Subgroups — C₇₁×#61941 #31882813

Order 18176.

1646 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3398	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3398	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3376	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3374	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3369	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3225	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3223	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3219	C₂	1	1	yes	maximal, characteristic
14	C₇₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3120	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₇₁	—	2	2	no	—
21	#559×C₇₁	C₂²	1	2	yes	—
22	Q₈²×C₇₁	C₂²	1	1	yes	characteristic
23	#557×C₇₁	C₂²	1	1	yes	characteristic
24	#557×C₇₁	C₂²	1	2	yes	—
25	#557×C₇₁	C₂²	1	2	yes	—
26	#556×C₇₁	—	2	1	no	—
27	#556×C₇₁	—	2	1	no	—
28	#556×C₇₁	C₂²	1	2	yes	—
29	#556×C₇₁	C₂²	1	1	yes	characteristic
30	#556×C₇₁	C₂²	1	2	yes	—
31	#556×C₇₁	C₂²	1	2	yes	—
32	#554×C₇₁	—	2	1	no	—
33	#554×C₇₁	C₂²	1	1	yes	characteristic
34	#552×C₇₁	—	2	2	no	—
35	#552×C₇₁	—	2	1	no	—
36	#544×C₇₁	—	2	1	no	—
37	#542×C₇₁	C₂²	1	2	yes	—
38	#541×C₇₁	—	2	1	no	—
39	#541×C₇₁	—	2	2	no	—
40	#541×C₇₁	C₂²	1	2	yes	—
41	#539×C₇₁	—	2	1	no	—
42	#539×C₇₁	—	2	1	no	—
43	#536×C₇₁	C₂²	1	2	yes	—
44	#533×C₇₁	C₂²	1	1	yes	characteristic
45	#533×C₇₁	C₂²	1	1	yes	characteristic
46	#532×C₇₁	C₂²	1	1	yes	characteristic
47	#529×C₇₁	—	2	2	no	—
48	#529×C₇₁	C₂²	1	1	yes	characteristic
49	#520×C₇₁	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
51	#497×C₇₁	C₂²	1	1	yes	characteristic
52	#497×C₇₁	C₂²	1	2	yes	—
53	#497×C₇₁	C₂²	1	2	yes	—
54	#497×C₇₁	C₂²	1	2	yes	—
55	#496×C₇₁	C₂²	1	1	yes	characteristic
56	#495×C₇₁	C₂²	1	2	yes	—
57	#494×C₇₁	C₂²	1	2	yes	—
58	#491×C₇₁	C₂²	1	1	yes	characteristic
59	#491×C₇₁	C₂²	1	2	yes	—
60	#490×C₇₁	C₂²	1	1	yes	characteristic
61	#489×C₇₁	C₂²	1	2	yes	—
62	#489×C₇₁	C₂²	1	2	yes	—
63	#488×C₇₁	C₂²	1	2	yes	—
64	#487×C₇₁	C₂²	1	2	yes	—
65	#484×C₇₁	C₂²	1	1	yes	characteristic
66	#483×C₇₁	C₂²	1	2	yes	—
67	#481×C₇₁	C₂²	1	1	yes	characteristic
68	#479×C₇₁	C₂²	1	2	yes	—
69	#479×C₇₁	C₂²	1	2	yes	—
70	#478×C₇₁	C₂²	1	2	yes	—
71	#476×C₇₁	C₂²	1	2	yes	—
72	#475×C₇₁	C₂²	1	2	yes	—
73	#475×C₇₁	C₂²	1	2	yes	—
74	#464×C₇₁	C₂²	1	2	yes	—
75	#464×C₇₁	C₂²	1	2	yes	—
76	#464×C₇₁	C₂²	1	2	yes	—
77	#464×C₇₁	C₂²	1	2	yes	—
78	#464×C₇₁	C₂²	1	2	yes	—
79	#464×C₇₁	C₂²	1	2	yes	—
80	#463×C₇₁	C₂²	1	2	yes	—
81	#463×C₇₁	C₂²	1	2	yes	—
82	#463×C₇₁	C₂²	1	2	yes	—
83	#462×C₇₁	C₂²	1	2	yes	—
84	#462×C₇₁	C₂²	1	2	yes	—
85	#462×C₇₁	C₂²	1	2	yes	—
86	#462×C₇₁	C₂²	1	2	yes	—
87	#462×C₇₁	C₂²	1	2	yes	—
88	#462×C₇₁	C₂²	1	2	yes	—
89	#461×C₇₁	C₂²	1	2	yes	—
90	#461×C₇₁	C₂²	1	2	yes	—
91	#460×C₇₁	C₂²	1	2	yes	—
92	#452×C₇₁	C₂²	1	2	yes	—
93	#452×C₇₁	C₂²	1	2	yes	—
94	#452×C₇₁	C₂²	1	2	yes	—
95	#451×C₇₁	C₂²	1	2	yes	—
96	#451×C₇₁	C₂²	1	1	yes	characteristic
97	#449×C₇₁	C₂²	1	2	yes	—
98	#448×C₇₁	C₂²	1	1	yes	characteristic
99	#446×C₇₁	C₂²	1	2	yes	—
100	#446×C₇₁	C₂²	1	2	yes	—
101	#446×C₇₁	C₂²	1	2	yes	—
102	#446×C₇₁	C₂²	1	2	yes	—
103	#442×C₇₁	C₂²	1	2	yes	—
104	#441×C₇₁	C₂²	1	2	yes	—
105	#441×C₇₁	C₂²	1	2	yes	—
106	#441×C₇₁	C₂²	1	2	yes	—
107	#441×C₇₁	C₂²	1	2	yes	—
108	#441×C₇₁	C₂²	1	2	yes	—
109	#440×C₇₁	C₂²	1	2	yes	—
110	#440×C₇₁	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
115	#433×C₇₁	C₂²	1	2	yes	—
116	#433×C₇₁	C₂²	1	2	yes	—
117	#432×C₇₁	C₂²	1	1	yes	characteristic
118	#432×C₇₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₇₁	C₂³	1	2	yes	—
120	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
132	C₂×D₈×C₇₁	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₇₁	—	2	2	no	—
134	C₄⋊Q₈×C₇₁	—	2	2	no	—
135	C₄⋊Q₈×C₇₁	—	2	1	no	—
136	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
137	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
138	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
140	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
145	#127×C₇₁	C₂³	1	1	yes	characteristic
146	#126×C₇₁	—	2	2	no	—
147	#126×C₇₁	—	2	2	no	—
148	#126×C₇₁	—	2	2	no	—
149	#126×C₇₁	—	2	2	no	—
150	#126×C₇₁	—	2	2	no	—
151	#126×C₇₁	—	2	2	no	—
152	#126×C₇₁	—	2	2	no	—
153	#126×C₇₁	—	2	2	no	—
154	#126×C₇₁	—	2	2	no	—
155	#126×C₇₁	—	2	2	no	—
156	#126×C₇₁	—	2	1	no	—
157	#125×C₇₁	—	2	2	no	—
158	#125×C₇₁	—	2	2	no	—
159	#125×C₇₁	—	2	2	no	—
160	#125×C₇₁	—	2	2	no	—
161	#125×C₇₁	—	2	2	no	—
162	#125×C₇₁	—	2	2	no	—
163	#125×C₇₁	—	2	2	no	—
164	#125×C₇₁	—	2	2	no	—
165	#125×C₇₁	—	2	1	no	—
166	#125×C₇₁	—	2	1	no	—
167	#125×C₇₁	D₄	1	2	yes	—
168	#125×C₇₁	C₂³	1	2	yes	—
169	#125×C₇₁	C₂³	1	1	yes	characteristic
170	#124×C₇₁	—	2	2	no	—
171	#124×C₇₁	—	2	2	no	—
172	#124×C₇₁	C₂³	1	2	yes	—
173	#124×C₇₁	C₂³	1	2	yes	—
174	#124×C₇₁	C₂³	1	2	yes	—
175	#124×C₇₁	C₂³	1	2	yes	—
176	#124×C₇₁	C₂³	1	1	yes	characteristic
177	#123×C₇₁	—	2	1	no	—
178	#123×C₇₁	—	2	2	no	—
179	#123×C₇₁	—	2	2	no	—
180	#123×C₇₁	—	2	2	no	—
181	#123×C₇₁	—	2	2	no	—
182	#123×C₇₁	—	2	2	no	—
183	C₂²⋊Q₈×C₇₁	—	2	2	no	—
184	C₂²⋊Q₈×C₇₁	—	2	2	no	—
185	C₂²⋊Q₈×C₇₁	—	2	1	no	—
186	C₂²⋊Q₈×C₇₁	—	2	1	no	—
187	C₂²⋊Q₈×C₇₁	—	2	2	no	—
188	C₂²⋊Q₈×C₇₁	—	2	1	no	—
189	C₂²⋊Q₈×C₇₁	—	2	2	no	—
190	C₂²⋊Q₈×C₇₁	—	2	2	no	—
191	C₂²⋊Q₈×C₇₁	—	2	2	no	—
192	C₂²⋊Q₈×C₇₁	—	2	2	no	—
193	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
195	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
196	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
198	#121×C₇₁	—	2	1	no	—
199	#121×C₇₁	—	2	1	no	—
200	#121×C₇₁	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₇₁	—	2	2	no	—
202	C₄×Q₈×C₇₁	—	2	1	no	—
203	C₄×Q₈×C₇₁	—	2	1	no	—
204	C₄×Q₈×C₇₁	—	2	2	no	—
205	C₄×Q₈×C₇₁	—	2	1	no	—
206	C₄×Q₈×C₇₁	—	2	1	no	—
207	C₄×Q₈×C₇₁	—	2	1	no	—
208	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
220	C₄×D₄×C₇₁	—	2	1	no	—
221	C₄×D₄×C₇₁	—	2	2	no	—
222	C₄×D₄×C₇₁	—	2	2	no	—
223	C₄×D₄×C₇₁	—	2	2	no	—
224	C₄×D₄×C₇₁	—	2	1	no	—
225	C₄×D₄×C₇₁	—	2	1	no	—
226	C₄×D₄×C₇₁	C₂³	1	2	yes	—
227	C₄×D₄×C₇₁	C₂³	1	2	yes	—
228	C₄×D₄×C₇₁	C₂³	1	2	yes	—
229	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
230	#117×C₇₁	—	2	1	no	—
231	#117×C₇₁	—	2	2	no	—
232	#117×C₇₁	—	2	2	no	—
233	#117×C₇₁	—	2	2	no	—
234	#117×C₇₁	—	2	2	no	—
235	#117×C₇₁	—	2	1	no	—
236	#117×C₇₁	—	2	1	no	—
237	#117×C₇₁	C₂³	1	2	yes	—
238	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
239	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
240	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
241	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₇₁	—	2	1	no	—
243	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
244	#107×C₇₁	C₂³	1	2	yes	—
245	#106×C₇₁	C₂³	1	2	yes	—
246	#106×C₇₁	C₂³	1	2	yes	—
247	#106×C₇₁	C₂³	1	2	yes	—
248	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
249	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
250	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
251	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
254	#103×C₇₁	C₂³	1	2	yes	—
255	#103×C₇₁	C₂³	1	2	yes	—
256	#103×C₇₁	C₂³	1	2	yes	—
257	#103×C₇₁	C₂³	1	2	yes	—
258	#103×C₇₁	C₂³	1	2	yes	—
259	#103×C₇₁	C₂³	1	2	yes	—
260	#103×C₇₁	C₂³	1	2	yes	—
261	#103×C₇₁	C₂³	1	2	yes	—
262	#103×C₇₁	C₂³	1	2	yes	—
263	#103×C₇₁	C₂³	1	2	yes	—
264	#103×C₇₁	C₂³	1	2	yes	—
265	#102×C₇₁	C₂³	1	2	yes	—
266	#102×C₇₁	C₂³	1	2	yes	—
267	#102×C₇₁	C₂³	1	2	yes	—
268	#102×C₇₁	C₂³	1	2	yes	—
269	#102×C₇₁	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
273	#97×C₇₁	C₂³	1	2	yes	—
274	#97×C₇₁	C₂³	1	1	yes	characteristic
275	#97×C₇₁	C₂³	1	1	yes	characteristic
276	#97×C₇₁	C₂³	1	2	yes	—
277	#97×C₇₁	C₂³	1	2	yes	—
278	C₄×C₈×C₇₁	C₂³	1	2	yes	—
279	C₄×C₈×C₇₁	C₂³	1	2	yes	—
280	#41×C₇₁	—	4	2	no	—
281	#41×C₇₁	—	4	2	no	—
282	C₂×Q₈×C₇₁	—	2	1	no	—
283	C₂×Q₈×C₇₁	—	2	1	no	—
284	C₂×Q₈×C₇₁	—	2	2	no	—
285	C₂×Q₈×C₇₁	—	4	2	no	—
286	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
287	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
289	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
290	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
291	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
293	C₂×D₄×C₇₁	—	2	2	no	—
294	C₂×D₄×C₇₁	—	2	1	no	—
295	C₂×D₄×C₇₁	—	2	1	no	—
296	C₂×D₄×C₇₁	—	2	1	no	—
297	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
298	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇₁	—	2	1	no	—
300	C₂²×C₄×C₇₁	—	2	1	no	—
301	C₂²×C₄×C₇₁	—	2	1	no	—
302	C₂²×C₄×C₇₁	—	2	2	no	—
303	C₂²×C₄×C₇₁	—	2	2	no	—
304	C₂²×C₄×C₇₁	—	2	2	no	—
305	C₂²×C₄×C₇₁	—	2	2	no	—
306	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
309	Q₁₆×C₇₁	—	4	2	no	—
310	Q₁₆×C₇₁	—	4	2	no	—
311	Q₁₆×C₇₁	—	4	2	no	—
312	Q₁₆×C₇₁	—	4	2	no	—
313	Q₁₆×C₇₁	—	4	2	no	—
314	Q₁₆×C₇₁	—	4	2	no	—
315	SD₁₆×C₇₁	—	4	2	no	—
316	SD₁₆×C₇₁	—	4	2	no	—
317	SD₁₆×C₇₁	—	4	2	no	—
318	SD₁₆×C₇₁	—	4	2	no	—
319	SD₁₆×C₇₁	—	4	2	no	—
320	D₈×C₇₁	—	4	2	no	—
321	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
322	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
323	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
324	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₇₁	—	2	1	no	—
326	C₄⋊C₄×C₇₁	—	2	1	no	—
327	C₄⋊C₄×C₇₁	—	2	2	no	—
328	C₄⋊C₄×C₇₁	—	2	2	no	—
329	C₄⋊C₄×C₇₁	—	2	2	no	—
330	C₄⋊C₄×C₇₁	—	2	2	no	—
331	C₄⋊C₄×C₇₁	—	2	2	no	—
332	C₄⋊C₄×C₇₁	—	2	1	no	—
333	C₄⋊C₄×C₇₁	—	2	2	no	—
334	C₄⋊C₄×C₇₁	—	2	2	no	—
335	C₄⋊C₄×C₇₁	—	2	2	no	—
336	C₄⋊C₄×C₇₁	—	2	1	no	—
337	C₄⋊C₄×C₇₁	—	2	1	no	—
338	C₄⋊C₄×C₇₁	—	2	1	no	—
339	C₄⋊C₄×C₇₁	—	2	1	no	—
340	C₄⋊C₄×C₇₁	—	2	1	no	—
341	C₄⋊C₄×C₇₁	—	2	2	no	—
342	C₄⋊C₄×C₇₁	—	2	2	no	—
343	C₄⋊C₄×C₇₁	—	2	2	no	—
344	C₄⋊C₄×C₇₁	—	2	2	no	—
345	C₄⋊C₄×C₇₁	—	2	1	no	—
346	C₄⋊C₄×C₇₁	—	2	2	no	—
347	C₄⋊C₄×C₇₁	—	2	2	no	—
348	C₄⋊C₄×C₇₁	—	2	2	no	—
349	C₄⋊C₄×C₇₁	—	2	2	no	—
350	C₄⋊C₄×C₇₁	—	2	2	no	—
351	C₄⋊C₄×C₇₁	—	2	2	no	—
352	C₄⋊C₄×C₇₁	—	2	1	no	—
353	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
366	C₂²⋊C₄×C₇₁	—	2	2	no	—
367	C₂²⋊C₄×C₇₁	—	2	1	no	—
368	C₂²⋊C₄×C₇₁	—	2	2	no	—
369	C₂²⋊C₄×C₇₁	—	2	1	no	—
370	C₂²⋊C₄×C₇₁	—	2	2	no	—
371	C₂²⋊C₄×C₇₁	—	2	2	no	—
372	C₂²⋊C₄×C₇₁	—	2	1	no	—
373	C₂²⋊C₄×C₇₁	—	2	1	no	—
374	C₂²⋊C₄×C₇₁	—	2	2	no	—
375	C₂²⋊C₄×C₇₁	—	2	2	no	—
376	C₂²⋊C₄×C₇₁	—	2	2	no	—
377	C₂²⋊C₄×C₇₁	—	2	2	no	—
378	C₂²⋊C₄×C₇₁	—	2	2	no	—
379	C₂²⋊C₄×C₇₁	—	2	2	no	—
380	C₂²⋊C₄×C₇₁	—	2	2	no	—
381	C₂²⋊C₄×C₇₁	—	2	1	no	—
382	C₂²⋊C₄×C₇₁	—	2	2	no	—
383	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
385	C₄²×C₇₁	—	2	2	no	—
386	C₄²×C₇₁	—	2	2	no	—
387	C₄²×C₇₁	—	2	2	no	—
388	C₄²×C₇₁	—	2	2	no	—
389	C₄²×C₇₁	—	2	2	no	—
390	C₄²×C₇₁	—	2	1	no	—
391	C₄²×C₇₁	—	2	2	no	—
392	C₄²×C₇₁	—	2	2	no	—
393	C₄²×C₇₁	—	2	2	no	—
394	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₇₁	C₂⁴	1	2	yes	—
397	C₄²×C₇₁	C₂⁴	1	2	yes	—
398	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
399	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
400	C₂³×C₇₁	—	2	1	no	—
401	C₂³×C₇₁	—	2	2	no	—
402	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
403	Q₈×C₇₁	—	2	2	no	—
404	Q₈×C₇₁	—	2	2	no	—
405	Q₈×C₇₁	—	2	2	no	—
406	Q₈×C₇₁	—	2	2	no	—
407	Q₈×C₇₁	—	2	2	no	—
408	Q₈×C₇₁	—	2	2	no	—
409	Q₈×C₇₁	—	2	2	no	—
410	Q₈×C₇₁	—	4	1	no	—
411	Q₈×C₇₁	—	4	1	no	—
412	Q₈×C₇₁	—	4	2	no	—
413	Q₈×C₇₁	—	4	2	no	—
414	Q₈×C₇₁	—	8	1	no	—
415	Q₈×C₇₁	—	8	2	no	—
416	D₄×C₇₁	—	2	2	no	—
417	D₄×C₇₁	—	2	2	no	—
418	D₄×C₇₁	—	2	2	no	—
419	D₄×C₇₁	—	4	2	no	—
420	D₄×C₇₁	—	4	4	no	—
421	D₄×C₇₁	—	8	1	no	—
422	D₄×C₇₁	—	8	1	no	—
423	C₂×C₄×C₇₁	—	2	2	no	—
424	C₂×C₄×C₇₁	—	2	2	no	—
425	C₂×C₄×C₇₁	—	2	2	no	—
426	C₂×C₄×C₇₁	—	2	1	no	—
427	C₂×C₄×C₇₁	—	2	1	no	—
428	C₂×C₄×C₇₁	—	2	2	no	—
429	C₂×C₄×C₇₁	—	2	1	no	—
430	C₂×C₄×C₇₁	—	2	2	no	—
431	C₂×C₄×C₇₁	—	2	2	no	—
432	C₂×C₄×C₇₁	—	4	1	no	—
433	C₂×C₄×C₇₁	—	4	1	no	—
434	C₂×C₄×C₇₁	—	4	2	no	—
435	C₂×C₄×C₇₁	—	4	4	no	—
436	C₂×C₄×C₇₁	—	4	2	no	—
437	C₂×C₄×C₇₁	—	8	2	no	—
438	C₂×C₄×C₇₁	—	8	2	no	—
439	C₂×C₄×C₇₁	—	8	2	no	—
440	C₂×C₄×C₇₁	—	8	1	no	—
441	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
451	C₈×C₇₁	—	2	2	no	—
452	C₈×C₇₁	—	2	2	no	—
453	C₈×C₇₁	—	2	2	no	—
454	C₈×C₇₁	—	2	2	no	—
455	C₂²×C₇₁	—	2	1	no	—
456	C₂²×C₇₁	—	2	1	no	—
457	C₂²×C₇₁	—	2	1	no	—
458	C₂²×C₇₁	—	4	1	no	—
459	C₂²×C₇₁	—	4	2	no	—
460	C₂²×C₇₁	—	4	1	no	—
461	C₂²×C₇₁	—	4	2	no	—
462	C₂²×C₇₁	—	4	2	no	—
463	C₂²×C₇₁	—	4	1	no	—
464	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₇₁	—	2	1	no	—
466	C₄×C₇₁	—	2	1	no	—
467	C₄×C₇₁	—	2	1	no	—
468	C₄×C₇₁	—	2	1	no	—
469	C₄×C₇₁	—	2	2	no	—
470	C₄×C₇₁	—	2	2	no	—
471	C₄×C₇₁	—	2	2	no	—
472	C₄×C₇₁	—	2	2	no	—
473	C₄×C₇₁	—	2	1	no	—
474	C₄×C₇₁	—	4	1	no	—
475	C₄×C₇₁	—	4	2	no	—
476	C₄×C₇₁	—	4	2	no	—
477	C₄×C₇₁	—	4	1	no	—
478	C₄×C₇₁	—	4	2	no	—
479	C₄×C₇₁	—	4	2	no	—
480	C₄×C₇₁	—	4	2	no	—
481	C₄×C₇₁	—	4	1	no	—
482	C₄×C₇₁	#585	1	2	yes	—
483	#61941	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
484	C₂×C₇₁	—	4	1	no	—
485	C₂×C₇₁	—	8	1	no	—
486	C₂×C₇₁	—	8	2	no	—
487	C₂×C₇₁	#3487	1	1	yes	characteristic
488	C₂×C₇₁	#3586	1	1	yes	characteristic
489	C₂×C₇₁	#3586	1	1	yes	characteristic
490	#3555	C₂×C₇₁	1	1	yes	characteristic, complemented
491	#3507	C₂×C₇₁	1	1	yes	characteristic, complemented
492	#3402	C₂×C₇₁	1	2	yes	complemented
493	#3401	C₂×C₇₁	1	2	yes	complemented
494	#3398	C₂×C₇₁	1	2	yes	complemented
495	#3398	C₂×C₇₁	1	2	yes	complemented
496	#3376	C₂×C₇₁	1	2	yes	complemented
497	#3374	C₂×C₇₁	1	2	yes	complemented
498	#3371	C₂×C₇₁	1	2	yes	complemented
499	#3369	C₂×C₇₁	1	2	yes	complemented
500	#3225	C₂×C₇₁	1	2	yes	complemented
501	#3223	C₂×C₇₁	1	2	yes	complemented
502	#3219	C₂×C₇₁	1	1	yes	characteristic
503	#3216	C₂×C₇₁	1	1	yes	characteristic, complemented
504	#3125	C₂×C₇₁	1	2	yes	complemented
505	#3120	C₂×C₇₁	1	2	yes	complemented
506	#3117	C₂×C₇₁	1	1	yes	characteristic, complemented
507	#3113	C₂×C₇₁	1	1	yes	characteristic, complemented
508	#2987	C₂×C₇₁	1	1	yes	characteristic, complemented
509	C₇₁	#61941	1	1	yes	characteristic, direct product factor, Sylow
510	#563	—	2	2	no	—
511	#559	C₂²×C₇₁	1	2	yes	—
512	Q₈²	C₂²×C₇₁	1	1	yes	characteristic
513	#557	C₂²×C₇₁	1	2	yes	—
514	#557	C₂²×C₇₁	1	1	yes	characteristic
515	#557	C₂²×C₇₁	1	2	yes	—
516	#556	—	2	1	no	—
517	#556	—	2	1	no	—
518	#556	C₂²×C₇₁	1	2	yes	—
519	#556	C₂²×C₇₁	1	2	yes	—
520	#556	C₂²×C₇₁	1	2	yes	—
521	#556	C₂²×C₇₁	1	1	yes	characteristic
522	#554	—	2	1	no	—
523	#554	C₂²×C₇₁	1	1	yes	characteristic
524	#552	—	2	2	no	—
525	#552	—	2	1	no	—
526	#544	—	2	1	no	—
527	#542	C₂²×C₇₁	1	2	yes	—
528	#541	—	2	1	no	—
529	#541	—	2	2	no	—
530	#541	C₂²×C₇₁	1	2	yes	—
531	#539	—	2	1	no	—
532	#539	—	2	1	no	—
533	#536	C₂²×C₇₁	1	2	yes	—
534	#533	C₂²×C₇₁	1	1	yes	characteristic
535	#533	C₂²×C₇₁	1	1	yes	characteristic
536	#532	C₂²×C₇₁	1	1	yes	characteristic
537	#529	—	2	2	no	—
538	#529	C₂²×C₇₁	1	1	yes	characteristic
539	#520	C₂²×C₇₁	1	2	yes	—
540	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
541	#497	C₂²×C₇₁	1	1	yes	characteristic
542	#497	C₂²×C₇₁	1	2	yes	—
543	#497	C₂²×C₇₁	1	2	yes	—
544	#497	C₂²×C₇₁	1	2	yes	—
545	#496	C₂²×C₇₁	1	1	yes	characteristic
546	#495	C₂²×C₇₁	1	2	yes	—
547	#494	C₂²×C₇₁	1	2	yes	—
548	#491	C₂²×C₇₁	1	1	yes	characteristic
549	#491	C₂²×C₇₁	1	2	yes	—
550	#490	C₂²×C₇₁	1	1	yes	characteristic
551	#489	C₂²×C₇₁	1	2	yes	—
552	#489	C₂²×C₇₁	1	2	yes	—
553	#488	C₂²×C₇₁	1	2	yes	—
554	#487	C₂²×C₇₁	1	2	yes	—
555	#484	C₂²×C₇₁	1	1	yes	characteristic
556	#483	C₂²×C₇₁	1	2	yes	—
557	#481	C₂²×C₇₁	1	1	yes	characteristic
558	#479	C₂²×C₇₁	1	2	yes	—
559	#479	C₂²×C₇₁	1	2	yes	—
560	#478	C₂²×C₇₁	1	2	yes	—
561	#476	C₂²×C₇₁	1	2	yes	—
562	#475	C₂²×C₇₁	1	2	yes	—
563	#475	C₂²×C₇₁	1	2	yes	—
564	#464	C₂²×C₇₁	1	2	yes	—
565	#464	C₂²×C₇₁	1	2	yes	—
566	#464	C₂²×C₇₁	1	2	yes	—
567	#464	C₂²×C₇₁	1	2	yes	—
568	#464	C₂²×C₇₁	1	2	yes	—
569	#464	C₂²×C₇₁	1	2	yes	—
570	#463	C₂²×C₇₁	1	2	yes	—
571	#463	C₂²×C₇₁	1	2	yes	—
572	#463	C₂²×C₇₁	1	2	yes	—
573	#462	C₂²×C₇₁	1	2	yes	—
574	#462	C₂²×C₇₁	1	2	yes	—
575	#462	C₂²×C₇₁	1	2	yes	—
576	#462	C₂²×C₇₁	1	2	yes	—
577	#462	C₂²×C₇₁	1	2	yes	—
578	#462	C₂²×C₇₁	1	2	yes	—
579	#461	C₂²×C₇₁	1	2	yes	—
580	#461	C₂²×C₇₁	1	2	yes	—
581	#460	C₂²×C₇₁	1	2	yes	—
582	#452	C₂²×C₇₁	1	2	yes	—
583	#452	C₂²×C₇₁	1	2	yes	—
584	#452	C₂²×C₇₁	1	2	yes	—
585	#451	C₂²×C₇₁	1	2	yes	—
586	#451	C₂²×C₇₁	1	1	yes	characteristic
587	#449	C₂²×C₇₁	1	2	yes	—
588	#448	C₂²×C₇₁	1	1	yes	characteristic
589	#446	C₂²×C₇₁	1	2	yes	—
590	#446	C₂²×C₇₁	1	2	yes	—
591	#446	C₂²×C₇₁	1	2	yes	—
592	#446	C₂²×C₇₁	1	2	yes	—
593	#442	C₂²×C₇₁	1	2	yes	—
594	#441	C₂²×C₇₁	1	2	yes	—
595	#441	C₂²×C₇₁	1	2	yes	—
596	#441	C₂²×C₇₁	1	2	yes	—
597	#441	C₂²×C₇₁	1	2	yes	—
598	#441	C₂²×C₇₁	1	2	yes	—
599	#440	C₂²×C₇₁	1	2	yes	—
600	#440	C₂²×C₇₁	1	2	yes	—
601	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	—
602	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
603	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
604	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
605	#433	C₂²×C₇₁	1	2	yes	—
606	#433	C₂²×C₇₁	1	2	yes	—
607	#432	C₂²×C₇₁	1	1	yes	characteristic
608	#432	C₂²×C₇₁	1	1	yes	characteristic
609	C₂×#41	C₂³×C₇₁	1	2	yes	—
610	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
611	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
612	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
613	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
614	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
615	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
616	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
618	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
619	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
622	C₂×D₈	C₂³×C₇₁	1	2	yes	—
623	C₄⋊Q₈	—	2	2	no	—
624	C₄⋊Q₈	—	2	2	no	—
625	C₄⋊Q₈	—	2	1	no	—
626	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
627	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
628	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
629	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
630	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
631	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
632	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
633	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
634	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
635	#127	C₂³×C₇₁	1	1	yes	characteristic
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	—	2	2	no	—
644	#126	—	2	2	no	—
645	#126	—	2	2	no	—
646	#126	—	2	1	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	2	no	—
650	#125	—	2	2	no	—
651	#125	—	2	2	no	—
652	#125	—	2	2	no	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	1	no	—
656	#125	—	2	1	no	—
657	#125	D₄×C₇₁	1	2	yes	—
658	#125	C₂³×C₇₁	1	1	yes	characteristic
659	#125	C₂³×C₇₁	1	2	yes	—
660	#124	—	2	2	no	—
661	#124	—	2	2	no	—
662	#124	C₂³×C₇₁	1	1	yes	characteristic
663	#124	C₂³×C₇₁	1	2	yes	—
664	#124	C₂³×C₇₁	1	2	yes	—
665	#124	C₂³×C₇₁	1	2	yes	—
666	#124	C₂³×C₇₁	1	2	yes	—
667	#123	—	2	1	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	1	no	—
676	C₂²⋊Q₈	—	2	1	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	1	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
684	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
685	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
686	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
687	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
688	#121	—	2	1	no	—
689	#121	—	2	1	no	—
690	#121	C₂³×C₇₁	1	1	yes	characteristic
691	C₄×Q₈	—	2	2	no	—
692	C₄×Q₈	—	2	1	no	—
693	C₄×Q₈	—	2	1	no	—
694	C₄×Q₈	—	2	2	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
699	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
700	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
701	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
702	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
704	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
705	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
706	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
707	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
708	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
709	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	—	2	1	no	—
716	C₄×D₄	C₂³×C₇₁	1	2	yes	—
717	C₄×D₄	C₂³×C₇₁	1	2	yes	—
718	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
719	C₄×D₄	C₂³×C₇₁	1	2	yes	—
720	#117	—	2	1	no	—
721	#117	—	2	2	no	—
722	#117	—	2	2	no	—
723	#117	—	2	2	no	—
724	#117	—	2	2	no	—
725	#117	—	2	1	no	—
726	#117	—	2	1	no	—
727	#117	C₂³×C₇₁	1	2	yes	—
728	C₂×C₄⋊C₄	—	2	1	no	—
729	C₂×C₄⋊C₄	—	2	2	no	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
732	C₂×C₄²	—	2	1	no	—
733	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
734	#107	C₂³×C₇₁	1	2	yes	—
735	#106	C₂³×C₇₁	1	2	yes	—
736	#106	C₂³×C₇₁	1	2	yes	—
737	#106	C₂³×C₇₁	1	2	yes	—
738	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
739	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
740	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
741	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
742	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
743	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
744	#103	C₂³×C₇₁	1	2	yes	—
745	#103	C₂³×C₇₁	1	2	yes	—
746	#103	C₂³×C₇₁	1	2	yes	—
747	#103	C₂³×C₇₁	1	2	yes	—
748	#103	C₂³×C₇₁	1	2	yes	—
749	#103	C₂³×C₇₁	1	2	yes	—
750	#103	C₂³×C₇₁	1	2	yes	—
751	#103	C₂³×C₇₁	1	2	yes	—
752	#103	C₂³×C₇₁	1	2	yes	—
753	#103	C₂³×C₇₁	1	2	yes	—
754	#103	C₂³×C₇₁	1	2	yes	—
755	#102	C₂³×C₇₁	1	2	yes	—
756	#102	C₂³×C₇₁	1	2	yes	—
757	#102	C₂³×C₇₁	1	2	yes	—
758	#102	C₂³×C₇₁	1	2	yes	—
759	#102	C₂³×C₇₁	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
761	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
763	#97	C₂³×C₇₁	1	2	yes	—
764	#97	C₂³×C₇₁	1	1	yes	characteristic
765	#97	C₂³×C₇₁	1	1	yes	characteristic
766	#97	C₂³×C₇₁	1	2	yes	—
767	#97	C₂³×C₇₁	1	2	yes	—
768	C₄×C₈	C₂³×C₇₁	1	2	yes	—
769	C₄×C₈	C₂³×C₇₁	1	2	yes	—
770	#41	—	4	2	no	—
771	#41	—	4	2	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
777	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
778	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
779	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
782	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
788	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
799	Q₁₆	—	4	2	no	—
800	Q₁₆	—	4	2	no	—
801	Q₁₆	—	4	2	no	—
802	Q₁₆	—	4	2	no	—
803	Q₁₆	—	4	2	no	—
804	Q₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	SD₁₆	—	4	2	no	—
807	SD₁₆	—	4	2	no	—
808	SD₁₆	—	4	2	no	—
809	SD₁₆	—	4	2	no	—
810	D₈	—	4	2	no	—
811	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
812	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
813	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
814	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
844	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
845	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
846	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
847	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
848	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
849	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
850	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
851	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
855	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	1	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	1	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	1	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
874	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	1	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
885	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
886	C₄²	C₂⁴×C₇₁	1	2	yes	—
887	C₄²	C₂⁴×C₇₁	1	2	yes	—
888	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
889	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
890	C₂³	—	2	1	no	—
891	C₂³	—	2	2	no	—
892	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	4	1	no	—
901	Q₈	—	4	1	no	—
902	Q₈	—	4	2	no	—
903	Q₈	—	4	2	no	—
904	Q₈	—	8	1	no	—
905	Q₈	—	8	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	2	2	no	—
908	D₄	—	2	2	no	—
909	D₄	—	4	2	no	—
910	D₄	—	4	4	no	—
911	D₄	—	8	1	no	—
912	D₄	—	8	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	—	8	1	no	—
931	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
935	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
938	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
939	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
940	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
941	C₈	—	2	2	no	—
942	C₈	—	2	2	no	—
943	C₈	—	2	2	no	—
944	C₈	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	1	no	—
972	C₄	#585×C₇₁	1	2	yes	—
973	C₂	—	4	1	no	—
974	C₂	—	8	1	no	—
975	C₂	—	8	2	no	—
976	C₂	C₇₁×#3487	1	1	yes	characteristic
977	C₂	C₇₁×#3586	1	1	yes	characteristic
978	C₂	C₇₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₇₁×#3219	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ #533×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3555	C₂	semidirect
2. C₇₁×#3507	C₂	semidirect
3. C₇₁×#3402	C₂	semidirect
4. C₇₁×#3401	C₂	semidirect
5. C₇₁×#3398	C₂	semidirect
6. C₇₁×#3398	C₂	semidirect
7. C₇₁×#3376	C₂	semidirect
8. C₇₁×#3374	C₂	semidirect
9. C₇₁×#3371	C₂	semidirect
10. C₇₁×#3369	C₂	semidirect
11. C₇₁×#3225	C₂	semidirect
12. C₇₁×#3223	C₂	semidirect
14. C₇₁×#3216	C₂	semidirect
15. C₇₁×#3125	C₂	semidirect
16. C₇₁×#3120	C₂	semidirect
17. C₇₁×#3117	C₂	semidirect
18. C₇₁×#3113	C₂	semidirect
19. C₇₁×#2987	C₂	semidirect
483. #61941	C₇₁	direct (N × H)
490. #3555	C₂×C₇₁	semidirect
491. #3507	C₂×C₇₁	semidirect
492. #3402	C₂×C₇₁	semidirect
493. #3401	C₂×C₇₁	semidirect
494. #3398	C₂×C₇₁	semidirect
495. #3398	C₂×C₇₁	semidirect
496. #3376	C₂×C₇₁	semidirect
497. #3374	C₂×C₇₁	semidirect
498. #3371	C₂×C₇₁	semidirect
499. #3369	C₂×C₇₁	semidirect
500. #3225	C₂×C₇₁	semidirect
501. #3223	C₂×C₇₁	semidirect
503. #3216	C₂×C₇₁	semidirect
504. #3125	C₂×C₇₁	semidirect
505. #3120	C₂×C₇₁	semidirect
506. #3117	C₂×C₇₁	semidirect
507. #3113	C₂×C₇₁	semidirect
508. #2987	C₂×C₇₁	semidirect
509. C₇₁	#61941	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₁×#3555	2
C₇₁×#3507	2
C₇₁×#3402	2
C₇₁×#3401	2
C₇₁×#3398	2
C₇₁×#3376	2
C₇₁×#3374	2
C₇₁×#3371	2
C₇₁×#3369	2
C₇₁×#3225	2
C₇₁×#3223	2
C₇₁×#3219	2
C₇₁×#3216	2
C₇₁×#3125	2
C₇₁×#3120	2
C₇₁×#3117	2
C₇₁×#3113	2
C₇₁×#2987	2
#61941	71

Subgroups — C71×#61941 #31882813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61941 #31882813