Subgroups — C₃₁×#22607 #21479366

Order 7936.

692 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	C₃₁×#2924	C₂	1	2	yes	maximal
2	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1946	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1922	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1826	C₂	1	2	yes	maximal
6	C₃₁×#1810	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1773	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1752	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₃₁×#117	C₂²	1	2	yes	—
11	C₃₁×#433	—	2	4	no	—
12	C₃₁×#432	—	2	2	no	—
13	C₃₁×#431	—	2	2	no	—
14	C₂×C₃₁×#108	C₂²	1	2	yes	—
15	C₃₁×#427	C₄	1	1	yes	characteristic, complemented
16	C₃₁×#427	C₄	1	1	yes	characteristic, complemented
17	C₃₁×#427	C₄	1	2	yes	complemented
18	C₃₁×#427	C₂²	1	2	yes	—
19	C₃₁×#427	C₂²	1	1	yes	characteristic
20	C₃₁×#427	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#107	C₄	1	1	yes	characteristic, complemented
22	C₂×C₃₁×#107	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃₁×#106	C₄	1	2	yes	complemented
24	C₃₁×#424	C₂²	1	4	yes	—
25	C₃₁×#407	C₂²	1	2	yes	—
26	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₃₁×#405	C₂²	1	4	yes	—
28	C₂×C₃₁×#97	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#341	C₂²	1	2	yes	—
31	C₃₁×#339	C₂²	1	4	yes	—
32	C₃₁×#339	C₂²	1	4	yes	—
33	C₃₁×#336	C₂²	1	2	yes	—
34	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
36	C₂²×C₈×C₃₁	—	2	4	no	—
37	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₃₁×#117	—	2	2	no	—
45	C₃₁×#117	—	2	2	no	—
46	C₃₁×#117	C₂×C₄	1	2	yes	—
47	C₃₁×#117	C₂×C₄	1	2	yes	—
48	C₃₁×#117	C₂³	1	2	yes	—
49	C₃₁×#117	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
54	C₂×C₄²×C₃₁	—	2	2	no	—
55	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
56	C₃₁×#108	—	2	4	no	—
57	C₃₁×#107	C₂×C₄	1	2	yes	—
58	C₃₁×#107	C₂×C₄	1	2	yes	—
59	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
60	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
61	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
62	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
63	C₃₁×#106	C₂×C₄	1	2	yes	—
64	C₃₁×#106	C₂×C₄	1	2	yes	—
65	C₃₁×#106	C₂×C₄	1	2	yes	—
66	C₃₁×#106	C₂×C₄	1	2	yes	—
67	C₃₁×C₄⋊C₈	—	2	4	no	—
68	C₃₁×C₄⋊C₈	—	2	4	no	—
69	C₃₁×C₂²⋊C₈	—	2	2	no	—
70	C₃₁×C₂²⋊C₈	—	2	2	no	—
71	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
72	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
73	C₃₁×#97	—	2	4	no	—
74	C₃₁×#97	—	2	4	no	—
75	C₄×C₈×C₃₁	—	2	4	no	—
76	C₃₁×#95	—	2	1	no	—
77	C₂⁴×C₃₁	#41	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	—	2	2	no	—
79	C₂²×C₄×C₃₁	—	2	2	no	—
80	C₂²×C₄×C₃₁	—	2	2	no	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	—	2	2	no	—
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
89	M₁₆×C₃₁	—	2	4	no	—
90	M₁₆×C₃₁	—	2	4	no	—
91	C₂×C₈×C₃₁	—	2	2	no	—
92	C₂×C₈×C₃₁	—	2	2	no	—
93	C₂×C₈×C₃₁	—	2	2	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₃₁	#41	1	4	yes	—
105	C₄⋊C₄×C₃₁	—	2	2	no	—
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
108	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
109	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
111	C₂²⋊C₄×C₃₁	—	2	2	no	—
112	C₂²⋊C₄×C₃₁	—	2	2	no	—
113	C₂²⋊C₄×C₃₁	—	2	2	no	—
114	C₂²⋊C₄×C₃₁	—	2	2	no	—
115	C₂²⋊C₄×C₃₁	—	4	2	no	—
116	C₄²×C₃₁	—	2	2	no	—
117	C₄²×C₃₁	—	2	2	no	—
118	C₄²×C₃₁	—	2	2	no	—
119	C₄²×C₃₁	—	2	2	no	—
120	C₄²×C₃₁	—	2	2	no	—
121	C₄²×C₃₁	—	2	2	no	—
122	#22607	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₃₁	—	2	2	no	—
124	C₂³×C₃₁	—	2	2	no	—
125	C₂³×C₃₁	—	4	1	no	—
126	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
127	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
128	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	—	2	1	no	—
132	C₂×C₄×C₃₁	—	2	1	no	—
133	C₂×C₄×C₃₁	—	2	1	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	4	4	no	—
141	C₂×C₄×C₃₁	—	4	2	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	8	2	no	—
145	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
150	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
151	C₈×C₃₁	—	2	1	no	—
152	C₈×C₃₁	—	2	1	no	—
153	C₈×C₃₁	—	2	4	no	—
154	C₈×C₃₁	—	4	4	no	—
155	C₈×C₃₁	#117	1	2	yes	—
156	C₈×C₃₁	#117	1	2	yes	—
157	#2924	C₂×C₃₁	1	2	yes	—
158	C₂×#427	C₂×C₃₁	1	1	yes	characteristic
159	#1946	C₂×C₃₁	1	2	yes	complemented
160	#1922	C₂×C₃₁	1	4	yes	complemented
161	#1826	C₂×C₃₁	1	2	yes	—
162	#1810	C₂×C₃₁	1	1	yes	characteristic
163	#1773	C₂×C₃₁	1	2	yes	complemented
164	#1752	C₂×C₃₁	1	1	yes	characteristic
165	C₂²×C₃₁	—	2	1	no	—
166	C₂²×C₃₁	—	2	1	no	—
167	C₂²×C₃₁	—	2	1	no	—
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	2	1	no	—
172	C₂²×C₃₁	—	4	4	no	—
173	C₂²×C₃₁	#444	1	2	yes	—
174	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₃₁	#552	1	2	yes	—
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	4	2	no	—
179	C₄×C₃₁	—	4	2	no	—
180	C₄×C₃₁	—	4	2	no	—
181	C₄×C₃₁	—	4	2	no	—
182	C₄×C₃₁	—	8	2	no	—
183	C₄×C₃₁	C₂×#117	1	1	yes	characteristic
184	C₄×C₃₁	#519	1	1	yes	characteristic
185	C₄×C₃₁	#547	1	2	yes	—
186	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
187	C₂×#117	C₂²×C₃₁	1	2	yes	—
188	#433	—	2	4	no	—
189	#432	—	2	2	no	—
190	#431	—	2	2	no	—
191	C₂×#108	C₂²×C₃₁	1	2	yes	—
192	#427	C₄×C₃₁	1	1	yes	characteristic, complemented
193	#427	C₄×C₃₁	1	1	yes	characteristic, complemented
194	#427	C₄×C₃₁	1	2	yes	complemented
195	#427	C₂²×C₃₁	1	2	yes	—
196	#427	C₂²×C₃₁	1	1	yes	characteristic
197	#427	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×#107	C₄×C₃₁	1	1	yes	characteristic, complemented
199	C₂×#107	C₄×C₃₁	1	1	yes	characteristic, complemented
200	C₂×#106	C₄×C₃₁	1	2	yes	complemented
201	#424	C₂²×C₃₁	1	4	yes	—
202	#407	C₂²×C₃₁	1	2	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
204	#405	C₂²×C₃₁	1	4	yes	—
205	C₂×#97	C₂²×C₃₁	1	2	yes	—
206	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
207	#341	C₂²×C₃₁	1	2	yes	—
208	#339	C₂²×C₃₁	1	4	yes	—
209	#339	C₂²×C₃₁	1	4	yes	—
210	#336	C₂²×C₃₁	1	2	yes	—
211	C₂×C₃₁	—	2	2	no	—
212	C₂×C₃₁	—	2	2	no	—
213	C₂×C₃₁	—	4	1	no	—
214	C₂×C₃₁	#2344	1	1	yes	characteristic
215	C₂×C₃₁	C₂×#444	1	1	yes	characteristic
216	C₂×C₃₁	#2957	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
218	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
221	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
226	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	C₂×C₄×C₃₁	1	2	yes	—
230	#117	C₂×C₄×C₃₁	1	2	yes	—
231	#117	C₂³×C₃₁	1	2	yes	—
232	#117	C₂³×C₃₁	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
239	#108	—	2	4	no	—
240	#107	C₂×C₄×C₃₁	1	2	yes	—
241	#107	C₂×C₄×C₃₁	1	2	yes	—
242	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
243	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
244	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
245	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
246	#106	C₂×C₄×C₃₁	1	2	yes	—
247	#106	C₂×C₄×C₃₁	1	2	yes	—
248	#106	C₂×C₄×C₃₁	1	2	yes	—
249	#106	C₂×C₄×C₃₁	1	2	yes	—
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
255	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
256	#97	—	2	4	no	—
257	#97	—	2	4	no	—
258	C₄×C₈	—	2	4	no	—
259	#95	—	2	1	no	—
260	C₃₁	#22607	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	#41×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
273	M₁₆	—	2	4	no	—
274	M₁₆	—	2	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
286	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
287	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
288	C₂×C₈	#41×C₃₁	1	4	yes	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
292	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
293	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
294	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	4	1	no	—
309	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
310	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
311	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
333	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	4	no	—
337	C₈	—	4	4	no	—
338	C₈	C₃₁×#117	1	2	yes	—
339	C₈	C₃₁×#117	1	2	yes	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	4	no	—
348	C₂²	C₃₁×#444	1	2	yes	—
349	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
350	C₂²	C₃₁×#552	1	2	yes	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	—	8	2	no	—
358	C₄	C₂×C₃₁×#117	1	1	yes	characteristic
359	C₄	C₃₁×#519	1	1	yes	characteristic
360	C₄	C₃₁×#547	1	2	yes	—
361	C₂	—	2	2	no	—
362	C₂	—	2	2	no	—
363	C₂	—	4	1	no	—
364	C₂	C₃₁×#2344	1	1	yes	characteristic
365	C₂	C₂×C₃₁×#444	1	1	yes	characteristic
366	C₂	C₃₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₂⁴×C₃₁	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₃₁×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#1946	C₂	semidirect
4. C₃₁×#1922	C₂	semidirect
7. C₃₁×#1773	C₂	semidirect
15. C₃₁×#427	C₄	semidirect
16. C₃₁×#427	C₄	semidirect
17. C₃₁×#427	C₄	semidirect
21. C₂×C₃₁×#107	C₄	semidirect
22. C₂×C₃₁×#107	C₄	semidirect
23. C₂×C₃₁×#106	C₄	semidirect
122. #22607	C₃₁	direct (N × H)
159. #1946	C₂×C₃₁	semidirect
160. #1922	C₂×C₃₁	semidirect
163. #1773	C₂×C₃₁	semidirect
192. #427	C₄×C₃₁	semidirect
193. #427	C₄×C₃₁	semidirect
194. #427	C₄×C₃₁	semidirect
198. C₂×#107	C₄×C₃₁	semidirect
199. C₂×#107	C₄×C₃₁	semidirect
200. C₂×#106	C₄×C₃₁	semidirect
260. C₃₁	#22607	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×#2924	2
C₂×C₃₁×#427	2
C₃₁×#1946	2
C₃₁×#1922	2
C₃₁×#1826	2
C₃₁×#1810	2
C₃₁×#1773	2
C₃₁×#1752	2
#22607	31

Subgroups — C31×#22607 #21479366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22607 #21479366