Subgroups — C₃₁×#33215 #21489974

Order 7936.

810 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2628	C₂	1	2	yes	maximal
4	C₃₁×#1993	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1944	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1942	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1846	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1809	C₂	1	2	yes	maximal
9	C₃₁×#1808	C₂	1	2	yes	maximal
10	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
14	C₃₁×#500	—	2	4	no	—
15	C₂×C₃₁×#107	C₂²	1	2	yes	—
16	C₂×C₃₁×#107	C₂²	1	2	yes	—
17	C₂×C₃₁×#107	C₂²	1	2	yes	—
18	C₂×C₃₁×#106	C₂²	1	2	yes	—
19	C₃₁×#405	—	2	4	no	—
20	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#400	—	2	2	no	—
25	C₃₁×#399	—	2	2	no	—
26	C₃₁×#395	—	2	2	no	—
27	C₃₁×#393	—	2	2	no	—
28	C₃₁×#389	C₂²	1	4	yes	—
29	C₃₁×#382	C₂²	1	2	yes	—
30	C₃₁×#380	C₂²	1	4	yes	—
31	C₃₁×#340	C₂²	1	4	yes	—
32	C₃₁×#340	C₂²	1	4	yes	—
33	C₂²×Q₈×C₃₁	—	2	2	no	—
34	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₃₁	—	2	2	no	—
36	C₂×M₁₆×C₃₁	—	2	2	no	—
37	C₂×M₁₆×C₃₁	Q₈	1	4	yes	complemented
38	C₂²×C₈×C₃₁	—	2	2	no	—
39	C₂²×C₈×C₃₁	—	2	2	no	—
40	C₂²×C₈×C₃₁	Q₈	1	4	yes	complemented
41	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₃₁×C₄⋊Q₈	—	2	4	no	—
46	C₃₁×C₄⋊Q₈	—	2	4	no	—
47	C₃₁×#117	—	2	2	no	—
48	C₃₁×#117	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
60	C₃₁×#107	—	2	4	no	—
61	C₃₁×#107	—	2	4	no	—
62	C₃₁×#107	—	2	4	no	—
63	C₃₁×#106	—	2	4	no	—
64	C₃₁×#97	—	2	2	no	—
65	C₃₁×#97	—	2	2	no	—
66	C₄×C₈×C₃₁	—	2	2	no	—
67	C₄×C₈×C₃₁	D₄	1	4	yes	—
68	C₃₁×#95	—	2	4	no	—
69	C₃₁×#95	—	2	2	no	—
70	C₃₁×#95	—	2	2	no	—
71	C₃₁×#95	—	2	4	no	—
72	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₃₁	—	4	4	no	—
74	C₂×Q₈×C₃₁	—	8	4	no	—
75	C₂²×C₄×C₃₁	—	2	1	no	—
76	C₂²×C₄×C₃₁	—	2	1	no	—
77	C₂²×C₄×C₃₁	—	2	1	no	—
78	C₂²×C₄×C₃₁	—	2	1	no	—
79	C₂²×C₄×C₃₁	—	2	4	no	—
80	C₂²×C₄×C₃₁	—	2	4	no	—
81	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
89	M₁₆×C₃₁	—	2	8	no	—
90	C₂×C₈×C₃₁	—	2	1	no	—
91	C₂×C₈×C₃₁	—	2	1	no	—
92	C₂×C₈×C₃₁	—	2	1	no	—
93	C₂×C₈×C₃₁	—	2	1	no	—
94	C₂×C₈×C₃₁	—	2	8	no	—
95	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
97	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
98	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
99	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
100	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
101	C₂×C₈×C₃₁	#41	1	2	yes	—
102	C₂×C₈×C₃₁	#41	1	2	yes	—
103	C₄⋊C₄×C₃₁	—	2	2	no	—
104	C₄⋊C₄×C₃₁	—	2	2	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	4	no	—
107	C₄⋊C₄×C₃₁	—	2	4	no	—
108	C₄⋊C₄×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	4	4	no	—
110	C₄⋊C₄×C₃₁	—	8	4	no	—
111	C₂²⋊C₄×C₃₁	—	2	2	no	—
112	C₂²⋊C₄×C₃₁	—	2	2	no	—
113	C₂²⋊C₄×C₃₁	—	8	4	no	—
114	C₄²×C₃₁	—	2	1	no	—
115	C₄²×C₃₁	—	2	1	no	—
116	C₄²×C₃₁	C₂×D₄	1	2	yes	—
117	C₄²×C₃₁	#41	1	2	yes	—
118	#33215	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₃₁	—	2	1	no	—
120	C₂³×C₃₁	—	2	1	no	—
121	C₂³×C₃₁	—	2	2	no	—
122	C₂³×C₃₁	—	2	2	no	—
123	C₂³×C₃₁	C₄⋊Q₈	1	2	yes	—
124	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₃₁	—	8	8	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	2	1	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	1	no	—
135	C₂×C₄×C₃₁	—	2	1	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	4	4	no	—
139	C₂×C₄×C₃₁	—	4	4	no	—
140	C₂×C₄×C₃₁	—	4	4	no	—
141	C₂×C₄×C₃₁	—	4	4	no	—
142	C₂×C₄×C₃₁	—	4	4	no	—
143	C₂×C₄×C₃₁	—	4	4	no	—
144	C₂×C₄×C₃₁	#121	1	2	yes	—
145	C₂×C₄×C₃₁	#121	1	2	yes	—
146	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
147	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
153	C₈×C₃₁	—	2	2	no	—
154	C₈×C₃₁	—	2	2	no	—
155	C₈×C₃₁	C₂²⋊Q₈	1	4	yes	—
156	C₈×C₃₁	C₂²⋊Q₈	1	4	yes	—
157	C₂×#500	C₂×C₃₁	1	1	yes	characteristic, complemented
158	C₂×#405	C₂×C₃₁	1	1	yes	characteristic
159	#2628	C₂×C₃₁	1	2	yes	—
160	#1993	C₂×C₃₁	1	2	yes	complemented
161	#1944	C₂×C₃₁	1	2	yes	complemented
162	#1942	C₂×C₃₁	1	2	yes	complemented
163	#1846	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#1809	C₂×C₃₁	1	2	yes	—
165	#1808	C₂×C₃₁	1	2	yes	—
166	C₂²×C₃₁	—	2	2	no	—
167	C₂²×C₃₁	—	2	4	no	—
168	C₂²×C₃₁	—	4	2	no	—
169	C₂²×C₃₁	—	4	1	no	—
170	C₂²×C₃₁	—	4	1	no	—
171	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
172	C₂²×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
173	C₂²×C₃₁	#532	1	1	yes	characteristic
174	C₂²×C₃₁	#576	1	2	yes	—
175	C₂²×C₃₁	#578	1	2	yes	—
176	C₄×C₃₁	—	2	2	no	—
177	C₄×C₃₁	—	2	2	no	—
178	C₄×C₃₁	—	2	2	no	—
179	C₄×C₃₁	—	4	1	no	—
180	C₄×C₃₁	—	4	1	no	—
181	C₄×C₃₁	—	8	4	no	—
182	C₄×C₃₁	—	8	4	no	—
183	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
184	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
185	C₄×C₃₁	#533	1	1	yes	characteristic
186	C₄×C₃₁	#533	1	1	yes	characteristic
187	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
188	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
189	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
190	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
191	#500	—	2	4	no	—
192	C₂×#107	C₂²×C₃₁	1	2	yes	—
193	C₂×#107	C₂²×C₃₁	1	2	yes	—
194	C₂×#107	C₂²×C₃₁	1	2	yes	—
195	C₂×#106	C₂²×C₃₁	1	2	yes	—
196	#405	—	2	4	no	—
197	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
201	#400	—	2	2	no	—
202	#399	—	2	2	no	—
203	#395	—	2	2	no	—
204	#393	—	2	2	no	—
205	#389	C₂²×C₃₁	1	4	yes	—
206	#382	C₂²×C₃₁	1	2	yes	—
207	#380	C₂²×C₃₁	1	4	yes	—
208	#340	C₂²×C₃₁	1	4	yes	—
209	#340	C₂²×C₃₁	1	4	yes	—
210	C₂×C₃₁	—	4	2	no	—
211	C₂×C₃₁	#2857	1	1	yes	characteristic
212	C₂×C₃₁	#3058	1	1	yes	characteristic
213	C₂×C₃₁	#3059	1	1	yes	characteristic
214	C₂×C₃₁	#3164	1	2	yes	—
215	C₂×C₃₁	#3175	1	2	yes	—
216	C₂²×Q₈	—	2	2	no	—
217	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	Q₈×C₃₁	1	4	yes	complemented
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	Q₈×C₃₁	1	4	yes	complemented
224	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
228	C₄⋊Q₈	—	2	4	no	—
229	C₄⋊Q₈	—	2	4	no	—
230	#117	—	2	2	no	—
231	#117	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	4	no	—
234	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
235	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
237	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
238	C₂×C₂²⋊C₄	—	2	4	no	—
239	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
243	#107	—	2	4	no	—
244	#107	—	2	4	no	—
245	#107	—	2	4	no	—
246	#106	—	2	4	no	—
247	#97	—	2	2	no	—
248	#97	—	2	2	no	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	D₄×C₃₁	1	4	yes	—
251	#95	—	2	4	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	4	no	—
255	C₃₁	#33215	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
257	C₂×Q₈	—	4	4	no	—
258	C₂×Q₈	—	8	4	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
271	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
273	M₁₆	—	2	8	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	8	no	—
279	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
280	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
281	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
282	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
283	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
284	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
285	C₂×C₈	#41×C₃₁	1	2	yes	—
286	C₂×C₈	#41×C₃₁	1	2	yes	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₄⋊C₄	—	8	4	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	8	4	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	C₂×D₄×C₃₁	1	2	yes	—
301	C₄²	#41×C₃₁	1	2	yes	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	C₃₁×C₄⋊Q₈	1	2	yes	—
307	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
308	Q₈	—	8	8	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	C₃₁×#121	1	2	yes	—
328	C₂×C₄	C₃₁×#121	1	2	yes	—
329	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
330	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	C₃₁×C₂²⋊Q₈	1	4	yes	—
339	C₈	C₃₁×C₂²⋊Q₈	1	4	yes	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
346	C₂²	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
347	C₂²	C₃₁×#532	1	1	yes	characteristic
348	C₂²	C₃₁×#576	1	2	yes	—
349	C₂²	C₃₁×#578	1	2	yes	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	1	no	—
355	C₄	—	8	4	no	—
356	C₄	—	8	4	no	—
357	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
358	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
359	C₄	C₃₁×#533	1	1	yes	characteristic
360	C₄	C₃₁×#533	1	1	yes	characteristic
361	C₂	—	4	2	no	—
362	C₂	C₃₁×#2857	1	1	yes	characteristic
363	C₂	C₃₁×#3058	1	1	yes	characteristic
364	C₂	C₃₁×#3059	1	1	yes	characteristic
365	C₂	C₃₁×#3164	1	2	yes	—
366	C₂	C₃₁×#3175	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#500	C₂	semidirect
4. C₃₁×#1993	C₂	semidirect
5. C₃₁×#1944	C₂	semidirect
6. C₃₁×#1942	C₂	semidirect
7. C₃₁×#1846	C₂	semidirect
37. C₂×M₁₆×C₃₁	Q₈	semidirect
40. C₂²×C₈×C₃₁	Q₈	semidirect
118. #33215	C₃₁	direct (N × H)
157. C₂×#500	C₂×C₃₁	semidirect
160. #1993	C₂×C₃₁	semidirect
161. #1944	C₂×C₃₁	semidirect
162. #1942	C₂×C₃₁	semidirect
163. #1846	C₂×C₃₁	semidirect
220. C₂×M₁₆	Q₈×C₃₁	semidirect
223. C₂²×C₈	Q₈×C₃₁	semidirect
255. C₃₁	#33215	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×#500	2
C₂×C₃₁×#405	2
C₃₁×#2628	2
C₃₁×#1993	2
C₃₁×#1944	2
C₃₁×#1942	2
C₃₁×#1846	2
C₃₁×#1809	2
C₃₁×#1808	2
#33215	31

Subgroups — C31×#33215 #21489974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33215 #21489974