Subgroups — C₃₁×#20012 #21476771

Order 7936.

606 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1678	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1667	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1630	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1622	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#559	C₂²	1	2	yes	—
13	C₃₁×#554	C₂²	1	2	yes	—
14	C₃₁×#500	C₂²	1	1	yes	characteristic
15	C₃₁×#495	—	2	1	no	—
16	C₃₁×#493	C₂²	1	1	yes	characteristic
17	C₃₁×#492	C₂²	1	2	yes	—
18	C₃₁×#488	—	2	2	no	—
19	C₃₁×#486	C₂²	1	2	yes	—
20	C₃₁×#484	—	2	2	no	—
21	C₃₁×#478	—	2	2	no	—
22	C₃₁×#477	C₂²	1	2	yes	—
23	C₃₁×#477	C₂²	1	2	yes	—
24	C₃₁×#467	—	2	1	no	—
25	C₃₁×#463	—	2	2	no	—
26	C₃₁×#463	—	2	2	no	—
27	C₃₁×#460	C₂²	1	2	yes	—
28	C₃₁×#459	C₂²	1	2	yes	—
29	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₃₁	—	2	1	no	—
34	C₄×D₈×C₃₁	—	2	2	no	—
35	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#107	—	2	1	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#334	C₂²	1	1	yes	characteristic
39	C₃₁×#333	C₂²	1	2	yes	—
40	C₃₁×#331	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₃₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₃₁	—	2	2	no	—
47	C₂×SD₁₆×C₃₁	—	4	2	no	—
48	C₂×SD₁₆×C₃₁	D₄	1	1	yes	characteristic
49	C₂×D₈×C₃₁	—	2	2	no	—
50	C₂×D₈×C₃₁	—	2	1	no	—
51	C₂×D₈×C₃₁	—	2	1	no	—
52	C₂²×C₈×C₃₁	—	2	1	no	—
53	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₃₁×#127	C₂³	1	2	yes	—
55	C₃₁×#125	—	2	2	no	—
56	C₃₁×#124	—	2	2	no	—
57	C₃₁×#124	—	2	2	no	—
58	C₃₁×#123	—	4	2	no	—
59	C₃₁×C₂²⋊Q₈	—	2	2	no	—
60	C₃₁×C₂²⋊Q₈	—	4	2	no	—
61	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
63	C₄×D₄×C₃₁	—	2	2	no	—
64	C₄×D₄×C₃₁	—	2	2	no	—
65	C₄×D₄×C₃₁	—	2	2	no	—
66	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	1	no	—
70	C₃₁×#107	—	2	2	no	—
71	C₃₁×#107	—	2	2	no	—
72	C₃₁×#107	D₄	1	1	yes	characteristic
73	C₃₁×#106	D₄	1	1	yes	characteristic
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	—	2	2	no	—
76	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
78	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	D₄	1	1	yes	characteristic
82	C₃₁×#103	D₄	1	2	yes	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	—	2	2	no	—
87	C₃₁×#102	D₄	1	1	yes	characteristic
88	C₃₁×C₂²⋊C₈	—	2	1	no	—
89	C₄×C₈×C₃₁	—	2	2	no	—
90	C₄×C₈×C₃₁	—	2	1	no	—
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₃₁	—	2	2	no	—
98	C₂×D₄×C₃₁	—	2	2	no	—
99	C₂×D₄×C₃₁	—	2	2	no	—
100	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	4	2	no	—
103	C₂²×C₄×C₃₁	—	4	2	no	—
104	Q₁₆×C₃₁	—	2	2	no	—
105	SD₁₆×C₃₁	—	2	2	no	—
106	SD₁₆×C₃₁	—	8	4	no	—
107	SD₁₆×C₃₁	—	8	2	no	—
108	D₈×C₃₁	—	4	4	no	—
109	D₈×C₃₁	—	4	2	no	—
110	D₈×C₃₁	—	8	1	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	1	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	2	1	no	—
115	C₂×C₈×C₃₁	—	4	2	no	—
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	4	2	no	—
125	C₄⋊C₄×C₃₁	—	4	2	no	—
126	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₃₁	—	2	1	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₃₁	—	4	2	no	—
134	C₄²×C₃₁	—	2	1	no	—
135	C₄²×C₃₁	—	2	2	no	—
136	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
137	#20012	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₃₁	—	2	1	no	—
139	C₂³×C₃₁	—	4	2	no	—
140	Q₈×C₃₁	—	2	1	no	—
141	Q₈×C₃₁	—	2	2	no	—
142	Q₈×C₃₁	—	2	2	no	—
143	Q₈×C₃₁	—	2	1	no	—
144	Q₈×C₃₁	—	8	2	no	—
145	D₄×C₃₁	—	2	1	no	—
146	D₄×C₃₁	—	4	2	no	—
147	D₄×C₃₁	—	4	2	no	—
148	D₄×C₃₁	—	4	2	no	—
149	D₄×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	8	2	no	—
151	D₄×C₃₁	#135	1	2	yes	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	1	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	4	1	no	—
158	C₂×C₄×C₃₁	—	4	1	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	16	2	no	—
161	C₂×C₄×C₃₁	—	16	2	no	—
162	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
165	C₈×C₃₁	—	2	2	no	—
166	C₈×C₃₁	—	2	1	no	—
167	C₈×C₃₁	—	2	1	no	—
168	C₈×C₃₁	—	2	1	no	—
169	C₈×C₃₁	—	4	1	no	—
170	C₈×C₃₁	—	4	2	no	—
171	C₈×C₃₁	—	4	1	no	—
172	C₈×C₃₁	#135	1	2	yes	—
173	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#3361	C₂×C₃₁	1	2	yes	complemented
175	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1706	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1678	C₂×C₃₁	1	2	yes	complemented
178	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#1667	C₂×C₃₁	1	1	yes	characteristic
180	#1630	C₂×C₃₁	1	2	yes	complemented
181	#1622	C₂×C₃₁	1	2	yes	complemented
182	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	—	4	1	no	—
186	C₂²×C₃₁	—	4	1	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	D₄²	1	1	yes	characteristic
191	C₄×C₃₁	—	2	1	no	—
192	C₄×C₃₁	—	4	1	no	—
193	C₄×C₃₁	—	4	2	no	—
194	C₄×C₃₁	—	4	1	no	—
195	C₄×C₃₁	—	4	1	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
199	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
200	C₄×C₃₁	#577	1	1	yes	characteristic
201	C₄×C₃₁	#578	1	1	yes	characteristic
202	#559	C₂²×C₃₁	1	2	yes	—
203	#554	C₂²×C₃₁	1	2	yes	—
204	#500	C₂²×C₃₁	1	1	yes	characteristic
205	#495	—	2	1	no	—
206	#493	C₂²×C₃₁	1	1	yes	characteristic
207	#492	C₂²×C₃₁	1	2	yes	—
208	#488	—	2	2	no	—
209	#486	C₂²×C₃₁	1	2	yes	—
210	#484	—	2	2	no	—
211	#478	—	2	2	no	—
212	#477	C₂²×C₃₁	1	2	yes	—
213	#477	C₂²×C₃₁	1	2	yes	—
214	#467	—	2	1	no	—
215	#463	—	2	2	no	—
216	#463	—	2	2	no	—
217	#460	C₂²×C₃₁	1	2	yes	—
218	#459	C₂²×C₃₁	1	2	yes	—
219	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
220	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
221	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
222	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
223	C₄×D₈	—	2	1	no	—
224	C₄×D₈	—	2	2	no	—
225	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
226	C₂×#107	—	2	1	no	—
227	#335	C₂²×C₃₁	1	1	yes	characteristic
228	#334	C₂²×C₃₁	1	1	yes	characteristic
229	#333	C₂²×C₃₁	1	2	yes	—
230	#331	C₂²×C₃₁	1	2	yes	—
231	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
232	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
233	D₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
234	C₈²	C₂²×C₃₁	1	1	yes	characteristic
235	C₂×C₃₁	—	4	2	no	—
236	C₂×C₃₁	—	16	2	no	—
237	C₂×C₃₁	#3284	1	1	yes	characteristic
238	C₂×C₃₁	#3285	1	1	yes	characteristic
239	C₂×C₃₁	#3292	1	1	yes	characteristic
240	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	4	2	no	—
243	C₂×SD₁₆	D₄×C₃₁	1	1	yes	characteristic
244	C₂×D₈	—	2	2	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
249	#127	C₂³×C₃₁	1	2	yes	—
250	#125	—	2	2	no	—
251	#124	—	2	2	no	—
252	#124	—	2	2	no	—
253	#123	—	4	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	4	2	no	—
256	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
257	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	2	2	no	—
263	#107	—	2	1	no	—
264	#107	—	2	1	no	—
265	#107	—	2	2	no	—
266	#107	—	2	2	no	—
267	#107	D₄×C₃₁	1	1	yes	characteristic
268	#106	D₄×C₃₁	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	D₄×C₃₁	1	1	yes	characteristic
277	#103	D₄×C₃₁	1	2	yes	—
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	D₄×C₃₁	1	1	yes	characteristic
283	C₂²⋊C₈	—	2	1	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
289	C₃₁	#20012	1	1	yes	characteristic, direct product factor, Sylow
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	Q₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	8	4	no	—
303	SD₁₆	—	8	2	no	—
304	D₈	—	4	4	no	—
305	D₈	—	4	2	no	—
306	D₈	—	8	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
323	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
324	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
333	C₂³	—	2	1	no	—
334	C₂³	—	4	2	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	2	1	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	8	2	no	—
346	D₄	C₃₁×#135	1	2	yes	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	16	2	no	—
356	C₂×C₄	—	16	2	no	—
357	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
359	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₈	C₃₁×#135	1	2	yes	—
368	C₂²	—	2	2	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	D₄²×C₃₁	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	2	no	—
381	C₄	—	8	2	no	—
382	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
383	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
384	C₄	C₃₁×#577	1	1	yes	characteristic
385	C₄	C₃₁×#578	1	1	yes	characteristic
386	C₂	—	4	2	no	—
387	C₂	—	16	2	no	—
388	C₂	C₃₁×#3284	1	1	yes	characteristic
389	C₂	C₃₁×#3285	1	1	yes	characteristic
390	C₂	C₃₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#1667	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3396	C₂	semidirect
2. C₃₁×#3361	C₂	semidirect
3. C₃₁×#3338	C₂	semidirect
4. C₃₁×#1706	C₂	semidirect
5. C₃₁×#1678	C₂	semidirect
6. C₃₁×#1676	C₂	semidirect
8. C₃₁×#1630	C₂	semidirect
9. C₃₁×#1622	C₂	semidirect
10. C₈×Q₁₆×C₃₁	C₂	semidirect
11. C₈×SD₁₆×C₃₁	C₂	semidirect
137. #20012	C₃₁	direct (N × H)
173. #3396	C₂×C₃₁	semidirect
174. #3361	C₂×C₃₁	semidirect
175. #3338	C₂×C₃₁	semidirect
176. #1706	C₂×C₃₁	semidirect
177. #1678	C₂×C₃₁	semidirect
178. #1676	C₂×C₃₁	semidirect
180. #1630	C₂×C₃₁	semidirect
181. #1622	C₂×C₃₁	semidirect
182. C₈×Q₁₆	C₂×C₃₁	semidirect
183. C₈×SD₁₆	C₂×C₃₁	semidirect
289. C₃₁	#20012	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×#3396	2
C₃₁×#3361	2
C₃₁×#3338	2
C₃₁×#1706	2
C₃₁×#1678	2
C₃₁×#1676	2
C₃₁×#1667	2
C₃₁×#1630	2
C₃₁×#1622	2
C₈×Q₁₆×C₃₁	2
C₈×SD₁₆×C₃₁	2
#20012	31

Subgroups — C31×#20012 #21476771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20012 #21476771