Subgroups — C₃₁×#20016 #21476775

Order 7936.

584 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1671	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1646	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1638	C₂	1	2	yes	maximal, complemented
10	C₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#556	C₂²	1	2	yes	—
13	C₃₁×#555	C₂²	1	2	yes	—
14	C₃₁×#500	C₂²	1	1	yes	characteristic
15	C₃₁×#498	C₂²	1	2	yes	—
16	C₃₁×#495	—	2	1	no	—
17	C₃₁×#494	C₂²	1	1	yes	characteristic
18	C₃₁×#487	C₂²	1	2	yes	—
19	C₃₁×#485	—	2	2	no	—
20	C₃₁×#482	—	2	2	no	—
21	C₃₁×#482	—	2	2	no	—
22	C₃₁×#477	C₂²	1	2	yes	—
23	C₃₁×#476	C₂²	1	2	yes	—
24	C₃₁×#474	C₂²	1	2	yes	—
25	C₃₁×#466	—	2	1	no	—
26	C₃₁×#465	—	2	2	no	—
27	C₃₁×#464	—	2	2	no	—
28	C₃₁×#461	C₂²	1	2	yes	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₄×Q₁₆×C₃₁	—	2	1	no	—
31	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₃₁	C₂²	1	2	yes	—
34	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#427	—	2	1	no	—
36	C₃₁×#427	—	2	2	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×#332	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×D₄⋊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	—	2	1	no	—
46	C₂×Q₁₆×C₃₁	—	2	1	no	—
47	C₂×SD₁₆×C₃₁	—	2	2	no	—
48	C₂×SD₁₆×C₃₁	D₄	1	1	yes	characteristic
49	C₂×D₈×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	—	2	2	no	—
51	C₂²×C₈×C₃₁	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₃₁×#126	—	4	2	no	—
55	C₃₁×#124	—	2	2	no	—
56	C₃₁×#124	—	4	2	no	—
57	C₃₁×C₂²⋊Q₈	—	2	2	no	—
58	C₃₁×#121	—	2	2	no	—
59	C₃₁×#121	—	2	2	no	—
60	C₄×Q₈×C₃₁	—	2	2	no	—
61	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₃₁	C₂³	1	2	yes	—
63	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×#117	—	2	2	no	—
65	C₃₁×#117	—	2	2	no	—
66	C₃₁×#117	—	2	2	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	2	no	—
70	C₃₁×#107	—	2	2	no	—
71	C₃₁×#107	D₄	1	1	yes	characteristic
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×#106	—	2	2	no	—
74	C₃₁×#106	—	2	2	no	—
75	C₃₁×#106	D₄	1	1	yes	characteristic
76	C₃₁×C₄⋊C₈	—	2	1	no	—
77	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
78	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	4	2	no	—
83	C₃₁×#103	D₄	1	1	yes	characteristic
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	D₄	1	2	yes	—
87	C₃₁×#102	D₄	1	1	yes	characteristic
88	C₃₁×C₂²⋊C₈	—	2	1	no	—
89	C₃₁×C₂²⋊C₈	—	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	—	2	2	no	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₁	—	2	1	no	—
101	C₂²×C₄×C₃₁	—	2	2	no	—
102	Q₁₆×C₃₁	—	4	2	no	—
103	Q₁₆×C₃₁	—	8	1	no	—
104	SD₁₆×C₃₁	—	2	2	no	—
105	SD₁₆×C₃₁	—	8	2	no	—
106	D₈×C₃₁	—	2	2	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	1	no	—
111	C₂×C₈×C₃₁	—	4	4	no	—
112	C₂×C₈×C₃₁	—	4	2	no	—
113	C₂×C₈×C₃₁	C₂×D₄	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	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	4	2	no	—
123	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂²⋊C₄×C₃₁	—	2	1	no	—
127	C₂²⋊C₄×C₃₁	—	2	2	no	—
128	C₂²⋊C₄×C₃₁	—	4	2	no	—
129	C₂²⋊C₄×C₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₄²×C₃₁	—	2	1	no	—
133	C₄²×C₃₁	—	4	2	no	—
134	C₄²×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
136	#20016	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	2	no	—
138	C₂³×C₃₁	—	2	1	no	—
139	Q₈×C₃₁	—	2	1	no	—
140	Q₈×C₃₁	—	2	1	no	—
141	Q₈×C₃₁	—	4	2	no	—
142	Q₈×C₃₁	—	4	2	no	—
143	Q₈×C₃₁	—	8	2	no	—
144	D₄×C₃₁	—	2	2	no	—
145	D₄×C₃₁	—	2	1	no	—
146	D₄×C₃₁	—	2	2	no	—
147	D₄×C₃₁	—	2	1	no	—
148	D₄×C₃₁	—	16	2	no	—
149	C₂×C₄×C₃₁	—	2	1	no	—
150	C₂×C₄×C₃₁	—	2	1	no	—
151	C₂×C₄×C₃₁	—	2	1	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	1	no	—
155	C₂×C₄×C₃₁	—	4	1	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₈×C₃₁	—	2	1	no	—
163	C₈×C₃₁	—	2	1	no	—
164	C₈×C₃₁	—	4	1	no	—
165	C₈×C₃₁	—	4	2	no	—
166	C₈×C₃₁	—	4	1	no	—
167	C₈×C₃₁	—	4	1	no	—
168	C₈×C₃₁	#135	1	2	yes	—
169	C₈×C₃₁	#135	1	2	yes	—
170	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#3341	C₂×C₃₁	1	1	yes	characteristic
172	#3340	C₂×C₃₁	1	2	yes	complemented
173	#1707	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1671	C₂×C₃₁	1	2	yes	complemented
176	#1669	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1646	C₂×C₃₁	1	2	yes	complemented
178	#1638	C₂×C₃₁	1	2	yes	complemented
179	C₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
180	C₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	1	no	—
183	C₂²×C₃₁	—	4	1	no	—
184	C₂²×C₃₁	—	4	2	no	—
185	C₂²×C₃₁	—	4	1	no	—
186	C₂²×C₃₁	—	4	2	no	—
187	C₂²×C₃₁	D₄²	1	1	yes	characteristic
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	4	2	no	—
190	C₄×C₃₁	—	4	1	no	—
191	C₄×C₃₁	—	4	1	no	—
192	C₄×C₃₁	—	4	1	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
196	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
197	C₄×C₃₁	#577	1	1	yes	characteristic
198	C₄×C₃₁	#578	1	1	yes	characteristic
199	#556	C₂²×C₃₁	1	2	yes	—
200	#555	C₂²×C₃₁	1	2	yes	—
201	#500	C₂²×C₃₁	1	1	yes	characteristic
202	#498	C₂²×C₃₁	1	2	yes	—
203	#495	—	2	1	no	—
204	#494	C₂²×C₃₁	1	1	yes	characteristic
205	#487	C₂²×C₃₁	1	2	yes	—
206	#485	—	2	2	no	—
207	#482	—	2	2	no	—
208	#482	—	2	2	no	—
209	#477	C₂²×C₃₁	1	2	yes	—
210	#476	C₂²×C₃₁	1	2	yes	—
211	#474	C₂²×C₃₁	1	2	yes	—
212	#466	—	2	1	no	—
213	#465	—	2	2	no	—
214	#464	—	2	2	no	—
215	#461	C₂²×C₃₁	1	2	yes	—
216	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
217	C₄×Q₁₆	—	2	1	no	—
218	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
219	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
220	C₈×D₄	C₂²×C₃₁	1	2	yes	—
221	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
222	#427	—	2	1	no	—
223	#427	—	2	2	no	—
224	#335	C₂²×C₃₁	1	1	yes	characteristic
225	#334	C₂²×C₃₁	1	1	yes	characteristic
226	#333	C₂²×C₃₁	1	2	yes	—
227	#332	C₂²×C₃₁	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
229	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
230	D₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₈²	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×C₃₁	—	8	2	no	—
233	C₂×C₃₁	—	8	1	no	—
234	C₂×C₃₁	#3283	1	1	yes	characteristic
235	C₂×C₃₁	#3284	1	1	yes	characteristic
236	C₂×C₃₁	#3290	1	1	yes	characteristic
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×SD₁₆	D₄×C₃₁	1	1	yes	characteristic
241	C₂×D₈	D₄×C₃₁	1	1	yes	characteristic
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
245	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
246	#126	—	4	2	no	—
247	#124	—	2	2	no	—
248	#124	—	4	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
255	C₄×D₄	C₂³×C₃₁	1	2	yes	—
256	#117	—	2	2	no	—
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#107	—	2	1	no	—
260	#107	—	2	1	no	—
261	#107	—	2	2	no	—
262	#107	—	2	2	no	—
263	#107	D₄×C₃₁	1	1	yes	characteristic
264	#106	—	2	2	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	#106	D₄×C₃₁	1	1	yes	characteristic
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
270	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
271	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	4	2	no	—
275	#103	D₄×C₃₁	1	1	yes	characteristic
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	D₄×C₃₁	1	2	yes	—
279	#102	D₄×C₃₁	1	1	yes	characteristic
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
286	C₃₁	#20016	1	1	yes	characteristic, direct product factor, Sylow
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	Q₁₆	—	4	2	no	—
296	Q₁₆	—	8	1	no	—
297	SD₁₆	—	2	2	no	—
298	SD₁₆	—	8	2	no	—
299	D₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	2	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
317	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	4	2	no	—
327	C₄²	—	4	2	no	—
328	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	2	1	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	1	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	8	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	2	1	no	—
338	D₄	—	2	2	no	—
339	D₄	—	2	1	no	—
340	D₄	—	16	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
353	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	4	1	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	1	no	—
359	C₈	—	4	1	no	—
360	C₈	C₃₁×#135	1	2	yes	—
361	C₈	C₃₁×#135	1	2	yes	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	D₄²×C₃₁	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
377	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
378	C₄	C₃₁×#577	1	1	yes	characteristic
379	C₄	C₃₁×#578	1	1	yes	characteristic
380	C₂	—	8	2	no	—
381	C₂	—	8	1	no	—
382	C₂	C₃₁×#3283	1	1	yes	characteristic
383	C₂	C₃₁×#3284	1	1	yes	characteristic
384	C₂	C₃₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#3341	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×#3393	C₂	semidirect
3. C₃₁×#3340	C₂	semidirect
4. C₃₁×#1707	C₂	semidirect
5. C₃₁×#1676	C₂	semidirect
6. C₃₁×#1671	C₂	semidirect
7. C₃₁×#1669	C₂	semidirect
8. C₃₁×#1646	C₂	semidirect
9. C₃₁×#1638	C₂	semidirect
10. C₈×SD₁₆×C₃₁	C₂	semidirect
11. C₈×D₈×C₃₁	C₂	semidirect
136. #20016	C₃₁	direct (N × H)
170. #3393	C₂×C₃₁	semidirect
172. #3340	C₂×C₃₁	semidirect
173. #1707	C₂×C₃₁	semidirect
174. #1676	C₂×C₃₁	semidirect
175. #1671	C₂×C₃₁	semidirect
176. #1669	C₂×C₃₁	semidirect
177. #1646	C₂×C₃₁	semidirect
178. #1638	C₂×C₃₁	semidirect
179. C₈×SD₁₆	C₂×C₃₁	semidirect
180. C₈×D₈	C₂×C₃₁	semidirect
286. C₃₁	#20016	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×#3393	2
C₃₁×#3341	2
C₃₁×#3340	2
C₃₁×#1707	2
C₃₁×#1676	2
C₃₁×#1671	2
C₃₁×#1669	2
C₃₁×#1646	2
C₃₁×#1638	2
C₈×SD₁₆×C₃₁	2
C₈×D₈×C₃₁	2
#20016	31

Subgroups — C31×#20016 #21476775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20016 #21476775