Subgroups — C₃₁×#61836 #21518595

Order 7936.

1724 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3388	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3381	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3371	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3117	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3103	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	C₂²	1	1	yes	characteristic
19	C₃₁×#559	C₂²	1	2	yes	—
20	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#557	—	2	1	no	—
22	C₃₁×#557	—	2	1	no	—
23	C₃₁×#557	—	2	2	no	—
24	C₃₁×#557	C₂²	1	2	yes	—
25	C₃₁×#557	C₂²	1	2	yes	—
26	C₃₁×#557	C₂²	1	4	yes	—
27	C₃₁×#554	C₂²	1	1	yes	characteristic
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#550	C₂²	1	1	yes	characteristic
30	C₃₁×#548	—	2	1	no	—
31	C₃₁×#547	—	2	1	no	—
32	C₃₁×#547	—	2	2	no	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#542	—	2	1	no	—
35	C₃₁×#532	C₂²	1	2	yes	—
36	C₃₁×#532	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
38	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₃₁×#529	C₂²	1	1	yes	characteristic
40	C₃₁×#529	C₂²	1	2	yes	—
41	C₂×C₃₁×#125	—	2	2	no	—
42	C₂×C₃₁×#125	C₂²	1	2	yes	—
43	C₃₁×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
45	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	4	yes	—
49	C₃₁×#501	C₂²	1	2	yes	—
50	C₃₁×#499	C₂²	1	4	yes	—
51	C₃₁×#498	C₂²	1	2	yes	—
52	C₃₁×#490	C₂²	1	4	yes	—
53	C₃₁×#489	C₂²	1	2	yes	—
54	C₃₁×#488	C₂²	1	4	yes	—
55	C₃₁×#486	C₂²	1	2	yes	—
56	C₃₁×#484	C₂²	1	2	yes	—
57	C₃₁×#483	C₂²	1	1	yes	characteristic
58	C₃₁×#481	C₂²	1	2	yes	—
59	C₃₁×#481	C₂²	1	2	yes	—
60	C₃₁×#481	C₂²	1	2	yes	—
61	C₃₁×#480	C₂²	1	1	yes	characteristic
62	C₃₁×#480	C₂²	1	2	yes	—
63	C₃₁×#479	C₂²	1	2	yes	—
64	C₃₁×#479	C₂²	1	4	yes	—
65	C₃₁×#479	C₂²	1	4	yes	—
66	C₃₁×#478	C₂²	1	4	yes	—
67	C₃₁×#478	C₂²	1	4	yes	—
68	C₃₁×#478	C₂²	1	4	yes	—
69	C₃₁×#477	C₂²	1	2	yes	—
70	C₃₁×#476	C₂²	1	4	yes	—
71	C₃₁×#475	C₂²	1	4	yes	—
72	C₃₁×#475	C₂²	1	2	yes	—
73	C₃₁×#474	C₂²	1	2	yes	—
74	C₃₁×#464	C₂²	1	2	yes	—
75	C₃₁×#464	C₂²	1	4	yes	—
76	C₃₁×#460	C₂²	1	4	yes	—
77	C₃₁×#460	C₂²	1	2	yes	—
78	C₃₁×#451	C₂²	1	1	yes	characteristic
79	C₃₁×#448	C₂²	1	1	yes	characteristic
80	C₃₁×#448	C₂²	1	2	yes	—
81	C₃₁×#446	C₂²	1	2	yes	—
82	C₃₁×#446	C₂²	1	4	yes	—
83	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
84	C₃₁×#441	C₂²	1	4	yes	—
85	C₃₁×#440	C₂²	1	4	yes	—
86	C₃₁×#440	C₂²	1	4	yes	—
87	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
89	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
90	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
91	C₃₁×#432	C₂²	1	1	yes	characteristic
92	C₃₁×#432	C₂²	1	2	yes	—
93	C₃₁×#431	C₂²	1	2	yes	—
94	C₃₁×#431	C₂²	1	1	yes	characteristic
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂²×Q₈×C₃₁	—	2	1	no	—
99	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
100	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
104	C₃₁×C₄⋊Q₈	—	2	2	no	—
105	C₃₁×C₄⋊Q₈	—	2	2	no	—
106	C₃₁×C₄⋊Q₈	—	2	4	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	2	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	—	2	1	no	—
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×#127	C₂³	1	1	yes	characteristic
116	C₃₁×#127	C₂³	1	2	yes	—
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	1	no	—
119	C₃₁×#125	—	2	4	no	—
120	C₃₁×#125	—	2	4	no	—
121	C₃₁×#125	—	2	4	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	C₂³	1	4	yes	—
126	C₃₁×#125	C₂³	1	4	yes	—
127	C₃₁×#125	C₂³	1	2	yes	—
128	C₃₁×#125	C₂³	1	1	yes	characteristic
129	C₃₁×#124	—	2	1	no	—
130	C₃₁×#124	—	2	2	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	—	2	1	no	—
133	C₃₁×#124	C₂³	1	2	yes	—
134	C₃₁×#124	C₂³	1	1	yes	characteristic
135	C₃₁×#123	—	2	2	no	—
136	C₃₁×#123	—	2	1	no	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	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	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
146	C₃₁×#121	—	2	1	no	—
147	C₃₁×#121	—	2	2	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	C₂³	1	1	yes	characteristic
151	C₃₁×#121	C₂³	1	2	yes	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	—	2	4	no	—
156	C₄×Q₈×C₃₁	—	2	2	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	—	2	1	no	—
159	C₄×Q₈×C₃₁	—	2	1	no	—
160	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	D₄	1	2	yes	—
162	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
164	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	1	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₃₁	C₂³	1	2	yes	—
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	2	yes	—
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₃₁×#117	—	2	2	no	—
184	C₃₁×#117	—	2	1	no	—
185	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
186	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
187	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
188	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
189	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
190	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄²×C₃₁	—	2	2	no	—
197	C₂×C₄²×C₃₁	—	2	1	no	—
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₃₁×#107	C₂³	1	2	yes	—
201	C₃₁×#107	C₂³	1	4	yes	—
202	C₃₁×#107	C₂³	1	4	yes	—
203	C₃₁×#106	C₂³	1	4	yes	—
204	C₃₁×#106	C₂³	1	4	yes	—
205	C₃₁×#106	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
211	C₃₁×#103	C₂³	1	2	yes	—
212	C₃₁×#103	C₂³	1	2	yes	—
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#103	C₂³	1	2	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	2	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₃₁×#97	C₂³	1	2	yes	—
225	C₃₁×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₃₁	C₂³	1	4	yes	—
227	C₄×C₈×C₃₁	C₂³	1	2	yes	—
228	#41×C₃₁	—	4	4	no	—
229	#41×C₃₁	—	8	4	no	—
230	#41×C₃₁	—	8	2	no	—
231	C₂×Q₈×C₃₁	—	2	4	no	—
232	C₂×Q₈×C₃₁	—	2	1	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	4	2	no	—
238	C₂×Q₈×C₃₁	—	4	4	no	—
239	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
242	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
244	C₂×D₄×C₃₁	—	2	1	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	1	no	—
250	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₃₁	—	2	1	no	—
253	C₂²×C₄×C₃₁	—	2	1	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	Q₁₆×C₃₁	—	2	4	no	—
266	SD₁₆×C₃₁	—	2	4	no	—
267	SD₁₆×C₃₁	—	2	8	no	—
268	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
269	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
270	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	—	2	4	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	—	2	4	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	4	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₃₁	—	2	1	no	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	1	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	1	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₄²×C₃₁	—	2	4	no	—
317	C₄²×C₃₁	—	2	4	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	—	2	1	no	—
322	C₄²×C₃₁	C₂×D₄	1	2	yes	—
323	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₃₁	C₂×D₄	1	2	yes	—
325	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₃₁	C₂⁴	1	2	yes	—
327	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₄²×C₃₁	C₂⁴	1	2	yes	—
330	#61836	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	1	no	—
333	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₃₁	—	2	4	no	—
335	Q₈×C₃₁	—	2	2	no	—
336	Q₈×C₃₁	—	2	2	no	—
337	Q₈×C₃₁	—	2	2	no	—
338	Q₈×C₃₁	—	2	2	no	—
339	Q₈×C₃₁	—	4	2	no	—
340	Q₈×C₃₁	—	4	4	no	—
341	Q₈×C₃₁	—	4	4	no	—
342	Q₈×C₃₁	—	8	2	no	—
343	Q₈×C₃₁	—	8	1	no	—
344	Q₈×C₃₁	2₋¹⁺⁴	1	4	yes	—
345	D₄×C₃₁	—	2	2	no	—
346	D₄×C₃₁	—	2	4	no	—
347	D₄×C₃₁	—	4	4	no	—
348	D₄×C₃₁	—	4	2	no	—
349	D₄×C₃₁	—	4	4	no	—
350	D₄×C₃₁	—	4	2	no	—
351	D₄×C₃₁	—	8	2	no	—
352	D₄×C₃₁	—	8	1	no	—
353	C₂×C₄×C₃₁	—	2	4	no	—
354	C₂×C₄×C₃₁	—	2	4	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	1	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	4	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	1	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	4	2	no	—
366	C₂×C₄×C₃₁	—	4	4	no	—
367	C₂×C₄×C₃₁	—	4	4	no	—
368	C₂×C₄×C₃₁	—	4	2	no	—
369	C₂×C₄×C₃₁	—	4	2	no	—
370	C₂×C₄×C₃₁	—	8	2	no	—
371	C₂×C₄×C₃₁	—	8	2	no	—
372	C₂×C₄×C₃₁	—	8	2	no	—
373	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
383	C₈×C₃₁	—	2	2	no	—
384	C₈×C₃₁	—	2	4	no	—
385	C₈×C₃₁	—	2	2	no	—
386	#3522	C₂×C₃₁	1	1	yes	characteristic
387	C₂×#557	C₂×C₃₁	1	1	yes	characteristic, complemented
388	#3388	C₂×C₃₁	1	4	yes	complemented
389	#3387	C₂×C₃₁	1	2	yes	complemented
390	#3381	C₂×C₃₁	1	2	yes	complemented
391	#3371	C₂×C₃₁	1	4	yes	complemented
392	#3368	C₂×C₃₁	1	2	yes	complemented
393	#3365	C₂×C₃₁	1	2	yes	complemented
394	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
395	#3234	C₂×C₃₁	1	2	yes	complemented
396	#3232	C₂×C₃₁	1	2	yes	complemented
397	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
398	#3117	C₂×C₃₁	1	2	yes	complemented
399	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
400	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#3103	C₂×C₃₁	1	2	yes	complemented
402	#2984	C₂×C₃₁	1	1	yes	characteristic, complemented
403	C₂²×C₃₁	—	2	1	no	—
404	C₂²×C₃₁	—	2	1	no	—
405	C₂²×C₃₁	—	4	2	no	—
406	C₂²×C₃₁	—	4	1	no	—
407	C₂²×C₃₁	—	4	2	no	—
408	C₂²×C₃₁	—	4	1	no	—
409	C₂²×C₃₁	—	4	2	no	—
410	C₂²×C₃₁	—	4	1	no	—
411	C₂²×C₃₁	#577	1	2	yes	—
412	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₃₁	—	2	4	no	—
414	C₄×C₃₁	—	2	1	no	—
415	C₄×C₃₁	—	2	1	no	—
416	C₄×C₃₁	—	2	2	no	—
417	C₄×C₃₁	—	2	2	no	—
418	C₄×C₃₁	—	2	2	no	—
419	C₄×C₃₁	—	2	1	no	—
420	C₄×C₃₁	—	2	2	no	—
421	C₄×C₃₁	—	2	1	no	—
422	C₄×C₃₁	—	4	1	no	—
423	C₄×C₃₁	—	4	1	no	—
424	C₄×C₃₁	—	4	4	no	—
425	C₄×C₃₁	—	4	2	no	—
426	C₄×C₃₁	—	4	2	no	—
427	C₄×C₃₁	—	4	1	no	—
428	C₄×C₃₁	#575	1	2	yes	—
429	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
430	#559	C₂²×C₃₁	1	1	yes	characteristic
431	#559	C₂²×C₃₁	1	2	yes	—
432	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
433	#557	—	2	1	no	—
434	#557	—	2	1	no	—
435	#557	—	2	2	no	—
436	#557	C₂²×C₃₁	1	2	yes	—
437	#557	C₂²×C₃₁	1	2	yes	—
438	#557	C₂²×C₃₁	1	4	yes	—
439	#554	C₂²×C₃₁	1	1	yes	characteristic
440	#554	C₂²×C₃₁	1	2	yes	—
441	#550	C₂²×C₃₁	1	1	yes	characteristic
442	#548	—	2	1	no	—
443	#547	—	2	1	no	—
444	#547	—	2	2	no	—
445	#542	—	2	2	no	—
446	#542	—	2	1	no	—
447	#532	C₂²×C₃₁	1	2	yes	—
448	#532	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	—	2	1	no	—
450	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
451	#529	C₂²×C₃₁	1	1	yes	characteristic
452	#529	C₂²×C₃₁	1	2	yes	—
453	C₂×#125	—	2	2	no	—
454	C₂×#125	C₂²×C₃₁	1	2	yes	—
455	#520	—	2	1	no	—
456	C₂×C₄×Q₈	—	2	1	no	—
457	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
458	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
460	#501	C₂²×C₃₁	1	4	yes	—
461	#501	C₂²×C₃₁	1	2	yes	—
462	#499	C₂²×C₃₁	1	4	yes	—
463	#498	C₂²×C₃₁	1	2	yes	—
464	#490	C₂²×C₃₁	1	4	yes	—
465	#489	C₂²×C₃₁	1	2	yes	—
466	#488	C₂²×C₃₁	1	4	yes	—
467	#486	C₂²×C₃₁	1	2	yes	—
468	#484	C₂²×C₃₁	1	2	yes	—
469	#483	C₂²×C₃₁	1	1	yes	characteristic
470	#481	C₂²×C₃₁	1	2	yes	—
471	#481	C₂²×C₃₁	1	2	yes	—
472	#481	C₂²×C₃₁	1	2	yes	—
473	#480	C₂²×C₃₁	1	1	yes	characteristic
474	#480	C₂²×C₃₁	1	2	yes	—
475	#479	C₂²×C₃₁	1	2	yes	—
476	#479	C₂²×C₃₁	1	4	yes	—
477	#479	C₂²×C₃₁	1	4	yes	—
478	#478	C₂²×C₃₁	1	4	yes	—
479	#478	C₂²×C₃₁	1	4	yes	—
480	#478	C₂²×C₃₁	1	4	yes	—
481	#477	C₂²×C₃₁	1	2	yes	—
482	#476	C₂²×C₃₁	1	4	yes	—
483	#475	C₂²×C₃₁	1	4	yes	—
484	#475	C₂²×C₃₁	1	2	yes	—
485	#474	C₂²×C₃₁	1	2	yes	—
486	#464	C₂²×C₃₁	1	2	yes	—
487	#464	C₂²×C₃₁	1	4	yes	—
488	#460	C₂²×C₃₁	1	4	yes	—
489	#460	C₂²×C₃₁	1	2	yes	—
490	#451	C₂²×C₃₁	1	1	yes	characteristic
491	#448	C₂²×C₃₁	1	1	yes	characteristic
492	#448	C₂²×C₃₁	1	2	yes	—
493	#446	C₂²×C₃₁	1	2	yes	—
494	#446	C₂²×C₃₁	1	4	yes	—
495	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
496	#441	C₂²×C₃₁	1	4	yes	—
497	#440	C₂²×C₃₁	1	4	yes	—
498	#440	C₂²×C₃₁	1	4	yes	—
499	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
500	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
501	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
502	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
503	#432	C₂²×C₃₁	1	1	yes	characteristic
504	#432	C₂²×C₃₁	1	2	yes	—
505	#431	C₂²×C₃₁	1	2	yes	—
506	#431	C₂²×C₃₁	1	1	yes	characteristic
507	C₂×C₃₁	—	2	2	no	—
508	C₂×C₃₁	—	8	2	no	—
509	C₂×C₃₁	—	8	1	no	—
510	C₂×C₃₁	#3486	1	1	yes	characteristic
511	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
512	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
513	C₂×#41	—	2	1	no	—
514	C₂×#41	—	2	2	no	—
515	C₂×#41	—	2	1	no	—
516	C₂²×Q₈	—	2	1	no	—
517	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
518	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
519	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
520	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
521	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	4	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
533	#127	C₂³×C₃₁	1	1	yes	characteristic
534	#127	C₂³×C₃₁	1	2	yes	—
535	#126	—	2	2	no	—
536	#126	—	2	1	no	—
537	#125	—	2	4	no	—
538	#125	—	2	4	no	—
539	#125	—	2	4	no	—
540	#125	—	2	4	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	C₂³×C₃₁	1	4	yes	—
544	#125	C₂³×C₃₁	1	4	yes	—
545	#125	C₂³×C₃₁	1	2	yes	—
546	#125	C₂³×C₃₁	1	1	yes	characteristic
547	#124	—	2	1	no	—
548	#124	—	2	2	no	—
549	#124	—	2	2	no	—
550	#124	—	2	1	no	—
551	#124	C₂³×C₃₁	1	2	yes	—
552	#124	C₂³×C₃₁	1	1	yes	characteristic
553	#123	—	2	2	no	—
554	#123	—	2	1	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	#121	—	2	1	no	—
565	#121	—	2	2	no	—
566	#121	—	2	1	no	—
567	#121	—	2	2	no	—
568	#121	C₂³×C₃₁	1	1	yes	characteristic
569	#121	C₂³×C₃₁	1	2	yes	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	4	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
579	C₄×Q₈	D₄×C₃₁	1	2	yes	—
580	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
582	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
583	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
584	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
585	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
587	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₄×D₄	C₂³×C₃₁	1	2	yes	—
598	C₄×D₄	C₂³×C₃₁	1	2	yes	—
599	C₄×D₄	C₂³×C₃₁	1	2	yes	—
600	C₄×D₄	C₂³×C₃₁	1	2	yes	—
601	#117	—	2	2	no	—
602	#117	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	2	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	2	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₄²	—	2	2	no	—
615	C₂×C₄²	—	2	1	no	—
616	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
617	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
618	#107	C₂³×C₃₁	1	2	yes	—
619	#107	C₂³×C₃₁	1	4	yes	—
620	#107	C₂³×C₃₁	1	4	yes	—
621	#106	C₂³×C₃₁	1	4	yes	—
622	#106	C₂³×C₃₁	1	4	yes	—
623	#106	C₂³×C₃₁	1	2	yes	—
624	#106	C₂³×C₃₁	1	4	yes	—
625	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
626	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
627	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
628	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
629	#103	C₂³×C₃₁	1	2	yes	—
630	#103	C₂³×C₃₁	1	2	yes	—
631	#103	C₂³×C₃₁	1	4	yes	—
632	#103	C₂³×C₃₁	1	2	yes	—
633	#103	C₂³×C₃₁	1	4	yes	—
634	#102	C₂³×C₃₁	1	4	yes	—
635	#102	C₂³×C₃₁	1	4	yes	—
636	#102	C₂³×C₃₁	1	2	yes	—
637	#102	C₂³×C₃₁	1	4	yes	—
638	#102	C₂³×C₃₁	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
640	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
641	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
642	#97	C₂³×C₃₁	1	2	yes	—
643	#97	C₂³×C₃₁	1	4	yes	—
644	C₄×C₈	C₂³×C₃₁	1	4	yes	—
645	C₄×C₈	C₂³×C₃₁	1	2	yes	—
646	C₃₁	#61836	1	1	yes	characteristic, direct product factor, Sylow
647	#41	—	4	4	no	—
648	#41	—	8	4	no	—
649	#41	—	8	2	no	—
650	C₂×Q₈	—	2	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×Q₈	—	4	4	no	—
658	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
659	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
660	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
661	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
662	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
670	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
680	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
684	Q₁₆	—	2	4	no	—
685	SD₁₆	—	2	4	no	—
686	SD₁₆	—	2	8	no	—
687	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
688	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
689	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
715	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
719	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
721	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	1	no	—
741	C₄²	C₂×D₄×C₃₁	1	2	yes	—
742	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₃₁	1	2	yes	—
744	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₄²	C₂⁴×C₃₁	1	2	yes	—
746	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
747	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
748	C₄²	C₂⁴×C₃₁	1	2	yes	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	1	no	—
751	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	4	no	—
759	Q₈	—	4	4	no	—
760	Q₈	—	8	2	no	—
761	Q₈	—	8	1	no	—
762	Q₈	C₃₁×2₋¹⁺⁴	1	4	yes	—
763	D₄	—	2	2	no	—
764	D₄	—	2	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	2	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	2	no	—
769	D₄	—	8	2	no	—
770	D₄	—	8	1	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	—	8	2	no	—
791	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
800	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
801	C₈	—	2	2	no	—
802	C₈	—	2	4	no	—
803	C₈	—	2	2	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	C₃₁×#577	1	2	yes	—
813	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
814	C₄	—	2	4	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	4	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	1	no	—
829	C₄	C₃₁×#575	1	2	yes	—
830	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
831	C₂	—	2	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	8	1	no	—
834	C₂	C₃₁×#3486	1	1	yes	characteristic
835	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
836	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3522	C₂
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
2. C₂×C₃₁×#557	C₂	semidirect
3. C₃₁×#3388	C₂	semidirect
4. C₃₁×#3387	C₂	semidirect
5. C₃₁×#3381	C₂	semidirect
6. C₃₁×#3371	C₂	semidirect
7. C₃₁×#3368	C₂	semidirect
8. C₃₁×#3365	C₂	semidirect
9. C₃₁×#3239	C₂	semidirect
10. C₃₁×#3234	C₂	semidirect
11. C₃₁×#3232	C₂	semidirect
12. C₃₁×#3227	C₂	semidirect
13. C₃₁×#3117	C₂	semidirect
14. C₃₁×#3112	C₂	semidirect
15. C₃₁×#3108	C₂	semidirect
16. C₃₁×#3103	C₂	semidirect
17. C₃₁×#2984	C₂	semidirect
330. #61836	C₃₁	direct (N × H)
387. C₂×#557	C₂×C₃₁	semidirect
388. #3388	C₂×C₃₁	semidirect
389. #3387	C₂×C₃₁	semidirect
390. #3381	C₂×C₃₁	semidirect
391. #3371	C₂×C₃₁	semidirect
392. #3368	C₂×C₃₁	semidirect
393. #3365	C₂×C₃₁	semidirect
394. #3239	C₂×C₃₁	semidirect
395. #3234	C₂×C₃₁	semidirect
396. #3232	C₂×C₃₁	semidirect
397. #3227	C₂×C₃₁	semidirect
398. #3117	C₂×C₃₁	semidirect
399. #3112	C₂×C₃₁	semidirect
400. #3108	C₂×C₃₁	semidirect
401. #3103	C₂×C₃₁	semidirect
402. #2984	C₂×C₃₁	semidirect
646. C₃₁	#61836	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×#3522	2
C₂×C₃₁×#557	2
C₃₁×#3388	2
C₃₁×#3387	2
C₃₁×#3381	2
C₃₁×#3371	2
C₃₁×#3368	2
C₃₁×#3365	2
C₃₁×#3239	2
C₃₁×#3234	2
C₃₁×#3232	2
C₃₁×#3227	2
C₃₁×#3117	2
C₃₁×#3112	2
C₃₁×#3108	2
C₃₁×#3103	2
C₃₁×#2984	2
#61836	31

Subgroups — C31×#61836 #21518595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61836 #21518595