Subgroups — C₃₁×#19256 #21476015

Order 7936.

690 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3077	C₂	1	2	yes	maximal
3	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1683	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1675	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1669	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1550	C₂	1	2	yes	maximal, complemented
9	C₂³×C₈×C₃₁	—	2	1	no	—
10	C₃₁×#533	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
13	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
14	C₃₁×#487	C₂²	1	2	yes	complemented
15	C₃₁×#478	—	2	4	no	—
16	C₃₁×#476	C₂²	1	4	yes	—
17	C₃₁×#474	C₂²	1	4	yes	—
18	C₃₁×#467	—	2	1	no	—
19	C₃₁×#467	—	2	1	no	—
20	C₄×Q₁₆×C₃₁	—	2	1	no	—
21	C₄×Q₁₆×C₃₁	—	2	1	no	—
22	C₈×D₄×C₃₁	—	2	1	no	—
23	C₈×D₄×C₃₁	—	2	1	no	—
24	C₈×D₄×C₃₁	C₂²	1	2	yes	—
25	C₈×D₄×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#428	—	2	2	no	—
27	C₃₁×#423	C₂²	1	2	yes	—
28	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃₁×#418	—	2	2	no	—
30	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	2	yes	complemented
33	C₃₁×#335	C₂²	1	2	yes	complemented
34	C₃₁×#333	C₂²	1	4	yes	complemented
35	C₃₁×#332	C₂²	1	4	yes	complemented
36	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₃₁	—	2	1	no	—
38	C₂×Q₁₆×C₃₁	—	2	1	no	—
39	C₂×Q₁₆×C₃₁	—	2	1	no	—
40	C₂×M₁₆×C₃₁	—	2	2	no	—
41	C₂²×C₈×C₃₁	—	2	1	no	—
42	C₂²×C₈×C₃₁	—	2	2	no	—
43	C₂²×C₈×C₃₁	—	2	2	no	—
44	C₂²×C₈×C₃₁	—	4	4	no	—
45	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
47	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
48	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
49	C₃₁×#125	—	2	2	no	—
50	C₃₁×C₂²⋊Q₈	—	2	2	no	—
51	C₃₁×C₂²⋊Q₈	—	2	2	no	—
52	C₄×Q₈×C₃₁	—	2	2	no	—
53	C₄×Q₈×C₃₁	—	2	2	no	—
54	C₄×D₄×C₃₁	—	2	1	no	—
55	C₄×D₄×C₃₁	—	2	1	no	—
56	C₄×D₄×C₃₁	D₄	1	2	yes	—
57	C₄×D₄×C₃₁	C₂³	1	2	yes	—
58	C₃₁×#117	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#107	—	2	1	no	—
63	C₃₁×#107	—	2	1	no	—
64	C₃₁×#107	—	2	4	no	—
65	C₃₁×#106	—	2	4	no	—
66	C₃₁×C₄⋊C₈	—	2	1	no	—
67	C₃₁×C₄⋊C₈	—	2	2	no	—
68	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
69	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
70	C₃₁×#103	—	2	2	no	—
71	C₃₁×#103	—	2	2	no	—
72	C₃₁×#102	—	2	4	no	—
73	C₃₁×#102	—	2	4	no	—
74	C₃₁×C₂²⋊C₈	—	2	2	no	—
75	C₃₁×C₂²⋊C₈	—	2	2	no	—
76	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
77	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂⁴×C₃₁	—	2	1	no	—
81	C₂×Q₈×C₃₁	—	2	2	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	1	no	—
84	C₂×D₄×C₃₁	—	2	2	no	—
85	C₂×D₄×C₃₁	Q₁₆	1	4	yes	complemented
86	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₃₁	—	2	1	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	—	2	2	no	—
90	C₂²×C₄×C₃₁	—	4	2	no	—
91	C₂²×C₄×C₃₁	—	4	2	no	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
95	Q₁₆×C₃₁	—	4	2	no	—
96	Q₁₆×C₃₁	—	4	2	no	—
97	M₁₆×C₃₁	—	4	4	no	—
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	4	no	—
101	C₂×C₈×C₃₁	—	4	1	no	—
102	C₂×C₈×C₃₁	—	4	4	no	—
103	C₂×C₈×C₃₁	—	4	2	no	—
104	C₂×C₈×C₃₁	—	4	4	no	—
105	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₄⋊C₄×C₃₁	—	2	1	no	—
110	C₄⋊C₄×C₃₁	—	2	2	no	—
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	—	4	2	no	—
115	C₄⋊C₄×C₃₁	—	4	2	no	—
116	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²⋊C₄×C₃₁	—	2	2	no	—
118	C₂²⋊C₄×C₃₁	—	2	2	no	—
119	C₂²⋊C₄×C₃₁	—	4	2	no	—
120	C₄²×C₃₁	—	4	2	no	—
121	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₃₁	#41	1	1	yes	characteristic
124	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
125	#19256	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₃₁	—	2	2	no	—
127	C₂³×C₃₁	—	2	4	no	—
128	C₂³×C₃₁	—	4	2	no	—
129	C₂³×C₃₁	—	4	2	no	—
130	C₂³×C₃₁	#121	1	1	yes	characteristic
131	Q₈×C₃₁	—	4	2	no	—
132	Q₈×C₃₁	—	4	2	no	—
133	Q₈×C₃₁	—	8	2	no	—
134	D₄×C₃₁	—	2	2	no	—
135	D₄×C₃₁	—	2	4	no	—
136	D₄×C₃₁	C₂×Q₁₆	1	4	yes	—
137	C₂×C₄×C₃₁	—	2	1	no	—
138	C₂×C₄×C₃₁	—	2	1	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	4	1	no	—
141	C₂×C₄×C₃₁	—	4	4	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
148	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
149	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
151	C₂×C₄×C₃₁	#135	1	2	yes	—
152	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
155	C₈×C₃₁	—	2	1	no	—
156	C₈×C₃₁	—	2	1	no	—
157	C₈×C₃₁	—	2	1	no	—
158	C₈×C₃₁	—	4	4	no	—
159	C₈×C₃₁	—	4	2	no	—
160	C₈×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
161	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#3077	C₂×C₃₁	1	2	yes	—
163	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
164	#1683	C₂×C₃₁	1	4	yes	complemented
165	#1675	C₂×C₃₁	1	2	yes	complemented
166	#1669	C₂×C₃₁	1	2	yes	complemented
167	#1567	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#1550	C₂×C₃₁	1	2	yes	complemented
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	2	4	no	—
172	C₂²×C₃₁	—	4	8	no	—
173	C₂²×C₃₁	—	4	2	no	—
174	C₂²×C₃₁	—	4	2	no	—
175	C₂²×C₃₁	#467	1	2	yes	—
176	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	4	2	no	—
181	C₄×C₃₁	—	8	2	no	—
182	C₄×C₃₁	—	8	2	no	—
183	C₄×C₃₁	#467	1	2	yes	—
184	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
185	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
186	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₄×C₃₁	#575	1	1	yes	characteristic
188	C₂³×C₈	—	2	1	no	—
189	#533	C₂²×C₃₁	1	2	yes	—
190	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
191	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
192	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
193	#487	C₂²×C₃₁	1	2	yes	complemented
194	#478	—	2	4	no	—
195	#476	C₂²×C₃₁	1	4	yes	—
196	#474	C₂²×C₃₁	1	4	yes	—
197	#467	—	2	1	no	—
198	#467	—	2	1	no	—
199	C₄×Q₁₆	—	2	1	no	—
200	C₄×Q₁₆	—	2	1	no	—
201	C₈×D₄	—	2	1	no	—
202	C₈×D₄	—	2	1	no	—
203	C₈×D₄	C₂²×C₃₁	1	2	yes	—
204	C₈×D₄	C₂²×C₃₁	1	2	yes	—
205	#428	—	2	2	no	—
206	#423	C₂²×C₃₁	1	2	yes	—
207	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
208	#418	—	2	2	no	—
209	C₂×C₂²⋊C₈	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
211	#335	C₂²×C₃₁	1	2	yes	complemented
212	#335	C₂²×C₃₁	1	2	yes	complemented
213	#333	C₂²×C₃₁	1	4	yes	complemented
214	#332	C₂²×C₃₁	1	4	yes	complemented
215	C₂×C₃₁	—	2	2	no	—
216	C₂×C₃₁	—	4	4	no	—
217	C₂×C₃₁	#3036	1	1	yes	characteristic
218	C₂×C₃₁	C₂×#467	1	1	yes	characteristic
219	C₂×C₃₁	#3067	1	1	yes	characteristic
220	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
221	C₂³×C₄	—	2	1	no	—
222	C₂×Q₁₆	—	2	1	no	—
223	C₂×Q₁₆	—	2	1	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	4	4	no	—
229	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
230	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
231	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
232	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
233	#125	—	2	2	no	—
234	C₂²⋊Q₈	—	2	2	no	—
235	C₂²⋊Q₈	—	2	2	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	D₄×C₃₁	1	2	yes	—
241	C₄×D₄	C₂³×C₃₁	1	2	yes	—
242	#117	—	2	2	no	—
243	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
246	#107	—	2	1	no	—
247	#107	—	2	1	no	—
248	#107	—	2	4	no	—
249	#106	—	2	4	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
253	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
254	#103	—	2	2	no	—
255	#103	—	2	2	no	—
256	#102	—	2	4	no	—
257	#102	—	2	4	no	—
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
261	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
264	C₃₁	#19256	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	—	2	1	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	Q₁₆×C₃₁	1	4	yes	complemented
271	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
280	Q₁₆	—	4	2	no	—
281	Q₁₆	—	4	2	no	—
282	M₁₆	—	4	4	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	4	1	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₄²	—	4	2	no	—
306	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₄²	#41×C₃₁	1	1	yes	characteristic
309	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₃₁×#121	1	1	yes	characteristic
315	Q₈	—	4	2	no	—
316	Q₈	—	4	2	no	—
317	Q₈	—	8	2	no	—
318	D₄	—	2	4	no	—
319	D₄	—	2	2	no	—
320	D₄	C₂×Q₁₆×C₃₁	1	4	yes	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
332	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
333	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
334	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
335	C₂×C₄	C₃₁×#135	1	2	yes	—
336	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	4	4	no	—
343	C₈	—	4	2	no	—
344	C₈	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	4	8	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	C₃₁×#467	1	2	yes	—
352	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	8	2	no	—
358	C₄	—	8	2	no	—
359	C₄	C₃₁×#467	1	2	yes	—
360	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
361	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
362	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₄	C₃₁×#575	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	4	4	no	—
366	C₂	C₃₁×#3036	1	1	yes	characteristic
367	C₂	C₂×C₃₁×#467	1	1	yes	characteristic
368	C₂	C₃₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3170	C₂	semidirect
4. C₃₁×#1683	C₂	semidirect
5. C₃₁×#1675	C₂	semidirect
6. C₃₁×#1669	C₂	semidirect
7. C₃₁×#1567	C₂	semidirect
8. C₃₁×#1550	C₂	semidirect
12. C₃₁×#500	C₂²	semidirect
13. C₃₁×#494	C₂²	semidirect
14. C₃₁×#487	C₂²	semidirect
32. C₃₁×#335	C₂²	semidirect
33. C₃₁×#335	C₂²	semidirect
34. C₃₁×#333	C₂²	semidirect
35. C₃₁×#332	C₂²	semidirect
85. C₂×D₄×C₃₁	Q₁₆	semidirect
125. #19256	C₃₁	direct (N × H)
161. #3170	C₂×C₃₁	semidirect
164. #1683	C₂×C₃₁	semidirect
165. #1675	C₂×C₃₁	semidirect
166. #1669	C₂×C₃₁	semidirect
167. #1567	C₂×C₃₁	semidirect
168. #1550	C₂×C₃₁	semidirect
191. #500	C₂²×C₃₁	semidirect
192. #494	C₂²×C₃₁	semidirect
193. #487	C₂²×C₃₁	semidirect
211. #335	C₂²×C₃₁	semidirect
212. #335	C₂²×C₃₁	semidirect
213. #333	C₂²×C₃₁	semidirect
214. #332	C₂²×C₃₁	semidirect
264. C₃₁	#19256	direct (N × H)
270. C₂×D₄	Q₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3170	2
C₃₁×#3077	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1683	2
C₃₁×#1675	2
C₃₁×#1669	2
C₃₁×#1567	2
C₃₁×#1550	2
#19256	31

Subgroups — C31×#19256 #21476015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19256 #21476015