Subgroups — C₇₁×#61422 #31882294

Order 18176.

1844 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3402	C₂	1	4	yes	maximal, complemented
4	C₇₁×#3400	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3398	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3398	C₂	1	4	yes	maximal, complemented
7	C₇₁×#3395	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3394	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3156	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3046	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3044	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3035	C₂	1	1	yes	maximal, characteristic
14	C₂×#462×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#2947	C₂	1	2	yes	maximal, complemented
17	C₄×#137×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₇₁	C₂²	1	2	yes	—
19	C₂×#137×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#137×C₇₁	C₂²	1	2	yes	—
21	C₂×#135×C₇₁	C₂²	1	2	yes	—
22	C₂²×Q₁₆×C₇₁	C₂²	1	2	yes	—
23	#559×C₇₁	C₂²	1	2	yes	—
24	#557×C₇₁	C₂²	1	2	yes	—
25	#557×C₇₁	C₂²	1	2	yes	—
26	#557×C₇₁	C₂²	1	2	yes	—
27	#556×C₇₁	—	2	1	no	—
28	#556×C₇₁	C₂²	1	2	yes	—
29	#556×C₇₁	C₂²	1	4	yes	—
30	#556×C₇₁	C₂²	1	2	yes	—
31	#554×C₇₁	—	2	1	no	—
32	#552×C₇₁	—	2	2	no	—
33	#552×C₇₁	—	2	2	no	—
34	#552×C₇₁	—	2	2	no	—
35	#541×C₇₁	—	2	2	no	—
36	#539×C₇₁	—	2	2	no	—
37	#536×C₇₁	C₂²	1	2	yes	—
38	#536×C₇₁	C₂²	1	2	yes	—
39	#533×C₇₁	—	2	1	no	—
40	#533×C₇₁	—	2	1	no	—
41	#533×C₇₁	C₂²	1	1	yes	characteristic
42	#532×C₇₁	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
44	#529×C₇₁	—	2	2	no	—
45	#520×C₇₁	C₂²	1	2	yes	—
46	#519×C₇₁	C₂²	1	2	yes	—
47	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
49	#497×C₇₁	C₂²	1	4	yes	—
50	#497×C₇₁	C₂²	1	4	yes	—
51	#497×C₇₁	C₂²	1	4	yes	—
52	#495×C₇₁	C₂²	1	4	yes	—
53	#494×C₇₁	C₂²	1	2	yes	—
54	#494×C₇₁	C₂²	1	4	yes	—
55	#492×C₇₁	C₂²	1	2	yes	—
56	#464×C₇₁	C₂²	1	4	yes	—
57	#464×C₇₁	C₂²	1	4	yes	—
58	#464×C₇₁	C₂²	1	4	yes	—
59	#464×C₇₁	C₂²	1	2	yes	—
60	#463×C₇₁	C₂²	1	4	yes	—
61	#463×C₇₁	C₂²	1	2	yes	—
62	#462×C₇₁	C₂²	1	4	yes	—
63	#462×C₇₁	C₂²	1	4	yes	—
64	#462×C₇₁	C₂²	1	4	yes	—
65	#462×C₇₁	C₂²	1	2	yes	—
66	#462×C₇₁	C₂²	1	1	yes	characteristic
67	#462×C₇₁	C₂²	1	2	yes	—
68	#462×C₇₁	C₂²	1	4	yes	—
69	#461×C₇₁	C₂²	1	4	yes	—
70	#461×C₇₁	C₂²	1	1	yes	characteristic
71	#460×C₇₁	C₂²	1	1	yes	characteristic
72	#459×C₇₁	C₂²	1	1	yes	characteristic
73	#446×C₇₁	C₂²	1	2	yes	—
74	#446×C₇₁	C₂²	1	4	yes	—
75	C₈×Q₈×C₇₁	C₂²	1	2	yes	—
76	#441×C₇₁	C₂²	1	2	yes	—
77	#441×C₇₁	C₂²	1	4	yes	—
78	#440×C₇₁	C₂²	1	4	yes	—
79	#440×C₇₁	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	—
81	C₄×Q₁₆×C₇₁	C₂²	1	4	yes	—
82	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
83	C₄×SD₁₆×C₇₁	C₂²	1	4	yes	—
84	#428×C₇₁	C₂²	1	1	yes	characteristic
85	#424×C₇₁	C₂²	1	2	yes	—
86	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
87	#419×C₇₁	C₂²	1	1	yes	characteristic
88	#417×C₇₁	C₂²	1	1	yes	characteristic
89	#416×C₇₁	C₂²	1	2	yes	—
90	C₂×#103×C₇₁	C₂²	1	2	yes	—
91	#405×C₇₁	C₂²	1	2	yes	—
92	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₇₁	C₂³	1	2	yes	—
94	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
96	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
97	#137×C₇₁	—	2	8	no	—
98	#137×C₇₁	—	2	4	no	—
99	#137×C₇₁	—	4	4	no	—
100	#135×C₇₁	—	4	4	no	—
101	C₂×Q₁₆×C₇₁	—	4	4	no	—
102	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
107	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
113	C₂×D₈×C₇₁	C₂³	1	2	yes	—
114	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₇₁	—	2	1	no	—
118	C₄⋊Q₈×C₇₁	—	2	1	no	—
119	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
120	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
121	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
123	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
125	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
126	#127×C₇₁	C₂³	1	1	yes	characteristic
127	#126×C₇₁	—	2	4	no	—
128	#126×C₇₁	—	2	4	no	—
129	#126×C₇₁	—	2	4	no	—
130	#126×C₇₁	—	2	4	no	—
131	#125×C₇₁	—	2	2	no	—
132	#125×C₇₁	—	2	2	no	—
133	#125×C₇₁	—	2	2	no	—
134	#125×C₇₁	—	2	4	no	—
135	#125×C₇₁	—	2	4	no	—
136	#125×C₇₁	—	2	4	no	—
137	#125×C₇₁	D₄	1	2	yes	—
138	#124×C₇₁	—	2	2	no	—
139	#124×C₇₁	C₂³	1	4	yes	—
140	#124×C₇₁	C₂³	1	2	yes	—
141	#124×C₇₁	C₂³	1	4	yes	—
142	#123×C₇₁	—	2	4	no	—
143	#123×C₇₁	—	2	4	no	—
144	#123×C₇₁	—	2	4	no	—
145	C₂²⋊Q₈×C₇₁	—	2	2	no	—
146	C₂²⋊Q₈×C₇₁	—	2	2	no	—
147	C₂²⋊Q₈×C₇₁	—	2	4	no	—
148	C₂²⋊Q₈×C₇₁	—	2	2	no	—
149	C₂²⋊Q₈×C₇₁	—	2	2	no	—
150	C₂²⋊Q₈×C₇₁	—	2	2	no	—
151	C₂²⋊Q₈×C₇₁	—	2	2	no	—
152	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
153	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
154	#121×C₇₁	—	2	1	no	—
155	#121×C₇₁	—	2	1	no	—
156	C₄×Q₈×C₇₁	—	2	2	no	—
157	C₄×Q₈×C₇₁	—	2	2	no	—
158	C₄×Q₈×C₇₁	—	2	2	no	—
159	C₄×Q₈×C₇₁	—	2	2	no	—
160	C₄×Q₈×C₇₁	—	2	2	no	—
161	C₄×Q₈×C₇₁	—	2	1	no	—
162	C₄×Q₈×C₇₁	—	2	1	no	—
163	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
165	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
167	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
168	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
171	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
172	C₄×D₄×C₇₁	—	2	1	no	—
173	C₄×D₄×C₇₁	—	2	1	no	—
174	C₄×D₄×C₇₁	—	2	2	no	—
175	C₄×D₄×C₇₁	—	2	4	no	—
176	C₄×D₄×C₇₁	—	2	1	no	—
177	C₄×D₄×C₇₁	—	2	1	no	—
178	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₇₁	C₂³	1	4	yes	—
180	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
181	#117×C₇₁	—	2	2	no	—
182	#117×C₇₁	—	2	4	no	—
183	#117×C₇₁	—	2	2	no	—
184	#117×C₇₁	—	2	2	no	—
185	#117×C₇₁	—	2	4	no	—
186	#117×C₇₁	—	2	1	no	—
187	#117×C₇₁	C₂³	1	1	yes	characteristic
188	#117×C₇₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
190	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
193	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇₁	—	2	1	no	—
195	C₂×C₄²×C₇₁	—	2	1	no	—
196	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
197	#107×C₇₁	C₂³	1	2	yes	—
198	#106×C₇₁	C₂³	1	2	yes	—
199	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
200	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
201	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
202	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
203	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
204	#103×C₇₁	C₂³	1	4	yes	—
205	#103×C₇₁	C₂³	1	4	yes	—
206	#103×C₇₁	C₂³	1	2	yes	—
207	#103×C₇₁	C₂³	1	2	yes	—
208	#103×C₇₁	C₂³	1	2	yes	—
209	#103×C₇₁	C₂³	1	2	yes	—
210	#103×C₇₁	C₂³	1	2	yes	—
211	#102×C₇₁	C₂³	1	2	yes	—
212	#102×C₇₁	C₂³	1	2	yes	—
213	#102×C₇₁	C₂³	1	2	yes	—
214	#97×C₇₁	C₂³	1	4	yes	—
215	#97×C₇₁	C₂³	1	2	yes	—
216	C₄×C₈×C₇₁	C₂³	1	4	yes	—
217	C₄×C₈×C₇₁	C₂³	1	2	yes	—
218	#41×C₇₁	—	2	4	no	—
219	#41×C₇₁	—	2	2	no	—
220	#41×C₇₁	—	2	2	no	—
221	#41×C₇₁	—	2	4	no	—
222	C₂×Q₈×C₇₁	—	2	1	no	—
223	C₂×Q₈×C₇₁	—	2	2	no	—
224	C₂×Q₈×C₇₁	—	2	4	no	—
225	C₂×Q₈×C₇₁	—	2	2	no	—
226	C₂×Q₈×C₇₁	—	2	2	no	—
227	C₂×Q₈×C₇₁	—	2	4	no	—
228	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₇₁	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
234	C₂×D₄×C₇₁	—	2	2	no	—
235	C₂×D₄×C₇₁	—	2	1	no	—
236	C₂×D₄×C₇₁	—	2	1	no	—
237	C₂×D₄×C₇₁	—	2	1	no	—
238	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
239	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₇₁	—	2	1	no	—
241	C₂²×C₄×C₇₁	—	2	2	no	—
242	C₂²×C₄×C₇₁	—	2	1	no	—
243	C₂²×C₄×C₇₁	—	2	1	no	—
244	C₂²×C₄×C₇₁	—	2	1	no	—
245	C₂²×C₄×C₇₁	—	2	1	no	—
246	C₂²×C₄×C₇₁	—	2	2	no	—
247	C₂²×C₄×C₇₁	—	2	4	no	—
248	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
251	Q₁₆×C₇₁	—	2	4	no	—
252	Q₁₆×C₇₁	—	2	8	no	—
253	Q₁₆×C₇₁	—	4	4	no	—
254	Q₁₆×C₇₁	—	4	4	no	—
255	Q₁₆×C₇₁	—	4	2	no	—
256	Q₁₆×C₇₁	—	4	4	no	—
257	SD₁₆×C₇₁	—	2	8	no	—
258	SD₁₆×C₇₁	—	2	4	no	—
259	SD₁₆×C₇₁	—	4	2	no	—
260	SD₁₆×C₇₁	—	4	2	no	—
261	SD₁₆×C₇₁	—	4	4	no	—
262	D₈×C₇₁	—	4	2	no	—
263	M₁₆×C₇₁	—	2	2	no	—
264	M₁₆×C₇₁	#41	1	4	yes	—
265	C₂×C₈×C₇₁	—	2	4	no	—
266	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
267	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
268	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
269	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₇₁	—	2	1	no	—
271	C₄⋊C₄×C₇₁	—	2	2	no	—
272	C₄⋊C₄×C₇₁	—	2	2	no	—
273	C₄⋊C₄×C₇₁	—	2	4	no	—
274	C₄⋊C₄×C₇₁	—	2	2	no	—
275	C₄⋊C₄×C₇₁	—	2	2	no	—
276	C₄⋊C₄×C₇₁	—	2	2	no	—
277	C₄⋊C₄×C₇₁	—	2	2	no	—
278	C₄⋊C₄×C₇₁	—	2	1	no	—
279	C₄⋊C₄×C₇₁	—	2	1	no	—
280	C₄⋊C₄×C₇₁	—	2	4	no	—
281	C₄⋊C₄×C₇₁	—	2	4	no	—
282	C₄⋊C₄×C₇₁	—	2	4	no	—
283	C₄⋊C₄×C₇₁	—	2	1	no	—
284	C₄⋊C₄×C₇₁	—	2	1	no	—
285	C₄⋊C₄×C₇₁	—	2	4	no	—
286	C₄⋊C₄×C₇₁	—	2	4	no	—
287	C₄⋊C₄×C₇₁	—	2	4	no	—
288	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
290	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
291	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
292	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
294	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
297	C₂²⋊C₄×C₇₁	—	2	1	no	—
298	C₂²⋊C₄×C₇₁	—	2	2	no	—
299	C₂²⋊C₄×C₇₁	—	2	4	no	—
300	C₂²⋊C₄×C₇₁	—	2	1	no	—
301	C₂²⋊C₄×C₇₁	—	2	1	no	—
302	C₂²⋊C₄×C₇₁	—	2	4	no	—
303	C₂²⋊C₄×C₇₁	—	2	4	no	—
304	C₂²⋊C₄×C₇₁	—	2	4	no	—
305	C₂²⋊C₄×C₇₁	—	2	2	no	—
306	C₂²⋊C₄×C₇₁	—	2	4	no	—
307	C₂²⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
308	C₄²×C₇₁	—	2	2	no	—
309	C₄²×C₇₁	—	2	1	no	—
310	C₄²×C₇₁	—	2	2	no	—
311	C₄²×C₇₁	—	2	1	no	—
312	C₄²×C₇₁	—	2	1	no	—
313	C₄²×C₇₁	—	2	4	no	—
314	C₄²×C₇₁	—	2	4	no	—
315	C₄²×C₇₁	—	2	4	no	—
316	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
319	C₄²×C₇₁	C₂⁴	1	4	yes	—
320	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
321	C₂³×C₇₁	—	2	1	no	—
322	C₂³×C₇₁	—	2	2	no	—
323	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₇₁	—	2	4	no	—
325	Q₈×C₇₁	—	2	2	no	—
326	Q₈×C₇₁	—	2	4	no	—
327	Q₈×C₇₁	—	2	2	no	—
328	Q₈×C₇₁	—	2	1	no	—
329	Q₈×C₇₁	—	2	1	no	—
330	Q₈×C₇₁	—	2	4	no	—
331	Q₈×C₇₁	—	2	2	no	—
332	Q₈×C₇₁	—	2	2	no	—
333	Q₈×C₇₁	—	4	2	no	—
334	Q₈×C₇₁	—	4	2	no	—
335	Q₈×C₇₁	—	4	4	no	—
336	D₄×C₇₁	—	2	1	no	—
337	D₄×C₇₁	—	2	2	no	—
338	D₄×C₇₁	—	2	1	no	—
339	D₄×C₇₁	—	2	2	no	—
340	D₄×C₇₁	—	4	4	no	—
341	D₄×C₇₁	—	4	2	no	—
342	D₄×C₇₁	—	4	2	no	—
343	D₄×C₇₁	—	8	1	no	—
344	C₂×C₄×C₇₁	—	2	2	no	—
345	C₂×C₄×C₇₁	—	2	1	no	—
346	C₂×C₄×C₇₁	—	2	1	no	—
347	C₂×C₄×C₇₁	—	2	2	no	—
348	C₂×C₄×C₇₁	—	2	2	no	—
349	C₂×C₄×C₇₁	—	2	2	no	—
350	C₂×C₄×C₇₁	—	2	4	no	—
351	C₂×C₄×C₇₁	—	2	1	no	—
352	C₂×C₄×C₇₁	—	4	1	no	—
353	C₂×C₄×C₇₁	—	4	2	no	—
354	C₂×C₄×C₇₁	—	4	2	no	—
355	C₂×C₄×C₇₁	—	4	4	no	—
356	C₂×C₄×C₇₁	—	4	2	no	—
357	C₂×C₄×C₇₁	—	4	4	no	—
358	C₂×C₄×C₇₁	—	4	2	no	—
359	C₂×C₄×C₇₁	—	8	4	no	—
360	C₂×C₄×C₇₁	—	8	1	no	—
361	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
365	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
369	C₂×C₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
370	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
371	C₈×C₇₁	—	2	2	no	—
372	C₈×C₇₁	—	2	2	no	—
373	C₈×C₇₁	—	2	2	no	—
374	C₈×C₇₁	C₂×#41	1	4	yes	—
375	C₂²×C₇₁	—	2	1	no	—
376	C₂²×C₇₁	—	2	1	no	—
377	C₂²×C₇₁	—	4	1	no	—
378	C₂²×C₇₁	—	4	2	no	—
379	C₂²×C₇₁	—	4	1	no	—
380	C₂²×C₇₁	—	4	2	no	—
381	C₂²×C₇₁	—	4	1	no	—
382	C₂²×C₇₁	—	4	2	no	—
383	C₂²×C₇₁	#550	1	2	yes	—
384	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₇₁	—	2	1	no	—
386	C₄×C₇₁	—	2	1	no	—
387	C₄×C₇₁	—	2	4	no	—
388	C₄×C₇₁	—	2	1	no	—
389	C₄×C₇₁	—	2	4	no	—
390	C₄×C₇₁	—	4	1	no	—
391	C₄×C₇₁	—	4	2	no	—
392	C₄×C₇₁	—	4	2	no	—
393	C₄×C₇₁	—	4	1	no	—
394	C₄×C₇₁	—	4	2	no	—
395	C₄×C₇₁	—	4	4	no	—
396	C₄×C₇₁	—	4	1	no	—
397	C₄×C₇₁	#550	1	2	yes	—
398	C₄×C₇₁	#578	1	2	yes	—
399	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
400	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	#61422	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂×C₇₁	—	2	2	no	—
403	C₂×C₇₁	—	8	1	no	—
404	C₂×C₇₁	—	8	2	no	—
405	C₂×C₇₁	C₂×#550	1	1	yes	characteristic
406	C₂×C₇₁	C₂×#578	1	1	yes	characteristic
407	C₂×C₇₁	#3586	1	1	yes	characteristic
408	#3509	C₂×C₇₁	1	1	yes	characteristic, complemented
409	#3507	C₂×C₇₁	1	1	yes	characteristic, complemented
410	#3402	C₂×C₇₁	1	4	yes	complemented
411	#3400	C₂×C₇₁	1	2	yes	complemented
412	#3398	C₂×C₇₁	1	2	yes	complemented
413	#3398	C₂×C₇₁	1	4	yes	complemented
414	#3395	C₂×C₇₁	1	2	yes	complemented
415	#3394	C₂×C₇₁	1	2	yes	complemented
416	#3156	C₂×C₇₁	1	2	yes	complemented
417	#3152	C₂×C₇₁	1	1	yes	characteristic, complemented
418	#3046	C₂×C₇₁	1	2	yes	complemented
419	#3044	C₂×C₇₁	1	2	yes	complemented
420	#3035	C₂×C₇₁	1	1	yes	characteristic
421	C₂×#462	C₂×C₇₁	1	1	yes	characteristic, complemented
422	#2962	C₂×C₇₁	1	1	yes	characteristic, complemented
423	#2947	C₂×C₇₁	1	2	yes	complemented
424	C₄×#137	C₂×C₇₁	1	1	yes	characteristic, complemented
425	C₇₁	#61422	1	1	yes	characteristic, direct product factor, Sylow
426	C₂×#137	C₂²×C₇₁	1	2	yes	—
427	C₂×#137	C₂²×C₇₁	1	1	yes	characteristic
428	C₂×#137	C₂²×C₇₁	1	2	yes	—
429	C₂×#135	C₂²×C₇₁	1	2	yes	—
430	C₂²×Q₁₆	C₂²×C₇₁	1	2	yes	—
431	#559	C₂²×C₇₁	1	2	yes	—
432	#557	C₂²×C₇₁	1	2	yes	—
433	#557	C₂²×C₇₁	1	2	yes	—
434	#557	C₂²×C₇₁	1	2	yes	—
435	#556	—	2	1	no	—
436	#556	C₂²×C₇₁	1	2	yes	—
437	#556	C₂²×C₇₁	1	4	yes	—
438	#556	C₂²×C₇₁	1	2	yes	—
439	#554	—	2	1	no	—
440	#552	—	2	2	no	—
441	#552	—	2	2	no	—
442	#552	—	2	2	no	—
443	#541	—	2	2	no	—
444	#539	—	2	2	no	—
445	#536	C₂²×C₇₁	1	2	yes	—
446	#536	C₂²×C₇₁	1	2	yes	—
447	#533	—	2	1	no	—
448	#533	—	2	1	no	—
449	#533	C₂²×C₇₁	1	1	yes	characteristic
450	#532	C₂²×C₇₁	1	1	yes	characteristic
451	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
452	#529	—	2	2	no	—
453	#520	C₂²×C₇₁	1	2	yes	—
454	#519	C₂²×C₇₁	1	2	yes	—
455	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
457	#497	C₂²×C₇₁	1	4	yes	—
458	#497	C₂²×C₇₁	1	4	yes	—
459	#497	C₂²×C₇₁	1	4	yes	—
460	#495	C₂²×C₇₁	1	4	yes	—
461	#494	C₂²×C₇₁	1	2	yes	—
462	#494	C₂²×C₇₁	1	4	yes	—
463	#492	C₂²×C₇₁	1	2	yes	—
464	#464	C₂²×C₇₁	1	4	yes	—
465	#464	C₂²×C₇₁	1	2	yes	—
466	#464	C₂²×C₇₁	1	4	yes	—
467	#464	C₂²×C₇₁	1	4	yes	—
468	#463	C₂²×C₇₁	1	4	yes	—
469	#463	C₂²×C₇₁	1	2	yes	—
470	#462	C₂²×C₇₁	1	2	yes	—
471	#462	C₂²×C₇₁	1	1	yes	characteristic
472	#462	C₂²×C₇₁	1	4	yes	—
473	#462	C₂²×C₇₁	1	4	yes	—
474	#462	C₂²×C₇₁	1	4	yes	—
475	#462	C₂²×C₇₁	1	2	yes	—
476	#462	C₂²×C₇₁	1	4	yes	—
477	#461	C₂²×C₇₁	1	1	yes	characteristic
478	#461	C₂²×C₇₁	1	4	yes	—
479	#460	C₂²×C₇₁	1	1	yes	characteristic
480	#459	C₂²×C₇₁	1	1	yes	characteristic
481	#446	C₂²×C₇₁	1	2	yes	—
482	#446	C₂²×C₇₁	1	4	yes	—
483	C₈×Q₈	C₂²×C₇₁	1	2	yes	—
484	#441	C₂²×C₇₁	1	2	yes	—
485	#441	C₂²×C₇₁	1	4	yes	—
486	#440	C₂²×C₇₁	1	4	yes	—
487	#440	C₂²×C₇₁	1	2	yes	—
488	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	—
489	C₄×Q₁₆	C₂²×C₇₁	1	4	yes	—
490	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
491	C₄×SD₁₆	C₂²×C₇₁	1	4	yes	—
492	#428	C₂²×C₇₁	1	1	yes	characteristic
493	#424	C₂²×C₇₁	1	2	yes	—
494	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
495	#419	C₂²×C₇₁	1	1	yes	characteristic
496	#417	C₂²×C₇₁	1	1	yes	characteristic
497	#416	C₂²×C₇₁	1	2	yes	—
498	C₂×#103	C₂²×C₇₁	1	2	yes	—
499	#405	C₂²×C₇₁	1	2	yes	—
500	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
501	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
502	C₂×#41	C₂³×C₇₁	1	2	yes	—
503	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
504	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
505	#137	—	2	8	no	—
506	#137	—	2	4	no	—
507	#137	—	4	4	no	—
508	#135	—	4	4	no	—
509	C₂×Q₁₆	—	4	4	no	—
510	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
511	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
512	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
513	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
514	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
515	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
517	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
518	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
519	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
520	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
521	C₂×D₈	C₂³×C₇₁	1	2	yes	—
522	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
523	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
528	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
533	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
534	#127	C₂³×C₇₁	1	1	yes	characteristic
535	#126	—	2	4	no	—
536	#126	—	2	4	no	—
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	4	no	—
543	#125	—	2	4	no	—
544	#125	—	2	4	no	—
545	#125	D₄×C₇₁	1	2	yes	—
546	#124	—	2	2	no	—
547	#124	C₂³×C₇₁	1	2	yes	—
548	#124	C₂³×C₇₁	1	4	yes	—
549	#124	C₂³×C₇₁	1	4	yes	—
550	#123	—	2	4	no	—
551	#123	—	2	4	no	—
552	#123	—	2	4	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	4	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
561	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
572	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
573	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
574	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
576	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
577	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
578	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
579	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	4	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
587	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
588	C₄×D₄	C₂³×C₇₁	1	4	yes	—
589	#117	—	2	2	no	—
590	#117	—	2	4	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	—	2	4	no	—
594	#117	—	2	1	no	—
595	#117	C₂³×C₇₁	1	1	yes	characteristic
596	#117	C₂³×C₇₁	1	2	yes	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
602	C₂×C₄²	—	2	1	no	—
603	C₂×C₄²	—	2	1	no	—
604	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
605	#107	C₂³×C₇₁	1	2	yes	—
606	#106	C₂³×C₇₁	1	2	yes	—
607	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
608	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
609	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
610	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
611	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
612	#103	C₂³×C₇₁	1	4	yes	—
613	#103	C₂³×C₇₁	1	4	yes	—
614	#103	C₂³×C₇₁	1	2	yes	—
615	#103	C₂³×C₇₁	1	2	yes	—
616	#103	C₂³×C₇₁	1	2	yes	—
617	#103	C₂³×C₇₁	1	2	yes	—
618	#103	C₂³×C₇₁	1	2	yes	—
619	#102	C₂³×C₇₁	1	2	yes	—
620	#102	C₂³×C₇₁	1	2	yes	—
621	#102	C₂³×C₇₁	1	2	yes	—
622	#97	C₂³×C₇₁	1	2	yes	—
623	#97	C₂³×C₇₁	1	4	yes	—
624	C₄×C₈	C₂³×C₇₁	1	2	yes	—
625	C₄×C₈	C₂³×C₇₁	1	4	yes	—
626	#41	—	2	2	no	—
627	#41	—	2	4	no	—
628	#41	—	2	2	no	—
629	#41	—	2	4	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	2	4	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	4	no	—
636	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
637	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
638	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
639	C₂×Q₈	C₂⁴×C₇₁	1	4	yes	—
640	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
641	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
647	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
659	Q₁₆	—	2	4	no	—
660	Q₁₆	—	2	8	no	—
661	Q₁₆	—	4	4	no	—
662	Q₁₆	—	4	4	no	—
663	Q₁₆	—	4	2	no	—
664	Q₁₆	—	4	4	no	—
665	SD₁₆	—	2	8	no	—
666	SD₁₆	—	2	4	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	4	no	—
670	D₈	—	4	2	no	—
671	M₁₆	—	2	2	no	—
672	M₁₆	#41×C₇₁	1	4	yes	—
673	C₂×C₈	—	2	4	no	—
674	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
675	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
676	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
677	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
697	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
699	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
700	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
702	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
703	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
704	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
726	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
727	C₄²	C₂⁴×C₇₁	1	4	yes	—
728	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
732	Q₈	—	2	4	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	2	4	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	2	4	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	4	2	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	4	no	—
744	D₄	—	2	1	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	2	no	—
751	D₄	—	8	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
771	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
773	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
776	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
777	C₂×C₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
778	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₈	C₂×#41×C₇₁	1	4	yes	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	2	no	—
791	C₂²	#550×C₇₁	1	2	yes	—
792	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
793	C₄	—	2	1	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	4	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	4	no	—
805	C₄	#550×C₇₁	1	2	yes	—
806	C₄	#578×C₇₁	1	2	yes	—
807	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
808	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
809	C₂	—	2	2	no	—
810	C₂	—	8	1	no	—
811	C₂	—	8	2	no	—
812	C₂	C₂×#550×C₇₁	1	1	yes	characteristic
813	C₂	C₂×#578×C₇₁	1	1	yes	characteristic
814	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×#3035	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×#3509	C₂	semidirect
2. C₇₁×#3507	C₂	semidirect
3. C₇₁×#3402	C₂	semidirect
4. C₇₁×#3400	C₂	semidirect
5. C₇₁×#3398	C₂	semidirect
6. C₇₁×#3398	C₂	semidirect
7. C₇₁×#3395	C₂	semidirect
8. C₇₁×#3394	C₂	semidirect
9. C₇₁×#3156	C₂	semidirect
10. C₇₁×#3152	C₂	semidirect
11. C₇₁×#3046	C₂	semidirect
12. C₇₁×#3044	C₂	semidirect
14. C₂×#462×C₇₁	C₂	semidirect
15. C₇₁×#2962	C₂	semidirect
16. C₇₁×#2947	C₂	semidirect
17. C₄×#137×C₇₁	C₂	semidirect
401. #61422	C₇₁	direct (N × H)
408. #3509	C₂×C₇₁	semidirect
409. #3507	C₂×C₇₁	semidirect
410. #3402	C₂×C₇₁	semidirect
411. #3400	C₂×C₇₁	semidirect
412. #3398	C₂×C₇₁	semidirect
413. #3398	C₂×C₇₁	semidirect
414. #3395	C₂×C₇₁	semidirect
415. #3394	C₂×C₇₁	semidirect
416. #3156	C₂×C₇₁	semidirect
417. #3152	C₂×C₇₁	semidirect
418. #3046	C₂×C₇₁	semidirect
419. #3044	C₂×C₇₁	semidirect
421. C₂×#462	C₂×C₇₁	semidirect
422. #2962	C₂×C₇₁	semidirect
423. #2947	C₂×C₇₁	semidirect
424. C₄×#137	C₂×C₇₁	semidirect
425. C₇₁	#61422	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×#3509	2
C₇₁×#3507	2
C₇₁×#3402	2
C₇₁×#3400	2
C₇₁×#3398	2
C₇₁×#3395	2
C₇₁×#3394	2
C₇₁×#3156	2
C₇₁×#3152	2
C₇₁×#3046	2
C₇₁×#3044	2
C₇₁×#3035	2
C₂×#462×C₇₁	2
C₇₁×#2962	2
C₇₁×#2947	2
C₄×#137×C₇₁	2
#61422	71

Subgroups — C71×#61422 #31882294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61422 #31882294