Subgroups — C₃₁×#61895 #21518654

Order 7936.

1794 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3371	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3117	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3105	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#559	—	2	2	no	—
17	C₃₁×#559	—	2	2	no	—
18	C₃₁×#559	C₂²	1	4	yes	—
19	C₃₁×#559	C₂²	1	4	yes	—
20	C₃₁×#559	C₂²	1	2	yes	complemented
21	C₃₁×#557	C₂²	1	2	yes	complemented
22	C₃₁×#556	—	2	2	no	—
23	C₃₁×#556	C₂²	1	2	yes	complemented
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#539	—	2	1	no	—
27	C₃₁×#539	—	2	1	no	—
28	C₃₁×#536	—	2	1	no	—
29	C₃₁×#533	C₂²	1	1	yes	characteristic
30	C₃₁×#532	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
32	C₃₁×#529	C₂²	1	2	yes	—
33	C₃₁×#529	C₂²	1	2	yes	—
34	C₂×C₃₁×#124	—	2	1	no	—
35	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#123	—	2	1	no	—
38	C₂×C₃₁×#123	—	2	1	no	—
39	C₃₁×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	—	2	1	no	—
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#497	C₂²	1	2	yes	complemented
46	C₃₁×#496	C₂²	1	4	yes	—
47	C₃₁×#496	C₂²	1	2	yes	complemented
48	C₃₁×#495	C₂²	1	4	yes	complemented
49	C₃₁×#490	C₂²	1	4	yes	—
50	C₃₁×#489	C₂²	1	2	yes	complemented
51	C₃₁×#489	C₂²	1	2	yes	complemented
52	C₃₁×#488	C₂²	1	4	yes	complemented
53	C₃₁×#484	C₂²	1	2	yes	—
54	C₃₁×#481	C₂²	1	2	yes	—
55	C₃₁×#479	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#476	C₂²	1	2	yes	complemented
58	C₃₁×#474	C₂²	1	2	yes	complemented
59	C₃₁×#464	C₂²	1	4	yes	complemented
60	C₃₁×#464	C₂²	1	4	yes	complemented
61	C₃₁×#464	C₂²	1	4	yes	complemented
62	C₃₁×#463	C₂²	1	4	yes	complemented
63	C₃₁×#463	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#461	C₂²	1	2	yes	complemented
66	C₃₁×#460	C₂²	1	4	yes	—
67	C₃₁×#459	C₂²	1	4	yes	—
68	C₃₁×#459	C₂²	1	2	yes	complemented
69	C₃₁×#451	C₂²	1	2	yes	—
70	C₃₁×#450	C₂²	1	2	yes	—
71	C₃₁×#450	C₂²	1	2	yes	—
72	C₃₁×#448	C₂²	1	2	yes	—
73	C₃₁×#447	C₂²	1	2	yes	—
74	C₃₁×#447	C₂²	1	2	yes	—
75	C₃₁×#446	C₂²	1	4	yes	complemented
76	C₃₁×#446	C₂²	1	4	yes	complemented
77	C₃₁×#442	C₂²	1	4	yes	complemented
78	C₃₁×#441	C₂²	1	4	yes	complemented
79	C₃₁×#440	C₂²	1	4	yes	complemented
80	C₃₁×#440	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
82	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
83	C₃₁×#432	C₂²	1	1	yes	characteristic
84	C₃₁×#432	C₂²	1	1	yes	characteristic
85	C₃₁×#432	C₂²	1	2	yes	—
86	C₃₁×#431	C₂²	1	2	yes	—
87	C₂×#41×C₃₁	—	2	1	no	—
88	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
89	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	—	2	1	no	—
91	C₂²×D₄×C₃₁	—	2	1	no	—
92	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	—	2	1	no	—
95	C₂³×C₄×C₃₁	—	2	1	no	—
96	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×D₈×C₃₁	C₂³	1	4	yes	—
101	C₂×D₈×C₃₁	C₂³	1	4	yes	—
102	C₃₁×C₄⋊Q₈	—	2	2	no	—
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₃₁×#127	—	2	2	no	—
107	C₃₁×#127	C₂³	1	4	yes	—
108	C₃₁×#127	C₂³	1	1	yes	characteristic
109	C₃₁×#126	—	2	2	no	—
110	C₃₁×#126	—	2	2	no	—
111	C₃₁×#126	—	2	2	no	—
112	C₃₁×#126	—	2	2	no	—
113	C₃₁×#125	—	2	2	no	—
114	C₃₁×#125	—	2	2	no	—
115	C₃₁×#125	—	2	1	no	—
116	C₃₁×#125	C₂³	1	2	yes	—
117	C₃₁×#125	C₂³	1	2	yes	—
118	C₃₁×#124	—	2	4	no	—
119	C₃₁×#124	—	2	4	no	—
120	C₃₁×#124	—	2	2	no	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	—	2	1	no	—
123	C₃₁×#124	—	2	1	no	—
124	C₃₁×#124	—	2	1	no	—
125	C₃₁×#124	C₂³	1	2	yes	—
126	C₃₁×#124	C₂³	1	2	yes	—
127	C₃₁×#124	C₂³	1	4	yes	—
128	C₃₁×#124	C₂³	1	2	yes	—
129	C₃₁×#124	C₂³	1	2	yes	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	4	no	—
133	C₃₁×#123	—	2	4	no	—
134	C₃₁×#123	—	2	4	no	—
135	C₃₁×#123	—	2	4	no	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	1	no	—
141	C₃₁×C₂²⋊Q₈	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	C₂³	1	2	yes	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	2	no	—
148	C₄×Q₈×C₃₁	—	2	1	no	—
149	C₄×Q₈×C₃₁	D₄	1	2	yes	—
150	C₄×Q₈×C₃₁	D₄	1	2	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
153	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	4	no	—
160	C₄×D₄×C₃₁	—	2	4	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₄×D₄×C₃₁	C₂³	1	4	yes	—
168	C₄×D₄×C₃₁	C₂³	1	2	yes	—
169	C₄×D₄×C₃₁	C₂³	1	2	yes	—
170	C₄×D₄×C₃₁	C₂³	1	2	yes	—
171	C₄×D₄×C₃₁	C₂³	1	2	yes	—
172	C₃₁×#117	—	2	1	no	—
173	C₃₁×#117	—	2	2	no	—
174	C₃₁×#117	—	2	2	no	—
175	C₃₁×#117	—	2	2	no	—
176	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
188	C₂×C₄²×C₃₁	—	2	1	no	—
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₃₁×#107	C₂³	1	4	yes	—
193	C₃₁×#106	C₂³	1	4	yes	—
194	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
195	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
196	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
197	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
198	C₃₁×#103	C₂³	1	4	yes	—
199	C₃₁×#103	C₂³	1	4	yes	—
200	C₃₁×#103	C₂³	1	4	yes	—
201	C₃₁×#102	C₂³	1	4	yes	—
202	C₃₁×#102	C₂³	1	4	yes	—
203	C₃₁×#102	C₂³	1	4	yes	—
204	C₃₁×#102	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃₁×#97	C₂³	1	2	yes	—
209	C₃₁×#97	C₂³	1	4	yes	—
210	C₃₁×#97	C₂³	1	2	yes	—
211	C₄×C₈×C₃₁	C₂³	1	4	yes	—
212	C₂⁴×C₃₁	—	2	1	no	—
213	C₂⁴×C₃₁	—	2	1	no	—
214	#41×C₃₁	—	4	4	no	—
215	C₂×Q₈×C₃₁	—	2	1	no	—
216	C₂×Q₈×C₃₁	—	2	1	no	—
217	C₂×Q₈×C₃₁	—	2	1	no	—
218	C₂×Q₈×C₃₁	—	4	2	no	—
219	C₂×Q₈×C₃₁	—	4	2	no	—
220	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
224	C₂×D₄×C₃₁	—	2	2	no	—
225	C₂×D₄×C₃₁	—	2	1	no	—
226	C₂×D₄×C₃₁	—	2	1	no	—
227	C₂×D₄×C₃₁	—	2	1	no	—
228	C₂×D₄×C₃₁	—	2	4	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	4	no	—
231	C₂×D₄×C₃₁	—	4	2	no	—
232	C₂×D₄×C₃₁	—	4	2	no	—
233	C₂×D₄×C₃₁	—	4	4	no	—
234	C₂×D₄×C₃₁	—	8	2	no	—
235	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	—	2	1	no	—
239	C₂²×C₄×C₃₁	—	2	1	no	—
240	C₂²×C₄×C₃₁	—	2	2	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	2	no	—
243	C₂²×C₄×C₃₁	—	2	4	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	8	2	no	—
247	C₂²×C₄×C₃₁	—	8	2	no	—
248	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	Q₁₆×C₃₁	—	4	4	no	—
256	SD₁₆×C₃₁	—	4	4	no	—
257	SD₁₆×C₃₁	—	4	4	no	—
258	SD₁₆×C₃₁	—	4	4	no	—
259	D₈×C₃₁	—	4	4	no	—
260	D₈×C₃₁	—	4	4	no	—
261	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
262	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	—	2	4	no	—
267	C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	2	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	2	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	2	no	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	—	2	2	no	—
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	2	no	—
303	C₂²⋊C₄×C₃₁	—	2	2	no	—
304	C₄²×C₃₁	—	2	4	no	—
305	C₄²×C₃₁	—	2	2	no	—
306	C₄²×C₃₁	—	2	2	no	—
307	C₄²×C₃₁	—	2	2	no	—
308	C₄²×C₃₁	C₂×D₄	1	2	yes	—
309	C₄²×C₃₁	C₂×D₄	1	2	yes	—
310	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₃₁	C₂⁴	1	2	yes	—
313	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₄²×C₃₁	C₂⁴	1	2	yes	—
316	#61895	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂³×C₃₁	—	2	2	no	—
318	C₂³×C₃₁	—	2	2	no	—
319	C₂³×C₃₁	—	2	2	no	—
320	C₂³×C₃₁	—	4	2	no	—
321	C₂³×C₃₁	—	4	2	no	—
322	C₂³×C₃₁	—	4	2	no	—
323	C₂³×C₃₁	—	4	2	no	—
324	C₂³×C₃₁	—	4	2	no	—
325	C₂³×C₃₁	—	4	2	no	—
326	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₃₁	—	2	4	no	—
328	Q₈×C₃₁	—	2	4	no	—
329	Q₈×C₃₁	—	4	2	no	—
330	Q₈×C₃₁	—	4	2	no	—
331	Q₈×C₃₁	—	4	2	no	—
332	Q₈×C₃₁	—	4	2	no	—
333	Q₈×C₃₁	—	8	1	no	—
334	D₄×C₃₁	—	2	4	no	—
335	D₄×C₃₁	—	2	2	no	—
336	D₄×C₃₁	—	2	4	no	—
337	D₄×C₃₁	—	2	2	no	—
338	D₄×C₃₁	—	4	2	no	—
339	D₄×C₃₁	—	4	2	no	—
340	D₄×C₃₁	—	4	8	no	—
341	D₄×C₃₁	—	4	2	no	—
342	D₄×C₃₁	—	4	4	no	—
343	D₄×C₃₁	—	8	1	no	—
344	D₄×C₃₁	—	8	4	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	4	1	no	—
355	C₂×C₄×C₃₁	—	4	1	no	—
356	C₂×C₄×C₃₁	—	4	1	no	—
357	C₂×C₄×C₃₁	—	4	4	no	—
358	C₂×C₄×C₃₁	—	4	2	no	—
359	C₂×C₄×C₃₁	—	4	2	no	—
360	C₂×C₄×C₃₁	—	8	2	no	—
361	C₂×C₄×C₃₁	—	8	2	no	—
362	C₂×C₄×C₃₁	—	8	4	no	—
363	C₂×C₄×C₃₁	—	8	2	no	—
364	C₂×C₄×C₃₁	—	8	2	no	—
365	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
375	C₈×C₃₁	—	2	4	no	—
376	C₈×C₃₁	—	2	4	no	—
377	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
378	C₂×#559	C₂×C₃₁	1	1	yes	characteristic, complemented
379	#3403	C₂×C₃₁	1	4	yes	complemented
380	#3401	C₂×C₃₁	1	4	yes	complemented
381	#3371	C₂×C₃₁	1	4	yes	complemented
382	#3370	C₂×C₃₁	1	4	yes	complemented
383	#3217	C₂×C₃₁	1	2	yes	complemented
384	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
385	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
386	#3211	C₂×C₃₁	1	2	yes	complemented
387	#3117	C₂×C₃₁	1	2	yes	complemented
388	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#3105	C₂×C₃₁	1	2	yes	complemented
391	#2983	C₂×C₃₁	1	1	yes	characteristic, complemented
392	C₂²×C₃₁	—	2	1	no	—
393	C₂²×C₃₁	—	2	1	no	—
394	C₂²×C₃₁	—	4	2	no	—
395	C₂²×C₃₁	—	4	2	no	—
396	C₂²×C₃₁	—	4	2	no	—
397	C₂²×C₃₁	—	4	2	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	—	4	2	no	—
400	C₂²×C₃₁	—	4	2	no	—
401	C₂²×C₃₁	—	4	2	no	—
402	C₂²×C₃₁	—	4	2	no	—
403	C₂²×C₃₁	—	8	4	no	—
404	C₂²×C₃₁	—	8	4	no	—
405	C₂²×C₃₁	#575	1	2	yes	—
406	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₃₁	—	2	2	no	—
408	C₄×C₃₁	—	2	1	no	—
409	C₄×C₃₁	—	2	1	no	—
410	C₄×C₃₁	—	2	2	no	—
411	C₄×C₃₁	—	2	1	no	—
412	C₄×C₃₁	—	2	1	no	—
413	C₄×C₃₁	—	2	2	no	—
414	C₄×C₃₁	—	2	1	no	—
415	C₄×C₃₁	—	2	2	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	2	no	—
418	C₄×C₃₁	—	4	2	no	—
419	C₄×C₃₁	—	4	2	no	—
420	C₄×C₃₁	—	4	2	no	—
421	C₄×C₃₁	#585	1	2	yes	—
422	#559	—	2	2	no	—
423	#559	—	2	2	no	—
424	#559	C₂²×C₃₁	1	4	yes	—
425	#559	C₂²×C₃₁	1	4	yes	—
426	#559	C₂²×C₃₁	1	2	yes	complemented
427	#557	C₂²×C₃₁	1	2	yes	complemented
428	#556	—	2	2	no	—
429	#556	C₂²×C₃₁	1	2	yes	complemented
430	#554	C₂²×C₃₁	1	2	yes	complemented
431	#552	—	2	2	no	—
432	#539	—	2	1	no	—
433	#539	—	2	1	no	—
434	#536	—	2	1	no	—
435	#533	C₂²×C₃₁	1	1	yes	characteristic
436	#532	C₂²×C₃₁	1	1	yes	characteristic
437	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
438	#529	C₂²×C₃₁	1	2	yes	—
439	#529	C₂²×C₃₁	1	2	yes	—
440	C₂×#124	—	2	1	no	—
441	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
442	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#123	—	2	1	no	—
444	C₂×#123	—	2	1	no	—
445	#520	—	2	1	no	—
446	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×C₄×D₄	—	2	1	no	—
449	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
451	#497	C₂²×C₃₁	1	2	yes	complemented
452	#496	C₂²×C₃₁	1	4	yes	—
453	#496	C₂²×C₃₁	1	2	yes	complemented
454	#495	C₂²×C₃₁	1	4	yes	complemented
455	#490	C₂²×C₃₁	1	4	yes	—
456	#489	C₂²×C₃₁	1	2	yes	complemented
457	#489	C₂²×C₃₁	1	2	yes	complemented
458	#488	C₂²×C₃₁	1	4	yes	complemented
459	#484	C₂²×C₃₁	1	2	yes	—
460	#481	C₂²×C₃₁	1	2	yes	—
461	#479	C₂²×C₃₁	1	4	yes	complemented
462	#478	C₂²×C₃₁	1	4	yes	complemented
463	#476	C₂²×C₃₁	1	2	yes	complemented
464	#474	C₂²×C₃₁	1	2	yes	complemented
465	#464	C₂²×C₃₁	1	4	yes	complemented
466	#464	C₂²×C₃₁	1	4	yes	complemented
467	#464	C₂²×C₃₁	1	4	yes	complemented
468	#463	C₂²×C₃₁	1	4	yes	complemented
469	#463	C₂²×C₃₁	1	4	yes	complemented
470	#463	C₂²×C₃₁	1	4	yes	complemented
471	#461	C₂²×C₃₁	1	2	yes	complemented
472	#460	C₂²×C₃₁	1	4	yes	—
473	#459	C₂²×C₃₁	1	4	yes	—
474	#459	C₂²×C₃₁	1	2	yes	complemented
475	#451	C₂²×C₃₁	1	2	yes	—
476	#450	C₂²×C₃₁	1	2	yes	—
477	#450	C₂²×C₃₁	1	2	yes	—
478	#448	C₂²×C₃₁	1	2	yes	—
479	#447	C₂²×C₃₁	1	2	yes	—
480	#447	C₂²×C₃₁	1	2	yes	—
481	#446	C₂²×C₃₁	1	4	yes	complemented
482	#446	C₂²×C₃₁	1	4	yes	complemented
483	#442	C₂²×C₃₁	1	4	yes	complemented
484	#441	C₂²×C₃₁	1	4	yes	complemented
485	#440	C₂²×C₃₁	1	4	yes	complemented
486	#440	C₂²×C₃₁	1	4	yes	complemented
487	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
488	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
489	#432	C₂²×C₃₁	1	1	yes	characteristic
490	#432	C₂²×C₃₁	1	1	yes	characteristic
491	#432	C₂²×C₃₁	1	2	yes	—
492	#431	C₂²×C₃₁	1	2	yes	—
493	C₂×C₃₁	—	2	2	no	—
494	C₂×C₃₁	—	8	2	no	—
495	C₂×C₃₁	—	8	2	no	—
496	C₂×C₃₁	—	8	2	no	—
497	C₂×C₃₁	#3487	1	1	yes	characteristic
498	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
499	C₂×C₃₁	#3585	1	1	yes	characteristic
500	C₂×#41	—	2	1	no	—
501	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
510	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
511	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
512	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
513	C₂×D₈	C₂³×C₃₁	1	4	yes	—
514	C₂×D₈	C₂³×C₃₁	1	4	yes	—
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
519	#127	—	2	2	no	—
520	#127	C₂³×C₃₁	1	4	yes	—
521	#127	C₂³×C₃₁	1	1	yes	characteristic
522	#126	—	2	2	no	—
523	#126	—	2	2	no	—
524	#126	—	2	2	no	—
525	#126	—	2	2	no	—
526	#125	—	2	2	no	—
527	#125	—	2	2	no	—
528	#125	—	2	1	no	—
529	#125	C₂³×C₃₁	1	2	yes	—
530	#125	C₂³×C₃₁	1	2	yes	—
531	#124	—	2	4	no	—
532	#124	—	2	4	no	—
533	#124	—	2	2	no	—
534	#124	—	2	2	no	—
535	#124	—	2	1	no	—
536	#124	—	2	1	no	—
537	#124	—	2	1	no	—
538	#124	C₂³×C₃₁	1	2	yes	—
539	#124	C₂³×C₃₁	1	4	yes	—
540	#124	C₂³×C₃₁	1	2	yes	—
541	#124	C₂³×C₃₁	1	2	yes	—
542	#124	C₂³×C₃₁	1	2	yes	—
543	#123	—	2	2	no	—
544	#123	—	2	2	no	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	#123	—	2	4	no	—
548	#123	—	2	4	no	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
557	#121	—	2	1	no	—
558	#121	C₂³×C₃₁	1	2	yes	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	D₄×C₃₁	1	2	yes	—
563	C₄×Q₈	D₄×C₃₁	1	2	yes	—
564	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
565	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
566	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
567	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
568	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
569	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	4	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	C₂³×C₃₁	1	4	yes	—
580	C₄×D₄	C₂³×C₃₁	1	2	yes	—
581	C₄×D₄	C₂³×C₃₁	1	2	yes	—
582	C₄×D₄	C₂³×C₃₁	1	2	yes	—
583	C₄×D₄	C₂³×C₃₁	1	2	yes	—
584	C₄×D₄	C₂³×C₃₁	1	2	yes	—
585	#117	—	2	1	no	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
592	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
593	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
605	#107	C₂³×C₃₁	1	4	yes	—
606	#106	C₂³×C₃₁	1	4	yes	—
607	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
608	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
609	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
610	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
611	#103	C₂³×C₃₁	1	4	yes	—
612	#103	C₂³×C₃₁	1	4	yes	—
613	#103	C₂³×C₃₁	1	4	yes	—
614	#102	C₂³×C₃₁	1	4	yes	—
615	#102	C₂³×C₃₁	1	4	yes	—
616	#102	C₂³×C₃₁	1	4	yes	—
617	#102	C₂³×C₃₁	1	4	yes	—
618	#102	C₂³×C₃₁	1	4	yes	—
619	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
620	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
621	#97	C₂³×C₃₁	1	2	yes	—
622	#97	C₂³×C₃₁	1	4	yes	—
623	#97	C₂³×C₃₁	1	2	yes	—
624	C₄×C₈	C₂³×C₃₁	1	4	yes	—
625	C₃₁	#61895	1	1	yes	characteristic, direct product factor, Sylow
626	C₂⁴	—	2	1	no	—
627	C₂⁴	—	2	1	no	—
628	#41	—	4	4	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	4	2	no	—
634	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
635	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
636	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
637	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	—	4	4	no	—
648	C₂×D₄	—	8	2	no	—
649	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
650	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	8	2	no	—
661	C₂²×C₄	—	8	2	no	—
662	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
669	Q₁₆	—	4	4	no	—
670	SD₁₆	—	4	4	no	—
671	SD₁₆	—	4	4	no	—
672	SD₁₆	—	4	4	no	—
673	D₈	—	4	4	no	—
674	D₈	—	4	4	no	—
675	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
676	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
692	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
693	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
694	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
695	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
696	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	C₂×D₄×C₃₁	1	2	yes	—
723	C₄²	C₂×D₄×C₃₁	1	2	yes	—
724	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
726	C₄²	C₂⁴×C₃₁	1	2	yes	—
727	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
729	C₄²	C₂⁴×C₃₁	1	2	yes	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	2	no	—
739	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
740	Q₈	—	2	4	no	—
741	Q₈	—	2	4	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	2	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	4	2	no	—
746	Q₈	—	8	1	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	2	no	—
749	D₄	—	2	4	no	—
750	D₄	—	2	2	no	—
751	D₄	—	4	2	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	8	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	8	1	no	—
757	D₄	—	8	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	—	8	2	no	—
775	C₂×C₄	—	8	4	no	—
776	C₂×C₄	—	8	2	no	—
777	C₂×C₄	—	8	2	no	—
778	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
780	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
781	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
787	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
788	C₈	—	2	4	no	—
789	C₈	—	2	4	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	8	4	no	—
802	C₂²	—	8	4	no	—
803	C₂²	C₃₁×#575	1	2	yes	—
804	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	2	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	C₃₁×#585	1	2	yes	—
820	C₂	—	2	2	no	—
821	C₂	—	8	2	no	—
822	C₂	—	8	2	no	—
823	C₂	—	8	2	no	—
824	C₂	C₃₁×#3487	1	1	yes	characteristic
825	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
826	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
2. C₂×C₃₁×#559	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3371	C₂	semidirect
6. C₃₁×#3370	C₂	semidirect
7. C₃₁×#3217	C₂	semidirect
8. C₃₁×#3215	C₂	semidirect
9. C₃₁×#3213	C₂	semidirect
10. C₃₁×#3211	C₂	semidirect
11. C₃₁×#3117	C₂	semidirect
12. C₃₁×#3110	C₂	semidirect
13. C₃₁×#3109	C₂	semidirect
14. C₃₁×#3105	C₂	semidirect
15. C₃₁×#2983	C₂	semidirect
20. C₃₁×#559	C₂²	semidirect
21. C₃₁×#557	C₂²	semidirect
23. C₃₁×#556	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
45. C₃₁×#497	C₂²	semidirect
47. C₃₁×#496	C₂²	semidirect
48. C₃₁×#495	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#489	C₂²	semidirect
52. C₃₁×#488	C₂²	semidirect
55. C₃₁×#479	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#474	C₂²	semidirect
59. C₃₁×#464	C₂²	semidirect
60. C₃₁×#464	C₂²	semidirect
61. C₃₁×#464	C₂²	semidirect
62. C₃₁×#463	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#461	C₂²	semidirect
68. C₃₁×#459	C₂²	semidirect
75. C₃₁×#446	C₂²	semidirect
76. C₃₁×#446	C₂²	semidirect
77. C₃₁×#442	C₂²	semidirect
78. C₃₁×#441	C₂²	semidirect
79. C₃₁×#440	C₂²	semidirect
80. C₃₁×#440	C₂²	semidirect
81. C₄×SD₁₆×C₃₁	C₂²	semidirect
82. C₄×D₈×C₃₁	C₂²	semidirect
316. #61895	C₃₁	direct (N × H)
377. #3507	C₂×C₃₁	semidirect
378. C₂×#559	C₂×C₃₁	semidirect
379. #3403	C₂×C₃₁	semidirect
380. #3401	C₂×C₃₁	semidirect
381. #3371	C₂×C₃₁	semidirect
382. #3370	C₂×C₃₁	semidirect
383. #3217	C₂×C₃₁	semidirect
384. #3215	C₂×C₃₁	semidirect
385. #3213	C₂×C₃₁	semidirect
386. #3211	C₂×C₃₁	semidirect
387. #3117	C₂×C₃₁	semidirect
388. #3110	C₂×C₃₁	semidirect
389. #3109	C₂×C₃₁	semidirect
390. #3105	C₂×C₃₁	semidirect
391. #2983	C₂×C₃₁	semidirect
426. #559	C₂²×C₃₁	semidirect
427. #557	C₂²×C₃₁	semidirect
429. #556	C₂²×C₃₁	semidirect
430. #554	C₂²×C₃₁	semidirect
451. #497	C₂²×C₃₁	semidirect
453. #496	C₂²×C₃₁	semidirect
454. #495	C₂²×C₃₁	semidirect
456. #489	C₂²×C₃₁	semidirect
457. #489	C₂²×C₃₁	semidirect
458. #488	C₂²×C₃₁	semidirect
461. #479	C₂²×C₃₁	semidirect
462. #478	C₂²×C₃₁	semidirect
463. #476	C₂²×C₃₁	semidirect
464. #474	C₂²×C₃₁	semidirect
465. #464	C₂²×C₃₁	semidirect
466. #464	C₂²×C₃₁	semidirect
467. #464	C₂²×C₃₁	semidirect
468. #463	C₂²×C₃₁	semidirect
469. #463	C₂²×C₃₁	semidirect
470. #463	C₂²×C₃₁	semidirect
471. #461	C₂²×C₃₁	semidirect
474. #459	C₂²×C₃₁	semidirect
481. #446	C₂²×C₃₁	semidirect
482. #446	C₂²×C₃₁	semidirect
483. #442	C₂²×C₃₁	semidirect
484. #441	C₂²×C₃₁	semidirect
485. #440	C₂²×C₃₁	semidirect
486. #440	C₂²×C₃₁	semidirect
487. C₄×SD₁₆	C₂²×C₃₁	semidirect
488. C₄×D₈	C₂²×C₃₁	semidirect
625. C₃₁	#61895	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×#3507	2
C₂×C₃₁×#559	2
C₃₁×#3403	2
C₃₁×#3401	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3217	2
C₃₁×#3215	2
C₃₁×#3213	2
C₃₁×#3211	2
C₃₁×#3117	2
C₃₁×#3110	2
C₃₁×#3109	2
C₃₁×#3105	2
C₃₁×#2983	2
#61895	31

Subgroups — C31×#61895 #21518654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61895 #21518654