Subgroups — C₃₁×#62102 #21518861

Order 7936.

1784 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3381	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3339	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3301	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3106	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	—	2	1	no	—
19	C₃₁×#559	C₂²	1	1	yes	characteristic
20	C₃₁×#557	C₂²	1	1	yes	characteristic
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#556	—	2	1	no	—
23	C₃₁×#556	C₂²	1	1	yes	characteristic
24	C₃₁×#555	C₂²	1	2	yes	—
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#553	—	2	2	no	—
27	C₃₁×#553	C₂²	1	2	yes	—
28	C₃₁×#553	C₂²	1	4	yes	—
29	C₃₁×#550	C₂²	1	1	yes	characteristic
30	C₃₁×#548	—	2	2	no	—
31	C₃₁×#548	C₂²	1	2	yes	—
32	C₃₁×#547	—	2	1	no	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#537	—	2	1	no	—
35	C₃₁×#533	C₂²	1	2	yes	—
36	C₃₁×#532	—	2	1	no	—
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	2	yes	—
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₃₁×#529	—	2	2	no	—
42	C₃₁×#529	C₂²	1	2	yes	—
43	C₃₁×#520	—	2	1	no	—
44	C₄×#41×C₃₁	—	2	1	no	—
45	C₄×#41×C₃₁	C₂²	1	2	yes	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#499	C₂²	1	4	yes	—
49	C₃₁×#498	C₂²	1	2	yes	—
50	C₃₁×#488	C₂²	1	4	yes	—
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	4	yes	—
53	C₃₁×#482	C₂²	1	4	yes	—
54	C₃₁×#482	C₂²	1	4	yes	—
55	C₃₁×#481	C₂²	1	2	yes	—
56	C₃₁×#481	C₂²	1	4	yes	—
57	C₃₁×#479	C₂²	1	4	yes	—
58	C₃₁×#478	C₂²	1	4	yes	—
59	C₃₁×#478	C₂²	1	4	yes	—
60	C₃₁×#477	C₂²	1	2	yes	—
61	C₃₁×#477	C₂²	1	2	yes	—
62	C₃₁×#477	C₂²	1	2	yes	—
63	C₃₁×#477	C₂²	1	2	yes	—
64	C₃₁×#476	C₂²	1	2	yes	—
65	C₃₁×#476	C₂²	1	2	yes	—
66	C₃₁×#475	C₂²	1	1	yes	characteristic
67	C₃₁×#475	C₂²	1	1	yes	characteristic
68	C₃₁×#474	C₂²	1	2	yes	—
69	C₃₁×#474	C₂²	1	2	yes	—
70	C₃₁×#466	C₂²	1	4	yes	—
71	C₃₁×#466	C₂²	1	4	yes	—
72	C₃₁×#465	C₂²	1	4	yes	—
73	C₃₁×#463	C₂²	1	4	yes	—
74	C₃₁×#460	C₂²	1	1	yes	characteristic
75	C₃₁×#460	C₂²	1	1	yes	characteristic
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#459	C₂²	1	2	yes	—
78	C₃₁×#449	C₂²	1	4	yes	—
79	C₃₁×#448	C₂²	1	2	yes	—
80	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
83	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
84	C₄×D₈×C₃₁	C₂²	1	4	yes	—
85	C₈×D₄×C₃₁	C₂²	1	4	yes	—
86	C₈×D₄×C₃₁	C₂²	1	2	yes	—
87	C₃₁×#431	C₂²	1	1	yes	characteristic
88	C₃₁×#431	C₂²	1	2	yes	—
89	C₃₁×#427	C₂²	1	4	yes	—
90	C₂×C₃₁×#107	C₂²	1	2	yes	—
91	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₃₁×#416	C₂²	1	4	yes	—
94	C₂×C₃₁×#103	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	2	yes	—
100	C₂²×Q₈×C₃₁	—	2	1	no	—
101	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×D₈×C₃₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×#127	—	2	1	no	—
115	C₃₁×#127	C₂³	1	1	yes	characteristic
116	C₃₁×#127	C₂³	1	1	yes	characteristic
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#126	—	2	2	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	C₂³	1	2	yes	—
123	C₃₁×#125	C₂³	1	4	yes	—
124	C₃₁×#124	—	2	1	no	—
125	C₃₁×#124	—	2	1	no	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	—	2	4	no	—
128	C₃₁×#124	—	2	1	no	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#124	—	2	1	no	—
131	C₃₁×#124	C₂³	1	2	yes	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×#123	—	2	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	2	no	—
145	C₃₁×#121	—	2	4	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	1	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	C₂³	1	2	yes	—
151	C₃₁×#121	C₂³	1	4	yes	—
152	C₃₁×#121	C₂³	1	2	yes	—
153	C₃₁×#121	C₂³	1	2	yes	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	—	2	1	no	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	—	2	1	no	—
158	C₄×Q₈×C₃₁	—	2	2	no	—
159	C₄×Q₈×C₃₁	—	2	2	no	—
160	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	2	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	—	2	2	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	4	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
179	C₄×D₄×C₃₁	D₄	1	2	yes	—
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	4	yes	—
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	2	yes	—
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₃₁×#117	—	2	2	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	—	2	2	no	—
189	C₃₁×#117	D₄	1	1	yes	characteristic
190	C₃₁×#117	D₄	1	2	yes	—
191	C₃₁×#117	C₂³	1	4	yes	—
192	C₃₁×#117	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	—	2	1	no	—
199	C₂×C₄²×C₃₁	—	2	2	no	—
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#107	C₂³	1	4	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#106	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×#106	C₂³	1	2	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₄×C₈×C₃₁	C₂³	1	4	yes	—
227	C₄×C₈×C₃₁	C₂³	1	2	yes	—
228	#41×C₃₁	—	2	4	no	—
229	#41×C₃₁	—	2	4	no	—
230	#41×C₃₁	—	4	2	no	—
231	#41×C₃₁	—	4	4	no	—
232	#41×C₃₁	—	4	4	no	—
233	#41×C₃₁	—	8	4	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	4	1	no	—
241	C₂×Q₈×C₃₁	—	8	2	no	—
242	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	1	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
257	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₁	—	2	1	no	—
259	C₂²×C₄×C₃₁	—	2	1	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	4	no	—
266	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	SD₁₆×C₃₁	—	2	4	no	—
273	SD₁₆×C₃₁	—	4	2	no	—
274	D₈×C₃₁	—	4	4	no	—
275	C₂×C₈×C₃₁	—	4	2	no	—
276	C₂×C₈×C₃₁	—	4	4	no	—
277	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
278	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
279	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
321	C₄²×C₃₁	—	2	1	no	—
322	C₄²×C₃₁	—	2	1	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	1	no	—
326	C₄²×C₃₁	—	2	1	no	—
327	C₄²×C₃₁	—	2	4	no	—
328	C₄²×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	C₂×D₄	1	2	yes	—
330	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₃₁	C₂⁴	1	2	yes	—
333	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
335	#62102	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₃₁	—	2	2	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
339	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₃₁	—	2	2	no	—
341	Q₈×C₃₁	—	2	1	no	—
342	Q₈×C₃₁	—	2	1	no	—
343	Q₈×C₃₁	—	2	1	no	—
344	Q₈×C₃₁	—	4	2	no	—
345	Q₈×C₃₁	—	4	4	no	—
346	Q₈×C₃₁	—	4	2	no	—
347	Q₈×C₃₁	—	4	2	no	—
348	Q₈×C₃₁	—	8	2	no	—
349	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
350	D₄×C₃₁	—	2	4	no	—
351	D₄×C₃₁	—	2	2	no	—
352	D₄×C₃₁	—	2	2	no	—
353	D₄×C₃₁	—	2	2	no	—
354	D₄×C₃₁	—	2	2	no	—
355	D₄×C₃₁	—	2	2	no	—
356	D₄×C₃₁	—	4	4	no	—
357	D₄×C₃₁	—	4	2	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	4	2	no	—
361	D₄×C₃₁	—	4	2	no	—
362	D₄×C₃₁	—	8	1	no	—
363	D₄×C₃₁	—	8	2	no	—
364	D₄×C₃₁	—	8	4	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	4	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	4	no	—
377	C₂×C₄×C₃₁	—	4	1	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	4	no	—
380	C₂×C₄×C₃₁	—	4	2	no	—
381	C₂×C₄×C₃₁	—	4	4	no	—
382	C₂×C₄×C₃₁	—	4	4	no	—
383	C₂×C₄×C₃₁	—	8	2	no	—
384	C₂×C₄×C₃₁	—	8	4	no	—
385	C₂×C₄×C₃₁	—	8	1	no	—
386	C₂×C₄×C₃₁	—	8	2	no	—
387	C₂×C₄×C₃₁	#135	1	4	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
397	C₈×C₃₁	—	2	2	no	—
398	C₈×C₃₁	—	2	4	no	—
399	C₈×C₃₁	—	2	2	no	—
400	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
402	#3381	C₂×C₃₁	1	2	yes	complemented
403	#3361	C₂×C₃₁	1	2	yes	complemented
404	#3340	C₂×C₃₁	1	2	yes	complemented
405	#3339	C₂×C₃₁	1	4	yes	complemented
406	#3305	C₂×C₃₁	1	2	yes	complemented
407	#3301	C₂×C₃₁	1	4	yes	complemented
408	#3247	C₂×C₃₁	1	2	yes	complemented
409	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
410	#3233	C₂×C₃₁	1	2	yes	complemented
411	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3106	C₂×C₃₁	1	2	yes	complemented
413	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3076	C₂×C₃₁	1	2	yes	complemented
415	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#2988	C₂×C₃₁	1	1	yes	characteristic, complemented
417	C₂²×C₃₁	—	2	1	no	—
418	C₂²×C₃₁	—	2	1	no	—
419	C₂²×C₃₁	—	2	2	no	—
420	C₂²×C₃₁	—	2	2	no	—
421	C₂²×C₃₁	—	2	2	no	—
422	C₂²×C₃₁	—	4	2	no	—
423	C₂²×C₃₁	—	4	2	no	—
424	C₂²×C₃₁	—	4	2	no	—
425	C₂²×C₃₁	—	4	2	no	—
426	C₂²×C₃₁	—	4	2	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	C₂×#135	1	2	yes	—
429	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
430	C₄×C₃₁	—	2	1	no	—
431	C₄×C₃₁	—	2	2	no	—
432	C₄×C₃₁	—	2	1	no	—
433	C₄×C₃₁	—	2	2	no	—
434	C₄×C₃₁	—	2	1	no	—
435	C₄×C₃₁	—	2	2	no	—
436	C₄×C₃₁	—	2	2	no	—
437	C₄×C₃₁	—	4	1	no	—
438	C₄×C₃₁	—	4	4	no	—
439	C₄×C₃₁	—	4	1	no	—
440	C₄×C₃₁	—	4	1	no	—
441	C₄×C₃₁	—	4	2	no	—
442	C₄×C₃₁	—	4	2	no	—
443	C₄×C₃₁	C₂×#135	1	2	yes	—
444	C₄×C₃₁	C₂×#135	1	2	yes	—
445	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₄×C₃₁	#585	1	1	yes	characteristic
447	#559	—	2	1	no	—
448	#559	C₂²×C₃₁	1	1	yes	characteristic
449	#557	C₂²×C₃₁	1	1	yes	characteristic
450	#556	—	2	1	no	—
451	#556	—	2	1	no	—
452	#556	C₂²×C₃₁	1	1	yes	characteristic
453	#555	C₂²×C₃₁	1	2	yes	—
454	#554	C₂²×C₃₁	1	2	yes	—
455	#553	—	2	2	no	—
456	#553	C₂²×C₃₁	1	2	yes	—
457	#553	C₂²×C₃₁	1	4	yes	—
458	#550	C₂²×C₃₁	1	1	yes	characteristic
459	#548	—	2	2	no	—
460	#548	C₂²×C₃₁	1	2	yes	—
461	#547	—	2	1	no	—
462	#542	—	2	2	no	—
463	#537	—	2	1	no	—
464	#533	C₂²×C₃₁	1	2	yes	—
465	#532	—	2	1	no	—
466	#532	C₂²×C₃₁	1	1	yes	characteristic
467	#532	C₂²×C₃₁	1	2	yes	—
468	#532	C₂²×C₃₁	1	1	yes	characteristic
469	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
470	#529	—	2	2	no	—
471	#529	C₂²×C₃₁	1	2	yes	—
472	#520	—	2	1	no	—
473	C₄×#41	—	2	1	no	—
474	C₄×#41	C₂²×C₃₁	1	2	yes	—
475	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
477	#499	C₂²×C₃₁	1	4	yes	—
478	#498	C₂²×C₃₁	1	2	yes	—
479	#488	C₂²×C₃₁	1	4	yes	—
480	#486	C₂²×C₃₁	1	2	yes	—
481	#485	C₂²×C₃₁	1	4	yes	—
482	#482	C₂²×C₃₁	1	4	yes	—
483	#482	C₂²×C₃₁	1	4	yes	—
484	#481	C₂²×C₃₁	1	2	yes	—
485	#481	C₂²×C₃₁	1	4	yes	—
486	#479	C₂²×C₃₁	1	4	yes	—
487	#478	C₂²×C₃₁	1	4	yes	—
488	#478	C₂²×C₃₁	1	4	yes	—
489	#477	C₂²×C₃₁	1	2	yes	—
490	#477	C₂²×C₃₁	1	2	yes	—
491	#477	C₂²×C₃₁	1	2	yes	—
492	#477	C₂²×C₃₁	1	2	yes	—
493	#476	C₂²×C₃₁	1	2	yes	—
494	#476	C₂²×C₃₁	1	2	yes	—
495	#475	C₂²×C₃₁	1	1	yes	characteristic
496	#475	C₂²×C₃₁	1	1	yes	characteristic
497	#474	C₂²×C₃₁	1	2	yes	—
498	#474	C₂²×C₃₁	1	2	yes	—
499	#466	C₂²×C₃₁	1	4	yes	—
500	#466	C₂²×C₃₁	1	4	yes	—
501	#465	C₂²×C₃₁	1	4	yes	—
502	#463	C₂²×C₃₁	1	4	yes	—
503	#460	C₂²×C₃₁	1	1	yes	characteristic
504	#460	C₂²×C₃₁	1	1	yes	characteristic
505	#459	C₂²×C₃₁	1	2	yes	—
506	#459	C₂²×C₃₁	1	2	yes	—
507	#449	C₂²×C₃₁	1	4	yes	—
508	#448	C₂²×C₃₁	1	2	yes	—
509	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
510	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
511	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
512	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
513	C₄×D₈	C₂²×C₃₁	1	4	yes	—
514	C₈×D₄	C₂²×C₃₁	1	4	yes	—
515	C₈×D₄	C₂²×C₃₁	1	2	yes	—
516	#431	C₂²×C₃₁	1	1	yes	characteristic
517	#431	C₂²×C₃₁	1	2	yes	—
518	#427	C₂²×C₃₁	1	4	yes	—
519	C₂×#107	C₂²×C₃₁	1	2	yes	—
520	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
521	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
522	#416	C₂²×C₃₁	1	4	yes	—
523	C₂×#103	C₂²×C₃₁	1	2	yes	—
524	C₂×C₃₁	—	2	2	no	—
525	C₂×C₃₁	—	4	2	no	—
526	C₂×C₃₁	—	8	2	no	—
527	C₂×C₃₁	—	8	2	no	—
528	C₂×C₃₁	#3489	1	1	yes	characteristic
529	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
530	C₂×C₃₁	#3585	1	1	yes	characteristic
531	C₂×#41	—	2	1	no	—
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
535	C₂×#41	C₂³×C₃₁	1	2	yes	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
538	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
540	C₂×D₈	C₂³×C₃₁	1	4	yes	—
541	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
542	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
550	#127	—	2	1	no	—
551	#127	C₂³×C₃₁	1	1	yes	characteristic
552	#127	C₂³×C₃₁	1	1	yes	characteristic
553	#126	—	2	2	no	—
554	#126	—	2	4	no	—
555	#126	—	2	2	no	—
556	#126	—	2	2	no	—
557	#125	—	2	2	no	—
558	#125	C₂³×C₃₁	1	2	yes	—
559	#125	C₂³×C₃₁	1	4	yes	—
560	#124	—	2	1	no	—
561	#124	—	2	1	no	—
562	#124	—	2	2	no	—
563	#124	—	2	4	no	—
564	#124	—	2	1	no	—
565	#124	—	2	2	no	—
566	#124	—	2	1	no	—
567	#124	C₂³×C₃₁	1	2	yes	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	4	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	4	no	—
582	#121	—	2	2	no	—
583	#121	—	2	1	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	C₂³×C₃₁	1	2	yes	—
587	#121	C₂³×C₃₁	1	2	yes	—
588	#121	C₂³×C₃₁	1	2	yes	—
589	#121	C₂³×C₃₁	1	4	yes	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	—	2	1	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
602	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	4	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
615	C₄×D₄	D₄×C₃₁	1	2	yes	—
616	C₄×D₄	C₂³×C₃₁	1	2	yes	—
617	C₄×D₄	C₂³×C₃₁	1	2	yes	—
618	C₄×D₄	C₂³×C₃₁	1	4	yes	—
619	C₄×D₄	C₂³×C₃₁	1	2	yes	—
620	C₄×D₄	C₂³×C₃₁	1	2	yes	—
621	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	—	2	2	no	—
625	#117	D₄×C₃₁	1	1	yes	characteristic
626	#117	D₄×C₃₁	1	2	yes	—
627	#117	C₂³×C₃₁	1	2	yes	—
628	#117	C₂³×C₃₁	1	4	yes	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	2	no	—
636	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
638	#107	C₂³×C₃₁	1	4	yes	—
639	#107	C₂³×C₃₁	1	4	yes	—
640	#107	C₂³×C₃₁	1	4	yes	—
641	#106	C₂³×C₃₁	1	2	yes	—
642	#106	C₂³×C₃₁	1	4	yes	—
643	#106	C₂³×C₃₁	1	2	yes	—
644	#106	C₂³×C₃₁	1	4	yes	—
645	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
646	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
647	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
648	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
649	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
650	#103	C₂³×C₃₁	1	4	yes	—
651	#103	C₂³×C₃₁	1	4	yes	—
652	#103	C₂³×C₃₁	1	2	yes	—
653	#103	C₂³×C₃₁	1	2	yes	—
654	#102	C₂³×C₃₁	1	4	yes	—
655	#102	C₂³×C₃₁	1	4	yes	—
656	#102	C₂³×C₃₁	1	2	yes	—
657	#102	C₂³×C₃₁	1	4	yes	—
658	#102	C₂³×C₃₁	1	4	yes	—
659	#102	C₂³×C₃₁	1	2	yes	—
660	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
661	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
662	C₄×C₈	C₂³×C₃₁	1	4	yes	—
663	C₄×C₈	C₂³×C₃₁	1	2	yes	—
664	C₃₁	#62102	1	1	yes	characteristic, direct product factor, Sylow
665	#41	—	2	4	no	—
666	#41	—	2	4	no	—
667	#41	—	4	2	no	—
668	#41	—	4	4	no	—
669	#41	—	4	4	no	—
670	#41	—	8	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	4	1	no	—
678	C₂×Q₈	—	8	2	no	—
679	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
680	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
692	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
693	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
694	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
704	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	4	2	no	—
711	D₈	—	4	4	no	—
712	C₂×C₈	—	4	2	no	—
713	C₂×C₈	—	4	4	no	—
714	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
715	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
716	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
756	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	4	no	—
765	C₄²	C₂×D₄×C₃₁	1	2	yes	—
766	C₄²	C₂×D₄×C₃₁	1	2	yes	—
767	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
769	C₄²	C₂⁴×C₃₁	1	2	yes	—
770	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
775	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
776	Q₈	—	2	2	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	4	no	—
782	Q₈	—	4	2	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	8	2	no	—
785	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	8	1	no	—
799	D₄	—	8	2	no	—
800	D₄	—	8	4	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	1	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₃₁×#135	1	4	yes	—
824	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
832	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
833	C₈	—	2	2	no	—
834	C₈	—	2	4	no	—
835	C₈	—	2	2	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	C₂×C₃₁×#135	1	2	yes	—
848	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	4	no	—
861	C₄	—	4	1	no	—
862	C₄	C₂×C₃₁×#135	1	2	yes	—
863	C₄	C₂×C₃₁×#135	1	2	yes	—
864	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
865	C₄	C₃₁×#585	1	1	yes	characteristic
866	C₂	—	2	2	no	—
867	C₂	—	4	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₃₁×#3489	1	1	yes	characteristic
871	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
872	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3381	C₂	semidirect
4. C₃₁×#3361	C₂	semidirect
5. C₃₁×#3340	C₂	semidirect
6. C₃₁×#3339	C₂	semidirect
7. C₃₁×#3305	C₂	semidirect
8. C₃₁×#3301	C₂	semidirect
9. C₃₁×#3247	C₂	semidirect
10. C₃₁×#3245	C₂	semidirect
11. C₃₁×#3233	C₂	semidirect
12. C₃₁×#3227	C₂	semidirect
13. C₃₁×#3106	C₂	semidirect
14. C₃₁×#3103	C₂	semidirect
15. C₃₁×#3076	C₂	semidirect
16. C₂×C₃₁×#477	C₂	semidirect
17. C₃₁×#2988	C₂	semidirect
335. #62102	C₃₁	direct (N × H)
400. #3511	C₂×C₃₁	semidirect
401. #3480	C₂×C₃₁	semidirect
402. #3381	C₂×C₃₁	semidirect
403. #3361	C₂×C₃₁	semidirect
404. #3340	C₂×C₃₁	semidirect
405. #3339	C₂×C₃₁	semidirect
406. #3305	C₂×C₃₁	semidirect
407. #3301	C₂×C₃₁	semidirect
408. #3247	C₂×C₃₁	semidirect
409. #3245	C₂×C₃₁	semidirect
410. #3233	C₂×C₃₁	semidirect
411. #3227	C₂×C₃₁	semidirect
412. #3106	C₂×C₃₁	semidirect
413. #3103	C₂×C₃₁	semidirect
414. #3076	C₂×C₃₁	semidirect
415. C₂×#477	C₂×C₃₁	semidirect
416. #2988	C₂×C₃₁	semidirect
664. C₃₁	#62102	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×#3511	2
C₃₁×#3480	2
C₃₁×#3381	2
C₃₁×#3361	2
C₃₁×#3340	2
C₃₁×#3339	2
C₃₁×#3305	2
C₃₁×#3301	2
C₃₁×#3247	2
C₃₁×#3245	2
C₃₁×#3233	2
C₃₁×#3227	2
C₃₁×#3106	2
C₃₁×#3103	2
C₃₁×#3076	2
C₂×C₃₁×#477	2
C₃₁×#2988	2
#62102	31

Subgroups — C31×#62102 #21518861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62102 #21518861