Subgroups — C₃₁×#33783 #21490542

Order 7936.

688 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	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2250	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2244	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2207	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2206	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2187	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2184	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2163	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₃₁	—	2	1	no	—
11	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁×#127	—	2	1	no	—
13	C₃₁×#529	—	2	1	no	—
14	C₂×C₃₁×SD₃₂	C₂²	1	4	yes	complemented
15	C₂×C₃₁×D₁₆	C₂²	1	4	yes	complemented
16	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
17	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
18	C₃₁×#493	—	2	1	no	—
19	C₃₁×#493	—	2	1	no	—
20	C₃₁×#493	C₂²	1	2	yes	—
21	C₃₁×#493	C₂²	1	2	yes	—
22	C₃₁×#488	—	2	1	no	—
23	C₃₁×#467	C₂²	1	1	yes	characteristic
24	C₃₁×#466	C₂²	1	1	yes	characteristic
25	C₃₁×#465	—	2	1	no	—
26	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₃₁	—	2	1	no	—
28	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	complemented
31	C₃₁×#357	C₂²	1	4	yes	complemented
32	C₃₁×#357	C₂²	1	4	yes	complemented
33	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₃₁×#346	C₂²	1	2	yes	complemented
35	C₂²×D₄×C₃₁	—	2	2	no	—
36	C₂²×D₄×C₃₁	—	4	1	no	—
37	C₂²×D₄×C₃₁	—	4	1	no	—
38	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
39	C₂×SD₁₆×C₃₁	—	2	1	no	—
40	C₂×D₈×C₃₁	—	2	2	no	—
41	C₂×D₈×C₃₁	—	2	2	no	—
42	C₂×D₈×C₃₁	—	2	2	no	—
43	C₂×D₈×C₃₁	—	4	4	no	—
44	C₂×D₈×C₃₁	—	4	4	no	—
45	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₃₁	C₂³	1	4	yes	—
47	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₃₁×#127	—	2	2	no	—
50	C₃₁×#127	—	2	2	no	—
51	C₃₁×#127	—	4	1	no	—
52	C₃₁×#127	—	4	1	no	—
53	C₃₁×#126	—	4	1	no	—
54	C₃₁×#125	—	2	1	no	—
55	C₃₁×#124	—	2	1	no	—
56	C₃₁×#123	—	4	1	no	—
57	C₃₁×C₂²⋊Q₈	—	2	1	no	—
58	C₃₁×#121	—	2	1	no	—
59	C₄×Q₈×C₃₁	—	2	1	no	—
60	C₄×D₄×C₃₁	—	2	1	no	—
61	C₄×D₄×C₃₁	—	4	1	no	—
62	C₃₁×#117	—	4	1	no	—
63	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
64	C₃₁×SD₃₂	—	4	4	no	—
65	C₃₁×D₁₆	—	4	4	no	—
66	C₂×C₁₆×C₃₁	C₂³	1	4	yes	—
67	C₃₁×#107	C₂³	1	1	yes	characteristic
68	C₃₁×#107	C₂³	1	1	yes	characteristic
69	C₃₁×#106	—	2	1	no	—
70	C₃₁×#103	—	2	1	no	—
71	C₃₁×#103	—	2	1	no	—
72	C₃₁×#102	—	2	1	no	—
73	C₃₁×#102	—	2	1	no	—
74	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
75	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
76	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
78	C₂⁴×C₃₁	—	4	2	no	—
79	C₂×Q₈×C₃₁	—	2	1	no	—
80	C₂×D₄×C₃₁	—	2	1	no	—
81	C₂×D₄×C₃₁	—	2	4	no	—
82	C₂×D₄×C₃₁	—	4	4	no	—
83	C₂×D₄×C₃₁	—	4	4	no	—
84	C₂×D₄×C₃₁	—	4	1	no	—
85	C₂×D₄×C₃₁	—	4	2	no	—
86	C₂×D₄×C₃₁	—	4	2	no	—
87	C₂×D₄×C₃₁	—	4	2	no	—
88	C₂×D₄×C₃₁	—	4	2	no	—
89	C₂×D₄×C₃₁	—	4	2	no	—
90	C₂×D₄×C₃₁	—	8	4	no	—
91	C₂×D₄×C₃₁	—	8	4	no	—
92	C₂²×C₄×C₃₁	—	4	1	no	—
93	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	Q₁₆×C₃₁	—	2	2	no	—
97	SD₁₆×C₃₁	—	4	2	no	—
98	D₈×C₃₁	—	2	2	no	—
99	D₈×C₃₁	—	2	4	no	—
100	D₈×C₃₁	—	2	4	no	—
101	D₈×C₃₁	—	4	4	no	—
102	D₈×C₃₁	—	4	4	no	—
103	D₈×C₃₁	—	4	4	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
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	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₃₁	—	2	1	no	—
111	C₄⋊C₄×C₃₁	—	2	1	no	—
112	C₄⋊C₄×C₃₁	—	4	1	no	—
113	C₄⋊C₄×C₃₁	—	4	1	no	—
114	C₄⋊C₄×C₃₁	—	4	1	no	—
115	C₄⋊C₄×C₃₁	—	4	1	no	—
116	C₂²⋊C₄×C₃₁	—	4	1	no	—
117	C₂²⋊C₄×C₃₁	—	4	1	no	—
118	C₂²⋊C₄×C₃₁	—	4	1	no	—
119	C₂²⋊C₄×C₃₁	—	4	1	no	—
120	C₂²⋊C₄×C₃₁	—	4	1	no	—
121	C₄²×C₃₁	—	4	1	no	—
122	C₄²×C₃₁	D₈	1	1	yes	characteristic
123	C₄²×C₃₁	D₈	1	1	yes	characteristic
124	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₁₆×C₃₁	—	2	4	no	—
127	#33783	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	4	1	no	—
129	C₂³×C₃₁	—	4	4	no	—
130	C₂³×C₃₁	—	8	4	no	—
131	C₂³×C₃₁	—	8	4	no	—
132	C₂³×C₃₁	—	8	4	no	—
133	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
134	Q₈×C₃₁	—	4	1	no	—
135	Q₈×C₃₁	—	4	1	no	—
136	D₄×C₃₁	—	4	4	no	—
137	D₄×C₃₁	—	4	1	no	—
138	D₄×C₃₁	—	4	4	no	—
139	D₄×C₃₁	—	4	1	no	—
140	D₄×C₃₁	—	8	4	no	—
141	D₄×C₃₁	—	8	4	no	—
142	D₄×C₃₁	—	8	4	no	—
143	D₄×C₃₁	—	8	4	no	—
144	D₄×C₃₁	—	8	2	no	—
145	D₄×C₃₁	—	8	4	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	1	no	—
152	C₂×C₄×C₃₁	—	4	1	no	—
153	C₂×C₄×C₃₁	—	8	2	no	—
154	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₃₁	—	2	1	no	—
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
163	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
164	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
165	C₂×#493	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#2250	C₂×C₃₁	1	2	yes	complemented
167	#2244	C₂×C₃₁	1	2	yes	complemented
168	#2207	C₂×C₃₁	1	2	yes	complemented
169	#2206	C₂×C₃₁	1	2	yes	complemented
170	#2187	C₂×C₃₁	1	2	yes	complemented
171	#2184	C₂×C₃₁	1	2	yes	complemented
172	#2163	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂²×C₃₁	—	2	1	no	—
174	C₂²×C₃₁	—	2	1	no	—
175	C₂²×C₃₁	—	8	1	no	—
176	C₂²×C₃₁	—	8	4	no	—
177	C₂²×C₃₁	—	8	4	no	—
178	C₂²×C₃₁	—	8	1	no	—
179	C₂²×C₃₁	—	8	4	no	—
180	C₂²×C₃₁	—	8	1	no	—
181	C₂²×C₃₁	—	16	8	no	—
182	C₂²×C₃₁	#509	1	2	yes	—
183	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
184	C₄×C₃₁	—	2	1	no	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	—	8	1	no	—
190	C₄×C₃₁	—	8	1	no	—
191	C₄×C₃₁	#509	1	2	yes	—
192	C₄×C₃₁	#535	1	1	yes	characteristic
193	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂²×D₈	—	2	1	no	—
195	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
196	C₂×#127	—	2	1	no	—
197	#529	—	2	1	no	—
198	C₂×SD₃₂	C₂²×C₃₁	1	4	yes	complemented
199	C₂×D₁₆	C₂²×C₃₁	1	4	yes	complemented
200	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
201	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
202	#493	—	2	1	no	—
203	#493	—	2	1	no	—
204	#493	C₂²×C₃₁	1	2	yes	—
205	#493	C₂²×C₃₁	1	2	yes	—
206	#488	—	2	1	no	—
207	#467	C₂²×C₃₁	1	1	yes	characteristic
208	#466	C₂²×C₃₁	1	1	yes	characteristic
209	#465	—	2	1	no	—
210	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
211	C₄×SD₁₆	—	2	1	no	—
212	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
213	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
214	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
215	#357	C₂²×C₃₁	1	4	yes	complemented
216	#357	C₂²×C₃₁	1	4	yes	complemented
217	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
218	#346	C₂²×C₃₁	1	2	yes	complemented
219	C₂×C₃₁	—	2	2	no	—
220	C₂×C₃₁	—	16	1	no	—
221	C₂×C₃₁	—	16	4	no	—
222	C₂×C₃₁	#3205	1	1	yes	characteristic
223	C₂×C₃₁	C₂×#509	1	1	yes	characteristic
224	C₂×C₃₁	C₂×#509	1	1	yes	characteristic
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	—	4	1	no	—
227	C₂²×D₄	—	4	1	no	—
228	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
229	C₂×SD₁₆	—	2	1	no	—
230	C₂×D₈	—	2	2	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	4	4	no	—
234	C₂×D₈	—	4	4	no	—
235	C₂×D₈	C₂³×C₃₁	1	4	yes	—
236	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
237	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
239	#127	—	2	2	no	—
240	#127	—	2	2	no	—
241	#127	—	4	1	no	—
242	#127	—	4	1	no	—
243	#126	—	4	1	no	—
244	#125	—	2	1	no	—
245	#124	—	2	1	no	—
246	#123	—	4	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	#121	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	4	1	no	—
252	#117	—	4	1	no	—
253	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
254	SD₃₂	—	4	4	no	—
255	D₁₆	—	4	4	no	—
256	C₂×C₁₆	C₂³×C₃₁	1	4	yes	—
257	#107	C₂³×C₃₁	1	1	yes	characteristic
258	#107	C₂³×C₃₁	1	1	yes	characteristic
259	#106	—	2	1	no	—
260	#103	—	2	1	no	—
261	#103	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	1	no	—
264	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
265	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
268	C₃₁	#33783	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	—	4	2	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	4	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂×D₄	—	8	4	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	Q₁₆	—	2	2	no	—
288	SD₁₆	—	4	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	4	no	—
291	D₈	—	2	4	no	—
292	D₈	—	4	4	no	—
293	D₈	—	4	4	no	—
294	D₈	—	4	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	D₈×C₃₁	1	1	yes	characteristic
314	C₄²	D₈×C₃₁	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₁₆	—	2	4	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	8	4	no	—
322	C₂³	—	8	4	no	—
323	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	1	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	2	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
353	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	1	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	16	8	no	—
363	C₂²	C₃₁×#509	1	2	yes	—
364	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₄	C₃₁×#509	1	2	yes	—
373	C₄	C₃₁×#535	1	1	yes	characteristic
374	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₂	—	2	2	no	—
376	C₂	—	16	4	no	—
377	C₂	—	16	1	no	—
378	C₂	C₃₁×#3205	1	1	yes	characteristic
379	C₂	C₂×C₃₁×#509	1	1	yes	characteristic
380	C₂	C₂×C₃₁×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3168	C₂	semidirect
2. C₂×C₃₁×#493	C₂	semidirect
3. C₃₁×#2250	C₂	semidirect
4. C₃₁×#2244	C₂	semidirect
5. C₃₁×#2207	C₂	semidirect
6. C₃₁×#2206	C₂	semidirect
7. C₃₁×#2187	C₂	semidirect
8. C₃₁×#2184	C₂	semidirect
9. C₃₁×#2163	C₂	semidirect
14. C₂×C₃₁×SD₃₂	C₂²	semidirect
15. C₂×C₃₁×D₁₆	C₂²	semidirect
16. C₃₁×#499	C₂²	semidirect
17. C₃₁×#495	C₂²	semidirect
26. C₄×Q₁₆×C₃₁	C₂²	semidirect
28. C₄×D₈×C₃₁	C₂²	semidirect
30. C₃₁×C₄⋊C₁₆	C₂²	semidirect
31. C₃₁×#357	C₂²	semidirect
32. C₃₁×#357	C₂²	semidirect
34. C₃₁×#346	C₂²	semidirect
127. #33783	C₃₁	direct (N × H)
164. #3168	C₂×C₃₁	semidirect
165. C₂×#493	C₂×C₃₁	semidirect
166. #2250	C₂×C₃₁	semidirect
167. #2244	C₂×C₃₁	semidirect
168. #2207	C₂×C₃₁	semidirect
169. #2206	C₂×C₃₁	semidirect
170. #2187	C₂×C₃₁	semidirect
171. #2184	C₂×C₃₁	semidirect
172. #2163	C₂×C₃₁	semidirect
198. C₂×SD₃₂	C₂²×C₃₁	semidirect
199. C₂×D₁₆	C₂²×C₃₁	semidirect
200. #499	C₂²×C₃₁	semidirect
201. #495	C₂²×C₃₁	semidirect
210. C₄×Q₁₆	C₂²×C₃₁	semidirect
212. C₄×D₈	C₂²×C₃₁	semidirect
214. C₄⋊C₁₆	C₂²×C₃₁	semidirect
215. #357	C₂²×C₃₁	semidirect
216. #357	C₂²×C₃₁	semidirect
218. #346	C₂²×C₃₁	semidirect
268. C₃₁	#33783	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×#3168	2
C₂×C₃₁×#493	2
C₃₁×#2250	2
C₃₁×#2244	2
C₃₁×#2207	2
C₃₁×#2206	2
C₃₁×#2187	2
C₃₁×#2184	2
C₃₁×#2163	2
#33783	31

Subgroups — C31×#33783 #21490542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33783 #21490542