteristic

100

#1990

C₂×C₃₁

yes

—

101

#1956

C₂×C₃₁

yes

characteristic

102

#1273

C₂×C₃₁

yes

characteristic

103

C₂²×C₃₁

#392

yes

characteristic

104

C₂²×C₃₁

#493

yes

characteristic

105

C₂²×C₃₁

#494

yes

—

106

C₂²×C₃₁

#496

yes

characteristic

107

C₂²×C₃₁

#497

yes

—

108

C₄×C₃₁

—

109

C₄×C₃₁

—

110

C₄×C₃₁

—

111

C₄×C₃₁

#447

yes

—

112

C₄×C₃₁

#451

yes

—

113

C₄×C₃₁

#459

yes

—

114

C₄×C₃₁

#462

yes

—

115

C₂²×Q₁₆

—

116

C₂×C₄⋊Q₈

C₂²×C₃₁

yes

—

117

C₂×C₄⋊Q₈

C₂²×C₃₁

yes

characteristic

118

#500

—

119

#500

—

120

#494

—

121

C₂×#107

—

122

C₂×#103

—

123

C₂×C₄×C₈

C₂²×C₃₁

yes

characteristic

124

C₂×C₄×C₈

C₂²×C₃₁

yes

—

125

#384

C₂²×C₃₁

yes

characteristic

126

#340

—

127

C₂×C₃₁

#1713

yes

characteristic

128

C₂×C₃₁

#1722

yes

characteristic

129

C₂×C₃₁

#1723

yes

—

130

C₂×C₃₁

#2011

yes

characteristic

131

C₂×C₃₁

#2016

yes

—

132

C₂²×Q₈

—

133

C₂²×Q₈

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

137

C₂²×C₈

D₄×C₃₁

yes

—

138

C₂²×C₈

D₄×C₃₁

yes

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

D₄×C₃₁

yes

—

145

C₄⋊Q₈

D₄×C₃₁

yes

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄²

C₂³×C₃₁

yes

characteristic

152

#107

—

153

#103

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₃₁

#10309

yes

characteristic, direct product factor, Sylow

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂×D₄×C₃₁

yes

characteristic

170

C₂²×C₄

C₂×D₄×C₃₁

yes

—

171

Q₁₆

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

D₈×C₃₁

yes

—

177

C₂×C₈

Q₁₆×C₃₁

yes

complemented

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄²

C₂×D₄×C₃₁

yes

—

187

C₄²

C₂×D₄×C₃₁

yes

characteristic

188

C₄²

#41×C₃₁

yes

characteristic

189

C₂³

C₃₁×#127

yes

characteristic

190

Q₈

—

191

Q₈

—

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

C₃₁×#120

yes

characteristic

203

C₂×C₄

C₃₁×#120

yes

—

204

C₂×C₄

C₃₁×#121

yes

characteristic

205

C₂×C₄

C₃₁×#121

yes

—

206

C₂×C₄

C₂×D₈×C₃₁

yes

—

207

C₂×C₄

C₂×Q₁₆×C₃₁

yes

—

208

C₂×C₄

C₃₁×AGL(1,ℤ/8)

yes

—

209

C₂×C₄

C₃₁×#137

yes

—

210

C₈

—

211

C₈

—

212

C₂²

C₃₁×#392

yes

characteristic

213

C₂²

C₃₁×#493

yes

characteristic

214

C₂²

C₃₁×#494

yes

—

215

C₂²

C₃₁×#496

yes

characteristic

216

C₂²

C₃₁×#497

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₃₁×#447

yes

—

221

C₄

C₃₁×#451

yes

—

222

C₄

C₃₁×#459

yes

—

223

C₄

C₃₁×#462

yes

—

224

C₂

C₃₁×#1713

yes

characteristic

225

C₂

C₃₁×#1722

yes

characteristic

226

C₂

C₃₁×#1723

yes

—

227

C₂

C₃₁×#2011

yes

characteristic

228

C₂

C₃₁×#2016

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₃₁

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₃₁

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

N	H ≅ G/N	type
62. C₂×C₈×C₃₁	Q₁₆	semidirect
74. #10309	C₃₁	direct (N × H)
157. C₃₁	#10309	direct (N × H)
177. C₂×C₈	Q₁₆×C₃₁	semidirect

H ≅ G/N

type

62. C₂×C₈×C₃₁

Q₁₆

semidirect

74. #10309

C₃₁

direct (N × H)

157. C₃₁

#10309

direct (N × H)

177. C₂×C₈

Q₁₆×C₃₁

semidirect

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

subgroup	index
C₂×C₃₁×#500	2
C₂×C₃₁×#494	2
C₃₁×#1990	2
C₃₁×#1956	2
C₃₁×#1273	2
#10309	31

subgroup

index

C₂×C₃₁×#500

C₂×C₃₁×#494

C₃₁×#1990

C₃₁×#1956

C₃₁×#1273

#10309

Subgroups — C₃₁×#10309 #21467068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C31×#10309 #21467068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10309 #21467068