Subgroups — C₃₁×#60714 #21517473

Order 7936.

2070 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3184	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3176	C₂	1	8	yes	maximal, complemented
4	C₃₁×#3169	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3138	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3058	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2948	C₂	1	4	yes	maximal, complemented
10	C₄×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×D₈×C₃₁	C₂²	1	4	yes	—
12	C₂×C₃₁×#131	C₂²	1	2	yes	—
13	C₃₁×#559	—	2	4	no	—
14	C₃₁×#550	—	2	4	no	—
15	C₃₁×#546	—	2	8	no	—
16	C₃₁×#540	C₂²	1	8	yes	complemented
17	C₃₁×#535	C₂²	1	4	yes	—
18	C₃₁×#533	C₂²	1	2	yes	—
19	C₃₁×#532	C₂²	1	8	yes	complemented
20	C₂×C₃₁×#127	C₂²	1	2	yes	—
21	C₃₁×#518	C₂²	1	4	yes	—
22	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#500	C₂²	1	2	yes	complemented
24	C₃₁×#499	C₂²	1	4	yes	complemented
25	C₃₁×#498	C₂²	1	2	yes	complemented
26	C₃₁×#493	C₂²	1	2	yes	—
27	C₃₁×#493	C₂²	1	4	yes	—
28	C₃₁×#493	C₂²	1	2	yes	—
29	C₃₁×#490	C₂²	1	8	yes	complemented
30	C₃₁×#486	C₂²	1	8	yes	complemented
31	C₃₁×#469	C₂²	1	16	yes	complemented
32	C₃₁×#466	C₂²	1	16	yes	complemented
33	C₃₁×#442	C₂²	1	16	yes	complemented
34	C₄×D₈×C₃₁	C₂²	1	16	yes	complemented
35	C₃₁×#427	C₂²	1	4	yes	—
36	C₃₁×#418	C₂²	1	8	yes	—
37	C₃₁×#405	C₂²	1	2	yes	—
38	C₃₁×#405	C₂²	1	4	yes	complemented
39	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
41	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	complemented
43	C₂×#41×C₃₁	—	2	8	no	—
44	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₁	—	2	4	no	—
46	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
47	C₂×D₈×C₃₁	—	2	16	no	—
48	C₂×D₈×C₃₁	C₂³	1	8	yes	—
49	C₂×D₈×C₃₁	C₂³	1	8	yes	—
50	C₃₁×#131	—	2	8	no	—
51	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
52	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
53	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
54	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
55	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
56	C₃₁×#127	—	2	4	no	—
57	C₃₁×#127	—	2	4	no	—
58	C₃₁×#127	C₂³	1	4	yes	—
59	C₃₁×#127	C₂³	1	4	yes	—
60	C₃₁×#125	C₂³	1	4	yes	—
61	C₃₁×#124	—	2	4	no	—
62	C₃₁×#124	—	2	8	no	—
63	C₃₁×#123	—	2	16	no	—
64	C₃₁×C₂²⋊Q₈	—	2	4	no	—
65	C₃₁×#121	—	2	8	no	—
66	C₃₁×#121	—	2	16	no	—
67	C₃₁×#121	C₂³	1	16	yes	—
68	C₃₁×#120	—	2	8	no	—
69	C₄×Q₈×C₃₁	—	2	4	no	—
70	C₄×Q₈×C₃₁	D₄	1	2	yes	—
71	C₄×D₄×C₃₁	—	2	8	no	—
72	C₄×D₄×C₃₁	—	2	8	no	—
73	C₄×D₄×C₃₁	D₄	1	4	yes	—
74	C₄×D₄×C₃₁	D₄	1	2	yes	—
75	C₄×D₄×C₃₁	C₂³	1	16	yes	—
76	C₃₁×#117	C₂³	1	4	yes	—
77	C₃₁×#117	C₂³	1	1	yes	characteristic
78	C₃₁×#117	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
80	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
82	C₃₁×#107	C₂³	1	8	yes	—
83	C₃₁×#106	C₂³	1	8	yes	—
84	C₃₁×#102	C₂³	1	32	yes	—
85	C₃₁×#97	C₂³	1	2	yes	—
86	C₃₁×#97	C₂³	1	4	yes	—
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₃₁	C₂³	1	2	yes	—
90	C₄×C₈×C₃₁	C₂³	1	2	yes	—
91	C₄×C₈×C₃₁	C₂³	1	4	yes	—
92	C₂⁴×C₃₁	—	2	4	no	—
93	#41×C₃₁	—	2	4	no	—
94	#41×C₃₁	—	8	16	no	—
95	C₂×Q₈×C₃₁	—	2	4	no	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₃₁	—	2	16	no	—
98	C₂×D₄×C₃₁	—	2	4	no	—
99	C₂×D₄×C₃₁	—	2	8	no	—
100	C₂×D₄×C₃₁	—	2	8	no	—
101	C₂×D₄×C₃₁	—	2	16	no	—
102	C₂×D₄×C₃₁	—	8	8	no	—
103	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₃₁	—	2	16	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
111	D₈×C₃₁	—	2	16	no	—
112	D₈×C₃₁	—	2	16	no	—
113	M₁₆×C₃₁	—	2	4	no	—
114	M₁₆×C₃₁	—	2	8	no	—
115	C₂×C₈×C₃₁	—	2	8	no	—
116	C₂×C₈×C₃₁	#41	1	8	yes	complemented
117	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
118	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
119	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
120	C₄⋊C₄×C₃₁	—	2	4	no	—
121	C₄⋊C₄×C₃₁	—	2	8	no	—
122	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
124	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
125	C₂²⋊C₄×C₃₁	—	2	4	no	—
126	C₂²⋊C₄×C₃₁	—	2	16	no	—
127	C₂²⋊C₄×C₃₁	—	2	16	no	—
128	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
130	C₄²×C₃₁	—	2	4	no	—
131	C₄²×C₃₁	C₂×D₄	1	4	yes	—
132	C₄²×C₃₁	C₂×D₄	1	2	yes	—
133	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
134	C₄²×C₃₁	C₂⁴	1	2	yes	—
135	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
136	#60714	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	8	no	—
138	C₂³×C₃₁	—	4	8	no	—
139	C₂³×C₃₁	—	8	8	no	—
140	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
141	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₃₁	—	2	2	no	—
143	Q₈×C₃₁	—	4	8	no	—
144	D₄×C₃₁	—	2	4	no	—
145	D₄×C₃₁	—	2	2	no	—
146	D₄×C₃₁	—	2	16	no	—
147	D₄×C₃₁	—	4	8	no	—
148	D₄×C₃₁	—	4	16	no	—
149	D₄×C₃₁	—	8	8	no	—
150	D₄×C₃₁	—	8	16	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	8	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	8	no	—
155	C₂×C₄×C₃₁	—	8	16	no	—
156	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
158	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
162	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
163	C₈×C₃₁	—	2	4	no	—
164	C₈×C₃₁	C₂×#41	1	4	yes	—
165	C₈×C₃₁	C₂×#41	1	4	yes	—
166	#3508	C₂×C₃₁	1	2	yes	complemented
167	#3184	C₂×C₃₁	1	4	yes	complemented
168	#3176	C₂×C₃₁	1	8	yes	complemented
169	#3169	C₂×C₃₁	1	4	yes	complemented
170	#3160	C₂×C₃₁	1	1	yes	characteristic, complemented
171	C₂×#493	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#3138	C₂×C₃₁	1	2	yes	complemented
173	#3058	C₂×C₃₁	1	4	yes	complemented
174	#2948	C₂×C₃₁	1	4	yes	complemented
175	C₄×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
176	C₂²×C₃₁	—	2	2	no	—
177	C₂²×C₃₁	—	2	2	no	—
178	C₂²×C₃₁	—	2	4	no	—
179	C₂²×C₃₁	—	4	8	no	—
180	C₂²×C₃₁	—	4	16	no	—
181	C₂²×C₃₁	—	16	8	no	—
182	C₂²×C₃₁	#532	1	2	yes	—
183	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	2	4	no	—
186	C₄×C₃₁	—	2	2	no	—
187	C₄×C₃₁	—	4	8	no	—
188	C₄×C₃₁	#532	1	2	yes	—
189	C₄×C₃₁	#576	1	4	yes	—
190	C₄×C₃₁	C₂²×#41	1	2	yes	—
191	C₂²×D₈	C₂²×C₃₁	1	4	yes	—
192	C₂×#131	C₂²×C₃₁	1	2	yes	—
193	#559	—	2	4	no	—
194	#550	—	2	4	no	—
195	#546	—	2	8	no	—
196	#540	C₂²×C₃₁	1	8	yes	complemented
197	#535	C₂²×C₃₁	1	4	yes	—
198	#533	C₂²×C₃₁	1	2	yes	—
199	#532	C₂²×C₃₁	1	8	yes	complemented
200	C₂×#127	C₂²×C₃₁	1	2	yes	—
201	#518	C₂²×C₃₁	1	4	yes	—
202	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
203	#500	C₂²×C₃₁	1	2	yes	complemented
204	#499	C₂²×C₃₁	1	4	yes	complemented
205	#498	C₂²×C₃₁	1	2	yes	complemented
206	#493	C₂²×C₃₁	1	2	yes	—
207	#493	C₂²×C₃₁	1	4	yes	—
208	#493	C₂²×C₃₁	1	2	yes	—
209	#490	C₂²×C₃₁	1	8	yes	complemented
210	#486	C₂²×C₃₁	1	8	yes	complemented
211	#469	C₂²×C₃₁	1	16	yes	complemented
212	#466	C₂²×C₃₁	1	16	yes	complemented
213	#442	C₂²×C₃₁	1	16	yes	complemented
214	C₄×D₈	C₂²×C₃₁	1	16	yes	complemented
215	#427	C₂²×C₃₁	1	4	yes	—
216	#418	C₂²×C₃₁	1	8	yes	—
217	#405	C₂²×C₃₁	1	2	yes	—
218	#405	C₂²×C₃₁	1	4	yes	complemented
219	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
220	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
221	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	complemented
223	C₂×C₃₁	—	2	2	no	—
224	C₂×C₃₁	—	4	2	no	—
225	C₂×C₃₁	—	8	8	no	—
226	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
227	C₂×C₃₁	C₂×#576	1	2	yes	—
228	C₂×#41	—	2	8	no	—
229	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
230	C₂²×D₄	—	2	4	no	—
231	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
232	C₂×D₈	—	2	16	no	—
233	C₂×D₈	C₂³×C₃₁	1	8	yes	—
234	C₂×D₈	C₂³×C₃₁	1	8	yes	—
235	#131	—	2	8	no	—
236	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
237	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
238	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
239	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
240	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
241	#127	—	2	4	no	—
242	#127	—	2	4	no	—
243	#127	C₂³×C₃₁	1	4	yes	—
244	#127	C₂³×C₃₁	1	4	yes	—
245	#125	C₂³×C₃₁	1	4	yes	—
246	#124	—	2	4	no	—
247	#124	—	2	8	no	—
248	#123	—	2	16	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	#121	—	2	8	no	—
251	#121	—	2	16	no	—
252	#121	C₂³×C₃₁	1	16	yes	—
253	#120	—	2	8	no	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	D₄×C₃₁	1	2	yes	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	—	2	8	no	—
258	C₄×D₄	D₄×C₃₁	1	4	yes	—
259	C₄×D₄	D₄×C₃₁	1	2	yes	—
260	C₄×D₄	C₂³×C₃₁	1	16	yes	—
261	#117	C₂³×C₃₁	1	4	yes	—
262	#117	C₂³×C₃₁	1	1	yes	characteristic
263	#117	C₂³×C₃₁	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	8	no	—
265	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
267	#107	C₂³×C₃₁	1	8	yes	—
268	#106	C₂³×C₃₁	1	8	yes	—
269	#102	C₂³×C₃₁	1	32	yes	—
270	#97	C₂³×C₃₁	1	2	yes	—
271	#97	C₂³×C₃₁	1	4	yes	—
272	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₃₁	1	2	yes	—
275	C₄×C₈	C₂³×C₃₁	1	2	yes	—
276	C₄×C₈	C₂³×C₃₁	1	4	yes	—
277	C₃₁	#60714	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	—	2	4	no	—
279	#41	—	2	4	no	—
280	#41	—	8	16	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
283	C₂×D₄	—	2	16	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	8	8	no	—
289	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
290	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
292	C₂²×C₄	—	2	16	no	—
293	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
297	D₈	—	2	16	no	—
298	D₈	—	2	16	no	—
299	M₁₆	—	2	4	no	—
300	M₁₆	—	2	8	no	—
301	C₂×C₈	—	2	8	no	—
302	C₂×C₈	#41×C₃₁	1	8	yes	complemented
303	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
304	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
305	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
309	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
310	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
315	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
316	C₄²	—	2	4	no	—
317	C₄²	C₂×D₄×C₃₁	1	4	yes	—
318	C₄²	C₂×D₄×C₃₁	1	2	yes	—
319	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
320	C₄²	C₂⁴×C₃₁	1	2	yes	—
321	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
322	C₂³	—	2	8	no	—
323	C₂³	—	4	8	no	—
324	C₂³	—	8	8	no	—
325	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
326	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
327	Q₈	—	2	2	no	—
328	Q₈	—	4	8	no	—
329	D₄	—	2	4	no	—
330	D₄	—	2	2	no	—
331	D₄	—	2	16	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	16	no	—
334	D₄	—	8	8	no	—
335	D₄	—	8	16	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	8	16	no	—
341	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
342	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
343	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
346	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
347	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	C₂×#41×C₃₁	1	4	yes	—
350	C₈	C₂×#41×C₃₁	1	4	yes	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	4	8	no	—
355	C₂²	—	4	16	no	—
356	C₂²	—	16	8	no	—
357	C₂²	C₃₁×#532	1	2	yes	—
358	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	4	no	—
361	C₄	—	2	2	no	—
362	C₄	—	4	8	no	—
363	C₄	C₃₁×#532	1	2	yes	—
364	C₄	C₃₁×#576	1	4	yes	—
365	C₄	C₂²×#41×C₃₁	1	2	yes	—
366	C₂	—	2	2	no	—
367	C₂	—	4	2	no	—
368	C₂	—	8	8	no	—
369	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
370	C₂	C₂×C₃₁×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3184	C₂	semidirect
3. C₃₁×#3176	C₂	semidirect
4. C₃₁×#3169	C₂	semidirect
5. C₃₁×#3160	C₂	semidirect
6. C₂×C₃₁×#493	C₂	semidirect
7. C₃₁×#3138	C₂	semidirect
8. C₃₁×#3058	C₂	semidirect
9. C₃₁×#2948	C₂	semidirect
10. C₄×C₃₁×#131	C₂	semidirect
16. C₃₁×#540	C₂²	semidirect
19. C₃₁×#532	C₂²	semidirect
23. C₃₁×#500	C₂²	semidirect
24. C₃₁×#499	C₂²	semidirect
25. C₃₁×#498	C₂²	semidirect
29. C₃₁×#490	C₂²	semidirect
30. C₃₁×#486	C₂²	semidirect
31. C₃₁×#469	C₂²	semidirect
32. C₃₁×#466	C₂²	semidirect
33. C₃₁×#442	C₂²	semidirect
34. C₄×D₈×C₃₁	C₂²	semidirect
38. C₃₁×#405	C₂²	semidirect
40. C₄×M₁₆×C₃₁	C₂²	semidirect
42. C₂×C₄×C₈×C₃₁	C₂²	semidirect
116. C₂×C₈×C₃₁	#41	semidirect
136. #60714	C₃₁	direct (N × H)
166. #3508	C₂×C₃₁	semidirect
167. #3184	C₂×C₃₁	semidirect
168. #3176	C₂×C₃₁	semidirect
169. #3169	C₂×C₃₁	semidirect
170. #3160	C₂×C₃₁	semidirect
171. C₂×#493	C₂×C₃₁	semidirect
172. #3138	C₂×C₃₁	semidirect
173. #3058	C₂×C₃₁	semidirect
174. #2948	C₂×C₃₁	semidirect
175. C₄×#131	C₂×C₃₁	semidirect
196. #540	C₂²×C₃₁	semidirect
199. #532	C₂²×C₃₁	semidirect
203. #500	C₂²×C₃₁	semidirect
204. #499	C₂²×C₃₁	semidirect
205. #498	C₂²×C₃₁	semidirect
209. #490	C₂²×C₃₁	semidirect
210. #486	C₂²×C₃₁	semidirect
211. #469	C₂²×C₃₁	semidirect
212. #466	C₂²×C₃₁	semidirect
213. #442	C₂²×C₃₁	semidirect
214. C₄×D₈	C₂²×C₃₁	semidirect
218. #405	C₂²×C₃₁	semidirect
220. C₄×M₁₆	C₂²×C₃₁	semidirect
222. C₂×C₄×C₈	C₂²×C₃₁	semidirect
277. C₃₁	#60714	direct (N × H)
302. C₂×C₈	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3508	2
C₃₁×#3184	2
C₃₁×#3176	2
C₃₁×#3169	2
C₃₁×#3160	2
C₂×C₃₁×#493	2
C₃₁×#3138	2
C₃₁×#3058	2
C₃₁×#2948	2
C₄×C₃₁×#131	2
#60714	31

Subgroups — C31×#60714 #21517473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60714 #21517473