Subgroups — C₃₁×#18070 #21474829

Order 7936.

600 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	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2969	C₂	1	2	yes	maximal, complemented
3	C₃₁×#1590	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1584	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1581	C₂	1	2	yes	maximal, complemented
6	C₈×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1482	C₂	1	2	yes	maximal, complemented
9	C₈×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#529	C₂²	1	2	yes	—
11	C₃₁×#499	C₄	1	1	yes	characteristic
12	C₃₁×#495	C₄	1	1	yes	characteristic
13	C₃₁×#488	C₄	1	2	yes	—
14	C₃₁×#467	C₄	1	1	yes	characteristic
15	C₃₁×#466	C₄	1	1	yes	characteristic
16	C₃₁×#465	C₄	1	2	yes	—
17	C₃₁×#446	C₂²	1	2	yes	—
18	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
21	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#436	—	2	2	no	—
23	C₃₁×#436	C₂²	1	2	yes	—
24	C₃₁×#435	—	2	2	no	—
25	C₈×D₄×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#433	—	2	2	no	—
27	C₃₁×#431	C₂²	1	2	yes	—
28	C₃₁×#431	C₂²	1	1	yes	characteristic
29	C₃₁×#405	—	2	2	no	—
30	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	2	yes	—
33	C₃₁×#334	C₂²	1	1	yes	characteristic
34	C₃₁×#334	C₂²	1	1	yes	characteristic
35	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
38	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
39	C₃₁×#322	C₂²	1	2	yes	—
40	C₈²×C₃₁	C₂²	1	2	yes	—
41	C₂×Q₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×SD₁₆×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₃₁	—	2	2	no	—
45	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
46	C₂²×C₈×C₃₁	—	2	2	no	—
47	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₃₁×#126	—	2	2	no	—
50	C₃₁×#125	C₂×C₄	1	2	yes	—
51	C₃₁×#124	C₂×C₄	1	2	yes	—
52	C₃₁×#123	—	2	2	no	—
53	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
54	C₃₁×#121	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
56	C₄×D₄×C₃₁	—	2	2	no	—
57	C₄×D₄×C₃₁	C₂³	1	2	yes	—
58	C₃₁×#117	—	2	2	no	—
59	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
60	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
61	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
62	C₃₁×#106	C₂×C₄	1	2	yes	—
63	C₃₁×C₄⋊C₈	—	2	2	no	—
64	C₃₁×C₄⋊C₈	—	2	2	no	—
65	C₃₁×C₄⋊C₈	—	2	1	no	—
66	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
67	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
68	C₃₁×#103	C₂×C₄	1	2	yes	—
69	C₃₁×#103	C₂×C₄	1	2	yes	—
70	C₃₁×#102	C₂×C₄	1	2	yes	—
71	C₃₁×#102	C₂×C₄	1	2	yes	—
72	C₃₁×C₂²⋊C₈	—	2	2	no	—
73	C₃₁×C₂²⋊C₈	—	2	1	no	—
74	C₃₁×C₂²⋊C₈	—	2	2	no	—
75	C₃₁×C₂²⋊C₈	—	2	2	no	—
76	C₃₁×#97	—	2	2	no	—
77	C₃₁×#97	D₄	1	1	yes	characteristic
78	C₃₁×#97	D₄	1	1	yes	characteristic
79	C₄×C₈×C₃₁	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₃₁	C₂³	1	2	yes	—
84	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₃₁	C₂³	1	2	yes	—
87	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
94	Q₁₆×C₃₁	—	4	1	no	—
95	SD₁₆×C₃₁	—	2	4	no	—
96	D₈×C₃₁	—	4	1	no	—
97	M₁₆×C₃₁	—	2	4	no	—
98	M₁₆×C₃₁	—	4	4	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	4	1	no	—
104	C₂×C₈×C₃₁	—	4	4	no	—
105	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
111	C₄⋊C₄×C₃₁	—	2	2	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
116	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
117	C₂²⋊C₄×C₃₁	—	2	2	no	—
118	C₂²⋊C₄×C₃₁	—	2	2	no	—
119	C₂²⋊C₄×C₃₁	—	2	2	no	—
120	C₂²⋊C₄×C₃₁	—	2	2	no	—
121	C₂²⋊C₄×C₃₁	—	2	2	no	—
122	C₄²×C₃₁	—	2	2	no	—
123	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₃₁	#41	1	1	yes	characteristic
126	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
127	#18070	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	2	no	—
129	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
130	Q₈×C₃₁	—	2	2	no	—
131	Q₈×C₃₁	—	2	2	no	—
132	D₄×C₃₁	—	2	2	no	—
133	D₄×C₃₁	—	2	2	no	—
134	D₄×C₃₁	—	8	2	no	—
135	C₂×C₄×C₃₁	—	2	1	no	—
136	C₂×C₄×C₃₁	—	2	1	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	4	1	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
150	C₈×C₃₁	—	2	1	no	—
151	C₈×C₃₁	—	2	1	no	—
152	C₈×C₃₁	—	2	1	no	—
153	C₈×C₃₁	—	2	2	no	—
154	C₈×C₃₁	—	4	2	no	—
155	C₈×C₃₁	—	4	2	no	—
156	C₈×C₃₁	—	4	2	no	—
157	C₈×C₃₁	#131	1	2	yes	—
158	C₈×C₃₁	#135	1	4	yes	—
159	#3168	C₂×C₃₁	1	1	yes	characteristic
160	#2969	C₂×C₃₁	1	2	yes	complemented
161	#1590	C₂×C₃₁	1	2	yes	complemented
162	#1584	C₂×C₃₁	1	2	yes	complemented
163	#1581	C₂×C₃₁	1	2	yes	complemented
164	C₈×SD₁₆	C₂×C₃₁	1	2	yes	complemented
165	#1564	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#1482	C₂×C₃₁	1	2	yes	complemented
167	C₈×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	4	2	no	—
172	C₂²×C₃₁	—	4	2	no	—
173	C₂²×C₃₁	—	4	2	no	—
174	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
175	C₄×C₃₁	—	2	1	no	—
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	4	2	no	—
180	C₄×C₃₁	—	4	2	no	—
181	C₄×C₃₁	—	4	2	no	—
182	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
183	C₄×C₃₁	#568	1	1	yes	characteristic
184	C₄×C₃₁	C₂×#135	1	2	yes	—
185	#529	C₂²×C₃₁	1	2	yes	—
186	#499	C₄×C₃₁	1	1	yes	characteristic
187	#495	C₄×C₃₁	1	1	yes	characteristic
188	#488	C₄×C₃₁	1	2	yes	—
189	#467	C₄×C₃₁	1	1	yes	characteristic
190	#466	C₄×C₃₁	1	1	yes	characteristic
191	#465	C₄×C₃₁	1	2	yes	—
192	#446	C₂²×C₃₁	1	2	yes	—
193	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
194	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
195	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
196	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
197	#436	—	2	2	no	—
198	#436	C₂²×C₃₁	1	2	yes	—
199	#435	—	2	2	no	—
200	C₈×D₄	C₂²×C₃₁	1	2	yes	—
201	#433	—	2	2	no	—
202	#431	C₂²×C₃₁	1	2	yes	—
203	#431	C₂²×C₃₁	1	1	yes	characteristic
204	#405	—	2	2	no	—
205	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
207	#335	C₂²×C₃₁	1	2	yes	—
208	#334	C₂²×C₃₁	1	1	yes	characteristic
209	#334	C₂²×C₃₁	1	1	yes	characteristic
210	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
211	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
212	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
213	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
214	#322	C₂²×C₃₁	1	2	yes	—
215	C₈²	C₂²×C₃₁	1	2	yes	—
216	C₂×C₃₁	—	4	1	no	—
217	C₂×C₃₁	—	8	2	no	—
218	C₂×C₃₁	#2935	1	1	yes	characteristic
219	C₂×C₃₁	C₄×#135	1	1	yes	characteristic
220	C₂×C₃₁	#2957	1	1	yes	characteristic
221	C₂×Q₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
222	C₂×SD₁₆	C₂×C₄×C₃₁	1	2	yes	—
223	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
228	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
229	#126	—	2	2	no	—
230	#125	C₂×C₄×C₃₁	1	2	yes	—
231	#124	C₂×C₄×C₃₁	1	2	yes	—
232	#123	—	2	2	no	—
233	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
234	#121	C₂×C₄×C₃₁	1	2	yes	—
235	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	C₂³×C₃₁	1	2	yes	—
238	#117	—	2	2	no	—
239	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
240	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
241	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
242	#106	C₂×C₄×C₃₁	1	2	yes	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
247	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
248	#103	C₂×C₄×C₃₁	1	2	yes	—
249	#103	C₂×C₄×C₃₁	1	2	yes	—
250	#102	C₂×C₄×C₃₁	1	2	yes	—
251	#102	C₂×C₄×C₃₁	1	2	yes	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₂²⋊C₈	—	2	1	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	#97	—	2	2	no	—
257	#97	D₄×C₃₁	1	1	yes	characteristic
258	#97	D₄×C₃₁	1	1	yes	characteristic
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
262	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₃₁	1	2	yes	—
264	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₃₁	1	2	yes	—
267	C₃₁	#18070	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
275	Q₁₆	—	4	1	no	—
276	SD₁₆	—	2	4	no	—
277	D₈	—	4	1	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	—	4	4	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
297	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₄²	#41×C₃₁	1	1	yes	characteristic
307	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
308	C₂³	—	2	2	no	—
309	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
310	Q₈	—	2	2	no	—
311	Q₈	—	2	2	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	2	no	—
314	D₄	—	8	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
325	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
326	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
327	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
330	C₈	—	2	1	no	—
331	C₈	—	2	1	no	—
332	C₈	—	2	1	no	—
333	C₈	—	2	2	no	—
334	C₈	—	4	2	no	—
335	C₈	—	4	2	no	—
336	C₈	—	4	2	no	—
337	C₈	C₃₁×#131	1	2	yes	—
338	C₈	C₃₁×#135	1	4	yes	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
354	C₄	C₃₁×#568	1	1	yes	characteristic
355	C₄	C₂×C₃₁×#135	1	2	yes	—
356	C₂	—	4	1	no	—
357	C₂	—	8	2	no	—
358	C₂	C₃₁×#2935	1	1	yes	characteristic
359	C₂	C₄×C₃₁×#135	1	1	yes	characteristic
360	C₂	C₃₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₃₁×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₄×M₁₆×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2969	C₂	semidirect
3. C₃₁×#1590	C₂	semidirect
4. C₃₁×#1584	C₂	semidirect
5. C₃₁×#1581	C₂	semidirect
6. C₈×SD₁₆×C₃₁	C₂	semidirect
7. C₃₁×#1564	C₂	semidirect
8. C₃₁×#1482	C₂	semidirect
9. C₈×M₁₆×C₃₁	C₂	semidirect
127. #18070	C₃₁	direct (N × H)
160. #2969	C₂×C₃₁	semidirect
161. #1590	C₂×C₃₁	semidirect
162. #1584	C₂×C₃₁	semidirect
163. #1581	C₂×C₃₁	semidirect
164. C₈×SD₁₆	C₂×C₃₁	semidirect
165. #1564	C₂×C₃₁	semidirect
166. #1482	C₂×C₃₁	semidirect
167. C₈×M₁₆	C₂×C₃₁	semidirect
267. C₃₁	#18070	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×#3168	2
C₃₁×#2969	2
C₃₁×#1590	2
C₃₁×#1584	2
C₃₁×#1581	2
C₈×SD₁₆×C₃₁	2
C₃₁×#1564	2
C₃₁×#1482	2
C₈×M₁₆×C₃₁	2
#18070	31

Subgroups — C31×#18070 #21474829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#18070 #21474829