Subgroups — C₃₁×#12980 #21469739

Order 7936.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#443	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#350	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#350	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1374	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#135	C₄	1	1	yes	characteristic
9	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
10	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
11	C₃₁×#504	—	2	2	no	—
12	C₃₁×#504	—	2	2	no	—
13	C₂×C₃₁×M₃₂	—	2	1	no	—
14	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₃₁	—	2	1	no	—
17	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#443	—	2	2	no	—
20	C₃₁×#443	—	2	2	no	—
21	C₂×C₃₁×#108	C₄	1	1	yes	characteristic
22	C₂×C₃₁×#104	C₄	1	1	yes	characteristic
23	C₂×C₃₁×#104	C₄	1	1	yes	characteristic
24	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#350	—	2	2	no	—
26	C₃₁×#350	—	2	2	no	—
27	C₃₁×C₂²⋊C₁₆	—	2	1	no	—
28	C₃₁×C₂²⋊C₁₆	—	2	1	no	—
29	C₂×#41×C₃₁	C₂×C₄	1	1	yes	characteristic
30	C₂×#41×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₃₁×#135	—	2	2	no	—
32	C₃₁×#135	—	2	2	no	—
33	C₂×Q₁₆×C₃₁	C₈	1	1	yes	characteristic
34	C₂×SD₁₆×C₃₁	C₈	1	1	yes	characteristic
35	C₂×SD₁₆×C₃₁	C₈	1	1	yes	characteristic
36	C₂×D₈×C₃₁	C₈	1	1	yes	characteristic
37	C₃₁×#131	—	2	1	no	—
38	C₃₁×#131	—	2	1	no	—
39	C₃₁×#131	—	2	1	no	—
40	C₃₁×#131	—	2	1	no	—
41	C₃₁×#131	—	2	1	no	—
42	C₃₁×#131	—	2	1	no	—
43	C₃₁×#131	D₄	1	2	yes	—
44	C₃₁×#131	D₄	1	2	yes	—
45	C₂×M₁₆×C₃₁	—	2	1	no	—
46	C₂×M₁₆×C₃₁	—	2	1	no	—
47	C₂×M₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	—	2	1	no	—
50	C₂²×C₈×C₃₁	—	2	1	no	—
51	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
54	C₃₁×M₃₂	—	2	4	no	—
55	C₃₁×M₃₂	—	2	1	no	—
56	C₃₁×M₃₂	—	2	1	no	—
57	C₃₁×M₃₂	—	2	1	no	—
58	C₃₁×M₃₂	D₄	1	2	yes	—
59	C₂×C₁₆×C₃₁	—	2	4	no	—
60	C₂×C₁₆×C₃₁	—	2	1	no	—
61	C₂×C₁₆×C₃₁	—	2	1	no	—
62	C₂×C₁₆×C₃₁	—	2	1	no	—
63	C₂×C₁₆×C₃₁	—	2	1	no	—
64	C₂×C₁₆×C₃₁	—	2	1	no	—
65	C₂×C₁₆×C₃₁	—	2	1	no	—
66	C₂×C₁₆×C₃₁	—	2	1	no	—
67	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
69	C₃₁×#108	—	2	2	no	—
70	C₃₁×#104	—	2	2	no	—
71	C₃₁×#104	—	2	2	no	—
72	C₄×C₈×C₃₁	—	2	1	no	—
73	C₄×C₈×C₃₁	—	2	1	no	—
74	#41×C₃₁	—	2	1	no	—
75	#41×C₃₁	—	2	1	no	—
76	#41×C₃₁	—	2	1	no	—
77	#41×C₃₁	—	2	1	no	—
78	#41×C₃₁	—	2	1	no	—
79	#41×C₃₁	—	2	1	no	—
80	#41×C₃₁	C₂²⋊C₄	1	2	yes	—
81	#41×C₃₁	M₁₆	1	2	yes	—
82	C₂×Q₈×C₃₁	C₂×C₈	1	1	yes	characteristic
83	C₂×Q₈×C₃₁	C₂×C₈	1	1	yes	characteristic
84	C₂×D₄×C₃₁	—	2	1	no	—
85	C₂×D₄×C₃₁	—	2	1	no	—
86	C₂×D₄×C₃₁	C₂×C₈	1	1	yes	characteristic
87	C₂×D₄×C₃₁	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
92	Q₁₆×C₃₁	—	2	2	no	—
93	SD₁₆×C₃₁	—	2	2	no	—
94	SD₁₆×C₃₁	—	2	2	no	—
95	D₈×C₃₁	—	2	2	no	—
96	M₁₆×C₃₁	—	2	1	no	—
97	M₁₆×C₃₁	—	2	2	no	—
98	M₁₆×C₃₁	—	2	2	no	—
99	M₁₆×C₃₁	—	2	1	no	—
100	M₁₆×C₃₁	—	2	1	no	—
101	M₁₆×C₃₁	—	4	1	no	—
102	M₁₆×C₃₁	—	4	1	no	—
103	M₁₆×C₃₁	C₂²⋊C₄	1	2	yes	—
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	2	no	—
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	4	1	no	—
111	C₂×C₈×C₃₁	—	4	1	no	—
112	C₂×C₈×C₃₁	C₂×C₈	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×C₈	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
119	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
120	C₄²×C₃₁	—	2	1	no	—
121	C₄²×C₃₁	—	2	1	no	—
122	C₁₆×C₃₁	—	2	1	no	—
123	C₁₆×C₃₁	—	2	2	no	—
124	C₁₆×C₃₁	—	2	1	no	—
125	C₁₆×C₃₁	—	4	1	no	—
126	C₁₆×C₃₁	—	4	1	no	—
127	#12980	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	1	no	—
129	C₂³×C₃₁	—	2	1	no	—
130	C₂³×C₃₁	#131	1	1	yes	characteristic
131	Q₈×C₃₁	—	2	1	no	—
132	Q₈×C₃₁	—	2	1	no	—
133	Q₈×C₃₁	—	2	1	no	—
134	Q₈×C₃₁	C₂²⋊C₈	1	2	yes	—
135	D₄×C₃₁	—	2	2	no	—
136	D₄×C₃₁	—	2	2	no	—
137	D₄×C₃₁	—	2	1	no	—
138	D₄×C₃₁	—	2	1	no	—
139	D₄×C₃₁	—	2	1	no	—
140	D₄×C₃₁	—	4	1	no	—
141	D₄×C₃₁	—	4	1	no	—
142	D₄×C₃₁	C₂²⋊C₈	1	2	yes	—
143	C₂×C₄×C₃₁	—	2	1	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	—	2	1	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	1	no	—
152	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
157	C₂×C₄×C₃₁	#131	1	1	yes	characteristic
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	—	2	1	no	—
161	C₈×C₃₁	—	4	1	no	—
162	C₈×C₃₁	#120	1	1	yes	characteristic
163	C₈×C₃₁	#121	1	1	yes	characteristic
164	C₈×C₃₁	#121	1	1	yes	characteristic
165	C₈×C₃₁	#123	1	1	yes	characteristic
166	C₂×#504	C₂×C₃₁	1	1	yes	characteristic, complemented
167	C₂×#443	C₂×C₃₁	1	1	yes	characteristic
168	C₂×#350	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂×#350	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#2113	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#1376	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#1374	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂²×C₃₁	—	2	1	no	—
174	C₂²×C₃₁	—	2	1	no	—
175	C₂²×C₃₁	—	2	2	no	—
176	C₂²×C₃₁	—	4	1	no	—
177	C₂²×C₃₁	—	4	1	no	—
178	C₂²×C₃₁	—	4	1	no	—
179	C₂²×C₃₁	—	4	1	no	—
180	C₂²×C₃₁	—	4	1	no	—
181	C₂²×C₃₁	#408	1	1	yes	characteristic
182	C₂²×C₃₁	C₈×D₄	1	1	yes	characteristic
183	C₂²×C₃₁	#435	1	1	yes	characteristic
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	4	1	no	—
187	C₄×C₃₁	#386	1	1	yes	characteristic
188	C₄×C₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
189	C₄×C₃₁	C₈×D₄	1	1	yes	characteristic
190	C₄×C₃₁	#435	1	1	yes	characteristic
191	C₂×#135	C₄×C₃₁	1	1	yes	characteristic
192	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
194	#504	—	2	2	no	—
195	#504	—	2	2	no	—
196	C₂×M₃₂	—	2	1	no	—
197	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
199	C₂²×C₁₆	—	2	1	no	—
200	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
201	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
202	#443	—	2	2	no	—
203	#443	—	2	2	no	—
204	C₂×#108	C₄×C₃₁	1	1	yes	characteristic
205	C₂×#104	C₄×C₃₁	1	1	yes	characteristic
206	C₂×#104	C₄×C₃₁	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
208	#350	—	2	2	no	—
209	#350	—	2	2	no	—
210	C₂²⋊C₁₆	—	2	1	no	—
211	C₂²⋊C₁₆	—	2	1	no	—
212	C₂×C₃₁	—	2	1	no	—
213	C₂×C₃₁	—	2	1	no	—
214	C₂×C₃₁	—	4	2	no	—
215	C₂×C₃₁	—	8	1	no	—
216	C₂×C₃₁	#1869	1	1	yes	characteristic
217	C₂×C₃₁	#2170	1	1	yes	characteristic
218	C₂×C₃₁	#2171	1	1	yes	characteristic
219	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic
220	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic
221	#135	—	2	2	no	—
222	#135	—	2	2	no	—
223	C₂×Q₁₆	C₈×C₃₁	1	1	yes	characteristic
224	C₂×SD₁₆	C₈×C₃₁	1	1	yes	characteristic
225	C₂×SD₁₆	C₈×C₃₁	1	1	yes	characteristic
226	C₂×D₈	C₈×C₃₁	1	1	yes	characteristic
227	#131	—	2	1	no	—
228	#131	—	2	1	no	—
229	#131	—	2	1	no	—
230	#131	—	2	1	no	—
231	#131	—	2	1	no	—
232	#131	—	2	1	no	—
233	#131	D₄×C₃₁	1	2	yes	—
234	#131	D₄×C₃₁	1	2	yes	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
238	C₂×M₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
244	M₃₂	—	2	4	no	—
245	M₃₂	—	2	1	no	—
246	M₃₂	—	2	1	no	—
247	M₃₂	—	2	1	no	—
248	M₃₂	D₄×C₃₁	1	2	yes	—
249	C₂×C₁₆	—	2	4	no	—
250	C₂×C₁₆	—	2	1	no	—
251	C₂×C₁₆	—	2	1	no	—
252	C₂×C₁₆	—	2	1	no	—
253	C₂×C₁₆	—	2	1	no	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	2	1	no	—
256	C₂×C₁₆	—	2	1	no	—
257	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
258	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
259	#108	—	2	2	no	—
260	#104	—	2	2	no	—
261	#104	—	2	2	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	—	2	1	no	—
264	C₃₁	#12980	1	1	yes	characteristic, direct product factor, Sylow
265	#41	—	2	1	no	—
266	#41	—	2	1	no	—
267	#41	—	2	1	no	—
268	#41	—	2	1	no	—
269	#41	—	2	1	no	—
270	#41	—	2	1	no	—
271	#41	C₂²⋊C₄×C₃₁	1	2	yes	—
272	#41	M₁₆×C₃₁	1	2	yes	—
273	C₂×Q₈	C₂×C₈×C₃₁	1	1	yes	characteristic
274	C₂×Q₈	C₂×C₈×C₃₁	1	1	yes	characteristic
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	C₂×C₈×C₃₁	1	1	yes	characteristic
278	C₂×D₄	C₂×C₈×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
283	Q₁₆	—	2	2	no	—
284	SD₁₆	—	2	2	no	—
285	SD₁₆	—	2	2	no	—
286	D₈	—	2	2	no	—
287	M₁₆	—	2	1	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	2	1	no	—
291	M₁₆	—	2	1	no	—
292	M₁₆	—	4	1	no	—
293	M₁₆	—	4	1	no	—
294	M₁₆	C₂²⋊C₄×C₃₁	1	2	yes	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	C₂×C₈×C₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂×C₈×C₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
310	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	2	no	—
315	C₁₆	—	2	1	no	—
316	C₁₆	—	4	1	no	—
317	C₁₆	—	4	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₃₁×#131	1	1	yes	characteristic
321	Q₈	—	2	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	C₃₁×C₂²⋊C₈	1	2	yes	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	C₃₁×C₂²⋊C₈	1	2	yes	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
347	C₂×C₄	C₃₁×#131	1	1	yes	characteristic
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	2	2	no	—
351	C₈	—	4	1	no	—
352	C₈	C₃₁×#120	1	1	yes	characteristic
353	C₈	C₃₁×#121	1	1	yes	characteristic
354	C₈	C₃₁×#121	1	1	yes	characteristic
355	C₈	C₃₁×#123	1	1	yes	characteristic
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	C₃₁×#408	1	1	yes	characteristic
365	C₂²	C₈×D₄×C₃₁	1	1	yes	characteristic
366	C₂²	C₃₁×#435	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	1	no	—
370	C₄	C₃₁×#386	1	1	yes	characteristic
371	C₄	C₂×C₃₁×C₂²⋊C₈	1	1	yes	characteristic
372	C₄	C₈×D₄×C₃₁	1	1	yes	characteristic
373	C₄	C₃₁×#435	1	1	yes	characteristic
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	4	2	no	—
377	C₂	—	8	1	no	—
378	C₂	C₃₁×#1869	1	1	yes	characteristic
379	C₂	C₃₁×#2170	1	1	yes	characteristic
380	C₂	C₃₁×#2171	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₃₁
Frattini, cosocle	C₂²×C₈	C₂³×C₃₁
socle	C₂²×C₃₁	C₈×D₄
prime radical	C₂×C₃₁×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ C₂²×C₁₆×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#504	C₂	semidirect
3. C₂×C₃₁×#350	C₂	semidirect
4. C₂×C₃₁×#350	C₂	semidirect
5. C₃₁×#2113	C₂	semidirect
6. C₃₁×#1376	C₂	semidirect
7. C₃₁×#1374	C₂	semidirect
127. #12980	C₃₁	direct (N × H)
166. C₂×#504	C₂×C₃₁	semidirect
168. C₂×#350	C₂×C₃₁	semidirect
169. C₂×#350	C₂×C₃₁	semidirect
170. #2113	C₂×C₃₁	semidirect
171. #1376	C₂×C₃₁	semidirect
172. #1374	C₂×C₃₁	semidirect
264. C₃₁	#12980	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#504	2
C₂×C₃₁×#443	2
C₂×C₃₁×#350	2
C₃₁×#2113	2
C₃₁×#1376	2
C₃₁×#1374	2
#12980	31

Subgroups — C31×#12980 #21469739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#12980 #21469739