Subgroups — C₂×C₃₁×#529 #16843372

Order 3968.

1232 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#529	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃₁×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#123	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#117	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
15	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#126	C₂²	1	16	yes	complemented
21	C₃₁×#125	C₂²	1	8	yes	complemented
22	C₃₁×#124	C₂²	1	8	yes	complemented
23	C₃₁×#123	C₂²	1	16	yes	complemented
24	C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	complemented
25	C₃₁×#121	C₂²	1	8	yes	—
26	C₄×Q₈×C₃₁	C₂²	1	8	yes	complemented
27	C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
28	C₄×D₄×C₃₁	C₂²	1	16	yes	complemented
29	C₃₁×#117	C₂²	1	16	yes	complemented
30	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
38	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
39	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
41	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
46	C₂×C₄²×C₃₁	C₂²	1	8	yes	complemented
47	C₂⁴×C₃₁	C₂³	1	2	yes	—
48	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
49	C₂×Q₈×C₃₁	—	2	4	no	—
50	C₂×Q₈×C₃₁	C₂³	1	4	yes	—
51	C₂×D₄×C₃₁	—	2	8	no	—
52	C₂×D₄×C₃₁	—	2	4	no	—
53	C₂×D₄×C₃₁	C₂³	1	8	yes	—
54	C₂×D₄×C₃₁	C₂³	1	4	yes	—
55	C₂²×C₄×C₃₁	—	2	4	no	—
56	C₂²×C₄×C₃₁	—	2	4	no	—
57	C₂²×C₄×C₃₁	—	2	8	no	—
58	C₂²×C₄×C₃₁	—	2	4	no	—
59	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
64	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
65	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
66	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
67	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
68	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
69	C₂²×C₄×C₃₁	C₂³	1	8	yes	—
70	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
72	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
73	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
74	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
75	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
76	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
77	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
78	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
79	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
80	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
81	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
82	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
83	C₄²×C₃₁	C₂³	1	4	yes	—
84	C₄²×C₃₁	C₂³	1	4	yes	—
85	C₄²×C₃₁	C₂³	1	4	yes	—
86	C₄²×C₃₁	C₂³	1	4	yes	—
87	C₄²×C₃₁	C₂³	1	8	yes	—
88	C₂³×C₃₁	—	2	2	no	—
89	C₂³×C₃₁	—	2	2	no	—
90	C₂³×C₃₁	—	2	4	no	—
91	C₂³×C₃₁	—	2	4	no	—
92	C₂³×C₃₁	—	2	4	no	—
93	C₂³×C₃₁	#41	1	4	yes	—
94	C₂³×C₃₁	C₂⁴	1	4	yes	—
95	C₂³×C₃₁	C₂⁴	1	2	yes	—
96	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
97	Q₈×C₃₁	—	2	8	no	—
98	D₄×C₃₁	—	2	16	no	—
99	D₄×C₃₁	—	2	8	no	—
100	C₂×C₄×C₃₁	—	2	8	no	—
101	C₂×C₄×C₃₁	—	2	2	no	—
102	C₂×C₄×C₃₁	—	2	2	no	—
103	C₂×C₄×C₃₁	—	2	2	no	—
104	C₂×C₄×C₃₁	—	2	2	no	—
105	C₂×C₄×C₃₁	—	2	4	no	—
106	C₂×C₄×C₃₁	—	2	4	no	—
107	C₂×C₄×C₃₁	—	2	4	no	—
108	C₂×C₄×C₃₁	—	2	8	no	—
109	C₂×C₄×C₃₁	—	2	16	no	—
110	C₂×C₄×C₃₁	—	2	8	no	—
111	C₂×C₄×C₃₁	#41	1	4	yes	—
112	C₂×C₄×C₃₁	#41	1	4	yes	—
113	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
114	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
115	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
116	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
117	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
118	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
119	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
120	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
121	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
122	C₂×#529	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂²×C₃₁	—	2	8	no	—
124	C₂²×C₃₁	—	2	2	no	—
125	C₂²×C₃₁	—	2	2	no	—
126	C₂²×C₃₁	—	2	4	no	—
127	C₂²×C₃₁	—	2	4	no	—
128	C₂²×C₃₁	—	2	4	no	—
129	C₂²×C₃₁	—	4	8	no	—
130	C₂²×C₃₁	C₂×#41	1	4	yes	—
131	C₂²×C₃₁	C₂×#41	1	2	yes	—
132	C₂²×C₃₁	C₂×#41	1	2	yes	—
133	C₂²×C₃₁	C₂×#41	1	2	yes	—
134	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
135	C₄×C₃₁	—	2	2	no	—
136	C₄×C₃₁	—	2	2	no	—
137	C₄×C₃₁	—	2	2	no	—
138	C₄×C₃₁	—	2	2	no	—
139	C₄×C₃₁	—	2	4	no	—
140	C₄×C₃₁	—	2	4	no	—
141	C₄×C₃₁	—	2	4	no	—
142	C₄×C₃₁	C₂×#41	1	4	yes	—
143	C₄×C₃₁	C₂×#41	1	4	yes	—
144	#529	C₂×C₃₁	1	16	yes	direct product factor
145	C₂×#126	C₂×C₃₁	1	2	yes	complemented
146	C₂×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
147	C₂×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
148	C₂×#123	C₂×C₃₁	1	2	yes	complemented
149	C₂×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
150	C₂×#121	C₂×C₃₁	1	1	yes	characteristic
151	C₂×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
152	C₂×C₄×D₄	C₂×C₃₁	1	2	yes	complemented
153	C₂×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
154	C₂×#117	C₂×C₃₁	1	2	yes	complemented
155	C₂²×C₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
156	C₂×C₃₁	—	2	4	no	—
157	C₂×C₃₁	—	4	4	no	—
158	C₂×C₃₁	#529	1	4	yes	direct product factor
159	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
160	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
161	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
162	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic
163	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
164	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
165	C₂³×C₄	C₂²×C₃₁	1	2	yes	—
166	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
167	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
168	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
169	#126	C₂²×C₃₁	1	16	yes	complemented
170	#125	C₂²×C₃₁	1	8	yes	complemented
171	#124	C₂²×C₃₁	1	8	yes	complemented
172	#123	C₂²×C₃₁	1	16	yes	complemented
173	C₂²⋊Q₈	C₂²×C₃₁	1	8	yes	complemented
174	#121	C₂²×C₃₁	1	8	yes	—
175	C₄×Q₈	C₂²×C₃₁	1	8	yes	complemented
176	C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
177	C₄×D₄	C₂²×C₃₁	1	16	yes	complemented
178	#117	C₂²×C₃₁	1	16	yes	complemented
179	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
180	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
181	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
182	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
183	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
186	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
190	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
191	C₂×C₄²	C₂²×C₃₁	1	2	yes	—
192	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₃₁	1	8	yes	complemented
196	C₃₁	C₂×#529	1	1	yes	characteristic, direct product factor, Sylow
197	C₂⁴	C₂³×C₃₁	1	2	yes	—
198	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
199	C₂×Q₈	—	2	4	no	—
200	C₂×Q₈	C₂³×C₃₁	1	4	yes	—
201	C₂×D₄	—	2	8	no	—
202	C₂×D₄	—	2	4	no	—
203	C₂×D₄	C₂³×C₃₁	1	8	yes	—
204	C₂×D₄	C₂³×C₃₁	1	4	yes	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	2	4	no	—
207	C₂²×C₄	—	2	8	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
210	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
211	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
213	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
214	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
215	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
216	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
217	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
218	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
219	C₂²×C₄	C₂³×C₃₁	1	8	yes	—
220	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
221	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
222	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
223	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
224	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
225	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
226	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
227	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
228	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
229	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
230	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
231	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
232	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
233	C₄²	C₂³×C₃₁	1	4	yes	—
234	C₄²	C₂³×C₃₁	1	4	yes	—
235	C₄²	C₂³×C₃₁	1	4	yes	—
236	C₄²	C₂³×C₃₁	1	4	yes	—
237	C₄²	C₂³×C₃₁	1	8	yes	—
238	C₂³	—	2	2	no	—
239	C₂³	—	2	2	no	—
240	C₂³	—	2	4	no	—
241	C₂³	—	2	4	no	—
242	C₂³	—	2	4	no	—
243	C₂³	#41×C₃₁	1	4	yes	—
244	C₂³	C₂⁴×C₃₁	1	4	yes	—
245	C₂³	C₂⁴×C₃₁	1	2	yes	—
246	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
247	Q₈	—	2	8	no	—
248	D₄	—	2	16	no	—
249	D₄	—	2	8	no	—
250	C₂×C₄	—	2	8	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	2	8	no	—
259	C₂×C₄	—	2	16	no	—
260	C₂×C₄	—	2	8	no	—
261	C₂×C₄	#41×C₃₁	1	4	yes	—
262	C₂×C₄	#41×C₃₁	1	4	yes	—
263	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
264	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
265	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
266	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
267	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
268	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
269	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
270	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
271	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
272	C₂²	—	2	8	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	4	no	—
276	C₂²	—	2	4	no	—
277	C₂²	—	2	4	no	—
278	C₂²	—	4	8	no	—
279	C₂²	C₂×#41×C₃₁	1	4	yes	—
280	C₂²	C₂×#41×C₃₁	1	2	yes	—
281	C₂²	C₂×#41×C₃₁	1	2	yes	—
282	C₂²	C₂×#41×C₃₁	1	2	yes	—
283	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
284	C₄	—	2	2	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	2	no	—
287	C₄	—	2	2	no	—
288	C₄	—	2	4	no	—
289	C₄	—	2	4	no	—
290	C₄	—	2	4	no	—
291	C₄	C₂×#41×C₃₁	1	4	yes	—
292	C₄	C₂×#41×C₃₁	1	4	yes	—
293	C₂	—	2	4	no	—
294	C₂	—	4	4	no	—
295	C₂	C₃₁×#529	1	4	yes	direct product factor
296	C₂	C₂²×#41×C₃₁	1	1	yes	characteristic
297	C₂	C₂²×#41×C₃₁	1	1	yes	characteristic
298	C₂	C₂²×#41×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁴
prime radical	C₂×C₃₁×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁×#529	C₂	direct (N × H)
2. C₂×C₃₁×#126	C₂	semidirect
3. C₂×C₃₁×#125	C₂	semidirect
4. C₂×C₃₁×#124	C₂	semidirect
5. C₂×C₃₁×#123	C₂	semidirect
6. C₂×C₃₁×C₂²⋊Q₈	C₂	semidirect
8. C₂×C₄×Q₈×C₃₁	C₂	semidirect
9. C₂×C₄×D₄×C₃₁	C₂	semidirect
10. C₂×C₄×D₄×C₃₁	C₂	semidirect
11. C₂×C₃₁×#117	C₂	semidirect
12. C₂²×C₄²×C₃₁	C₂	semidirect
20. C₃₁×#126	C₂²	semidirect
21. C₃₁×#125	C₂²	semidirect
22. C₃₁×#124	C₂²	semidirect
23. C₃₁×#123	C₂²	semidirect
24. C₃₁×C₂²⋊Q₈	C₂²	semidirect
26. C₄×Q₈×C₃₁	C₂²	semidirect
27. C₄×D₄×C₃₁	C₂²	semidirect
28. C₄×D₄×C₃₁	C₂²	semidirect
29. C₃₁×#117	C₂²	semidirect
46. C₂×C₄²×C₃₁	C₂²	semidirect
122. C₂×#529	C₃₁	direct (N × H)
144. #529	C₂×C₃₁	direct (N × H)
145. C₂×#126	C₂×C₃₁	semidirect
146. C₂×#125	C₂×C₃₁	semidirect
147. C₂×#124	C₂×C₃₁	semidirect
148. C₂×#123	C₂×C₃₁	semidirect
149. C₂×C₂²⋊Q₈	C₂×C₃₁	semidirect
151. C₂×C₄×Q₈	C₂×C₃₁	semidirect
152. C₂×C₄×D₄	C₂×C₃₁	semidirect
153. C₂×C₄×D₄	C₂×C₃₁	semidirect
154. C₂×#117	C₂×C₃₁	semidirect
155. C₂²×C₄²	C₂×C₃₁	semidirect
158. C₂×C₃₁	#529	direct (N × H)
169. #126	C₂²×C₃₁	semidirect
170. #125	C₂²×C₃₁	semidirect
171. #124	C₂²×C₃₁	semidirect
172. #123	C₂²×C₃₁	semidirect
173. C₂²⋊Q₈	C₂²×C₃₁	semidirect
175. C₄×Q₈	C₂²×C₃₁	semidirect
176. C₄×D₄	C₂²×C₃₁	semidirect
177. C₄×D₄	C₂²×C₃₁	semidirect
178. #117	C₂²×C₃₁	semidirect
195. C₂×C₄²	C₂²×C₃₁	semidirect
196. C₃₁	C₂×#529	direct (N × H)
295. C₂	C₃₁×#529	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#529	2
C₂×C₃₁×#126	2
C₂×C₃₁×#125	2
C₂×C₃₁×#124	2
C₂×C₃₁×#123	2
C₂×C₃₁×C₂²⋊Q₈	2
C₂×C₃₁×#121	2
C₂×C₄×Q₈×C₃₁	2
C₂×C₄×D₄×C₃₁	2
C₂×C₃₁×#117	2
C₂²×C₄²×C₃₁	2
C₂×#529	31

Subgroups — C2×C31×#529 #16843372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#529 #16843372