Subgroups — C₃₁×#35145 #21491904

Order 7936.

2262 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2860	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2664	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2662	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×#2591	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2583	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2561	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2539	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2413	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2411	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#529	—	2	8	no	—
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×#126	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃₁×#123	C₂²	1	2	yes	—
28	C₂×C₃₁×#123	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#120	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃₁×#117	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#400	C₂²	1	2	yes	complemented
45	C₃₁×#399	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	complemented
47	C₃₁×#398	C₂²	1	4	yes	complemented
48	C₃₁×#397	C₂²	1	2	yes	—
49	C₃₁×#396	C₂²	1	4	yes	—
50	C₃₁×#396	C₂²	1	4	yes	complemented
51	C₃₁×#395	C₂²	1	2	yes	complemented
52	C₃₁×#394	C₂²	1	4	yes	—
53	C₃₁×#394	C₂²	1	2	yes	complemented
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#392	C₂²	1	2	yes	—
56	C₃₁×#390	C₂²	1	4	yes	—
57	C₃₁×#390	C₂²	1	4	yes	—
58	C₃₁×#390	C₂²	1	4	yes	—
59	C₃₁×#389	C₂²	1	4	yes	complemented
60	C₃₁×#389	C₂²	1	4	yes	complemented
61	C₃₁×#389	C₂²	1	4	yes	complemented
62	C₃₁×#388	C₂²	1	4	yes	—
63	C₃₁×#388	C₂²	1	4	yes	—
64	C₃₁×#388	C₂²	1	4	yes	—
65	C₃₁×#388	C₂²	1	4	yes	—
66	C₃₁×#388	C₂²	1	4	yes	complemented
67	C₃₁×#388	C₂²	1	4	yes	complemented
68	C₃₁×#388	C₂²	1	4	yes	complemented
69	C₃₁×#387	C₂²	1	4	yes	complemented
70	C₃₁×#386	C₂²	1	2	yes	—
71	C₃₁×#386	C₂²	1	4	yes	—
72	C₃₁×#386	C₂²	1	2	yes	—
73	C₃₁×#385	C₂²	1	2	yes	—
74	C₃₁×#385	C₂²	1	2	yes	—
75	C₃₁×#385	C₂²	1	4	yes	complemented
76	C₃₁×#381	C₂²	1	2	yes	—
77	C₃₁×#379	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
79	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
83	C₃₁×#376	C₂²	1	2	yes	complemented
84	C₄³×C₃₁	C₂²	1	2	yes	complemented
85	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₃₁×#126	—	2	8	no	—
98	C₃₁×#126	—	2	8	no	—
99	C₃₁×#126	—	2	8	no	—
100	C₃₁×#126	—	2	8	no	—
101	C₃₁×#126	—	2	8	no	—
102	C₃₁×#125	—	2	4	no	—
103	C₃₁×#124	—	2	4	no	—
104	C₃₁×#123	—	2	8	no	—
105	C₃₁×#123	—	2	8	no	—
106	C₃₁×C₂²⋊Q₈	—	2	4	no	—
107	C₃₁×#121	—	2	4	no	—
108	C₃₁×#120	—	2	8	no	—
109	C₄×Q₈×C₃₁	—	2	4	no	—
110	C₄×D₄×C₃₁	—	2	8	no	—
111	C₄×D₄×C₃₁	—	2	4	no	—
112	C₃₁×#117	—	2	8	no	—
113	C₃₁×#117	—	2	8	no	—
114	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
115	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
116	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
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	2	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	2	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄²×C₃₁	D₄	1	8	yes	complemented
156	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
157	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
160	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
165	C₃₁×#95	C₂³	1	2	yes	—
166	C₃₁×#95	C₂³	1	4	yes	—
167	C₃₁×#95	C₂³	1	4	yes	—
168	C₃₁×#95	C₂³	1	4	yes	—
169	C₃₁×#95	C₂³	1	4	yes	—
170	C₃₁×#95	C₂³	1	2	yes	—
171	C₃₁×#95	C₂³	1	4	yes	—
172	C₃₁×#95	C₂³	1	4	yes	—
173	C₃₁×#95	C₂³	1	4	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	C₂×Q₈×C₃₁	—	2	2	no	—
182	C₂×Q₈×C₃₁	—	4	2	no	—
183	C₂×D₄×C₃₁	—	2	4	no	—
184	C₂×D₄×C₃₁	—	2	4	no	—
185	C₂×D₄×C₃₁	—	2	4	no	—
186	C₂×D₄×C₃₁	—	2	2	no	—
187	C₂×D₄×C₃₁	—	2	8	no	—
188	C₂×D₄×C₃₁	—	4	2	no	—
189	C₂×D₄×C₃₁	—	4	4	no	—
190	C₂×D₄×C₃₁	—	4	4	no	—
191	C₂²×C₄×C₃₁	—	2	4	no	—
192	C₂²×C₄×C₃₁	—	2	2	no	—
193	C₂²×C₄×C₃₁	—	2	2	no	—
194	C₂²×C₄×C₃₁	—	2	2	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	4	no	—
197	C₂²×C₄×C₃₁	—	4	2	no	—
198	C₂²×C₄×C₃₁	—	4	2	no	—
199	C₂²×C₄×C₃₁	—	4	4	no	—
200	C₂²×C₄×C₃₁	—	4	2	no	—
201	C₂²×C₄×C₃₁	—	4	2	no	—
202	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
219	C₄⋊C₄×C₃₁	—	2	4	no	—
220	C₄⋊C₄×C₃₁	—	2	4	no	—
221	C₄⋊C₄×C₃₁	—	2	4	no	—
222	C₄⋊C₄×C₃₁	—	2	4	no	—
223	C₄⋊C₄×C₃₁	—	2	4	no	—
224	C₄⋊C₄×C₃₁	—	2	4	no	—
225	C₄⋊C₄×C₃₁	—	2	4	no	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	2	no	—
228	C₄⋊C₄×C₃₁	—	2	4	no	—
229	C₄⋊C₄×C₃₁	—	2	2	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	8	no	—
232	C₄⋊C₄×C₃₁	—	2	8	no	—
233	C₄⋊C₄×C₃₁	—	4	4	no	—
234	C₄⋊C₄×C₃₁	—	4	4	no	—
235	C₂²⋊C₄×C₃₁	—	2	4	no	—
236	C₂²⋊C₄×C₃₁	—	2	4	no	—
237	C₂²⋊C₄×C₃₁	—	2	4	no	—
238	C₂²⋊C₄×C₃₁	—	2	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	4	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	8	no	—
248	C₂²⋊C₄×C₃₁	—	2	8	no	—
249	C₂²⋊C₄×C₃₁	—	4	4	no	—
250	C₂²⋊C₄×C₃₁	—	4	4	no	—
251	C₂²⋊C₄×C₃₁	—	4	4	no	—
252	C₂²⋊C₄×C₃₁	—	4	4	no	—
253	C₂²⋊C₄×C₃₁	#41	1	8	yes	—
254	C₄²×C₃₁	—	2	4	no	—
255	C₄²×C₃₁	—	2	8	no	—
256	C₄²×C₃₁	—	4	2	no	—
257	C₄²×C₃₁	—	4	4	no	—
258	C₄²×C₃₁	—	4	2	no	—
259	C₄²×C₃₁	C₂×D₄	1	4	yes	—
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	#35145	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂³×C₃₁	—	2	2	no	—
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	2	no	—
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	—	2	4	no	—
273	C₂³×C₃₁	—	2	4	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	C₂⁵	1	1	yes	characteristic
283	Q₈×C₃₁	—	4	4	no	—
284	D₄×C₃₁	—	4	4	no	—
285	D₄×C₃₁	—	4	8	no	—
286	D₄×C₃₁	—	8	8	no	—
287	C₂×C₄×C₃₁	—	2	8	no	—
288	C₂×C₄×C₃₁	—	2	2	no	—
289	C₂×C₄×C₃₁	—	2	2	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	2	no	—
292	C₂×C₄×C₃₁	—	2	4	no	—
293	C₂×C₄×C₃₁	—	2	4	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	4	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	4	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	4	no	—
307	C₂×C₄×C₃₁	—	2	4	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	4	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	2	4	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	4	4	no	—
314	C₂×C₄×C₃₁	—	4	4	no	—
315	C₂×C₄×C₃₁	—	4	8	no	—
316	C₂×C₄×C₃₁	—	4	4	no	—
317	C₂×C₄×C₃₁	—	4	4	no	—
318	C₂×C₄×C₃₁	—	4	4	no	—
319	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	C₂×#41	1	8	yes	—
326	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
327	C₂²×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
328	#2860	C₂×C₃₁	1	4	yes	complemented
329	#2664	C₂×C₃₁	1	2	yes	complemented
330	#2662	C₂×C₃₁	1	2	yes	complemented
331	#2604	C₂×C₃₁	1	2	yes	complemented
332	#2603	C₂×C₃₁	1	2	yes	complemented
333	#2601	C₂×C₃₁	1	4	yes	complemented
334	#2591	C₂×C₃₁	1	1	yes	characteristic, complemented
335	#2583	C₂×C₃₁	1	1	yes	characteristic, complemented
336	#2561	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#2539	C₂×C₃₁	1	1	yes	characteristic
338	#2413	C₂×C₃₁	1	2	yes	complemented
339	#2411	C₂×C₃₁	1	2	yes	complemented
340	#2322	C₂×C₃₁	1	2	yes	complemented
341	#2321	C₂×C₃₁	1	2	yes	complemented
342	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
343	C₂²×C₃₁	—	2	2	no	—
344	C₂²×C₃₁	—	2	2	no	—
345	C₂²×C₃₁	—	2	8	no	—
346	C₂²×C₃₁	—	4	2	no	—
347	C₂²×C₃₁	—	4	2	no	—
348	C₂²×C₃₁	—	4	2	no	—
349	C₂²×C₃₁	—	4	2	no	—
350	C₂²×C₃₁	—	4	2	no	—
351	C₂²×C₃₁	—	4	2	no	—
352	C₂²×C₃₁	—	4	4	no	—
353	C₂²×C₃₁	—	4	4	no	—
354	C₂²×C₃₁	—	4	4	no	—
355	C₂²×C₃₁	—	4	4	no	—
356	C₂²×C₃₁	—	8	8	no	—
357	C₂²×C₃₁	#532	1	4	yes	—
358	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
359	C₂²×C₃₁	C₂²×#41	1	2	yes	—
360	C₂²×C₃₁	#585	1	2	yes	—
361	C₂²×C₃₁	#585	1	2	yes	—
362	C₄×C₃₁	—	2	2	no	—
363	C₄×C₃₁	—	2	2	no	—
364	C₄×C₃₁	—	2	2	no	—
365	C₄×C₃₁	—	2	2	no	—
366	C₄×C₃₁	—	2	2	no	—
367	C₄×C₃₁	—	2	2	no	—
368	C₄×C₃₁	—	2	8	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	—	4	2	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	—	4	2	no	—
375	C₄×C₃₁	—	4	4	no	—
376	#529	—	2	8	no	—
377	C₂×#126	—	2	8	no	—
378	C₂×#126	C₂²×C₃₁	1	2	yes	—
379	C₂×#126	C₂²×C₃₁	1	2	yes	—
380	C₂×#126	C₂²×C₃₁	1	2	yes	—
381	C₂×#126	C₂²×C₃₁	1	2	yes	—
382	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
383	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
384	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
385	C₂×#123	C₂²×C₃₁	1	2	yes	—
386	C₂×#123	C₂²×C₃₁	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
388	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
389	C₂×#120	C₂²×C₃₁	1	2	yes	—
390	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
391	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
392	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	C₂×#117	C₂²×C₃₁	1	2	yes	—
394	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
395	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
398	C₂²×C₂²⋊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×C₄²	C₂²×C₃₁	1	1	yes	characteristic
402	#400	C₂²×C₃₁	1	2	yes	complemented
403	#399	C₂²×C₃₁	1	2	yes	—
404	#398	C₂²×C₃₁	1	2	yes	complemented
405	#398	C₂²×C₃₁	1	4	yes	complemented
406	#397	C₂²×C₃₁	1	2	yes	—
407	#396	C₂²×C₃₁	1	4	yes	—
408	#396	C₂²×C₃₁	1	4	yes	complemented
409	#395	C₂²×C₃₁	1	2	yes	complemented
410	#394	C₂²×C₃₁	1	4	yes	—
411	#394	C₂²×C₃₁	1	2	yes	complemented
412	#393	C₂²×C₃₁	1	2	yes	—
413	#392	C₂²×C₃₁	1	2	yes	—
414	#390	C₂²×C₃₁	1	4	yes	—
415	#390	C₂²×C₃₁	1	4	yes	—
416	#390	C₂²×C₃₁	1	4	yes	—
417	#389	C₂²×C₃₁	1	4	yes	complemented
418	#389	C₂²×C₃₁	1	4	yes	complemented
419	#389	C₂²×C₃₁	1	4	yes	complemented
420	#388	C₂²×C₃₁	1	4	yes	—
421	#388	C₂²×C₃₁	1	4	yes	—
422	#388	C₂²×C₃₁	1	4	yes	—
423	#388	C₂²×C₃₁	1	4	yes	—
424	#388	C₂²×C₃₁	1	4	yes	complemented
425	#388	C₂²×C₃₁	1	4	yes	complemented
426	#388	C₂²×C₃₁	1	4	yes	complemented
427	#387	C₂²×C₃₁	1	4	yes	complemented
428	#386	C₂²×C₃₁	1	2	yes	—
429	#386	C₂²×C₃₁	1	4	yes	—
430	#386	C₂²×C₃₁	1	2	yes	—
431	#385	C₂²×C₃₁	1	2	yes	—
432	#385	C₂²×C₃₁	1	2	yes	—
433	#385	C₂²×C₃₁	1	4	yes	complemented
434	#381	C₂²×C₃₁	1	2	yes	—
435	#379	C₂²×C₃₁	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
437	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
438	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
439	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
441	#376	C₂²×C₃₁	1	2	yes	complemented
442	C₄³	C₂²×C₃₁	1	2	yes	complemented
443	C₂×C₃₁	—	2	4	no	—
444	C₂×C₃₁	—	8	2	no	—
445	C₂×C₃₁	—	8	2	no	—
446	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
447	C₂×C₃₁	#3449	1	1	yes	characteristic
448	C₂×C₃₁	#3449	1	1	yes	characteristic
449	C₂×C₃₁	#3521	1	4	yes	—
450	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
451	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
453	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
455	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
460	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
462	#126	—	2	8	no	—
463	#126	—	2	8	no	—
464	#126	—	2	8	no	—
465	#126	—	2	8	no	—
466	#126	—	2	8	no	—
467	#125	—	2	4	no	—
468	#124	—	2	4	no	—
469	#123	—	2	8	no	—
470	#123	—	2	8	no	—
471	C₂²⋊Q₈	—	2	4	no	—
472	#121	—	2	4	no	—
473	#120	—	2	8	no	—
474	C₄×Q₈	—	2	4	no	—
475	C₄×D₄	—	2	8	no	—
476	C₄×D₄	—	2	4	no	—
477	#117	—	2	8	no	—
478	#117	—	2	8	no	—
479	C₂×C₄⋊C₄	—	2	4	no	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	2	4	no	—
482	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	4	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	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	4	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	2	yes	—
520	C₂×C₄²	D₄×C₃₁	1	8	yes	complemented
521	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
522	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
523	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
524	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
525	C₂×C₄²	C₂³×C₃₁	1	2	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	4	yes	—
535	#95	C₂³×C₃₁	1	4	yes	—
536	#95	C₂³×C₃₁	1	4	yes	—
537	#95	C₂³×C₃₁	1	4	yes	—
538	#95	C₂³×C₃₁	1	4	yes	—
539	C₃₁	#35145	1	1	yes	characteristic, direct product factor, Sylow
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	4	no	—
542	C₂⁴	—	4	2	no	—
543	C₂⁴	—	4	2	no	—
544	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
545	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
546	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	4	2	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
569	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
570	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	#41×C₃₁	1	8	yes	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	8	no	—
622	C₄²	—	4	2	no	—
623	C₄²	—	4	4	no	—
624	C₄²	—	4	2	no	—
625	C₄²	C₂×D₄×C₃₁	1	4	yes	—
626	C₄²	C₂×D₄×C₃₁	1	4	yes	—
627	C₄²	C₂×D₄×C₃₁	1	4	yes	—
628	C₄²	C₂×D₄×C₃₁	1	4	yes	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	4	4	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	8	8	no	—
645	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
646	C₂³	C₂×#41×C₃₁	1	4	yes	—
647	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
648	Q₈	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	8	no	—
651	D₄	—	8	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	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	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	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	—	4	4	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
687	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
690	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	8	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	8	8	no	—
705	C₂²	C₃₁×#532	1	4	yes	—
706	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
707	C₂²	C₂²×#41×C₃₁	1	2	yes	—
708	C₂²	C₃₁×#585	1	2	yes	—
709	C₂²	C₃₁×#585	1	2	yes	—
710	C₄	—	2	2	no	—
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	8	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	4	no	—
724	C₂	—	2	4	no	—
725	C₂	—	8	2	no	—
726	C₂	—	8	2	no	—
727	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
728	C₂	C₃₁×#3449	1	1	yes	characteristic
729	C₂	C₃₁×#3449	1	1	yes	characteristic
730	C₂	C₃₁×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2539	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. C₂×C₃₁×#529	C₂	semidirect
2. C₂²×C₃₁×#126	C₂	semidirect
3. C₃₁×#2860	C₂	semidirect
4. C₃₁×#2664	C₂	semidirect
5. C₃₁×#2662	C₂	semidirect
6. C₃₁×#2604	C₂	semidirect
7. C₃₁×#2603	C₂	semidirect
8. C₃₁×#2601	C₂	semidirect
9. C₃₁×#2591	C₂	semidirect
10. C₃₁×#2583	C₂	semidirect
11. C₃₁×#2561	C₂	semidirect
13. C₃₁×#2413	C₂	semidirect
14. C₃₁×#2411	C₂	semidirect
15. C₃₁×#2322	C₂	semidirect
16. C₃₁×#2321	C₂	semidirect
17. C₄×C₃₁×#117	C₂	semidirect
24. C₂×C₃₁×#126	C₂²	semidirect
25. C₂×C₃₁×#125	C₂²	semidirect
26. C₂×C₃₁×#124	C₂²	semidirect
32. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
34. C₂×C₄×D₄×C₃₁	C₂²	semidirect
36. C₂×C₃₁×#117	C₂²	semidirect
44. C₃₁×#400	C₂²	semidirect
46. C₃₁×#398	C₂²	semidirect
47. C₃₁×#398	C₂²	semidirect
50. C₃₁×#396	C₂²	semidirect
51. C₃₁×#395	C₂²	semidirect
53. C₃₁×#394	C₂²	semidirect
59. C₃₁×#389	C₂²	semidirect
60. C₃₁×#389	C₂²	semidirect
61. C₃₁×#389	C₂²	semidirect
66. C₃₁×#388	C₂²	semidirect
67. C₃₁×#388	C₂²	semidirect
68. C₃₁×#388	C₂²	semidirect
69. C₃₁×#387	C₂²	semidirect
75. C₃₁×#385	C₂²	semidirect
78. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
79. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
83. C₃₁×#376	C₂²	semidirect
84. C₄³×C₃₁	C₂²	semidirect
155. C₂×C₄²×C₃₁	D₄	semidirect
263. #35145	C₃₁	direct (N × H)
326. C₂×#529	C₂×C₃₁	semidirect
327. C₂²×#126	C₂×C₃₁	semidirect
328. #2860	C₂×C₃₁	semidirect
329. #2664	C₂×C₃₁	semidirect
330. #2662	C₂×C₃₁	semidirect
331. #2604	C₂×C₃₁	semidirect
332. #2603	C₂×C₃₁	semidirect
333. #2601	C₂×C₃₁	semidirect
334. #2591	C₂×C₃₁	semidirect
335. #2583	C₂×C₃₁	semidirect
336. #2561	C₂×C₃₁	semidirect
338. #2413	C₂×C₃₁	semidirect
339. #2411	C₂×C₃₁	semidirect
340. #2322	C₂×C₃₁	semidirect
341. #2321	C₂×C₃₁	semidirect
342. C₄×#117	C₂×C₃₁	semidirect
382. C₂×#126	C₂²×C₃₁	semidirect
383. C₂×#125	C₂²×C₃₁	semidirect
384. C₂×#124	C₂²×C₃₁	semidirect
390. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
392. C₂×C₄×D₄	C₂²×C₃₁	semidirect
394. C₂×#117	C₂²×C₃₁	semidirect
402. #400	C₂²×C₃₁	semidirect
404. #398	C₂²×C₃₁	semidirect
405. #398	C₂²×C₃₁	semidirect
408. #396	C₂²×C₃₁	semidirect
409. #395	C₂²×C₃₁	semidirect
411. #394	C₂²×C₃₁	semidirect
417. #389	C₂²×C₃₁	semidirect
418. #389	C₂²×C₃₁	semidirect
419. #389	C₂²×C₃₁	semidirect
424. #388	C₂²×C₃₁	semidirect
425. #388	C₂²×C₃₁	semidirect
426. #388	C₂²×C₃₁	semidirect
427. #387	C₂²×C₃₁	semidirect
433. #385	C₂²×C₃₁	semidirect
436. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
437. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
441. #376	C₂²×C₃₁	semidirect
442. C₄³	C₂²×C₃₁	semidirect
520. C₂×C₄²	D₄×C₃₁	semidirect
539. C₃₁	#35145	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×#529	2
C₂²×C₃₁×#126	2
C₃₁×#2860	2
C₃₁×#2664	2
C₃₁×#2662	2
C₃₁×#2604	2
C₃₁×#2603	2
C₃₁×#2601	2
C₃₁×#2591	2
C₃₁×#2583	2
C₃₁×#2561	2
C₃₁×#2539	2
C₃₁×#2413	2
C₃₁×#2411	2
C₃₁×#2322	2
C₃₁×#2321	2
C₄×C₃₁×#117	2
#35145	31

Subgroups — C31×#35145 #21491904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35145 #21491904