Subgroups — C₃₁×#35143 #21491902

Order 7936.

2418 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2852	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2637	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2636	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2604	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2603	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2601	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2579	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2534	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2406	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2404	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#126	—	2	8	no	—
20	C₂×C₃₁×#126	C₂²	1	2	yes	—
21	C₂×C₃₁×#126	C₂²	1	2	yes	—
22	C₂×C₃₁×#126	C₂²	1	2	yes	—
23	C₂×C₃₁×#126	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#120	C₂²	1	2	yes	—
26	C₄×#41×C₃₁	—	2	8	no	—
27	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
35	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
43	C₃₁×#400	C₂²	1	2	yes	complemented
44	C₃₁×#399	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	4	yes	complemented
46	C₃₁×#398	C₂²	1	2	yes	complemented
47	C₃₁×#397	C₂²	1	2	yes	—
48	C₃₁×#396	C₂²	1	4	yes	—
49	C₃₁×#396	C₂²	1	4	yes	complemented
50	C₃₁×#395	C₂²	1	2	yes	complemented
51	C₃₁×#394	C₂²	1	4	yes	—
52	C₃₁×#394	C₂²	1	2	yes	complemented
53	C₃₁×#393	C₂²	1	2	yes	—
54	C₃₁×#392	C₂²	1	2	yes	—
55	C₃₁×#390	C₂²	1	4	yes	—
56	C₃₁×#389	C₂²	1	4	yes	complemented
57	C₃₁×#388	C₂²	1	4	yes	—
58	C₃₁×#388	C₂²	1	4	yes	—
59	C₃₁×#388	C₂²	1	4	yes	—
60	C₃₁×#388	C₂²	1	4	yes	—
61	C₃₁×#388	C₂²	1	4	yes	complemented
62	C₃₁×#387	C₂²	1	4	yes	complemented
63	C₃₁×#387	C₂²	1	4	yes	complemented
64	C₃₁×#387	C₂²	1	4	yes	complemented
65	C₃₁×#386	C₂²	1	2	yes	—
66	C₃₁×#386	C₂²	1	4	yes	—
67	C₃₁×#386	C₂²	1	2	yes	—
68	C₃₁×#386	C₂²	1	4	yes	—
69	C₃₁×#386	C₂²	1	4	yes	—
70	C₃₁×#385	C₂²	1	2	yes	—
71	C₃₁×#385	C₂²	1	2	yes	—
72	C₃₁×#385	C₂²	1	4	yes	complemented
73	C₃₁×#385	C₂²	1	4	yes	complemented
74	C₃₁×#385	C₂²	1	4	yes	complemented
75	C₃₁×#383	C₂²	1	2	yes	complemented
76	C₃₁×#382	C₂²	1	2	yes	complemented
77	C₃₁×#381	C₂²	1	2	yes	—
78	C₃₁×#381	C₂²	1	1	yes	characteristic
79	C₃₁×#381	C₂²	1	1	yes	characteristic
80	C₃₁×#380	C₂²	1	2	yes	—
81	C₃₁×#379	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
84	C₃₁×#376	C₂²	1	2	yes	complemented
85	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
86	C₂×#41×C₃₁	—	2	8	no	—
87	C₂×#41×C₃₁	—	2	4	no	—
88	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
92	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₃₁×#126	—	2	8	no	—
102	C₃₁×#126	—	2	8	no	—
103	C₃₁×#126	—	2	8	no	—
104	C₃₁×#126	—	2	8	no	—
105	C₃₁×#123	—	2	8	no	—
106	C₃₁×#120	—	2	8	no	—
107	C₄×Q₈×C₃₁	—	2	4	no	—
108	C₄×Q₈×C₃₁	—	2	4	no	—
109	C₄×D₄×C₃₁	—	2	8	no	—
110	C₄×D₄×C₃₁	—	2	8	no	—
111	C₄×D₄×C₃₁	—	2	4	no	—
112	C₄×D₄×C₃₁	—	2	4	no	—
113	C₃₁×#117	—	2	4	no	—
114	C₃₁×#117	—	2	8	no	—
115	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
116	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
117	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₄²×C₃₁	—	2	8	no	—
153	C₂×C₄²×C₃₁	D₄	1	8	yes	complemented
154	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
158	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
162	C₃₁×#95	C₂³	1	2	yes	—
163	C₃₁×#95	C₂³	1	4	yes	—
164	C₃₁×#95	C₂³	1	4	yes	—
165	C₃₁×#95	C₂³	1	4	yes	—
166	C₃₁×#95	C₂³	1	4	yes	—
167	C₃₁×#95	C₂³	1	2	yes	—
168	C₃₁×#95	C₂³	1	4	yes	—
169	C₃₁×#95	C₂³	1	4	yes	—
170	C₃₁×#95	C₂³	1	4	yes	—
171	C₃₁×#95	C₂³	1	4	yes	—
172	C₃₁×#95	C₂³	1	2	yes	—
173	C₃₁×#95	C₂³	1	2	yes	—
174	C₂⁴×C₃₁	—	2	2	no	—
175	C₂⁴×C₃₁	—	2	4	no	—
176	C₂⁴×C₃₁	—	4	2	no	—
177	C₂⁴×C₃₁	—	4	2	no	—
178	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
179	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
180	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
181	#41×C₃₁	—	2	32	no	—
182	C₂×Q₈×C₃₁	—	2	2	no	—
183	C₂×Q₈×C₃₁	—	2	4	no	—
184	C₂×D₄×C₃₁	—	2	4	no	—
185	C₂×D₄×C₃₁	—	2	4	no	—
186	C₂×D₄×C₃₁	—	2	4	no	—
187	C₂×D₄×C₃₁	—	2	8	no	—
188	C₂×D₄×C₃₁	—	2	2	no	—
189	C₂×D₄×C₃₁	—	4	4	no	—
190	C₂×D₄×C₃₁	—	4	4	no	—
191	C₂×D₄×C₃₁	#41	1	8	yes	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
193	C₂²×C₄×C₃₁	—	2	4	no	—
194	C₂²×C₄×C₃₁	—	2	4	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	2	no	—
197	C₂²×C₄×C₃₁	—	2	2	no	—
198	C₂²×C₄×C₃₁	—	2	2	no	—
199	C₂²×C₄×C₃₁	—	2	4	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	2	4	no	—
202	C₂²×C₄×C₃₁	—	4	2	no	—
203	C₂²×C₄×C₃₁	—	4	2	no	—
204	C₂²×C₄×C₃₁	—	4	4	no	—
205	C₂²×C₄×C₃₁	—	4	4	no	—
206	C₂²×C₄×C₃₁	—	4	2	no	—
207	C₂²×C₄×C₃₁	—	4	2	no	—
208	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
225	C₄⋊C₄×C₃₁	—	2	4	no	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	4	no	—
228	C₄⋊C₄×C₃₁	—	2	4	no	—
229	C₄⋊C₄×C₃₁	—	2	4	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	—	2	4	no	—
233	C₄⋊C₄×C₃₁	—	2	2	no	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	2	8	no	—
236	C₄⋊C₄×C₃₁	—	4	4	no	—
237	C₄⋊C₄×C₃₁	—	4	4	no	—
238	C₄⋊C₄×C₃₁	—	4	4	no	—
239	C₂²⋊C₄×C₃₁	—	2	4	no	—
240	C₂²⋊C₄×C₃₁	—	2	4	no	—
241	C₂²⋊C₄×C₃₁	—	2	4	no	—
242	C₂²⋊C₄×C₃₁	—	2	8	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₃₁	—	2	4	no	—
249	C₂²⋊C₄×C₃₁	—	2	4	no	—
250	C₂²⋊C₄×C₃₁	—	2	4	no	—
251	C₂²⋊C₄×C₃₁	—	2	8	no	—
252	C₂²⋊C₄×C₃₁	—	4	4	no	—
253	C₂²⋊C₄×C₃₁	—	4	4	no	—
254	C₂²⋊C₄×C₃₁	—	4	4	no	—
255	C₂²⋊C₄×C₃₁	—	4	4	no	—
256	C₄²×C₃₁	—	2	4	no	—
257	C₄²×C₃₁	—	2	4	no	—
258	C₄²×C₃₁	—	2	4	no	—
259	C₄²×C₃₁	—	4	4	no	—
260	C₄²×C₃₁	C₂×D₄	1	4	yes	—
261	C₄²×C₃₁	C₂×D₄	1	4	yes	—
262	C₄²×C₃₁	C₂×D₄	1	4	yes	—
263	C₄²×C₃₁	C₂×D₄	1	4	yes	—
264	#35143	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₃₁	—	2	2	no	—
266	C₂³×C₃₁	—	2	2	no	—
267	C₂³×C₃₁	—	2	2	no	—
268	C₂³×C₃₁	—	2	2	no	—
269	C₂³×C₃₁	—	2	4	no	—
270	C₂³×C₃₁	—	2	4	no	—
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	—	2	4	no	—
273	C₂³×C₃₁	—	2	2	no	—
274	C₂³×C₃₁	—	2	4	no	—
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	4	4	no	—
277	C₂³×C₃₁	—	4	4	no	—
278	C₂³×C₃₁	—	4	4	no	—
279	C₂³×C₃₁	—	8	8	no	—
280	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
281	C₂³×C₃₁	C₂×#41	1	4	yes	—
282	C₂³×C₃₁	C₂×#41	1	4	yes	—
283	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
284	Q₈×C₃₁	—	2	8	no	—
285	D₄×C₃₁	—	2	8	no	—
286	D₄×C₃₁	—	2	16	no	—
287	D₄×C₃₁	—	8	8	no	—
288	C₂×C₄×C₃₁	—	2	16	no	—
289	C₂×C₄×C₃₁	—	2	8	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	2	no	—
292	C₂×C₄×C₃₁	—	2	2	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	2	2	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	2	2	no	—
297	C₂×C₄×C₃₁	—	2	2	no	—
298	C₂×C₄×C₃₁	—	2	2	no	—
299	C₂×C₄×C₃₁	—	2	2	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	4	no	—
304	C₂×C₄×C₃₁	—	2	4	no	—
305	C₂×C₄×C₃₁	—	2	4	no	—
306	C₂×C₄×C₃₁	—	2	4	no	—
307	C₂×C₄×C₃₁	—	2	4	no	—
308	C₂×C₄×C₃₁	—	2	4	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	2	4	no	—
312	C₂×C₄×C₃₁	—	2	4	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	4	no	—
315	C₂×C₄×C₃₁	—	4	4	no	—
316	C₂×C₄×C₃₁	—	4	4	no	—
317	C₂×C₄×C₃₁	—	4	8	no	—
318	C₂×C₄×C₃₁	—	4	8	no	—
319	C₂×C₄×C₃₁	—	4	4	no	—
320	C₂×C₄×C₃₁	—	4	4	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
329	C₂²×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
330	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#2852	C₂×C₃₁	1	4	yes	complemented
332	#2637	C₂×C₃₁	1	2	yes	complemented
333	#2636	C₂×C₃₁	1	2	yes	complemented
334	#2604	C₂×C₃₁	1	2	yes	complemented
335	#2603	C₂×C₃₁	1	2	yes	complemented
336	#2601	C₂×C₃₁	1	4	yes	complemented
337	#2579	C₂×C₃₁	1	2	yes	complemented
338	#2534	C₂×C₃₁	1	2	yes	complemented
339	#2484	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#2482	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#2406	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#2404	C₂×C₃₁	1	1	yes	characteristic
343	#2322	C₂×C₃₁	1	2	yes	complemented
344	#2321	C₂×C₃₁	1	2	yes	complemented
345	#2283	C₂×C₃₁	1	1	yes	characteristic, complemented
346	C₂²×C₃₁	—	2	2	no	—
347	C₂²×C₃₁	—	2	2	no	—
348	C₂²×C₃₁	—	2	8	no	—
349	C₂²×C₃₁	—	2	4	no	—
350	C₂²×C₃₁	—	2	8	no	—
351	C₂²×C₃₁	—	4	2	no	—
352	C₂²×C₃₁	—	4	2	no	—
353	C₂²×C₃₁	—	4	4	no	—
354	C₂²×C₃₁	—	4	2	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	—	4	2	no	—
357	C₂²×C₃₁	—	4	4	no	—
358	C₂²×C₃₁	—	4	4	no	—
359	C₂²×C₃₁	—	8	8	no	—
360	C₂²×C₃₁	#525	1	4	yes	—
361	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₃₁	C₂²×#41	1	2	yes	—
363	C₂²×C₃₁	#585	1	2	yes	—
364	C₂²×C₃₁	#585	1	2	yes	—
365	C₄×C₃₁	—	2	2	no	—
366	C₄×C₃₁	—	2	2	no	—
367	C₄×C₃₁	—	2	4	no	—
368	C₄×C₃₁	—	2	2	no	—
369	C₄×C₃₁	—	2	2	no	—
370	C₄×C₃₁	—	2	2	no	—
371	C₄×C₃₁	—	2	2	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	—	4	2	no	—
375	C₄×C₃₁	—	4	2	no	—
376	C₄×C₃₁	—	4	2	no	—
377	C₄×C₃₁	—	4	4	no	—
378	C₄×C₃₁	—	4	4	no	—
379	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
380	C₂×#126	—	2	8	no	—
381	C₂×#126	C₂²×C₃₁	1	2	yes	—
382	C₂×#126	C₂²×C₃₁	1	2	yes	—
383	C₂×#126	C₂²×C₃₁	1	2	yes	—
384	C₂×#126	C₂²×C₃₁	1	2	yes	—
385	C₂×#123	C₂²×C₃₁	1	2	yes	—
386	C₂×#120	C₂²×C₃₁	1	2	yes	—
387	C₄×#41	—	2	8	no	—
388	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
389	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
390	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
392	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
394	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
396	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
398	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
402	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
403	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
404	#400	C₂²×C₃₁	1	2	yes	complemented
405	#399	C₂²×C₃₁	1	2	yes	—
406	#398	C₂²×C₃₁	1	4	yes	complemented
407	#398	C₂²×C₃₁	1	2	yes	complemented
408	#397	C₂²×C₃₁	1	2	yes	—
409	#396	C₂²×C₃₁	1	4	yes	—
410	#396	C₂²×C₃₁	1	4	yes	complemented
411	#395	C₂²×C₃₁	1	2	yes	complemented
412	#394	C₂²×C₃₁	1	4	yes	—
413	#394	C₂²×C₃₁	1	2	yes	complemented
414	#393	C₂²×C₃₁	1	2	yes	—
415	#392	C₂²×C₃₁	1	2	yes	—
416	#390	C₂²×C₃₁	1	4	yes	—
417	#389	C₂²×C₃₁	1	4	yes	complemented
418	#388	C₂²×C₃₁	1	4	yes	—
419	#388	C₂²×C₃₁	1	4	yes	—
420	#388	C₂²×C₃₁	1	4	yes	—
421	#388	C₂²×C₃₁	1	4	yes	—
422	#388	C₂²×C₃₁	1	4	yes	complemented
423	#387	C₂²×C₃₁	1	4	yes	complemented
424	#387	C₂²×C₃₁	1	4	yes	complemented
425	#387	C₂²×C₃₁	1	4	yes	complemented
426	#386	C₂²×C₃₁	1	2	yes	—
427	#386	C₂²×C₃₁	1	4	yes	—
428	#386	C₂²×C₃₁	1	2	yes	—
429	#386	C₂²×C₃₁	1	4	yes	—
430	#386	C₂²×C₃₁	1	4	yes	—
431	#385	C₂²×C₃₁	1	2	yes	—
432	#385	C₂²×C₃₁	1	2	yes	—
433	#385	C₂²×C₃₁	1	4	yes	complemented
434	#385	C₂²×C₃₁	1	4	yes	complemented
435	#385	C₂²×C₃₁	1	4	yes	complemented
436	#383	C₂²×C₃₁	1	2	yes	complemented
437	#382	C₂²×C₃₁	1	2	yes	complemented
438	#381	C₂²×C₃₁	1	2	yes	—
439	#381	C₂²×C₃₁	1	1	yes	characteristic
440	#381	C₂²×C₃₁	1	1	yes	characteristic
441	#380	C₂²×C₃₁	1	2	yes	—
442	#379	C₂²×C₃₁	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
444	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
445	#376	C₂²×C₃₁	1	2	yes	complemented
446	C₂×C₃₁	—	2	4	no	—
447	C₂×C₃₁	—	4	4	no	—
448	C₂×C₃₁	—	8	2	no	—
449	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
450	C₂×C₃₁	#3449	1	1	yes	characteristic
451	C₂×C₃₁	#3449	1	1	yes	characteristic
452	C₂×C₃₁	#3521	1	4	yes	—
453	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
454	C₂×#41	—	2	8	no	—
455	C₂×#41	—	2	4	no	—
456	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
459	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
460	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
462	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
466	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
467	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
469	#126	—	2	8	no	—
470	#126	—	2	8	no	—
471	#126	—	2	8	no	—
472	#126	—	2	8	no	—
473	#123	—	2	8	no	—
474	#120	—	2	8	no	—
475	C₄×Q₈	—	2	4	no	—
476	C₄×Q₈	—	2	4	no	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	—	2	4	no	—
481	#117	—	2	4	no	—
482	#117	—	2	8	no	—
483	C₂×C₄⋊C₄	—	2	4	no	—
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	—	2	4	no	—
486	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
520	C₂×C₄²	—	2	8	no	—
521	C₂×C₄²	D₄×C₃₁	1	8	yes	complemented
522	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
523	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
524	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
525	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
526	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
530	#95	C₂³×C₃₁	1	4	yes	—
531	#95	C₂³×C₃₁	1	2	yes	—
532	#95	C₂³×C₃₁	1	2	yes	—
533	#95	C₂³×C₃₁	1	4	yes	—
534	#95	C₂³×C₃₁	1	2	yes	—
535	#95	C₂³×C₃₁	1	2	yes	—
536	#95	C₂³×C₃₁	1	4	yes	—
537	#95	C₂³×C₃₁	1	4	yes	—
538	#95	C₂³×C₃₁	1	4	yes	—
539	#95	C₂³×C₃₁	1	4	yes	—
540	#95	C₂³×C₃₁	1	4	yes	—
541	#95	C₂³×C₃₁	1	4	yes	—
542	C₃₁	#35143	1	1	yes	characteristic, direct product factor, Sylow
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	2	4	no	—
545	C₂⁴	—	4	2	no	—
546	C₂⁴	—	4	2	no	—
547	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
548	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
549	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
550	#41	—	2	32	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	#41×C₃₁	1	8	yes	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
578	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
579	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	4	4	no	—
629	C₄²	C₂×D₄×C₃₁	1	4	yes	—
630	C₄²	C₂×D₄×C₃₁	1	4	yes	—
631	C₄²	C₂×D₄×C₃₁	1	4	yes	—
632	C₄²	C₂×D₄×C₃₁	1	4	yes	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	8	8	no	—
648	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
649	C₂³	C₂×#41×C₃₁	1	4	yes	—
650	C₂³	C₂×#41×C₃₁	1	4	yes	—
651	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
652	Q₈	—	2	8	no	—
653	D₄	—	2	8	no	—
654	D₄	—	2	16	no	—
655	D₄	—	8	8	no	—
656	C₂×C₄	—	2	16	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	8	no	—
686	C₂×C₄	—	4	8	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
694	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
696	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	8	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	2	8	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	8	8	no	—
711	C₂²	C₃₁×#525	1	4	yes	—
712	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
713	C₂²	C₂²×#41×C₃₁	1	2	yes	—
714	C₂²	C₃₁×#585	1	2	yes	—
715	C₂²	C₃₁×#585	1	2	yes	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	4	no	—
729	C₄	—	4	4	no	—
730	C₂	—	2	4	no	—
731	C₂	—	4	4	no	—
732	C₂	—	8	2	no	—
733	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
734	C₂	C₃₁×#3449	1	1	yes	characteristic
735	C₂	C₃₁×#3449	1	1	yes	characteristic
736	C₂	C₃₁×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2404	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#126	C₂	semidirect
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#2852	C₂	semidirect
4. C₃₁×#2637	C₂	semidirect
5. C₃₁×#2636	C₂	semidirect
6. C₃₁×#2604	C₂	semidirect
7. C₃₁×#2603	C₂	semidirect
8. C₃₁×#2601	C₂	semidirect
9. C₃₁×#2579	C₂	semidirect
10. C₃₁×#2534	C₂	semidirect
11. C₃₁×#2484	C₂	semidirect
12. C₃₁×#2482	C₂	semidirect
13. C₃₁×#2406	C₂	semidirect
15. C₃₁×#2322	C₂	semidirect
16. C₃₁×#2321	C₂	semidirect
17. C₃₁×#2283	C₂	semidirect
27. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
28. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
31. C₂×C₄×D₄×C₃₁	C₂²	semidirect
32. C₂×C₄×D₄×C₃₁	C₂²	semidirect
34. C₂×C₃₁×#117	C₂²	semidirect
42. C₂²×C₄²×C₃₁	C₂²	semidirect
43. C₃₁×#400	C₂²	semidirect
45. C₃₁×#398	C₂²	semidirect
46. C₃₁×#398	C₂²	semidirect
49. C₃₁×#396	C₂²	semidirect
50. C₃₁×#395	C₂²	semidirect
52. C₃₁×#394	C₂²	semidirect
56. C₃₁×#389	C₂²	semidirect
61. C₃₁×#388	C₂²	semidirect
62. C₃₁×#387	C₂²	semidirect
63. C₃₁×#387	C₂²	semidirect
64. C₃₁×#387	C₂²	semidirect
72. C₃₁×#385	C₂²	semidirect
73. C₃₁×#385	C₂²	semidirect
74. C₃₁×#385	C₂²	semidirect
75. C₃₁×#383	C₂²	semidirect
76. C₃₁×#382	C₂²	semidirect
82. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
84. C₃₁×#376	C₂²	semidirect
153. C₂×C₄²×C₃₁	D₄	semidirect
264. #35143	C₃₁	direct (N × H)
329. C₂²×#126	C₂×C₃₁	semidirect
330. C₂×C₄×#41	C₂×C₃₁	semidirect
331. #2852	C₂×C₃₁	semidirect
332. #2637	C₂×C₃₁	semidirect
333. #2636	C₂×C₃₁	semidirect
334. #2604	C₂×C₃₁	semidirect
335. #2603	C₂×C₃₁	semidirect
336. #2601	C₂×C₃₁	semidirect
337. #2579	C₂×C₃₁	semidirect
338. #2534	C₂×C₃₁	semidirect
339. #2484	C₂×C₃₁	semidirect
340. #2482	C₂×C₃₁	semidirect
341. #2406	C₂×C₃₁	semidirect
343. #2322	C₂×C₃₁	semidirect
344. #2321	C₂×C₃₁	semidirect
345. #2283	C₂×C₃₁	semidirect
388. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
389. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
392. C₂×C₄×D₄	C₂²×C₃₁	semidirect
393. C₂×C₄×D₄	C₂²×C₃₁	semidirect
395. C₂×#117	C₂²×C₃₁	semidirect
403. C₂²×C₄²	C₂²×C₃₁	semidirect
404. #400	C₂²×C₃₁	semidirect
406. #398	C₂²×C₃₁	semidirect
407. #398	C₂²×C₃₁	semidirect
410. #396	C₂²×C₃₁	semidirect
411. #395	C₂²×C₃₁	semidirect
413. #394	C₂²×C₃₁	semidirect
417. #389	C₂²×C₃₁	semidirect
422. #388	C₂²×C₃₁	semidirect
423. #387	C₂²×C₃₁	semidirect
424. #387	C₂²×C₃₁	semidirect
425. #387	C₂²×C₃₁	semidirect
433. #385	C₂²×C₃₁	semidirect
434. #385	C₂²×C₃₁	semidirect
435. #385	C₂²×C₃₁	semidirect
436. #383	C₂²×C₃₁	semidirect
437. #382	C₂²×C₃₁	semidirect
443. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
445. #376	C₂²×C₃₁	semidirect
521. C₂×C₄²	D₄×C₃₁	semidirect
542. C₃₁	#35143	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#126	2
C₂×C₄×#41×C₃₁	2
C₃₁×#2852	2
C₃₁×#2637	2
C₃₁×#2636	2
C₃₁×#2604	2
C₃₁×#2603	2
C₃₁×#2601	2
C₃₁×#2579	2
C₃₁×#2534	2
C₃₁×#2484	2
C₃₁×#2482	2
C₃₁×#2406	2
C₃₁×#2404	2
C₃₁×#2322	2
C₃₁×#2321	2
C₃₁×#2283	2
#35143	31

Subgroups — C31×#35143 #21491902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35143 #21491902