Subgroups — C₃₁×#21659 #21478418

Order 7936.

722 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2932	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1963	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1938	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1937	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1837	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1765	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1764	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#131	C₂²	1	2	yes	—
13	C₃₁×#533	C₂²	1	1	yes	characteristic
14	C₃₁×#532	C₂²	1	1	yes	characteristic
15	C₃₁×#488	C₄	1	4	yes	complemented
16	C₃₁×#487	C₄	1	2	yes	complemented
17	C₃₁×#486	C₄	1	2	yes	complemented
18	C₃₁×#446	—	2	4	no	—
19	C₃₁×#435	—	2	4	no	—
20	C₃₁×#424	C₂²	1	2	yes	—
21	C₃₁×#423	C₂²	1	1	yes	characteristic
22	C₃₁×#423	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#104	C₂²	1	2	yes	—
24	C₂×C₃₁×#104	C₂²	1	2	yes	—
25	C₃₁×#416	C₂²	1	2	yes	—
26	C₃₁×#416	C₂²	1	2	yes	—
27	C₃₁×#408	C₂²	1	2	yes	—
28	C₃₁×#405	C₂²	1	2	yes	—
29	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#376	C₂²	1	1	yes	characteristic
36	C₃₁×#341	C₂²	1	2	yes	—
37	C₃₁×#341	C₂²	1	2	yes	—
38	C₃₁×#339	C₂²	1	2	yes	—
39	C₃₁×#339	C₂²	1	2	yes	—
40	C₂×#41×C₃₁	C₂³	1	2	yes	—
41	C₃₁×#131	—	2	4	no	—
42	C₃₁×#131	—	2	4	no	—
43	C₂×M₁₆×C₃₁	—	2	2	no	—
44	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
45	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₁	—	2	2	no	—
47	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₃₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
53	C₃₁×#127	C₂×C₄	1	1	yes	characteristic
54	C₃₁×#125	C₂×C₄	1	2	yes	—
55	C₃₁×#124	C₂×C₄	1	2	yes	—
56	C₃₁×C₂²⋊Q₈	—	2	2	no	—
57	C₃₁×#121	—	2	2	no	—
58	C₄×Q₈×C₃₁	—	2	2	no	—
59	C₄×D₄×C₃₁	—	2	2	no	—
60	C₃₁×#117	C₂³	1	2	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×C₄⋊C₈	—	2	4	no	—
65	C₃₁×C₄⋊C₈	—	2	2	no	—
66	C₃₁×C₄⋊C₈	—	2	2	no	—
67	C₃₁×#104	—	2	4	no	—
68	C₃₁×#104	—	2	4	no	—
69	C₃₁×#103	C₂×C₄	1	4	yes	—
70	C₃₁×#103	C₂×C₄	1	4	yes	—
71	C₃₁×#102	C₂×C₄	1	4	yes	—
72	C₃₁×#102	C₂×C₄	1	4	yes	—
73	C₃₁×C₂²⋊C₈	—	2	4	no	—
74	C₃₁×#97	—	2	2	no	—
75	C₃₁×#97	—	2	2	no	—
76	C₃₁×#97	—	2	2	no	—
77	C₃₁×#97	D₄	1	4	yes	—
78	C₄×C₈×C₃₁	—	2	2	no	—
79	C₄×C₈×C₃₁	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
83	C₃₁×#95	—	2	2	no	—
84	#41×C₃₁	—	2	2	no	—
85	#41×C₃₁	—	2	2	no	—
86	#41×C₃₁	—	2	2	no	—
87	#41×C₃₁	—	2	2	no	—
88	C₂×Q₈×C₃₁	—	2	2	no	—
89	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₃₁	—	2	2	no	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₃₁	—	2	1	no	—
94	C₂²×C₄×C₃₁	—	2	1	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	#41	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
98	M₁₆×C₃₁	—	2	2	no	—
99	M₁₆×C₃₁	—	2	2	no	—
100	M₁₆×C₃₁	—	2	2	no	—
101	M₁₆×C₃₁	—	2	2	no	—
102	M₁₆×C₃₁	—	4	4	no	—
103	C₂×C₈×C₃₁	—	2	1	no	—
104	C₂×C₈×C₃₁	—	2	1	no	—
105	C₂×C₈×C₃₁	—	2	1	no	—
106	C₂×C₈×C₃₁	—	2	1	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	4	4	no	—
112	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₃₁	#41	1	2	yes	—
117	C₂×C₈×C₃₁	#41	1	2	yes	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
122	C₂²⋊C₄×C₃₁	—	2	2	no	—
123	C₂²⋊C₄×C₃₁	—	2	4	no	—
124	C₄²×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	—	2	1	no	—
126	C₄²×C₃₁	—	2	1	no	—
127	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₃₁	C₂×D₄	1	2	yes	—
130	C₄²×C₃₁	#41	1	2	yes	—
131	C₄²×C₃₁	#41	1	2	yes	—
132	#21659	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₃₁	—	2	2	no	—
134	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
135	Q₈×C₃₁	—	2	2	no	—
136	Q₈×C₃₁	—	2	2	no	—
137	Q₈×C₃₁	—	8	2	no	—
138	D₄×C₃₁	—	2	2	no	—
139	D₄×C₃₁	—	2	2	no	—
140	D₄×C₃₁	—	4	2	no	—
141	D₄×C₃₁	—	4	2	no	—
142	D₄×C₃₁	—	8	2	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	—	2	2	no	—
162	C₈×C₃₁	—	2	2	no	—
163	C₈×C₃₁	—	4	2	no	—
164	C₈×C₃₁	—	4	2	no	—
165	C₈×C₃₁	#124	1	4	yes	—
166	#3131	C₂×C₃₁	1	1	yes	characteristic
167	#2961	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#2932	C₂×C₃₁	1	1	yes	characteristic
169	#1995	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#1963	C₂×C₃₁	1	1	yes	characteristic
171	#1938	C₂×C₃₁	1	2	yes	complemented
172	#1937	C₂×C₃₁	1	2	yes	complemented
173	#1837	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1765	C₂×C₃₁	1	2	yes	complemented
175	#1764	C₂×C₃₁	1	2	yes	complemented
176	#1726	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂²×C₃₁	—	2	2	no	—
178	C₂²×C₃₁	—	4	4	no	—
179	C₂²×C₃₁	—	4	2	no	—
180	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
181	C₂²×C₃₁	#529	1	1	yes	characteristic
182	C₂²×C₃₁	#529	1	1	yes	characteristic
183	C₄×C₃₁	—	2	2	no	—
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	4	2	no	—
187	C₄×C₃₁	—	4	4	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	C₄×#41	1	1	yes	characteristic
190	C₄×C₃₁	C₄×#41	1	1	yes	characteristic
191	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
192	C₄×C₃₁	#532	1	1	yes	characteristic
193	C₂×#131	C₂²×C₃₁	1	2	yes	—
194	#533	C₂²×C₃₁	1	1	yes	characteristic
195	#532	C₂²×C₃₁	1	1	yes	characteristic
196	#488	C₄×C₃₁	1	4	yes	complemented
197	#487	C₄×C₃₁	1	2	yes	complemented
198	#486	C₄×C₃₁	1	2	yes	complemented
199	#446	—	2	4	no	—
200	#435	—	2	4	no	—
201	#424	C₂²×C₃₁	1	2	yes	—
202	#423	C₂²×C₃₁	1	1	yes	characteristic
203	#423	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×#104	C₂²×C₃₁	1	2	yes	—
205	C₂×#104	C₂²×C₃₁	1	2	yes	—
206	#416	C₂²×C₃₁	1	2	yes	—
207	#416	C₂²×C₃₁	1	2	yes	—
208	#408	C₂²×C₃₁	1	2	yes	—
209	#405	C₂²×C₃₁	1	2	yes	—
210	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
216	#376	C₂²×C₃₁	1	1	yes	characteristic
217	#341	C₂²×C₃₁	1	2	yes	—
218	#341	C₂²×C₃₁	1	2	yes	—
219	#339	C₂²×C₃₁	1	2	yes	—
220	#339	C₂²×C₃₁	1	2	yes	—
221	C₂×C₃₁	—	2	1	no	—
222	C₂×C₃₁	—	2	1	no	—
223	C₂×C₃₁	—	8	2	no	—
224	C₂×C₃₁	C₄×#124	1	1	yes	characteristic
225	C₂×C₃₁	#2957	1	2	yes	—
226	C₂×#41	C₂³×C₃₁	1	2	yes	—
227	#131	—	2	4	no	—
228	#131	—	2	4	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
231	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
237	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
238	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
239	#127	C₂×C₄×C₃₁	1	1	yes	characteristic
240	#125	C₂×C₄×C₃₁	1	2	yes	—
241	#124	C₂×C₄×C₃₁	1	2	yes	—
242	C₂²⋊Q₈	—	2	2	no	—
243	#121	—	2	2	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	#117	C₂³×C₃₁	1	2	yes	—
247	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	2	2	no	—
253	#104	—	2	4	no	—
254	#104	—	2	4	no	—
255	#103	C₂×C₄×C₃₁	1	4	yes	—
256	#103	C₂×C₄×C₃₁	1	4	yes	—
257	#102	C₂×C₄×C₃₁	1	4	yes	—
258	#102	C₂×C₄×C₃₁	1	4	yes	—
259	C₂²⋊C₈	—	2	4	no	—
260	#97	—	2	2	no	—
261	#97	—	2	2	no	—
262	#97	—	2	2	no	—
263	#97	D₄×C₃₁	1	4	yes	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
268	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
269	#95	—	2	2	no	—
270	C₃₁	#21659	1	1	yes	characteristic, direct product factor, Sylow
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	#41×C₃₁	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	4	4	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
300	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
303	C₂×C₈	#41×C₃₁	1	2	yes	—
304	C₂×C₈	#41×C₃₁	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
315	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₃₁	1	2	yes	—
317	C₄²	#41×C₃₁	1	2	yes	—
318	C₄²	#41×C₃₁	1	2	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	Q₈	—	8	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
339	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
340	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₈	C₃₁×#124	1	4	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	2	no	—
355	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
356	C₂²	C₃₁×#529	1	1	yes	characteristic
357	C₂²	C₃₁×#529	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	4	no	—
363	C₄	—	4	2	no	—
364	C₄	C₄×#41×C₃₁	1	1	yes	characteristic
365	C₄	C₄×#41×C₃₁	1	1	yes	characteristic
366	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
367	C₄	C₃₁×#532	1	1	yes	characteristic
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	8	2	no	—
371	C₂	C₄×C₃₁×#124	1	1	yes	characteristic
372	C₂	C₃₁×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₃₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₃₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2961	C₂	semidirect
4. C₃₁×#1995	C₂	semidirect
6. C₃₁×#1938	C₂	semidirect
7. C₃₁×#1937	C₂	semidirect
8. C₃₁×#1837	C₂	semidirect
9. C₃₁×#1765	C₂	semidirect
10. C₃₁×#1764	C₂	semidirect
11. C₃₁×#1726	C₂	semidirect
15. C₃₁×#488	C₄	semidirect
16. C₃₁×#487	C₄	semidirect
17. C₃₁×#486	C₄	semidirect
132. #21659	C₃₁	direct (N × H)
167. #2961	C₂×C₃₁	semidirect
169. #1995	C₂×C₃₁	semidirect
171. #1938	C₂×C₃₁	semidirect
172. #1937	C₂×C₃₁	semidirect
173. #1837	C₂×C₃₁	semidirect
174. #1765	C₂×C₃₁	semidirect
175. #1764	C₂×C₃₁	semidirect
176. #1726	C₂×C₃₁	semidirect
196. #488	C₄×C₃₁	semidirect
197. #487	C₄×C₃₁	semidirect
198. #486	C₄×C₃₁	semidirect
270. C₃₁	#21659	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×#3131	2
C₃₁×#2961	2
C₃₁×#2932	2
C₃₁×#1995	2
C₃₁×#1963	2
C₃₁×#1938	2
C₃₁×#1937	2
C₃₁×#1837	2
C₃₁×#1765	2
C₃₁×#1764	2
C₃₁×#1726	2
#21659	31

Subgroups — C31×#21659 #21478418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21659 #21478418