Subgroups — C₃₁×#18064 #21474823

Order 7936.

718 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2974	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1594	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1581	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1580	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1490	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₃₁	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
11	C₄×D₈×C₃₁	C₄	1	2	yes	—
12	C₄×D₈×C₃₁	C₄	1	1	yes	characteristic
13	C₄×D₈×C₃₁	C₄	1	1	yes	characteristic
14	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₄×D₈×C₃₁	C₂²	1	2	yes	—
16	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#436	C₂²	1	4	yes	complemented
18	C₃₁×#435	—	2	4	no	—
19	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
20	C₃₁×#432	C₂²	1	2	yes	—
21	C₃₁×#431	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#107	C₄	1	1	yes	characteristic
23	C₂×C₃₁×#102	C₄	1	2	yes	—
24	C₃₁×#407	—	2	2	no	—
25	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
26	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#335	C₂²	1	2	yes	complemented
29	C₃₁×#334	C₂²	1	2	yes	complemented
30	C₃₁×D₄⋊C₈	C₂²	1	4	yes	complemented
31	C₃₁×D₄⋊C₈	C₂²	1	4	yes	complemented
32	C₃₁×#322	C₂²	1	2	yes	complemented
33	C₃₁×#322	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₃₁	—	2	2	no	—
36	C₂×D₈×C₃₁	—	2	4	no	—
37	C₂×D₈×C₃₁	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₃₁	—	2	1	no	—
41	C₂×M₁₆×C₃₁	—	2	4	no	—
42	C₂²×C₈×C₃₁	—	2	4	no	—
43	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₃₁	—	2	2	no	—
46	C₄×D₄×C₃₁	—	2	2	no	—
47	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₃₁	C₂³	1	2	yes	—
50	C₄×D₄×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×#107	C₂×C₄	1	2	yes	—
55	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
56	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
57	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
58	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
59	C₃₁×#102	C₂×C₄	1	2	yes	—
60	C₃₁×#102	C₂×C₄	1	2	yes	—
61	C₃₁×#102	C₂×C₄	1	2	yes	—
62	C₃₁×#102	C₂×C₄	1	2	yes	—
63	C₃₁×C₂²⋊C₈	—	2	2	no	—
64	C₃₁×C₂²⋊C₈	—	2	4	no	—
65	C₃₁×C₂²⋊C₈	—	2	4	no	—
66	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
67	C₃₁×#97	—	2	2	no	—
68	C₃₁×#97	—	2	1	no	—
69	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₃₁	C₂³	1	2	yes	—
72	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₃₁	C₂³	1	2	yes	—
75	C₂⁴×C₃₁	—	2	2	no	—
76	C₂×D₄×C₃₁	—	2	4	no	—
77	C₂×D₄×C₃₁	—	2	2	no	—
78	C₂×D₄×C₃₁	—	4	2	no	—
79	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
80	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	—	2	2	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	8	4	no	—
87	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
90	D₈×C₃₁	—	2	4	no	—
91	D₈×C₃₁	—	2	2	no	—
92	D₈×C₃₁	M₁₆	1	4	yes	complemented
93	M₁₆×C₃₁	—	4	2	no	—
94	M₁₆×C₃₁	—	8	4	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	4	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	4	1	no	—
99	C₂×C₈×C₃₁	—	8	4	no	—
100	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
105	C₄⋊C₄×C₃₁	—	2	2	no	—
106	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
108	C₂²⋊C₄×C₃₁	—	2	2	no	—
109	C₂²⋊C₄×C₃₁	—	2	2	no	—
110	C₂²⋊C₄×C₃₁	—	2	2	no	—
111	C₂²⋊C₄×C₃₁	—	2	2	no	—
112	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₃₁	#41	1	1	yes	characteristic
115	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
116	#18064	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	2	2	no	—
118	C₂³×C₃₁	—	2	2	no	—
119	C₂³×C₃₁	—	4	4	no	—
120	C₂³×C₃₁	—	4	4	no	—
121	C₂³×C₃₁	—	8	2	no	—
122	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
123	D₄×C₃₁	—	2	2	no	—
124	D₄×C₃₁	—	2	2	no	—
125	D₄×C₃₁	—	2	2	no	—
126	D₄×C₃₁	—	4	4	no	—
127	D₄×C₃₁	C₂×M₁₆	1	4	yes	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	4	4	no	—
135	C₂×C₄×C₃₁	—	4	4	no	—
136	C₂×C₄×C₃₁	—	8	2	no	—
137	C₂×C₄×C₃₁	—	8	2	no	—
138	C₂×C₄×C₃₁	—	8	2	no	—
139	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
145	C₈×C₃₁	—	2	1	no	—
146	C₈×C₃₁	—	2	1	no	—
147	C₈×C₃₁	—	2	1	no	—
148	C₈×C₃₁	—	2	4	no	—
149	C₈×C₃₁	—	4	2	no	—
150	C₈×C₃₁	—	4	4	no	—
151	C₈×C₃₁	C₂×M₁₆	1	2	yes	—
152	#2974	C₂×C₃₁	1	2	yes	complemented
153	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic
154	#1594	C₂×C₃₁	1	2	yes	complemented
155	#1581	C₂×C₃₁	1	4	yes	complemented
156	#1580	C₂×C₃₁	1	2	yes	complemented
157	#1568	C₂×C₃₁	1	1	yes	characteristic, complemented
158	#1490	C₂×C₃₁	1	2	yes	complemented
159	#1451	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂²×C₃₁	—	2	1	no	—
161	C₂²×C₃₁	—	2	1	no	—
162	C₂²×C₃₁	—	2	4	no	—
163	C₂²×C₃₁	—	4	2	no	—
164	C₂²×C₃₁	—	4	2	no	—
165	C₂²×C₃₁	—	4	2	no	—
166	C₂²×C₃₁	—	4	2	no	—
167	C₂²×C₃₁	—	4	2	no	—
168	C₂²×C₃₁	—	8	8	no	—
169	C₂²×C₃₁	#444	1	2	yes	—
170	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
171	C₄×C₃₁	—	2	1	no	—
172	C₄×C₃₁	—	2	1	no	—
173	C₄×C₃₁	—	2	1	no	—
174	C₄×C₃₁	—	2	1	no	—
175	C₄×C₃₁	—	4	2	no	—
176	C₄×C₃₁	—	4	2	no	—
177	C₄×C₃₁	C₂²×M₁₆	1	1	yes	characteristic
178	C₄×C₃₁	#568	1	1	yes	characteristic
179	C₄×C₃₁	#576	1	2	yes	—
180	C₂²×D₈	C₄×C₃₁	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
182	C₄×D₈	C₄×C₃₁	1	2	yes	—
183	C₄×D₈	C₄×C₃₁	1	1	yes	characteristic
184	C₄×D₈	C₄×C₃₁	1	1	yes	characteristic
185	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
186	C₄×D₈	C₂²×C₃₁	1	2	yes	—
187	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
188	#436	C₂²×C₃₁	1	4	yes	complemented
189	#435	—	2	4	no	—
190	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
191	#432	C₂²×C₃₁	1	2	yes	—
192	#431	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×#107	C₄×C₃₁	1	1	yes	characteristic
194	C₂×#102	C₄×C₃₁	1	2	yes	—
195	#407	—	2	2	no	—
196	C₂×C₂²⋊C₈	—	2	2	no	—
197	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
199	#335	C₂²×C₃₁	1	2	yes	complemented
200	#334	C₂²×C₃₁	1	2	yes	complemented
201	D₄⋊C₈	C₂²×C₃₁	1	4	yes	complemented
202	D₄⋊C₈	C₂²×C₃₁	1	4	yes	complemented
203	#322	C₂²×C₃₁	1	2	yes	complemented
204	#322	C₂²×C₃₁	1	2	yes	complemented
205	C₂×C₃₁	—	2	2	no	—
206	C₂×C₃₁	—	4	4	no	—
207	C₂×C₃₁	—	8	2	no	—
208	C₂×C₃₁	D₄×M₁₆	1	1	yes	characteristic
209	C₂×C₃₁	#2948	1	1	yes	characteristic
210	C₂×C₃₁	C₂×#444	1	1	yes	characteristic
211	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
212	C₂³×C₄	—	2	2	no	—
213	C₂×D₈	—	2	4	no	—
214	C₂×D₈	C₂×C₄×C₃₁	1	2	yes	—
215	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
216	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
217	C₂×M₁₆	—	2	1	no	—
218	C₂×M₁₆	—	2	4	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
221	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
225	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
226	C₄×D₄	C₂³×C₃₁	1	2	yes	—
227	C₄×D₄	C₂³×C₃₁	1	2	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
229	C₂×C₂²⋊C₄	—	2	2	no	—
230	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
231	#107	C₂×C₄×C₃₁	1	2	yes	—
232	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
233	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
234	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
235	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
236	#102	C₂×C₄×C₃₁	1	2	yes	—
237	#102	C₂×C₄×C₃₁	1	2	yes	—
238	#102	C₂×C₄×C₃₁	1	2	yes	—
239	#102	C₂×C₄×C₃₁	1	2	yes	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₂²⋊C₈	—	2	4	no	—
242	C₂²⋊C₈	—	2	4	no	—
243	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
244	#97	—	2	2	no	—
245	#97	—	2	1	no	—
246	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
247	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
248	C₄×C₈	C₂³×C₃₁	1	2	yes	—
249	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
250	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₃₁	1	2	yes	—
252	C₃₁	#18064	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	—	2	2	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
258	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	8	4	no	—
265	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
268	D₈	—	2	4	no	—
269	D₈	—	2	2	no	—
270	D₈	M₁₆×C₃₁	1	4	yes	complemented
271	M₁₆	—	4	2	no	—
272	M₁₆	—	8	4	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	4	1	no	—
277	C₂×C₈	—	8	4	no	—
278	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
279	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
280	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
281	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
282	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
285	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
291	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₄²	#41×C₃₁	1	1	yes	characteristic
293	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	8	2	no	—
299	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
300	D₄	—	2	2	no	—
301	D₄	—	2	2	no	—
302	D₄	—	2	2	no	—
303	D₄	—	4	4	no	—
304	D₄	C₂×M₁₆×C₃₁	1	4	yes	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	8	2	no	—
314	C₂×C₄	—	8	2	no	—
315	C₂×C₄	—	8	2	no	—
316	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
317	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
318	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
319	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
320	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
321	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
322	C₈	—	2	1	no	—
323	C₈	—	2	1	no	—
324	C₈	—	2	1	no	—
325	C₈	—	2	4	no	—
326	C₈	—	4	2	no	—
327	C₈	—	4	4	no	—
328	C₈	C₂×M₁₆×C₃₁	1	2	yes	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	8	8	no	—
338	C₂²	C₃₁×#444	1	2	yes	—
339	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	4	2	no	—
345	C₄	—	4	2	no	—
346	C₄	C₂²×M₁₆×C₃₁	1	1	yes	characteristic
347	C₄	C₃₁×#568	1	1	yes	characteristic
348	C₄	C₃₁×#576	1	2	yes	—
349	C₂	—	2	2	no	—
350	C₂	—	4	4	no	—
351	C₂	—	8	2	no	—
352	C₂	D₄×M₁₆×C₃₁	1	1	yes	characteristic
353	C₂	C₃₁×#2948	1	1	yes	characteristic
354	C₂	C₂×C₃₁×#444	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	C₂²×D₈×C₃₁	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₃₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2974	C₂	semidirect
3. C₃₁×#1594	C₂	semidirect
4. C₃₁×#1581	C₂	semidirect
5. C₃₁×#1580	C₂	semidirect
6. C₃₁×#1568	C₂	semidirect
7. C₃₁×#1490	C₂	semidirect
8. C₃₁×#1451	C₂	semidirect
17. C₃₁×#436	C₂²	semidirect
19. C₈×D₄×C₃₁	C₂²	semidirect
28. C₃₁×#335	C₂²	semidirect
29. C₃₁×#334	C₂²	semidirect
30. C₃₁×D₄⋊C₈	C₂²	semidirect
31. C₃₁×D₄⋊C₈	C₂²	semidirect
32. C₃₁×#322	C₂²	semidirect
33. C₃₁×#322	C₂²	semidirect
92. D₈×C₃₁	M₁₆	semidirect
116. #18064	C₃₁	direct (N × H)
152. #2974	C₂×C₃₁	semidirect
154. #1594	C₂×C₃₁	semidirect
155. #1581	C₂×C₃₁	semidirect
156. #1580	C₂×C₃₁	semidirect
157. #1568	C₂×C₃₁	semidirect
158. #1490	C₂×C₃₁	semidirect
159. #1451	C₂×C₃₁	semidirect
188. #436	C₂²×C₃₁	semidirect
190. C₈×D₄	C₂²×C₃₁	semidirect
199. #335	C₂²×C₃₁	semidirect
200. #334	C₂²×C₃₁	semidirect
201. D₄⋊C₈	C₂²×C₃₁	semidirect
202. D₄⋊C₈	C₂²×C₃₁	semidirect
203. #322	C₂²×C₃₁	semidirect
204. #322	C₂²×C₃₁	semidirect
252. C₃₁	#18064	direct (N × H)
270. D₈	M₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#2974	2
C₂×C₄×D₈×C₃₁	2
C₃₁×#1594	2
C₃₁×#1581	2
C₃₁×#1580	2
C₃₁×#1568	2
C₃₁×#1490	2
C₃₁×#1451	2
#18064	31

Subgroups — C31×#18064 #21474823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#18064 #21474823