Subgroups — C₃₁×#33052 #21489811

Order 7936.

1022 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#490	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2856	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1936	C₂	1	4	yes	maximal, complemented
8	C₃₁×#1893	C₂	1	4	yes	maximal, complemented
9	C₃₁×#1836	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
11	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#121	—	2	2	no	—
14	C₂×C₃₁×#121	C₂²	1	2	yes	—
15	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#490	—	2	4	no	—
17	C₂×C₃₁×#102	C₂²	1	4	yes	—
18	C₂×C₃₁×#102	C₂²	1	4	yes	—
19	C₂×C₃₁×#97	—	2	4	no	—
20	C₂×C₃₁×#97	C₂²	1	2	yes	—
21	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
23	C₃₁×#390	—	2	2	no	—
24	C₃₁×#390	C₂²	1	2	yes	—
25	C₃₁×#389	C₂²	1	2	yes	—
26	C₃₁×#387	—	2	2	no	—
27	C₃₁×#385	—	2	2	no	—
28	C₃₁×#384	C₂²	1	1	yes	characteristic
29	C₃₁×#382	C₂²	1	1	yes	characteristic
30	C₃₁×#380	C₂²	1	2	yes	—
31	C₃₁×#340	C₂²	1	4	yes	—
32	C₃₁×#340	C₂²	1	4	yes	—
33	C₂²×D₄×C₃₁	—	2	2	no	—
34	C₂²×D₄×C₃₁	—	2	2	no	—
35	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
36	C₂³×C₄×C₃₁	D₄	1	2	yes	—
37	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	—	2	4	no	—
39	C₂²×C₈×C₃₁	—	2	4	no	—
40	C₂²×C₈×C₃₁	—	2	4	no	—
41	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₃₁×#127	—	2	2	no	—
44	C₃₁×#127	—	2	2	no	—
45	C₃₁×#125	—	2	2	no	—
46	C₃₁×#125	—	2	2	no	—
47	C₃₁×#121	—	2	8	no	—
48	C₃₁×#121	—	4	8	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄²×C₃₁	—	2	2	no	—
59	C₂×C₄²×C₃₁	—	2	2	no	—
60	C₂×C₄²×C₃₁	D₄	1	2	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₃₁×#102	—	2	8	no	—
64	C₃₁×#102	—	2	8	no	—
65	C₃₁×#97	—	2	4	no	—
66	C₃₁×#97	—	2	2	no	—
67	C₃₁×#97	D₄	1	4	yes	complemented
68	C₃₁×#95	—	2	2	no	—
69	C₃₁×#95	—	2	2	no	—
70	C₃₁×#95	—	2	2	no	—
71	C₂⁴×C₃₁	—	2	2	no	—
72	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂×D₄×C₃₁	—	2	2	no	—
74	C₂×D₄×C₃₁	—	2	4	no	—
75	C₂×D₄×C₃₁	—	2	4	no	—
76	C₂×D₄×C₃₁	—	2	2	no	—
77	C₂×D₄×C₃₁	—	4	4	no	—
78	C₂×D₄×C₃₁	—	4	4	no	—
79	C₂×D₄×C₃₁	—	4	4	no	—
80	C₂×D₄×C₃₁	—	4	8	no	—
81	C₂×D₄×C₃₁	—	4	4	no	—
82	C₂²×C₄×C₃₁	—	2	1	no	—
83	C₂²×C₄×C₃₁	—	2	1	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	2	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	—	2	2	no	—
90	C₂²×C₄×C₃₁	—	4	2	no	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	#41	1	4	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₃₁	—	2	16	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
102	C₂×C₈×C₃₁	#41	1	4	yes	—
103	C₄⋊C₄×C₃₁	—	2	2	no	—
104	C₄⋊C₄×C₃₁	—	2	4	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	—	4	4	no	—
108	C₄⋊C₄×C₃₁	—	4	4	no	—
109	C₄⋊C₄×C₃₁	—	4	4	no	—
110	C₂²⋊C₄×C₃₁	—	4	8	no	—
111	C₂²⋊C₄×C₃₁	—	4	4	no	—
112	C₂²⋊C₄×C₃₁	—	4	4	no	—
113	C₄²×C₃₁	—	2	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	#33052	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	—	4	2	no	—
123	C₂³×C₃₁	—	4	2	no	—
124	C₂³×C₃₁	—	4	2	no	—
125	C₂³×C₃₁	—	4	4	no	—
126	C₂³×C₃₁	—	4	4	no	—
127	C₂³×C₃₁	#124	1	2	yes	—
128	C₂³×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
129	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
130	D₄×C₃₁	—	4	4	no	—
131	D₄×C₃₁	—	4	4	no	—
132	D₄×C₃₁	—	8	8	no	—
133	D₄×C₃₁	—	8	8	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	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	4	8	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	4	4	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	#121	1	4	yes	—
153	C₂×C₄×C₃₁	#124	1	2	yes	—
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
158	C₈×C₃₁	—	2	4	no	—
159	C₈×C₃₁	—	2	4	no	—
160	C₂×#490	C₂×C₃₁	1	1	yes	characteristic, complemented
161	C₂²×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#2856	C₂×C₃₁	1	1	yes	characteristic
163	#2851	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#1992	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#1961	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#1936	C₂×C₃₁	1	4	yes	complemented
167	#1893	C₂×C₃₁	1	4	yes	complemented
168	#1836	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂²×C₃₁	—	2	2	no	—
170	C₂²×C₃₁	—	2	2	no	—
171	C₂²×C₃₁	—	2	4	no	—
172	C₂²×C₃₁	—	2	4	no	—
173	C₂²×C₃₁	—	8	2	no	—
174	C₂²×C₃₁	—	8	2	no	—
175	C₂²×C₃₁	—	8	2	no	—
176	C₂²×C₃₁	—	8	4	no	—
177	C₂²×C₃₁	—	8	4	no	—
178	C₂²×C₃₁	#490	1	4	yes	complemented
179	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
180	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
181	C₂²×C₃₁	#532	1	1	yes	characteristic
182	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
183	C₂²×C₃₁	#575	1	2	yes	—
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	2	4	no	—
186	C₄×C₃₁	—	4	2	no	—
187	C₄×C₃₁	—	8	2	no	—
188	C₄×C₃₁	—	8	2	no	—
189	C₄×C₃₁	—	8	2	no	—
190	C₄×C₃₁	#525	1	2	yes	—
191	C₄×C₃₁	#529	1	2	yes	—
192	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
193	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×#121	—	2	2	no	—
196	C₂×#121	C₂²×C₃₁	1	2	yes	—
197	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
198	#490	—	2	4	no	—
199	C₂×#102	C₂²×C₃₁	1	4	yes	—
200	C₂×#102	C₂²×C₃₁	1	4	yes	—
201	C₂×#97	—	2	4	no	—
202	C₂×#97	C₂²×C₃₁	1	2	yes	—
203	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
205	#390	—	2	2	no	—
206	#390	C₂²×C₃₁	1	2	yes	—
207	#389	C₂²×C₃₁	1	2	yes	—
208	#387	—	2	2	no	—
209	#385	—	2	2	no	—
210	#384	C₂²×C₃₁	1	1	yes	characteristic
211	#382	C₂²×C₃₁	1	1	yes	characteristic
212	#380	C₂²×C₃₁	1	2	yes	—
213	#340	C₂²×C₃₁	1	4	yes	—
214	#340	C₂²×C₃₁	1	4	yes	—
215	C₂×C₃₁	—	2	4	no	—
216	C₂×C₃₁	—	16	2	no	—
217	C₂×C₃₁	#2850	1	1	yes	characteristic
218	C₂×C₃₁	#3055	1	2	yes	—
219	C₂×C₃₁	C₂×#490	1	1	yes	characteristic
220	C₂×C₃₁	#3135	1	1	yes	characteristic
221	C₂×C₃₁	#3180	1	2	yes	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
225	C₂³×C₄	D₄×C₃₁	1	2	yes	—
226	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
232	#127	—	2	2	no	—
233	#127	—	2	2	no	—
234	#125	—	2	2	no	—
235	#125	—	2	2	no	—
236	#121	—	2	8	no	—
237	#121	—	4	8	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	D₄×C₃₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
252	#102	—	2	8	no	—
253	#102	—	2	8	no	—
254	#97	—	2	4	no	—
255	#97	—	2	2	no	—
256	#97	D₄×C₃₁	1	4	yes	complemented
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	C₃₁	#33052	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	—	2	2	no	—
262	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	—	4	4	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	4	8	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	#41×C₃₁	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
286	C₂×C₈	—	2	16	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
292	C₂×C₈	#41×C₃₁	1	4	yes	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	8	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	C₂×D₄×C₃₁	1	2	yes	—
307	C₄²	#41×C₃₁	1	2	yes	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	C₃₁×#124	1	2	yes	—
317	C₂³	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
318	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
319	D₄	—	4	4	no	—
320	D₄	—	4	4	no	—
321	D₄	—	8	8	no	—
322	D₄	—	8	8	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	C₃₁×#121	1	4	yes	—
342	C₂×C₄	C₃₁×#124	1	2	yes	—
343	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
345	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
346	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
347	C₈	—	2	4	no	—
348	C₈	—	2	4	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	4	no	—
357	C₂²	—	8	4	no	—
358	C₂²	C₃₁×#490	1	4	yes	complemented
359	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
360	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
361	C₂²	C₃₁×#532	1	1	yes	characteristic
362	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
363	C₂²	C₃₁×#575	1	2	yes	—
364	C₄	—	2	2	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	2	no	—
367	C₄	—	8	2	no	—
368	C₄	—	8	2	no	—
369	C₄	—	8	2	no	—
370	C₄	C₃₁×#525	1	2	yes	—
371	C₄	C₃₁×#529	1	2	yes	—
372	C₂	—	2	4	no	—
373	C₂	—	16	2	no	—
374	C₂	C₃₁×#2850	1	1	yes	characteristic
375	C₂	C₃₁×#3055	1	2	yes	—
376	C₂	C₂×C₃₁×#490	1	1	yes	characteristic
377	C₂	C₃₁×#3135	1	1	yes	characteristic
378	C₂	C₃₁×#3180	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₃₁×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#490	C₂	semidirect
2. C₂²×C₃₁×#97	C₂	semidirect
4. C₃₁×#2851	C₂	semidirect
5. C₃₁×#1992	C₂	semidirect
6. C₃₁×#1961	C₂	semidirect
7. C₃₁×#1936	C₂	semidirect
8. C₃₁×#1893	C₂	semidirect
9. C₃₁×#1836	C₂	semidirect
67. C₃₁×#97	D₄	semidirect
118. #33052	C₃₁	direct (N × H)
160. C₂×#490	C₂×C₃₁	semidirect
161. C₂²×#97	C₂×C₃₁	semidirect
163. #2851	C₂×C₃₁	semidirect
164. #1992	C₂×C₃₁	semidirect
165. #1961	C₂×C₃₁	semidirect
166. #1936	C₂×C₃₁	semidirect
167. #1893	C₂×C₃₁	semidirect
168. #1836	C₂×C₃₁	semidirect
178. C₂²×C₃₁	#490	semidirect
256. #97	D₄×C₃₁	semidirect
260. C₃₁	#33052	direct (N × H)
358. C₂²	C₃₁×#490	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#490	2
C₂²×C₃₁×#97	2
C₃₁×#2856	2
C₃₁×#2851	2
C₃₁×#1992	2
C₃₁×#1961	2
C₃₁×#1936	2
C₃₁×#1893	2
C₃₁×#1836	2
#33052	31

Subgroups — C31×#33052 #21489811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33052 #21489811