Subgroups — C₇₁×#61939 #31882811

Order 18176.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1008 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×#3506	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×#3400	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3397	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3377	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3375	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3370	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3368	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3222	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3120	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₁×#3110	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	#559×C₇₁	C₂²	1	2	yes	—
23	Q₈²×C₇₁	C₂²	1	1	yes	characteristic, complemented
24	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
25	#557×C₇₁	C₂²	1	2	yes	complemented
26	#556×C₇₁	—	2	1	no	—
27	#556×C₇₁	C₂²	1	2	yes	—
28	#556×C₇₁	C₂²	1	2	yes	complemented
29	#556×C₇₁	C₂²	1	1	yes	characteristic, complemented
30	#555×C₇₁	—	2	1	no	—
31	#554×C₇₁	C₂²	1	1	yes	characteristic, complemented
32	#553×C₇₁	—	2	2	no	—
33	#552×C₇₁	—	2	1	no	—
34	#550×C₇₁	C₂²	1	2	yes	—
35	#547×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	#538×C₇₁	—	2	1	no	—
42	#538×C₇₁	—	2	1	no	—
43	#535×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	C₂²	1	1	yes	characteristic
48	#525×C₇₁	—	2	2	no	—
49	#520×C₇₁	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
51	#497×C₇₁	C₂²	1	2	yes	—
52	#497×C₇₁	C₂²	1	2	yes	complemented
53	#497×C₇₁	C₂²	1	1	yes	characteristic, complemented
54	#496×C₇₁	C₂²	1	2	yes	—
55	#496×C₇₁	C₂²	1	1	yes	characteristic, complemented
56	#495×C₇₁	C₂²	1	2	yes	—
57	#492×C₇₁	C₂²	1	2	yes	—
58	#491×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	#490×C₇₁	C₂²	1	2	yes	—
60	#490×C₇₁	C₂²	1	1	yes	characteristic, complemented
61	#489×C₇₁	C₂²	1	2	yes	—
62	#489×C₇₁	C₂²	1	2	yes	complemented
63	#488×C₇₁	C₂²	1	2	yes	—
64	#486×C₇₁	C₂²	1	2	yes	—
65	#484×C₇₁	C₂²	1	2	yes	—
66	#483×C₇₁	C₂²	1	1	yes	characteristic
67	#480×C₇₁	C₂²	1	1	yes	characteristic
68	#479×C₇₁	C₂²	1	2	yes	complemented
69	#478×C₇₁	C₂²	1	2	yes	—
70	#478×C₇₁	C₂²	1	2	yes	complemented
71	#477×C₇₁	C₂²	1	2	yes	complemented
72	#474×C₇₁	C₂²	1	2	yes	—
73	#474×C₇₁	C₂²	1	2	yes	complemented
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	complemented
78	#464×C₇₁	C₂²	1	2	yes	complemented
79	#463×C₇₁	C₂²	1	2	yes	—
80	#463×C₇₁	C₂²	1	2	yes	—
81	#463×C₇₁	C₂²	1	2	yes	complemented
82	#463×C₇₁	C₂²	1	2	yes	complemented
83	#462×C₇₁	C₂²	1	2	yes	complemented
84	#462×C₇₁	C₂²	1	2	yes	complemented
85	#461×C₇₁	C₂²	1	2	yes	—
86	#461×C₇₁	C₂²	1	2	yes	complemented
87	#460×C₇₁	C₂²	1	2	yes	—
88	#460×C₇₁	C₂²	1	2	yes	—
89	#460×C₇₁	C₂²	1	2	yes	—
90	#460×C₇₁	C₂²	1	2	yes	complemented
91	#459×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	#450×C₇₁	C₂²	1	2	yes	—
96	#450×C₇₁	C₂²	1	1	yes	characteristic
97	#449×C₇₁	C₂²	1	2	yes	—
98	#447×C₇₁	C₂²	1	1	yes	characteristic
99	#446×C₇₁	C₂²	1	2	yes	complemented
100	#446×C₇₁	C₂²	1	2	yes	complemented
101	#446×C₇₁	C₂²	1	2	yes	complemented
102	#446×C₇₁	C₂²	1	2	yes	complemented
103	#442×C₇₁	C₂²	1	2	yes	—
104	#441×C₇₁	C₂²	1	2	yes	complemented
105	#440×C₇₁	C₂²	1	2	yes	—
106	#440×C₇₁	C₂²	1	2	yes	—
107	#440×C₇₁	C₂²	1	2	yes	—
108	#440×C₇₁	C₂²	1	2	yes	complemented
109	#440×C₇₁	C₂²	1	2	yes	complemented
110	#440×C₇₁	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
114	C₄×D₈×C₇₁	C₂²	1	2	yes	complemented
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	—	2	2	no	—
120	C₂×#41×C₇₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇₁	—	2	1	no	—
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×SD₁₆×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×SD₁₆×C₇₁	C₂³	1	2	yes	—
133	C₂×D₈×C₇₁	C₂³	1	2	yes	—
134	C₂×D₈×C₇₁	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₇₁	—	2	2	no	—
136	C₄⋊Q₈×C₇₁	—	2	2	no	—
137	C₄⋊Q₈×C₇₁	—	2	1	no	—
138	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
139	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
140	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
141	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
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	2	yes	—
146	#127×C₇₁	C₂³	1	2	yes	—
147	#127×C₇₁	C₂³	1	1	yes	characteristic
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	1	no	—
163	#125×C₇₁	—	2	1	no	—
164	#125×C₇₁	D₄	1	2	yes	—
165	#125×C₇₁	C₂³	1	1	yes	characteristic
166	#125×C₇₁	C₂³	1	2	yes	—
167	#124×C₇₁	—	2	2	no	—
168	#124×C₇₁	—	2	2	no	—
169	#124×C₇₁	—	2	2	no	—
170	#124×C₇₁	C₂³	1	1	yes	characteristic
171	#124×C₇₁	C₂³	1	2	yes	—
172	#124×C₇₁	C₂³	1	2	yes	—
173	#124×C₇₁	C₂³	1	2	yes	—
174	#124×C₇₁	C₂³	1	2	yes	—
175	#123×C₇₁	—	2	1	no	—
176	#123×C₇₁	—	2	2	no	—
177	#123×C₇₁	—	2	2	no	—
178	#123×C₇₁	—	2	2	no	—
179	#123×C₇₁	—	2	2	no	—
180	#123×C₇₁	—	2	2	no	—
181	C₂²⋊Q₈×C₇₁	—	2	2	no	—
182	C₂²⋊Q₈×C₇₁	—	2	1	no	—
183	C₂²⋊Q₈×C₇₁	—	2	1	no	—
184	C₂²⋊Q₈×C₇₁	—	2	2	no	—
185	C₂²⋊Q₈×C₇₁	—	2	1	no	—
186	C₂²⋊Q₈×C₇₁	—	2	2	no	—
187	C₂²⋊Q₈×C₇₁	—	2	2	no	—
188	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
189	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
190	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
191	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
192	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
193	#121×C₇₁	—	2	1	no	—
194	#121×C₇₁	—	2	1	no	—
195	#121×C₇₁	—	2	2	no	—
196	#121×C₇₁	—	2	2	no	—
197	#121×C₇₁	—	2	2	no	—
198	#121×C₇₁	—	2	2	no	—
199	#121×C₇₁	—	2	2	no	—
200	#121×C₇₁	C₂³	1	1	yes	characteristic
201	#120×C₇₁	—	2	2	no	—
202	#120×C₇₁	—	2	2	no	—
203	C₄×Q₈×C₇₁	—	2	1	no	—
204	C₄×Q₈×C₇₁	—	2	1	no	—
205	C₄×Q₈×C₇₁	—	2	2	no	—
206	C₄×Q₈×C₇₁	—	2	1	no	—
207	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
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	1	yes	characteristic
214	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₇₁	—	2	1	no	—
218	C₄×D₄×C₇₁	—	2	2	no	—
219	C₄×D₄×C₇₁	—	2	2	no	—
220	C₄×D₄×C₇₁	—	2	2	no	—
221	C₄×D₄×C₇₁	—	2	2	no	—
222	C₄×D₄×C₇₁	—	2	1	no	—
223	C₄×D₄×C₇₁	—	2	1	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	2	yes	—
230	C₄×D₄×C₇₁	C₂³	1	2	yes	—
231	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
232	#117×C₇₁	—	2	1	no	—
233	#117×C₇₁	—	2	2	no	—
234	#117×C₇₁	—	2	2	no	—
235	#117×C₇₁	—	2	2	no	—
236	#117×C₇₁	—	2	1	no	—
237	#117×C₇₁	—	2	1	no	—
238	#117×C₇₁	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₇₁	—	2	1	no	—
243	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
244	#107×C₇₁	C₂³	1	2	yes	—
245	#107×C₇₁	C₂³	1	2	yes	—
246	#107×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	#102×C₇₁	C₂³	1	2	yes	—
262	#102×C₇₁	C₂³	1	2	yes	—
263	#102×C₇₁	C₂³	1	2	yes	—
264	#102×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	1	yes	characteristic
274	#97×C₇₁	C₂³	1	1	yes	characteristic
275	#97×C₇₁	C₂³	1	2	yes	—
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	C₂⁴×C₇₁	—	2	1	no	—
281	#41×C₇₁	—	4	2	no	—
282	#41×C₇₁	—	4	2	no	—
283	#41×C₇₁	—	8	4	no	—
284	C₂×Q₈×C₇₁	—	2	1	no	—
285	C₂×Q₈×C₇₁	—	2	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	1	yes	characteristic
292	C₂×D₄×C₇₁	—	2	2	no	—
293	C₂×D₄×C₇₁	—	2	1	no	—
294	C₂×D₄×C₇₁	—	2	1	no	—
295	C₂×D₄×C₇₁	—	2	1	no	—
296	C₂×D₄×C₇₁	—	2	2	no	—
297	C₂×D₄×C₇₁	—	2	2	no	—
298	C₂×D₄×C₇₁	—	2	1	no	—
299	C₂×D₄×C₇₁	—	2	2	no	—
300	C₂×D₄×C₇₁	—	2	2	no	—
301	C₂×D₄×C₇₁	—	4	2	no	—
302	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
303	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
304	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇₁	—	2	1	no	—
306	C₂²×C₄×C₇₁	—	2	1	no	—
307	C₂²×C₄×C₇₁	—	2	2	no	—
308	C₂²×C₄×C₇₁	—	2	2	no	—
309	C₂²×C₄×C₇₁	—	2	2	no	—
310	C₂²×C₄×C₇₁	—	2	2	no	—
311	C₂²×C₄×C₇₁	—	2	2	no	—
312	C₂²×C₄×C₇₁	—	2	2	no	—
313	C₂²×C₄×C₇₁	—	8	2	no	—
314	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
317	Q₁₆×C₇₁	—	4	2	no	—
318	Q₁₆×C₇₁	—	4	2	no	—
319	Q₁₆×C₇₁	—	4	2	no	—
320	SD₁₆×C₇₁	—	4	2	no	—
321	SD₁₆×C₇₁	—	4	2	no	—
322	SD₁₆×C₇₁	—	4	2	no	—
323	SD₁₆×C₇₁	—	4	2	no	—
324	SD₁₆×C₇₁	—	4	2	no	—
325	SD₁₆×C₇₁	—	4	2	no	—
326	SD₁₆×C₇₁	—	4	2	no	—
327	D₈×C₇₁	—	4	2	no	—
328	D₈×C₇₁	—	4	2	no	—
329	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
330	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
331	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
332	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₇₁	—	2	1	no	—
334	C₄⋊C₄×C₇₁	—	2	1	no	—
335	C₄⋊C₄×C₇₁	—	2	2	no	—
336	C₄⋊C₄×C₇₁	—	2	2	no	—
337	C₄⋊C₄×C₇₁	—	2	2	no	—
338	C₄⋊C₄×C₇₁	—	2	1	no	—
339	C₄⋊C₄×C₇₁	—	2	1	no	—
340	C₄⋊C₄×C₇₁	—	2	2	no	—
341	C₄⋊C₄×C₇₁	—	2	1	no	—
342	C₄⋊C₄×C₇₁	—	2	1	no	—
343	C₄⋊C₄×C₇₁	—	2	1	no	—
344	C₄⋊C₄×C₇₁	—	2	1	no	—
345	C₄⋊C₄×C₇₁	—	2	2	no	—
346	C₄⋊C₄×C₇₁	—	2	2	no	—
347	C₄⋊C₄×C₇₁	—	2	1	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	2	no	—
353	C₄⋊C₄×C₇₁	—	2	2	no	—
354	C₄⋊C₄×C₇₁	—	2	1	no	—
355	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
360	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
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	2	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	1	no	—
378	C₂²⋊C₄×C₇₁	—	2	1	no	—
379	C₂²⋊C₄×C₇₁	—	2	2	no	—
380	C₂²⋊C₄×C₇₁	—	2	2	no	—
381	C₂²⋊C₄×C₇₁	—	2	2	no	—
382	C₂²⋊C₄×C₇₁	—	2	2	no	—
383	C₂²⋊C₄×C₇₁	—	2	2	no	—
384	C₂²⋊C₄×C₇₁	—	2	2	no	—
385	C₂²⋊C₄×C₇₁	—	2	1	no	—
386	C₂²⋊C₄×C₇₁	—	2	2	no	—
387	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
389	C₄²×C₇₁	—	2	2	no	—
390	C₄²×C₇₁	—	2	2	no	—
391	C₄²×C₇₁	—	2	2	no	—
392	C₄²×C₇₁	—	2	1	no	—
393	C₄²×C₇₁	—	2	2	no	—
394	C₄²×C₇₁	—	2	2	no	—
395	C₄²×C₇₁	—	2	2	no	—
396	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₇₁	C₂⁴	1	2	yes	—
399	C₄²×C₇₁	C₂⁴	1	2	yes	—
400	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
401	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
402	C₂³×C₇₁	—	2	1	no	—
403	C₂³×C₇₁	—	2	2	no	—
404	C₂³×C₇₁	—	2	2	no	—
405	C₂³×C₇₁	—	4	2	no	—
406	C₂³×C₇₁	—	8	1	no	—
407	C₂³×C₇₁	—	8	1	no	—
408	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
409	Q₈×C₇₁	—	2	2	no	—
410	Q₈×C₇₁	—	2	2	no	—
411	Q₈×C₇₁	—	2	2	no	—
412	Q₈×C₇₁	—	2	2	no	—
413	Q₈×C₇₁	—	2	2	no	—
414	Q₈×C₇₁	—	4	1	no	—
415	Q₈×C₇₁	—	4	1	no	—
416	Q₈×C₇₁	—	4	2	no	—
417	Q₈×C₇₁	—	8	1	no	—
418	Q₈×C₇₁	—	8	2	no	—
419	D₄×C₇₁	—	2	2	no	—
420	D₄×C₇₁	—	2	2	no	—
421	D₄×C₇₁	—	2	2	no	—
422	D₄×C₇₁	—	2	2	no	—
423	D₄×C₇₁	—	2	2	no	—
424	D₄×C₇₁	—	4	2	no	—
425	D₄×C₇₁	—	4	2	no	—
426	D₄×C₇₁	—	4	4	no	—
427	D₄×C₇₁	—	8	1	no	—
428	D₄×C₇₁	—	8	2	no	—
429	D₄×C₇₁	—	8	2	no	—
430	D₄×C₇₁	—	8	2	no	—
431	D₄×C₇₁	—	8	2	no	—
432	D₄×C₇₁	—	8	1	no	—
433	C₂×C₄×C₇₁	—	2	2	no	—
434	C₂×C₄×C₇₁	—	2	2	no	—
435	C₂×C₄×C₇₁	—	2	1	no	—
436	C₂×C₄×C₇₁	—	2	1	no	—
437	C₂×C₄×C₇₁	—	2	2	no	—
438	C₂×C₄×C₇₁	—	2	2	no	—
439	C₂×C₄×C₇₁	—	2	1	no	—
440	C₂×C₄×C₇₁	—	2	2	no	—
441	C₂×C₄×C₇₁	—	4	1	no	—
442	C₂×C₄×C₇₁	—	4	1	no	—
443	C₂×C₄×C₇₁	—	4	2	no	—
444	C₂×C₄×C₇₁	—	4	4	no	—
445	C₂×C₄×C₇₁	—	4	4	no	—
446	C₂×C₄×C₇₁	—	8	2	no	—
447	C₂×C₄×C₇₁	—	8	2	no	—
448	C₂×C₄×C₇₁	—	8	2	no	—
449	C₂×C₄×C₇₁	—	8	2	no	—
450	C₂×C₄×C₇₁	—	8	1	no	—
451	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
461	C₈×C₇₁	—	2	2	no	—
462	C₈×C₇₁	—	2	2	no	—
463	C₈×C₇₁	—	2	2	no	—
464	C₈×C₇₁	—	2	2	no	—
465	C₂²×C₇₁	—	2	1	no	—
466	C₂²×C₇₁	—	2	1	no	—
467	C₂²×C₇₁	—	2	1	no	—
468	C₂²×C₇₁	—	4	2	no	—
469	C₂²×C₇₁	—	4	2	no	—
470	C₂²×C₇₁	—	4	1	no	—
471	C₂²×C₇₁	—	4	1	no	—
472	C₂²×C₇₁	—	4	2	no	—
473	C₂²×C₇₁	—	4	2	no	—
474	C₂²×C₇₁	—	4	2	no	—
475	C₂²×C₇₁	—	4	2	no	—
476	C₂²×C₇₁	—	4	1	no	—
477	C₂²×C₇₁	—	8	4	no	—
478	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
479	C₄×C₇₁	—	2	1	no	—
480	C₄×C₇₁	—	2	1	no	—
481	C₄×C₇₁	—	2	2	no	—
482	C₄×C₇₁	—	2	2	no	—
483	C₄×C₇₁	—	2	1	no	—
484	C₄×C₇₁	—	2	1	no	—
485	C₄×C₇₁	—	2	2	no	—
486	C₄×C₇₁	—	2	2	no	—
487	C₄×C₇₁	—	2	1	no	—
488	C₄×C₇₁	—	4	2	no	—
489	C₄×C₇₁	—	4	2	no	—
490	C₄×C₇₁	—	4	1	no	—
491	C₄×C₇₁	—	4	1	no	—
492	C₄×C₇₁	—	4	2	no	—
493	C₄×C₇₁	—	4	2	no	—
494	C₄×C₇₁	—	4	1	no	—
495	C₄×C₇₁	#585	1	2	yes	—
496	#61939	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂×C₇₁	—	4	1	no	—
498	C₂×C₇₁	—	8	2	no	—
499	C₂×C₇₁	—	8	1	no	—
500	C₂×C₇₁	—	8	2	no	—
501	C₂×C₇₁	#3487	1	1	yes	characteristic
502	C₂×C₇₁	#3585	1	1	yes	characteristic
503	C₂×C₇₁	#3586	1	1	yes	characteristic
504	#3555	C₂×C₇₁	1	1	yes	characteristic, complemented
505	#3506	C₂×C₇₁	1	1	yes	characteristic, complemented
506	#3402	C₂×C₇₁	1	2	yes	complemented
507	#3401	C₂×C₇₁	1	2	yes	complemented
508	#3400	C₂×C₇₁	1	2	yes	complemented
509	#3397	C₂×C₇₁	1	2	yes	complemented
510	#3377	C₂×C₇₁	1	2	yes	complemented
511	#3375	C₂×C₇₁	1	2	yes	complemented
512	#3370	C₂×C₇₁	1	2	yes	complemented
513	#3368	C₂×C₇₁	1	2	yes	complemented
514	#3224	C₂×C₇₁	1	2	yes	complemented
515	#3222	C₂×C₇₁	1	2	yes	complemented
516	#3219	C₂×C₇₁	1	1	yes	characteristic, complemented
517	#3216	C₂×C₇₁	1	1	yes	characteristic, complemented
518	#3124	C₂×C₇₁	1	2	yes	complemented
519	#3120	C₂×C₇₁	1	2	yes	complemented
520	#3114	C₂×C₇₁	1	1	yes	characteristic, complemented
521	#3110	C₂×C₇₁	1	1	yes	characteristic, complemented
522	#2987	C₂×C₇₁	1	1	yes	characteristic, complemented
523	C₇₁	#61939	1	1	yes	characteristic, direct product factor, Sylow
524	#563	—	2	2	no	—
525	#559	C₂²×C₇₁	1	2	yes	—
526	#559	C₂²×C₇₁	1	2	yes	—
527	Q₈²	C₂²×C₇₁	1	1	yes	characteristic, complemented
528	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
529	#557	C₂²×C₇₁	1	2	yes	complemented
530	#556	—	2	1	no	—
531	#556	C₂²×C₇₁	1	2	yes	—
532	#556	C₂²×C₇₁	1	2	yes	complemented
533	#556	C₂²×C₇₁	1	1	yes	characteristic, complemented
534	#555	—	2	1	no	—
535	#554	C₂²×C₇₁	1	1	yes	characteristic, complemented
536	#553	—	2	2	no	—
537	#552	—	2	1	no	—
538	#550	C₂²×C₇₁	1	2	yes	—
539	#547	—	2	1	no	—
540	#544	—	2	1	no	—
541	#542	C₂²×C₇₁	1	2	yes	—
542	#541	—	2	1	no	—
543	#541	—	2	2	no	—
544	#541	C₂²×C₇₁	1	2	yes	—
545	#538	—	2	1	no	—
546	#538	—	2	1	no	—
547	#535	C₂²×C₇₁	1	2	yes	—
548	#533	C₂²×C₇₁	1	1	yes	characteristic
549	#533	C₂²×C₇₁	1	1	yes	characteristic
550	#532	C₂²×C₇₁	1	1	yes	characteristic
551	#529	C₂²×C₇₁	1	1	yes	characteristic
552	#525	—	2	2	no	—
553	#520	C₂²×C₇₁	1	2	yes	—
554	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
555	#497	C₂²×C₇₁	1	2	yes	—
556	#497	C₂²×C₇₁	1	2	yes	complemented
557	#497	C₂²×C₇₁	1	1	yes	characteristic, complemented
558	#496	C₂²×C₇₁	1	2	yes	—
559	#496	C₂²×C₇₁	1	1	yes	characteristic, complemented
560	#495	C₂²×C₇₁	1	2	yes	—
561	#492	C₂²×C₇₁	1	2	yes	—
562	#491	C₂²×C₇₁	1	1	yes	characteristic, complemented
563	#490	C₂²×C₇₁	1	2	yes	—
564	#490	C₂²×C₇₁	1	1	yes	characteristic, complemented
565	#489	C₂²×C₇₁	1	2	yes	—
566	#489	C₂²×C₇₁	1	2	yes	complemented
567	#488	C₂²×C₇₁	1	2	yes	—
568	#486	C₂²×C₇₁	1	2	yes	—
569	#484	C₂²×C₇₁	1	2	yes	—
570	#483	C₂²×C₇₁	1	1	yes	characteristic
571	#480	C₂²×C₇₁	1	1	yes	characteristic
572	#479	C₂²×C₇₁	1	2	yes	complemented
573	#478	C₂²×C₇₁	1	2	yes	—
574	#478	C₂²×C₇₁	1	2	yes	complemented
575	#477	C₂²×C₇₁	1	2	yes	complemented
576	#474	C₂²×C₇₁	1	2	yes	—
577	#474	C₂²×C₇₁	1	2	yes	complemented
578	#464	C₂²×C₇₁	1	2	yes	—
579	#464	C₂²×C₇₁	1	2	yes	—
580	#464	C₂²×C₇₁	1	2	yes	—
581	#464	C₂²×C₇₁	1	2	yes	complemented
582	#464	C₂²×C₇₁	1	2	yes	complemented
583	#463	C₂²×C₇₁	1	2	yes	—
584	#463	C₂²×C₇₁	1	2	yes	—
585	#463	C₂²×C₇₁	1	2	yes	complemented
586	#463	C₂²×C₇₁	1	2	yes	complemented
587	#462	C₂²×C₇₁	1	2	yes	complemented
588	#462	C₂²×C₇₁	1	2	yes	complemented
589	#461	C₂²×C₇₁	1	2	yes	—
590	#461	C₂²×C₇₁	1	2	yes	complemented
591	#460	C₂²×C₇₁	1	2	yes	—
592	#460	C₂²×C₇₁	1	2	yes	—
593	#460	C₂²×C₇₁	1	2	yes	—
594	#460	C₂²×C₇₁	1	2	yes	complemented
595	#459	C₂²×C₇₁	1	2	yes	—
596	#452	C₂²×C₇₁	1	2	yes	—
597	#452	C₂²×C₇₁	1	2	yes	—
598	#452	C₂²×C₇₁	1	2	yes	—
599	#450	C₂²×C₇₁	1	2	yes	—
600	#450	C₂²×C₇₁	1	1	yes	characteristic
601	#449	C₂²×C₇₁	1	2	yes	—
602	#447	C₂²×C₇₁	1	1	yes	characteristic
603	#446	C₂²×C₇₁	1	2	yes	complemented
604	#446	C₂²×C₇₁	1	2	yes	complemented
605	#446	C₂²×C₇₁	1	2	yes	complemented
606	#446	C₂²×C₇₁	1	2	yes	complemented
607	#442	C₂²×C₇₁	1	2	yes	—
608	#441	C₂²×C₇₁	1	2	yes	complemented
609	#440	C₂²×C₇₁	1	2	yes	—
610	#440	C₂²×C₇₁	1	2	yes	—
611	#440	C₂²×C₇₁	1	2	yes	—
612	#440	C₂²×C₇₁	1	2	yes	complemented
613	#440	C₂²×C₇₁	1	2	yes	complemented
614	#440	C₂²×C₇₁	1	2	yes	complemented
615	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
616	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
617	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
618	C₄×D₈	C₂²×C₇₁	1	2	yes	complemented
619	#433	C₂²×C₇₁	1	2	yes	—
620	#433	C₂²×C₇₁	1	2	yes	—
621	#432	C₂²×C₇₁	1	1	yes	characteristic
622	#432	C₂²×C₇₁	1	1	yes	characteristic
623	C₂×#41	—	2	2	no	—
624	C₂×#41	C₂³×C₇₁	1	2	yes	—
625	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
626	C₂³×C₄	—	2	1	no	—
627	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
628	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
629	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
637	C₂×D₈	C₂³×C₇₁	1	2	yes	—
638	C₂×D₈	C₂³×C₇₁	1	2	yes	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	1	no	—
642	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
643	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
644	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
649	#127	C₂³×C₇₁	1	1	yes	characteristic
650	#127	C₂³×C₇₁	1	2	yes	—
651	#127	C₂³×C₇₁	1	2	yes	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	1	no	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	1	no	—
667	#125	—	2	1	no	—
668	#125	D₄×C₇₁	1	2	yes	—
669	#125	C₂³×C₇₁	1	1	yes	characteristic
670	#125	C₂³×C₇₁	1	2	yes	—
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	—	2	2	no	—
674	#124	C₂³×C₇₁	1	1	yes	characteristic
675	#124	C₂³×C₇₁	1	2	yes	—
676	#124	C₂³×C₇₁	1	2	yes	—
677	#124	C₂³×C₇₁	1	2	yes	—
678	#124	C₂³×C₇₁	1	2	yes	—
679	#123	—	2	1	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
693	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
694	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
695	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
697	#121	—	2	1	no	—
698	#121	—	2	1	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	C₂³×C₇₁	1	1	yes	characteristic
705	#120	—	2	2	no	—
706	#120	—	2	2	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	2	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
712	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
713	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
714	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
715	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
716	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
717	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
718	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
719	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	C₂³×C₇₁	1	2	yes	—
731	C₄×D₄	C₂³×C₇₁	1	2	yes	—
732	C₄×D₄	C₂³×C₇₁	1	2	yes	—
733	C₄×D₄	C₂³×C₇₁	1	2	yes	—
734	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₇₁	1	2	yes	—
736	#117	—	2	1	no	—
737	#117	—	2	2	no	—
738	#117	—	2	2	no	—
739	#117	—	2	2	no	—
740	#117	—	2	1	no	—
741	#117	—	2	1	no	—
742	#117	C₂³×C₇₁	1	2	yes	—
743	C₂×C₄⋊C₄	—	2	2	no	—
744	C₂×C₄⋊C₄	—	2	1	no	—
745	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	—	2	1	no	—
747	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
748	#107	C₂³×C₇₁	1	2	yes	—
749	#107	C₂³×C₇₁	1	2	yes	—
750	#107	C₂³×C₇₁	1	2	yes	—
751	#106	C₂³×C₇₁	1	2	yes	—
752	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
753	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
754	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
755	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
756	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
757	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
758	#103	C₂³×C₇₁	1	2	yes	—
759	#103	C₂³×C₇₁	1	2	yes	—
760	#103	C₂³×C₇₁	1	2	yes	—
761	#103	C₂³×C₇₁	1	2	yes	—
762	#103	C₂³×C₇₁	1	2	yes	—
763	#103	C₂³×C₇₁	1	2	yes	—
764	#103	C₂³×C₇₁	1	2	yes	—
765	#102	C₂³×C₇₁	1	2	yes	—
766	#102	C₂³×C₇₁	1	2	yes	—
767	#102	C₂³×C₇₁	1	2	yes	—
768	#102	C₂³×C₇₁	1	2	yes	—
769	#102	C₂³×C₇₁	1	2	yes	—
770	#102	C₂³×C₇₁	1	2	yes	—
771	#102	C₂³×C₇₁	1	2	yes	—
772	#102	C₂³×C₇₁	1	2	yes	—
773	#102	C₂³×C₇₁	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
775	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
777	#97	C₂³×C₇₁	1	1	yes	characteristic
778	#97	C₂³×C₇₁	1	1	yes	characteristic
779	#97	C₂³×C₇₁	1	2	yes	—
780	#97	C₂³×C₇₁	1	2	yes	—
781	#97	C₂³×C₇₁	1	2	yes	—
782	C₄×C₈	C₂³×C₇₁	1	2	yes	—
783	C₄×C₈	C₂³×C₇₁	1	2	yes	—
784	C₂⁴	—	2	1	no	—
785	#41	—	4	2	no	—
786	#41	—	4	2	no	—
787	#41	—	8	4	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
791	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
792	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
794	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
795	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
807	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
808	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	8	2	no	—
818	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
821	Q₁₆	—	4	2	no	—
822	Q₁₆	—	4	2	no	—
823	Q₁₆	—	4	2	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	D₈	—	4	2	no	—
832	D₈	—	4	2	no	—
833	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
834	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
835	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
836	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	1	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	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
860	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
861	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
862	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
863	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
865	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
869	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	1	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	1	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
901	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
902	C₄²	C₂⁴×C₇₁	1	2	yes	—
903	C₄²	C₂⁴×C₇₁	1	2	yes	—
904	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
905	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	8	1	no	—
911	C₂³	—	8	1	no	—
912	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
913	Q₈	—	2	2	no	—
914	Q₈	—	2	2	no	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	4	2	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	4	1	no	—
921	Q₈	—	8	1	no	—
922	Q₈	—	8	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	4	no	—
931	D₄	—	8	2	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	1	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	2	no	—
936	D₄	—	8	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	2	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	1	no	—
955	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
956	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
960	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
962	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
964	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
965	C₈	—	2	2	no	—
966	C₈	—	2	2	no	—
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	8	4	no	—
982	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	2	no	—
991	C₄	—	2	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	#585×C₇₁	1	2	yes	—
1000	C₂	—	4	1	no	—
1001	C₂	—	8	2	no	—
1002	C₂	—	8	2	no	—
1003	C₂	—	8	1	no	—
1004	C₂	C₇₁×#3487	1	1	yes	characteristic
1005	C₂	C₇₁×#3585	1	1	yes	characteristic
1006	C₂	C₇₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
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×#3506	C₂	semidirect
3. C₇₁×#3402	C₂	semidirect
4. C₇₁×#3401	C₂	semidirect
5. C₇₁×#3400	C₂	semidirect
6. C₇₁×#3397	C₂	semidirect
7. C₇₁×#3377	C₂	semidirect
8. C₇₁×#3375	C₂	semidirect
9. C₇₁×#3370	C₂	semidirect
10. C₇₁×#3368	C₂	semidirect
11. C₇₁×#3224	C₂	semidirect
12. C₇₁×#3222	C₂	semidirect
13. C₇₁×#3219	C₂	semidirect
14. C₇₁×#3216	C₂	semidirect
15. C₇₁×#3124	C₂	semidirect
16. C₇₁×#3120	C₂	semidirect
17. C₇₁×#3114	C₂	semidirect
18. C₇₁×#3110	C₂	semidirect
19. C₇₁×#2987	C₂	semidirect
23. Q₈²×C₇₁	C₂²	semidirect
24. #557×C₇₁	C₂²	semidirect
25. #557×C₇₁	C₂²	semidirect
28. #556×C₇₁	C₂²	semidirect
29. #556×C₇₁	C₂²	semidirect
31. #554×C₇₁	C₂²	semidirect
52. #497×C₇₁	C₂²	semidirect
53. #497×C₇₁	C₂²	semidirect
55. #496×C₇₁	C₂²	semidirect
58. #491×C₇₁	C₂²	semidirect
60. #490×C₇₁	C₂²	semidirect
62. #489×C₇₁	C₂²	semidirect
68. #479×C₇₁	C₂²	semidirect
70. #478×C₇₁	C₂²	semidirect
71. #477×C₇₁	C₂²	semidirect
73. #474×C₇₁	C₂²	semidirect
77. #464×C₇₁	C₂²	semidirect
78. #464×C₇₁	C₂²	semidirect
81. #463×C₇₁	C₂²	semidirect
82. #463×C₇₁	C₂²	semidirect
83. #462×C₇₁	C₂²	semidirect
84. #462×C₇₁	C₂²	semidirect
86. #461×C₇₁	C₂²	semidirect
90. #460×C₇₁	C₂²	semidirect
99. #446×C₇₁	C₂²	semidirect
100. #446×C₇₁	C₂²	semidirect
101. #446×C₇₁	C₂²	semidirect
102. #446×C₇₁	C₂²	semidirect
104. #441×C₇₁	C₂²	semidirect
108. #440×C₇₁	C₂²	semidirect
109. #440×C₇₁	C₂²	semidirect
110. #440×C₇₁	C₂²	semidirect
111. C₄×Q₁₆×C₇₁	C₂²	semidirect
112. C₄×Q₁₆×C₇₁	C₂²	semidirect
113. C₄×SD₁₆×C₇₁	C₂²	semidirect
114. C₄×D₈×C₇₁	C₂²	semidirect
496. #61939	C₇₁	direct (N × H)
504. #3555	C₂×C₇₁	semidirect
505. #3506	C₂×C₇₁	semidirect
506. #3402	C₂×C₇₁	semidirect
507. #3401	C₂×C₇₁	semidirect
508. #3400	C₂×C₇₁	semidirect
509. #3397	C₂×C₇₁	semidirect
510. #3377	C₂×C₇₁	semidirect
511. #3375	C₂×C₇₁	semidirect
512. #3370	C₂×C₇₁	semidirect
513. #3368	C₂×C₇₁	semidirect
514. #3224	C₂×C₇₁	semidirect
515. #3222	C₂×C₇₁	semidirect
516. #3219	C₂×C₇₁	semidirect
517. #3216	C₂×C₇₁	semidirect
518. #3124	C₂×C₇₁	semidirect
519. #3120	C₂×C₇₁	semidirect
520. #3114	C₂×C₇₁	semidirect
521. #3110	C₂×C₇₁	semidirect
522. #2987	C₂×C₇₁	semidirect
523. C₇₁	#61939	direct (N × H)
527. Q₈²	C₂²×C₇₁	semidirect
528. #557	C₂²×C₇₁	semidirect
529. #557	C₂²×C₇₁	semidirect
532. #556	C₂²×C₇₁	semidirect
533. #556	C₂²×C₇₁	semidirect
535. #554	C₂²×C₇₁	semidirect
556. #497	C₂²×C₇₁	semidirect
557. #497	C₂²×C₇₁	semidirect
559. #496	C₂²×C₇₁	semidirect
562. #491	C₂²×C₇₁	semidirect
564. #490	C₂²×C₇₁	semidirect
566. #489	C₂²×C₇₁	semidirect
572. #479	C₂²×C₇₁	semidirect
574. #478	C₂²×C₇₁	semidirect
575. #477	C₂²×C₇₁	semidirect
577. #474	C₂²×C₇₁	semidirect
581. #464	C₂²×C₇₁	semidirect
582. #464	C₂²×C₇₁	semidirect
585. #463	C₂²×C₇₁	semidirect
586. #463	C₂²×C₇₁	semidirect
587. #462	C₂²×C₇₁	semidirect
588. #462	C₂²×C₇₁	semidirect
590. #461	C₂²×C₇₁	semidirect
594. #460	C₂²×C₇₁	semidirect
603. #446	C₂²×C₇₁	semidirect
604. #446	C₂²×C₇₁	semidirect
605. #446	C₂²×C₇₁	semidirect
606. #446	C₂²×C₇₁	semidirect
608. #441	C₂²×C₇₁	semidirect
612. #440	C₂²×C₇₁	semidirect
613. #440	C₂²×C₇₁	semidirect
614. #440	C₂²×C₇₁	semidirect
615. C₄×Q₁₆	C₂²×C₇₁	semidirect
616. C₄×Q₁₆	C₂²×C₇₁	semidirect
617. C₄×SD₁₆	C₂²×C₇₁	semidirect
618. C₄×D₈	C₂²×C₇₁	semidirect

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×#3506	2
C₇₁×#3402	2
C₇₁×#3401	2
C₇₁×#3400	2
C₇₁×#3397	2
C₇₁×#3377	2
C₇₁×#3375	2
C₇₁×#3370	2
C₇₁×#3368	2
C₇₁×#3224	2
C₇₁×#3222	2
C₇₁×#3219	2
C₇₁×#3216	2
C₇₁×#3124	2
C₇₁×#3120	2
C₇₁×#3114	2
C₇₁×#3110	2
C₇₁×#2987	2
#61939	71

Subgroups — C71×#61939 #31882811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61939 #31882811