Subgroups — C₂×C₃₁×#1972 #21477985

Order 7936.

2006 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#102	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#390	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1972	C₂	1	8	yes	maximal, direct product factor
7	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
8	C₂²×D₈×C₃₁	—	2	4	no	—
9	C₂²×D₈×C₃₁	—	2	4	no	—
10	C₂²×D₈×C₃₁	C₄	1	8	yes	complemented
11	C₂²×D₈×C₃₁	C₂²	1	4	yes	—
12	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₃₁	—	2	4	no	—
16	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#106	—	2	4	no	—
18	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
19	C₂×C₃₁×#102	—	2	8	no	—
20	C₂×C₃₁×#102	C₂²	1	8	yes	complemented
21	C₂×C₃₁×#97	—	2	4	no	—
22	C₂×C₃₁×#97	C₂²	1	4	yes	complemented
23	C₃₁×#390	—	2	4	no	—
24	C₃₁×#390	C₂²	1	8	yes	complemented
25	C₂⁵×C₃₁	—	2	2	no	—
26	C₂²×D₄×C₃₁	—	2	4	no	—
27	C₂²×D₄×C₃₁	—	2	4	no	—
28	C₂²×D₄×C₃₁	—	2	4	no	—
29	C₂²×D₄×C₃₁	—	2	2	no	—
30	C₂²×D₄×C₃₁	—	2	4	no	—
31	C₂²×D₄×C₃₁	—	2	4	no	—
32	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	—
33	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
34	C₂³×C₄×C₃₁	—	2	2	no	—
35	C₂³×C₄×C₃₁	D₄	1	2	yes	—
36	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
37	C₂×D₈×C₃₁	—	2	32	no	—
38	C₂×D₈×C₃₁	—	2	8	no	—
39	C₂×D₈×C₃₁	—	2	8	no	—
40	C₂×D₈×C₃₁	C₂×C₄	1	16	yes	complemented
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	—	2	2	no	—
43	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₃₁	D₄	1	4	yes	—
45	C₂²×C₈×C₃₁	D₄	1	4	yes	—
46	C₂²×C₈×C₃₁	D₄	1	4	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
53	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
54	C₂×C₂²⋊C₄×C₃₁	—	4	16	no	—
55	C₂×C₄²×C₃₁	—	2	2	no	—
56	C₂×C₄²×C₃₁	—	2	2	no	—
57	C₂×C₄²×C₃₁	D₄	1	2	yes	—
58	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
59	C₃₁×#106	—	2	8	no	—
60	C₃₁×#102	—	2	16	no	—
61	C₃₁×#97	—	2	8	no	—
62	C₂⁴×C₃₁	—	2	8	no	—
63	C₂⁴×C₃₁	—	2	4	no	—
64	C₂⁴×C₃₁	—	4	4	no	—
65	C₂⁴×C₃₁	—	4	4	no	—
66	C₂⁴×C₃₁	—	4	8	no	—
67	C₂⁴×C₃₁	—	4	8	no	—
68	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₃₁	—	2	16	no	—
70	C₂×D₄×C₃₁	—	2	16	no	—
71	C₂×D₄×C₃₁	—	2	8	no	—
72	C₂×D₄×C₃₁	—	2	4	no	—
73	C₂×D₄×C₃₁	—	2	4	no	—
74	C₂×D₄×C₃₁	—	2	4	no	—
75	C₂×D₄×C₃₁	—	2	4	no	—
76	C₂×D₄×C₃₁	—	2	4	no	—
77	C₂×D₄×C₃₁	—	4	8	no	—
78	C₂×D₄×C₃₁	—	4	4	no	—
79	C₂×D₄×C₃₁	—	4	8	no	—
80	C₂×D₄×C₃₁	—	4	4	no	—
81	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
82	C₂²×C₄×C₃₁	—	2	4	no	—
83	C₂²×C₄×C₃₁	—	2	8	no	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	4	4	no	—
86	C₂²×C₄×C₃₁	—	4	8	no	—
87	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₃₁	#41	1	2	yes	—
94	C₂²×C₄×C₃₁	#41	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
96	D₈×C₃₁	—	2	32	no	—
97	C₂×C₈×C₃₁	—	2	8	no	—
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	C₂²⋊C₄	1	16	yes	complemented
101	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
103	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	4	no	—
107	C₄⋊C₄×C₃₁	—	4	4	no	—
108	C₂²⋊C₄×C₃₁	—	4	32	no	—
109	C₄²×C₃₁	—	2	4	no	—
110	C₄²×C₃₁	—	2	2	no	—
111	C₄²×C₃₁	—	2	2	no	—
112	C₂×#1972	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₃₁	—	2	8	no	—
114	C₂³×C₃₁	—	4	4	no	—
115	C₂³×C₃₁	—	4	4	no	—
116	C₂³×C₃₁	—	4	8	no	—
117	C₂³×C₃₁	—	4	8	no	—
118	C₂³×C₃₁	—	4	16	no	—
119	C₂³×C₃₁	—	4	32	no	—
120	C₂³×C₃₁	—	8	16	no	—
121	C₂³×C₃₁	—	8	8	no	—
122	C₂³×C₃₁	—	8	8	no	—
123	C₂³×C₃₁	C₄×D₄	1	2	yes	—
124	C₂³×C₃₁	#121	1	2	yes	—
125	C₂³×C₃₁	#127	1	2	yes	—
126	C₂³×C₃₁	AGL(1,ℤ/8)	1	8	yes	—
127	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
128	D₄×C₃₁	—	2	8	no	—
129	D₄×C₃₁	—	2	8	no	—
130	D₄×C₃₁	—	4	4	no	—
131	D₄×C₃₁	—	4	4	no	—
132	D₄×C₃₁	—	4	16	no	—
133	C₂×C₄×C₃₁	—	2	4	no	—
134	C₂×C₄×C₃₁	—	2	8	no	—
135	C₂×C₄×C₃₁	—	4	8	no	—
136	C₂×C₄×C₃₁	—	4	4	no	—
137	C₂×C₄×C₃₁	—	4	8	no	—
138	C₂×C₄×C₃₁	—	8	8	no	—
139	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
140	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
141	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₃₁	#121	1	4	yes	—
143	C₂×C₄×C₃₁	#121	1	2	yes	—
144	C₂×C₄×C₃₁	#124	1	4	yes	—
145	C₂×C₄×C₃₁	#127	1	2	yes	—
146	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
152	C₈×C₃₁	—	2	4	no	—
153	C₈×C₃₁	C₂×C₂²⋊C₄	1	8	yes	complemented
154	C₂³×D₈	C₂×C₃₁	1	1	yes	characteristic
155	C₂²×#106	C₂×C₃₁	1	1	yes	characteristic, complemented
156	C₂²×#102	C₂×C₃₁	1	2	yes	complemented
157	C₂²×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
158	C₂×#390	C₂×C₃₁	1	2	yes	complemented
159	#1972	C₂×C₃₁	1	8	yes	direct product factor
160	C₂²×C₃₁	—	4	16	no	—
161	C₂²×C₃₁	—	4	8	no	—
162	C₂²×C₃₁	—	8	4	no	—
163	C₂²×C₃₁	—	8	4	no	—
164	C₂²×C₃₁	—	8	32	no	—
165	C₂²×C₃₁	—	8	8	no	—
166	C₂²×C₃₁	#390	1	4	yes	—
167	C₂²×C₃₁	#442	1	8	yes	—
168	C₂²×C₃₁	#469	1	8	yes	—
169	C₂²×C₃₁	#496	1	8	yes	—
170	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
172	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
173	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
174	C₄×C₃₁	—	4	4	no	—
175	C₄×C₃₁	—	8	4	no	—
176	C₄×C₃₁	#390	1	4	yes	—
177	C₄×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₃₁	C₂×#121	1	1	yes	characteristic
180	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
181	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
182	C₂²×D₈	—	2	4	no	—
183	C₂²×D₈	—	2	4	no	—
184	C₂²×D₈	C₄×C₃₁	1	8	yes	complemented
185	C₂²×D₈	C₂²×C₃₁	1	4	yes	—
186	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
188	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
189	C₂²×C₂²⋊C₄	—	2	4	no	—
190	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
191	C₂×#106	—	2	4	no	—
192	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
193	C₂×#102	—	2	8	no	—
194	C₂×#102	C₂²×C₃₁	1	8	yes	complemented
195	C₂×#97	—	2	4	no	—
196	C₂×#97	C₂²×C₃₁	1	4	yes	complemented
197	#390	—	2	4	no	—
198	#390	C₂²×C₃₁	1	8	yes	complemented
199	C₂×C₃₁	—	8	8	no	—
200	C₂×C₃₁	#1972	1	8	yes	direct product factor
201	C₂×C₃₁	C₂×#390	1	1	yes	characteristic
202	C₂×C₃₁	C₂×#442	1	2	yes	—
203	C₂×C₃₁	C₂×#469	1	2	yes	—
204	C₂×C₃₁	C₂×#496	1	2	yes	—
205	C₂⁵	—	2	2	no	—
206	C₂²×D₄	—	2	4	no	—
207	C₂²×D₄	—	2	4	no	—
208	C₂²×D₄	—	2	4	no	—
209	C₂²×D₄	—	2	2	no	—
210	C₂²×D₄	—	2	4	no	—
211	C₂²×D₄	—	2	4	no	—
212	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	—
213	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	D₄×C₃₁	1	2	yes	—
216	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
217	C₂×D₈	—	2	32	no	—
218	C₂×D₈	—	2	8	no	—
219	C₂×D₈	—	2	8	no	—
220	C₂×D₈	C₂×C₄×C₃₁	1	16	yes	complemented
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
224	C₂²×C₈	D₄×C₃₁	1	4	yes	—
225	C₂²×C₈	D₄×C₃₁	1	4	yes	—
226	C₂²×C₈	D₄×C₃₁	1	4	yes	—
227	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
228	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
233	C₂×C₂²⋊C₄	—	2	16	no	—
234	C₂×C₂²⋊C₄	—	4	16	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	D₄×C₃₁	1	2	yes	—
238	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
239	#106	—	2	8	no	—
240	#102	—	2	16	no	—
241	#97	—	2	8	no	—
242	C₃₁	C₂×#1972	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁴	—	2	8	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	—	4	8	no	—
248	C₂⁴	—	4	8	no	—
249	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	4	8	no	—
259	C₂×D₄	—	4	4	no	—
260	C₂×D₄	—	4	8	no	—
261	C₂×D₄	—	4	4	no	—
262	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	—	4	8	no	—
268	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
270	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
271	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
274	C₂²×C₄	#41×C₃₁	1	2	yes	—
275	C₂²×C₄	#41×C₃₁	1	2	yes	—
276	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
277	D₈	—	2	32	no	—
278	C₂×C₈	—	2	8	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	C₂²⋊C₄×C₃₁	1	16	yes	complemented
282	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
283	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
284	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
285	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₂²⋊C₄	—	4	32	no	—
290	C₄²	—	2	4	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₂³	—	2	8	no	—
294	C₂³	—	4	32	no	—
295	C₂³	—	4	4	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	4	8	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	4	16	no	—
300	C₂³	—	8	16	no	—
301	C₂³	—	8	8	no	—
302	C₂³	—	8	8	no	—
303	C₂³	C₄×D₄×C₃₁	1	2	yes	—
304	C₂³	C₃₁×#121	1	2	yes	—
305	C₂³	C₃₁×#127	1	2	yes	—
306	C₂³	C₃₁×AGL(1,ℤ/8)	1	8	yes	—
307	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
308	D₄	—	2	8	no	—
309	D₄	—	2	8	no	—
310	D₄	—	4	4	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	16	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	8	8	no	—
319	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
320	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
321	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
322	C₂×C₄	C₃₁×#121	1	4	yes	—
323	C₂×C₄	C₃₁×#121	1	2	yes	—
324	C₂×C₄	C₃₁×#124	1	4	yes	—
325	C₂×C₄	C₃₁×#127	1	2	yes	—
326	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
332	C₈	—	2	4	no	—
333	C₈	C₂×C₂²⋊C₄×C₃₁	1	8	yes	complemented
334	C₂²	—	4	16	no	—
335	C₂²	—	4	8	no	—
336	C₂²	—	8	4	no	—
337	C₂²	—	8	4	no	—
338	C₂²	—	8	32	no	—
339	C₂²	—	8	8	no	—
340	C₂²	C₃₁×#390	1	4	yes	—
341	C₂²	C₃₁×#442	1	8	yes	—
342	C₂²	C₃₁×#469	1	8	yes	—
343	C₂²	C₃₁×#496	1	8	yes	—
344	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
345	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
346	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
347	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
348	C₄	—	4	4	no	—
349	C₄	—	8	4	no	—
350	C₄	C₃₁×#390	1	4	yes	—
351	C₄	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
352	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
353	C₄	C₂×C₃₁×#121	1	1	yes	characteristic
354	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
355	C₂	—	8	8	no	—
356	C₂	C₃₁×#1972	1	8	yes	direct product factor
357	C₂	C₂×C₃₁×#390	1	1	yes	characteristic
358	C₂	C₂×C₃₁×#442	1	2	yes	—
359	C₂	C₂×C₃₁×#469	1	2	yes	—
360	C₂	C₂×C₃₁×#496	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂³×D₈×C₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₁×#106	C₂	semidirect
3. C₂²×C₃₁×#102	C₂	semidirect
4. C₂²×C₃₁×#97	C₂	semidirect
5. C₂×C₃₁×#390	C₂	semidirect
6. C₃₁×#1972	C₂	direct (N × H)
10. C₂²×D₈×C₃₁	C₄	semidirect
18. C₂×C₃₁×#106	C₂²	semidirect
20. C₂×C₃₁×#102	C₂²	semidirect
22. C₂×C₃₁×#97	C₂²	semidirect
24. C₃₁×#390	C₂²	semidirect
40. C₂×D₈×C₃₁	C₂×C₄	semidirect
100. C₂×C₈×C₃₁	C₂²⋊C₄	semidirect
112. C₂×#1972	C₃₁	direct (N × H)
153. C₈×C₃₁	C₂×C₂²⋊C₄	semidirect
155. C₂²×#106	C₂×C₃₁	semidirect
156. C₂²×#102	C₂×C₃₁	semidirect
157. C₂²×#97	C₂×C₃₁	semidirect
158. C₂×#390	C₂×C₃₁	semidirect
159. #1972	C₂×C₃₁	direct (N × H)
184. C₂²×D₈	C₄×C₃₁	semidirect
192. C₂×#106	C₂²×C₃₁	semidirect
194. C₂×#102	C₂²×C₃₁	semidirect
196. C₂×#97	C₂²×C₃₁	semidirect
198. #390	C₂²×C₃₁	semidirect
200. C₂×C₃₁	#1972	direct (N × H)
220. C₂×D₈	C₂×C₄×C₃₁	semidirect
242. C₃₁	C₂×#1972	direct (N × H)
281. C₂×C₈	C₂²⋊C₄×C₃₁	semidirect
333. C₈	C₂×C₂²⋊C₄×C₃₁	semidirect
356. C₂	C₃₁×#1972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₃₁	2
C₂²×C₃₁×#106	2
C₂²×C₃₁×#102	2
C₂²×C₃₁×#97	2
C₂×C₃₁×#390	2
C₃₁×#1972	2
C₂×#1972	31

Subgroups — C2×C31×#1972 #21477985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1972 #21477985