Subgroups — C₇₁×#61546 #31882418

Order 18176.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3345	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3332	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3326	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3271	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#3179	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3125	C₂	1	2	yes	maximal, complemented
18	C₇₁×#3119	C₂	1	2	yes	maximal, complemented
19	C₇₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#2952	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₇₁	C₂²	1	1	yes	characteristic
25	C₂×#135×C₇₁	C₂²	1	2	yes	—
26	#559×C₇₁	—	2	1	no	—
27	#559×C₇₁	C₂²	1	1	yes	characteristic
28	Q₈²×C₇₁	C₂²	1	1	yes	characteristic
29	#557×C₇₁	C₂²	1	1	yes	characteristic
30	#554×C₇₁	—	2	1	no	—
31	#554×C₇₁	C₂²	1	1	yes	characteristic
32	#553×C₇₁	—	2	2	no	—
33	#553×C₇₁	C₂²	1	2	yes	—
34	#550×C₇₁	—	2	1	no	—
35	#550×C₇₁	C₂²	1	2	yes	—
36	#550×C₇₁	C₂²	1	1	yes	characteristic
37	#550×C₇₁	C₂²	1	1	yes	characteristic
38	#550×C₇₁	C₂²	1	1	yes	characteristic
39	#548×C₇₁	C₂²	1	2	yes	—
40	#547×C₇₁	—	2	2	no	—
41	#547×C₇₁	—	2	1	no	—
42	#547×C₇₁	C₂²	1	1	yes	characteristic
43	#547×C₇₁	C₂²	1	2	yes	—
44	#542×C₇₁	—	2	2	no	—
45	#542×C₇₁	C₂²	1	2	yes	—
46	#540×C₇₁	—	2	2	no	—
47	#540×C₇₁	C₂²	1	2	yes	—
48	#532×C₇₁	—	2	1	no	—
49	#532×C₇₁	—	2	1	no	—
50	#532×C₇₁	C₂²	1	1	yes	characteristic
51	#532×C₇₁	C₂²	1	1	yes	characteristic
52	#529×C₇₁	—	2	1	no	—
53	#529×C₇₁	—	2	1	no	—
54	#529×C₇₁	C₂²	1	1	yes	characteristic
55	#520×C₇₁	C₂²	1	2	yes	—
56	#520×C₇₁	C₂²	1	2	yes	—
57	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
59	#501×C₇₁	C₂²	1	2	yes	—
60	#498×C₇₁	C₂²	1	1	yes	characteristic
61	#496×C₇₁	C₂²	1	2	yes	—
62	#493×C₇₁	C₂²	1	1	yes	characteristic
63	#488×C₇₁	C₂²	1	2	yes	—
64	#486×C₇₁	C₂²	1	2	yes	—
65	#486×C₇₁	C₂²	1	1	yes	characteristic
66	#486×C₇₁	C₂²	1	1	yes	characteristic
67	#483×C₇₁	C₂²	1	2	yes	—
68	#482×C₇₁	C₂²	1	2	yes	—
69	#481×C₇₁	C₂²	1	2	yes	—
70	#481×C₇₁	C₂²	1	2	yes	—
71	#481×C₇₁	C₂²	1	2	yes	—
72	#480×C₇₁	C₂²	1	2	yes	—
73	#479×C₇₁	C₂²	1	2	yes	—
74	#478×C₇₁	C₂²	1	2	yes	—
75	#477×C₇₁	C₂²	1	1	yes	characteristic
76	#476×C₇₁	C₂²	1	1	yes	characteristic
77	#476×C₇₁	C₂²	1	2	yes	—
78	#475×C₇₁	C₂²	1	1	yes	characteristic
79	#475×C₇₁	C₂²	1	2	yes	—
80	#475×C₇₁	C₂²	1	1	yes	characteristic
81	#469×C₇₁	C₂²	1	2	yes	—
82	#469×C₇₁	C₂²	1	2	yes	—
83	#469×C₇₁	C₂²	1	2	yes	—
84	#468×C₇₁	C₂²	1	2	yes	—
85	#466×C₇₁	C₂²	1	2	yes	—
86	#465×C₇₁	C₂²	1	2	yes	—
87	#464×C₇₁	C₂²	1	2	yes	—
88	#463×C₇₁	C₂²	1	2	yes	—
89	#460×C₇₁	C₂²	1	1	yes	characteristic
90	#460×C₇₁	C₂²	1	1	yes	characteristic
91	#460×C₇₁	C₂²	1	1	yes	characteristic
92	#460×C₇₁	C₂²	1	2	yes	—
93	#459×C₇₁	C₂²	1	1	yes	characteristic
94	#459×C₇₁	C₂²	1	2	yes	—
95	#452×C₇₁	C₂²	1	2	yes	—
96	#449×C₇₁	C₂²	1	2	yes	—
97	#449×C₇₁	C₂²	1	2	yes	—
98	#449×C₇₁	C₂²	1	2	yes	—
99	#449×C₇₁	C₂²	1	2	yes	—
100	#448×C₇₁	C₂²	1	2	yes	—
101	#446×C₇₁	C₂²	1	1	yes	characteristic
102	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic
103	#442×C₇₁	C₂²	1	2	yes	—
104	#442×C₇₁	C₂²	1	2	yes	—
105	#442×C₇₁	C₂²	1	2	yes	—
106	#441×C₇₁	C₂²	1	1	yes	characteristic
107	#441×C₇₁	C₂²	1	2	yes	—
108	#441×C₇₁	C₂²	1	1	yes	characteristic
109	#440×C₇₁	C₂²	1	1	yes	characteristic
110	#440×C₇₁	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
112	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
120	C₄×D₈×C₇₁	C₂²	1	2	yes	—
121	#436×C₇₁	C₂²	1	2	yes	—
122	#436×C₇₁	C₂²	1	1	yes	characteristic
123	#435×C₇₁	C₂²	1	2	yes	—
124	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
125	#433×C₇₁	C₂²	1	2	yes	—
126	#431×C₇₁	C₂²	1	1	yes	characteristic
127	#428×C₇₁	C₂²	1	1	yes	characteristic
128	C₂×#106×C₇₁	C₂²	1	2	yes	—
129	#419×C₇₁	C₂²	1	1	yes	characteristic
130	#417×C₇₁	C₂²	1	2	yes	—
131	#417×C₇₁	C₂²	1	1	yes	characteristic
132	#417×C₇₁	C₂²	1	2	yes	—
133	#405×C₇₁	C₂²	1	2	yes	—
134	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₇₁	—	2	1	no	—
136	C₂×#41×C₇₁	—	2	2	no	—
137	C₂×#41×C₇₁	—	2	1	no	—
138	C₂×#41×C₇₁	—	2	1	no	—
139	C₂×#41×C₇₁	—	2	1	no	—
140	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₇₁	C₂³	1	2	yes	—
142	C₂×#41×C₇₁	C₂³	1	2	yes	—
143	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
144	#137×C₇₁	—	2	4	no	—
145	#135×C₇₁	—	2	8	no	—
146	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
153	C₂×D₈×C₇₁	C₂³	1	2	yes	—
154	C₂×D₈×C₇₁	C₂³	1	2	yes	—
155	C₂×D₈×C₇₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₇₁	—	2	1	no	—
161	C₄⋊Q₈×C₇₁	—	2	1	no	—
162	C₄⋊Q₈×C₇₁	—	2	2	no	—
163	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
166	#127×C₇₁	—	2	1	no	—
167	#127×C₇₁	—	2	1	no	—
168	#127×C₇₁	—	2	2	no	—
169	#127×C₇₁	C₂³	1	1	yes	characteristic
170	#127×C₇₁	C₂³	1	2	yes	—
171	#127×C₇₁	C₂³	1	1	yes	characteristic
172	#126×C₇₁	—	2	2	no	—
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	D₄	1	2	yes	—
175	#125×C₇₁	—	2	1	no	—
176	#125×C₇₁	—	2	2	no	—
177	#125×C₇₁	D₄	1	1	yes	characteristic
178	#125×C₇₁	C₂³	1	2	yes	—
179	#124×C₇₁	—	2	1	no	—
180	#124×C₇₁	—	2	2	no	—
181	#124×C₇₁	—	2	2	no	—
182	#124×C₇₁	—	2	1	no	—
183	#124×C₇₁	—	2	1	no	—
184	#124×C₇₁	D₄	1	1	yes	characteristic
185	#124×C₇₁	C₂³	1	2	yes	—
186	#123×C₇₁	—	2	2	no	—
187	#123×C₇₁	—	2	2	no	—
188	#123×C₇₁	—	2	2	no	—
189	#123×C₇₁	—	2	2	no	—
190	#123×C₇₁	—	2	2	no	—
191	#123×C₇₁	—	2	2	no	—
192	#123×C₇₁	—	2	2	no	—
193	#123×C₇₁	—	2	2	no	—
194	#123×C₇₁	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₇₁	—	2	1	no	—
196	C₂²⋊Q₈×C₇₁	—	2	2	no	—
197	C₂²⋊Q₈×C₇₁	—	2	2	no	—
198	C₂²⋊Q₈×C₇₁	—	2	2	no	—
199	C₂²⋊Q₈×C₇₁	—	2	2	no	—
200	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
201	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
202	#121×C₇₁	—	2	2	no	—
203	#121×C₇₁	—	2	2	no	—
204	#121×C₇₁	—	2	1	no	—
205	#121×C₇₁	—	2	1	no	—
206	#121×C₇₁	—	2	1	no	—
207	#121×C₇₁	—	2	2	no	—
208	#121×C₇₁	—	2	2	no	—
209	#121×C₇₁	—	2	2	no	—
210	#121×C₇₁	—	2	2	no	—
211	#121×C₇₁	—	2	2	no	—
212	#121×C₇₁	—	2	2	no	—
213	#121×C₇₁	—	2	2	no	—
214	#121×C₇₁	D₄	1	1	yes	characteristic
215	#121×C₇₁	C₂³	1	2	yes	—
216	#121×C₇₁	C₂³	1	2	yes	—
217	#121×C₇₁	C₂³	1	2	yes	—
218	#121×C₇₁	C₂³	1	2	yes	—
219	#121×C₇₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₇₁	—	2	1	no	—
221	C₄×Q₈×C₇₁	—	2	1	no	—
222	C₄×Q₈×C₇₁	—	2	1	no	—
223	C₄×Q₈×C₇₁	—	2	1	no	—
224	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₇₁	—	2	1	no	—
234	C₄×D₄×C₇₁	—	2	1	no	—
235	C₄×D₄×C₇₁	—	2	1	no	—
236	C₄×D₄×C₇₁	—	2	1	no	—
237	C₄×D₄×C₇₁	—	2	2	no	—
238	C₄×D₄×C₇₁	—	2	1	no	—
239	C₄×D₄×C₇₁	—	2	1	no	—
240	C₄×D₄×C₇₁	—	2	2	no	—
241	C₄×D₄×C₇₁	—	2	2	no	—
242	C₄×D₄×C₇₁	—	2	2	no	—
243	C₄×D₄×C₇₁	—	2	2	no	—
244	C₄×D₄×C₇₁	—	2	2	no	—
245	C₄×D₄×C₇₁	—	2	2	no	—
246	C₄×D₄×C₇₁	—	2	1	no	—
247	C₄×D₄×C₇₁	—	2	1	no	—
248	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₇₁	C₂³	1	2	yes	—
250	C₄×D₄×C₇₁	C₂³	1	2	yes	—
251	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₇₁	C₂³	1	2	yes	—
253	C₄×D₄×C₇₁	C₂³	1	2	yes	—
254	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₇₁	C₂³	1	2	yes	—
256	#117×C₇₁	—	2	2	no	—
257	#117×C₇₁	—	2	2	no	—
258	#117×C₇₁	—	2	1	no	—
259	#117×C₇₁	C₂³	1	1	yes	characteristic
260	#117×C₇₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
263	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
264	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₇₁	—	2	1	no	—
268	C₂×C₄²×C₇₁	—	2	1	no	—
269	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
270	#107×C₇₁	C₂³	1	1	yes	characteristic
271	#107×C₇₁	C₂³	1	1	yes	characteristic
272	#107×C₇₁	C₂³	1	2	yes	—
273	#106×C₇₁	C₂³	1	1	yes	characteristic
274	#106×C₇₁	C₂³	1	2	yes	—
275	#106×C₇₁	C₂³	1	2	yes	—
276	#106×C₇₁	C₂³	1	2	yes	—
277	#106×C₇₁	C₂³	1	1	yes	characteristic
278	#106×C₇₁	C₂³	1	2	yes	—
279	#106×C₇₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
284	#103×C₇₁	C₂³	1	1	yes	characteristic
285	#103×C₇₁	C₂³	1	1	yes	characteristic
286	#103×C₇₁	C₂³	1	2	yes	—
287	#103×C₇₁	C₂³	1	2	yes	—
288	#103×C₇₁	C₂³	1	1	yes	characteristic
289	#103×C₇₁	C₂³	1	1	yes	characteristic
290	#103×C₇₁	C₂³	1	1	yes	characteristic
291	#103×C₇₁	C₂³	1	1	yes	characteristic
292	#103×C₇₁	C₂³	1	2	yes	—
293	#102×C₇₁	C₂³	1	1	yes	characteristic
294	#102×C₇₁	C₂³	1	1	yes	characteristic
295	#102×C₇₁	C₂³	1	2	yes	—
296	#102×C₇₁	C₂³	1	2	yes	—
297	#102×C₇₁	C₂³	1	2	yes	—
298	#102×C₇₁	C₂³	1	2	yes	—
299	#102×C₇₁	C₂³	1	2	yes	—
300	#102×C₇₁	C₂³	1	2	yes	—
301	#102×C₇₁	C₂³	1	2	yes	—
302	#102×C₇₁	C₂³	1	2	yes	—
303	#102×C₇₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
307	#97×C₇₁	C₂³	1	1	yes	characteristic
308	#97×C₇₁	C₂³	1	2	yes	—
309	#97×C₇₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₁	C₂³	1	2	yes	—
311	C₄×C₈×C₇₁	C₂³	1	2	yes	—
312	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
314	#41×C₇₁	—	2	4	no	—
315	#41×C₇₁	—	2	4	no	—
316	#41×C₇₁	—	2	2	no	—
317	#41×C₇₁	—	4	1	no	—
318	#41×C₇₁	—	4	2	no	—
319	#41×C₇₁	—	4	2	no	—
320	#41×C₇₁	—	8	2	no	—
321	#41×C₇₁	—	8	2	no	—
322	#41×C₇₁	—	8	2	no	—
323	#41×C₇₁	—	8	4	no	—
324	#41×C₇₁	—	8	2	no	—
325	C₂×Q₈×C₇₁	—	2	1	no	—
326	C₂×Q₈×C₇₁	—	2	1	no	—
327	C₂×Q₈×C₇₁	—	2	2	no	—
328	C₂×Q₈×C₇₁	—	2	1	no	—
329	C₂×Q₈×C₇₁	—	2	2	no	—
330	C₂×Q₈×C₇₁	—	4	1	no	—
331	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₇₁	—	2	2	no	—
336	C₂×D₄×C₇₁	—	2	2	no	—
337	C₂×D₄×C₇₁	—	2	1	no	—
338	C₂×D₄×C₇₁	—	2	2	no	—
339	C₂×D₄×C₇₁	—	2	2	no	—
340	C₂×D₄×C₇₁	—	2	2	no	—
341	C₂×D₄×C₇₁	—	2	2	no	—
342	C₂×D₄×C₇₁	—	2	2	no	—
343	C₂×D₄×C₇₁	—	2	1	no	—
344	C₂×D₄×C₇₁	—	2	1	no	—
345	C₂×D₄×C₇₁	—	2	1	no	—
346	C₂×D₄×C₇₁	—	2	2	no	—
347	C₂×D₄×C₇₁	—	2	2	no	—
348	C₂×D₄×C₇₁	—	2	1	no	—
349	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₇₁	—	2	1	no	—
355	C₂²×C₄×C₇₁	—	2	1	no	—
356	C₂²×C₄×C₇₁	—	2	2	no	—
357	C₂²×C₄×C₇₁	—	2	2	no	—
358	C₂²×C₄×C₇₁	—	2	1	no	—
359	C₂²×C₄×C₇₁	—	2	1	no	—
360	C₂²×C₄×C₇₁	—	2	2	no	—
361	C₂²×C₄×C₇₁	—	2	2	no	—
362	C₂²×C₄×C₇₁	—	2	1	no	—
363	C₂²×C₄×C₇₁	—	2	2	no	—
364	C₂²×C₄×C₇₁	—	2	2	no	—
365	C₂²×C₄×C₇₁	—	2	2	no	—
366	C₂²×C₄×C₇₁	—	2	2	no	—
367	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
371	Q₁₆×C₇₁	—	2	2	no	—
372	Q₁₆×C₇₁	#41	1	4	yes	complemented
373	SD₁₆×C₇₁	—	2	4	no	—
374	SD₁₆×C₇₁	—	2	4	no	—
375	SD₁₆×C₇₁	—	2	2	no	—
376	SD₁₆×C₇₁	—	2	2	no	—
377	SD₁₆×C₇₁	—	4	2	no	—
378	D₈×C₇₁	—	2	4	no	—
379	D₈×C₇₁	—	4	2	no	—
380	D₈×C₇₁	—	4	2	no	—
381	M₁₆×C₇₁	—	2	2	no	—
382	M₁₆×C₇₁	—	4	1	no	—
383	M₁₆×C₇₁	—	4	2	no	—
384	C₂×C₈×C₇₁	—	2	4	no	—
385	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₇₁	—	2	1	no	—
392	C₄⋊C₄×C₇₁	—	2	1	no	—
393	C₄⋊C₄×C₇₁	—	2	2	no	—
394	C₄⋊C₄×C₇₁	—	2	2	no	—
395	C₄⋊C₄×C₇₁	—	2	2	no	—
396	C₄⋊C₄×C₇₁	—	2	2	no	—
397	C₄⋊C₄×C₇₁	—	2	1	no	—
398	C₄⋊C₄×C₇₁	—	2	1	no	—
399	C₄⋊C₄×C₇₁	—	2	1	no	—
400	C₄⋊C₄×C₇₁	—	2	1	no	—
401	C₄⋊C₄×C₇₁	—	2	1	no	—
402	C₄⋊C₄×C₇₁	—	2	1	no	—
403	C₄⋊C₄×C₇₁	—	2	1	no	—
404	C₄⋊C₄×C₇₁	—	2	2	no	—
405	C₄⋊C₄×C₇₁	—	2	2	no	—
406	C₄⋊C₄×C₇₁	—	2	2	no	—
407	C₄⋊C₄×C₇₁	—	2	2	no	—
408	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₇₁	—	2	1	no	—
421	C₂²⋊C₄×C₇₁	—	2	2	no	—
422	C₂²⋊C₄×C₇₁	—	2	2	no	—
423	C₂²⋊C₄×C₇₁	—	2	1	no	—
424	C₂²⋊C₄×C₇₁	—	2	1	no	—
425	C₂²⋊C₄×C₇₁	—	2	2	no	—
426	C₂²⋊C₄×C₇₁	—	2	2	no	—
427	C₂²⋊C₄×C₇₁	—	2	2	no	—
428	C₂²⋊C₄×C₇₁	—	2	2	no	—
429	C₂²⋊C₄×C₇₁	—	2	2	no	—
430	C₂²⋊C₄×C₇₁	—	2	2	no	—
431	C₂²⋊C₄×C₇₁	—	2	2	no	—
432	C₂²⋊C₄×C₇₁	—	2	2	no	—
433	C₂²⋊C₄×C₇₁	—	2	2	no	—
434	C₂²⋊C₄×C₇₁	—	2	2	no	—
435	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
440	C₄²×C₇₁	—	2	1	no	—
441	C₄²×C₇₁	—	2	1	no	—
442	C₄²×C₇₁	—	2	1	no	—
443	C₄²×C₇₁	—	2	1	no	—
444	C₄²×C₇₁	—	2	1	no	—
445	C₄²×C₇₁	—	2	1	no	—
446	C₄²×C₇₁	—	2	1	no	—
447	C₄²×C₇₁	—	2	2	no	—
448	C₄²×C₇₁	—	2	2	no	—
449	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₇₁	C₂⁴	1	2	yes	—
454	C₂³×C₇₁	—	2	2	no	—
455	C₂³×C₇₁	—	2	1	no	—
456	C₂³×C₇₁	—	2	2	no	—
457	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
458	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₇₁	—	2	2	no	—
460	Q₈×C₇₁	—	2	1	no	—
461	Q₈×C₇₁	—	2	1	no	—
462	Q₈×C₇₁	—	2	1	no	—
463	Q₈×C₇₁	—	2	1	no	—
464	Q₈×C₇₁	—	4	2	no	—
465	Q₈×C₇₁	—	4	2	no	—
466	Q₈×C₇₁	—	8	1	no	—
467	Q₈×C₇₁	—	8	2	no	—
468	Q₈×C₇₁	C₂×#41	1	2	yes	—
469	Q₈×C₇₁	C₂×#41	1	2	yes	—
470	D₄×C₇₁	—	2	2	no	—
471	D₄×C₇₁	—	2	2	no	—
472	D₄×C₇₁	—	2	2	no	—
473	D₄×C₇₁	—	2	1	no	—
474	D₄×C₇₁	—	2	2	no	—
475	D₄×C₇₁	—	2	1	no	—
476	D₄×C₇₁	—	2	2	no	—
477	D₄×C₇₁	—	4	2	no	—
478	D₄×C₇₁	—	4	2	no	—
479	D₄×C₇₁	—	4	4	no	—
480	D₄×C₇₁	—	4	4	no	—
481	D₄×C₇₁	—	4	4	no	—
482	D₄×C₇₁	—	4	2	no	—
483	D₄×C₇₁	—	4	2	no	—
484	D₄×C₇₁	—	8	1	no	—
485	D₄×C₇₁	—	8	2	no	—
486	D₄×C₇₁	—	8	1	no	—
487	D₄×C₇₁	—	8	2	no	—
488	D₄×C₇₁	—	8	2	no	—
489	D₄×C₇₁	—	8	2	no	—
490	D₄×C₇₁	—	8	2	no	—
491	D₄×C₇₁	—	8	2	no	—
492	C₂×C₄×C₇₁	—	2	1	no	—
493	C₂×C₄×C₇₁	—	2	1	no	—
494	C₂×C₄×C₇₁	—	2	2	no	—
495	C₂×C₄×C₇₁	—	2	2	no	—
496	C₂×C₄×C₇₁	—	2	1	no	—
497	C₂×C₄×C₇₁	—	2	1	no	—
498	C₂×C₄×C₇₁	—	2	2	no	—
499	C₂×C₄×C₇₁	—	2	1	no	—
500	C₂×C₄×C₇₁	—	2	1	no	—
501	C₂×C₄×C₇₁	—	2	1	no	—
502	C₂×C₄×C₇₁	—	2	1	no	—
503	C₂×C₄×C₇₁	—	2	1	no	—
504	C₂×C₄×C₇₁	—	2	2	no	—
505	C₂×C₄×C₇₁	—	2	2	no	—
506	C₂×C₄×C₇₁	—	4	1	no	—
507	C₂×C₄×C₇₁	—	4	4	no	—
508	C₂×C₄×C₇₁	—	4	4	no	—
509	C₂×C₄×C₇₁	—	4	2	no	—
510	C₂×C₄×C₇₁	—	4	2	no	—
511	C₂×C₄×C₇₁	—	4	2	no	—
512	C₂×C₄×C₇₁	—	4	2	no	—
513	C₂×C₄×C₇₁	—	8	1	no	—
514	C₂×C₄×C₇₁	—	8	2	no	—
515	C₂×C₄×C₇₁	—	8	2	no	—
516	C₂×C₄×C₇₁	—	8	2	no	—
517	C₂×C₄×C₇₁	—	8	2	no	—
518	C₂×C₄×C₇₁	—	8	2	no	—
519	C₂×C₄×C₇₁	—	8	2	no	—
520	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
529	C₈×C₇₁	—	2	2	no	—
530	C₈×C₇₁	—	2	1	no	—
531	C₈×C₇₁	—	2	1	no	—
532	C₈×C₇₁	—	2	1	no	—
533	C₈×C₇₁	—	2	2	no	—
534	C₈×C₇₁	C₂×#41	1	2	yes	—
535	C₂²×C₇₁	—	2	1	no	—
536	C₂²×C₇₁	—	2	2	no	—
537	C₂²×C₇₁	—	2	1	no	—
538	C₂²×C₇₁	—	2	2	no	—
539	C₂²×C₇₁	—	2	1	no	—
540	C₂²×C₇₁	—	2	2	no	—
541	C₂²×C₇₁	—	4	2	no	—
542	C₂²×C₇₁	—	4	1	no	—
543	C₂²×C₇₁	—	4	2	no	—
544	C₂²×C₇₁	—	4	2	no	—
545	C₂²×C₇₁	—	4	2	no	—
546	C₂²×C₇₁	—	4	1	no	—
547	C₂²×C₇₁	—	4	1	no	—
548	C₂²×C₇₁	—	4	2	no	—
549	C₂²×C₇₁	—	4	2	no	—
550	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₇₁	—	2	1	no	—
552	C₄×C₇₁	—	2	1	no	—
553	C₄×C₇₁	—	2	2	no	—
554	C₄×C₇₁	—	2	2	no	—
555	C₄×C₇₁	—	2	1	no	—
556	C₄×C₇₁	—	2	2	no	—
557	C₄×C₇₁	—	2	2	no	—
558	C₄×C₇₁	—	2	1	no	—
559	C₄×C₇₁	—	2	2	no	—
560	C₄×C₇₁	—	4	1	no	—
561	C₄×C₇₁	—	4	1	no	—
562	C₄×C₇₁	—	4	2	no	—
563	C₄×C₇₁	—	4	1	no	—
564	C₄×C₇₁	—	4	1	no	—
565	C₄×C₇₁	—	4	1	no	—
566	C₄×C₇₁	—	4	2	no	—
567	C₄×C₇₁	#577	1	2	yes	—
568	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
569	C₄×C₇₁	#585	1	1	yes	characteristic
570	#61546	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
571	C₂×C₇₁	—	4	1	no	—
572	C₂×C₇₁	—	4	2	no	—
573	C₂×C₇₁	—	8	2	no	—
574	C₂×C₇₁	—	8	1	no	—
575	C₂×C₇₁	—	8	2	no	—
576	C₂×C₇₁	D₄×#41	1	1	yes	characteristic
577	C₂×C₇₁	C₂×#577	1	1	yes	characteristic
578	C₂×C₇₁	#3585	1	1	yes	characteristic
579	#3522	C₂×C₇₁	1	1	yes	characteristic, complemented
580	#3517	C₂×C₇₁	1	1	yes	characteristic, complemented
581	#3399	C₂×C₇₁	1	1	yes	characteristic, complemented
582	#3387	C₂×C₇₁	1	1	yes	characteristic, complemented
583	#3365	C₂×C₇₁	1	1	yes	characteristic, complemented
584	#3362	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3345	C₂×C₇₁	1	2	yes	complemented
586	#3335	C₂×C₇₁	1	1	yes	characteristic, complemented
587	#3333	C₂×C₇₁	1	1	yes	characteristic, complemented
588	#3332	C₂×C₇₁	1	1	yes	characteristic, complemented
589	#3332	C₂×C₇₁	1	2	yes	complemented
590	#3326	C₂×C₇₁	1	2	yes	complemented
591	#3287	C₂×C₇₁	1	1	yes	characteristic, complemented
592	#3271	C₂×C₇₁	1	2	yes	complemented
593	#3184	C₂×C₇₁	1	1	yes	characteristic, complemented
594	#3179	C₂×C₇₁	1	2	yes	complemented
595	#3125	C₂×C₇₁	1	2	yes	complemented
596	#3119	C₂×C₇₁	1	2	yes	complemented
597	#3106	C₂×C₇₁	1	1	yes	characteristic, complemented
598	#3103	C₂×C₇₁	1	1	yes	characteristic, complemented
599	#2969	C₂×C₇₁	1	1	yes	characteristic, complemented
600	#2952	C₂×C₇₁	1	2	yes	complemented
601	C₄×#137	C₂×C₇₁	1	1	yes	characteristic, complemented
602	C₇₁	#61546	1	1	yes	characteristic, direct product factor, Sylow
603	C₂×#137	C₂²×C₇₁	1	1	yes	characteristic
604	C₂×#135	C₂²×C₇₁	1	2	yes	—
605	#559	—	2	1	no	—
606	#559	C₂²×C₇₁	1	1	yes	characteristic
607	Q₈²	C₂²×C₇₁	1	1	yes	characteristic
608	#557	C₂²×C₇₁	1	1	yes	characteristic
609	#554	—	2	1	no	—
610	#554	C₂²×C₇₁	1	1	yes	characteristic
611	#553	—	2	2	no	—
612	#553	C₂²×C₇₁	1	2	yes	—
613	#550	—	2	1	no	—
614	#550	C₂²×C₇₁	1	2	yes	—
615	#550	C₂²×C₇₁	1	1	yes	characteristic
616	#550	C₂²×C₇₁	1	1	yes	characteristic
617	#550	C₂²×C₇₁	1	1	yes	characteristic
618	#548	C₂²×C₇₁	1	2	yes	—
619	#547	—	2	2	no	—
620	#547	—	2	1	no	—
621	#547	C₂²×C₇₁	1	1	yes	characteristic
622	#547	C₂²×C₇₁	1	2	yes	—
623	#542	—	2	2	no	—
624	#542	C₂²×C₇₁	1	2	yes	—
625	#540	—	2	2	no	—
626	#540	C₂²×C₇₁	1	2	yes	—
627	#532	—	2	1	no	—
628	#532	—	2	1	no	—
629	#532	C₂²×C₇₁	1	1	yes	characteristic
630	#532	C₂²×C₇₁	1	1	yes	characteristic
631	#529	—	2	1	no	—
632	#529	—	2	1	no	—
633	#529	C₂²×C₇₁	1	1	yes	characteristic
634	#520	C₂²×C₇₁	1	2	yes	—
635	#520	C₂²×C₇₁	1	2	yes	—
636	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
637	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
638	#501	C₂²×C₇₁	1	2	yes	—
639	#498	C₂²×C₇₁	1	1	yes	characteristic
640	#496	C₂²×C₇₁	1	2	yes	—
641	#493	C₂²×C₇₁	1	1	yes	characteristic
642	#488	C₂²×C₇₁	1	2	yes	—
643	#486	C₂²×C₇₁	1	2	yes	—
644	#486	C₂²×C₇₁	1	1	yes	characteristic
645	#486	C₂²×C₇₁	1	1	yes	characteristic
646	#483	C₂²×C₇₁	1	2	yes	—
647	#482	C₂²×C₇₁	1	2	yes	—
648	#481	C₂²×C₇₁	1	2	yes	—
649	#481	C₂²×C₇₁	1	2	yes	—
650	#481	C₂²×C₇₁	1	2	yes	—
651	#480	C₂²×C₇₁	1	2	yes	—
652	#479	C₂²×C₇₁	1	2	yes	—
653	#478	C₂²×C₇₁	1	2	yes	—
654	#477	C₂²×C₇₁	1	1	yes	characteristic
655	#476	C₂²×C₇₁	1	1	yes	characteristic
656	#476	C₂²×C₇₁	1	2	yes	—
657	#475	C₂²×C₇₁	1	1	yes	characteristic
658	#475	C₂²×C₇₁	1	2	yes	—
659	#475	C₂²×C₇₁	1	1	yes	characteristic
660	#469	C₂²×C₇₁	1	2	yes	—
661	#469	C₂²×C₇₁	1	2	yes	—
662	#469	C₂²×C₇₁	1	2	yes	—
663	#468	C₂²×C₇₁	1	2	yes	—
664	#466	C₂²×C₇₁	1	2	yes	—
665	#465	C₂²×C₇₁	1	2	yes	—
666	#464	C₂²×C₇₁	1	2	yes	—
667	#463	C₂²×C₇₁	1	2	yes	—
668	#460	C₂²×C₇₁	1	1	yes	characteristic
669	#460	C₂²×C₇₁	1	1	yes	characteristic
670	#460	C₂²×C₇₁	1	1	yes	characteristic
671	#460	C₂²×C₇₁	1	2	yes	—
672	#459	C₂²×C₇₁	1	1	yes	characteristic
673	#459	C₂²×C₇₁	1	2	yes	—
674	#452	C₂²×C₇₁	1	2	yes	—
675	#449	C₂²×C₇₁	1	2	yes	—
676	#449	C₂²×C₇₁	1	2	yes	—
677	#449	C₂²×C₇₁	1	2	yes	—
678	#449	C₂²×C₇₁	1	2	yes	—
679	#448	C₂²×C₇₁	1	2	yes	—
680	#446	C₂²×C₇₁	1	1	yes	characteristic
681	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic
682	#442	C₂²×C₇₁	1	2	yes	—
683	#442	C₂²×C₇₁	1	2	yes	—
684	#442	C₂²×C₇₁	1	2	yes	—
685	#441	C₂²×C₇₁	1	1	yes	characteristic
686	#441	C₂²×C₇₁	1	2	yes	—
687	#441	C₂²×C₇₁	1	1	yes	characteristic
688	#440	C₂²×C₇₁	1	1	yes	characteristic
689	#440	C₂²×C₇₁	1	1	yes	characteristic
690	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
691	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
692	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
694	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
696	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
697	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
698	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
699	C₄×D₈	C₂²×C₇₁	1	2	yes	—
700	#436	C₂²×C₇₁	1	1	yes	characteristic
701	#436	C₂²×C₇₁	1	2	yes	—
702	#435	C₂²×C₇₁	1	2	yes	—
703	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
704	#433	C₂²×C₇₁	1	2	yes	—
705	#431	C₂²×C₇₁	1	1	yes	characteristic
706	#428	C₂²×C₇₁	1	1	yes	characteristic
707	C₂×#106	C₂²×C₇₁	1	2	yes	—
708	#419	C₂²×C₇₁	1	1	yes	characteristic
709	#417	C₂²×C₇₁	1	1	yes	characteristic
710	#417	C₂²×C₇₁	1	2	yes	—
711	#417	C₂²×C₇₁	1	2	yes	—
712	#405	C₂²×C₇₁	1	2	yes	—
713	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	2	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
720	C₂×#41	C₂³×C₇₁	1	2	yes	—
721	C₂×#41	C₂³×C₇₁	1	2	yes	—
722	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
723	#137	—	2	4	no	—
724	#135	—	2	8	no	—
725	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
732	C₂×D₈	C₂³×C₇₁	1	2	yes	—
733	C₂×D₈	C₂³×C₇₁	1	2	yes	—
734	C₂×D₈	C₂³×C₇₁	1	2	yes	—
735	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
738	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	—	2	2	no	—
742	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
745	#127	—	2	1	no	—
746	#127	—	2	1	no	—
747	#127	—	2	2	no	—
748	#127	C₂³×C₇₁	1	1	yes	characteristic
749	#127	C₂³×C₇₁	1	1	yes	characteristic
750	#127	C₂³×C₇₁	1	2	yes	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	D₄×C₇₁	1	2	yes	—
754	#125	—	2	1	no	—
755	#125	—	2	2	no	—
756	#125	D₄×C₇₁	1	1	yes	characteristic
757	#125	C₂³×C₇₁	1	2	yes	—
758	#124	—	2	1	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	D₄×C₇₁	1	1	yes	characteristic
764	#124	C₂³×C₇₁	1	2	yes	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	D₄×C₇₁	1	2	yes	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
780	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	D₄×C₇₁	1	1	yes	characteristic
794	#121	C₂³×C₇₁	1	2	yes	—
795	#121	C₂³×C₇₁	1	2	yes	—
796	#121	C₂³×C₇₁	1	2	yes	—
797	#121	C₂³×C₇₁	1	2	yes	—
798	#121	C₂³×C₇₁	1	2	yes	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
810	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
811	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₇₁	1	2	yes	—
830	C₄×D₄	C₂³×C₇₁	1	2	yes	—
831	C₄×D₄	C₂³×C₇₁	1	2	yes	—
832	C₄×D₄	C₂³×C₇₁	1	2	yes	—
833	C₄×D₄	C₂³×C₇₁	1	2	yes	—
834	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	C₂³×C₇₁	1	1	yes	characteristic
839	#117	C₂³×C₇₁	1	2	yes	—
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	—	2	2	no	—
842	C₂×C₄⋊C₄	—	2	2	no	—
843	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
845	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	—	2	1	no	—
848	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
849	#107	C₂³×C₇₁	1	1	yes	characteristic
850	#107	C₂³×C₇₁	1	1	yes	characteristic
851	#107	C₂³×C₇₁	1	2	yes	—
852	#106	C₂³×C₇₁	1	1	yes	characteristic
853	#106	C₂³×C₇₁	1	2	yes	—
854	#106	C₂³×C₇₁	1	2	yes	—
855	#106	C₂³×C₇₁	1	2	yes	—
856	#106	C₂³×C₇₁	1	1	yes	characteristic
857	#106	C₂³×C₇₁	1	2	yes	—
858	#106	C₂³×C₇₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
863	#103	C₂³×C₇₁	1	1	yes	characteristic
864	#103	C₂³×C₇₁	1	1	yes	characteristic
865	#103	C₂³×C₇₁	1	2	yes	—
866	#103	C₂³×C₇₁	1	2	yes	—
867	#103	C₂³×C₇₁	1	1	yes	characteristic
868	#103	C₂³×C₇₁	1	1	yes	characteristic
869	#103	C₂³×C₇₁	1	1	yes	characteristic
870	#103	C₂³×C₇₁	1	1	yes	characteristic
871	#103	C₂³×C₇₁	1	2	yes	—
872	#102	C₂³×C₇₁	1	1	yes	characteristic
873	#102	C₂³×C₇₁	1	1	yes	characteristic
874	#102	C₂³×C₇₁	1	2	yes	—
875	#102	C₂³×C₇₁	1	2	yes	—
876	#102	C₂³×C₇₁	1	2	yes	—
877	#102	C₂³×C₇₁	1	2	yes	—
878	#102	C₂³×C₇₁	1	2	yes	—
879	#102	C₂³×C₇₁	1	2	yes	—
880	#102	C₂³×C₇₁	1	2	yes	—
881	#102	C₂³×C₇₁	1	2	yes	—
882	#102	C₂³×C₇₁	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
886	#97	C₂³×C₇₁	1	1	yes	characteristic
887	#97	C₂³×C₇₁	1	1	yes	characteristic
888	#97	C₂³×C₇₁	1	2	yes	—
889	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₇₁	1	2	yes	—
892	C₄×C₈	C₂³×C₇₁	1	2	yes	—
893	#41	—	2	4	no	—
894	#41	—	2	4	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	4	no	—
903	#41	—	8	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
929	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
930	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
931	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
932	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
947	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
950	Q₁₆	—	2	2	no	—
951	Q₁₆	#41×C₇₁	1	4	yes	complemented
952	SD₁₆	—	2	4	no	—
953	SD₁₆	—	2	4	no	—
954	SD₁₆	—	2	2	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	2	4	no	—
958	D₈	—	4	2	no	—
959	D₈	—	4	2	no	—
960	M₁₆	—	2	2	no	—
961	M₁₆	—	4	1	no	—
962	M₁₆	—	4	2	no	—
963	C₂×C₈	—	2	4	no	—
964	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
966	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
968	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1029	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₇₁	1	2	yes	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1037	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	8	1	no	—
1046	Q₈	—	8	2	no	—
1047	Q₈	C₂×#41×C₇₁	1	2	yes	—
1048	Q₈	C₂×#41×C₇₁	1	2	yes	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	1	no	—
1065	D₄	—	8	1	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	4	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	1	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1107	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1108	C₈	—	2	2	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	C₂×#41×C₇₁	1	2	yes	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	#577×C₇₁	1	2	yes	—
1147	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
1148	C₄	#585×C₇₁	1	1	yes	characteristic
1149	C₂	—	4	1	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	8	1	no	—
1152	C₂	—	8	2	no	—
1153	C₂	—	8	2	no	—
1154	C₂	D₄×#41×C₇₁	1	1	yes	characteristic
1155	C₂	C₂×#577×C₇₁	1	1	yes	characteristic
1156	C₂	C₇₁×#3585	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 ◁ #529×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3522	C₂	semidirect
2. C₇₁×#3517	C₂	semidirect
3. C₇₁×#3399	C₂	semidirect
4. C₇₁×#3387	C₂	semidirect
5. C₇₁×#3365	C₂	semidirect
6. C₇₁×#3362	C₂	semidirect
7. C₇₁×#3345	C₂	semidirect
8. C₇₁×#3335	C₂	semidirect
9. C₇₁×#3333	C₂	semidirect
10. C₇₁×#3332	C₂	semidirect
11. C₇₁×#3332	C₂	semidirect
12. C₇₁×#3326	C₂	semidirect
13. C₇₁×#3287	C₂	semidirect
14. C₇₁×#3271	C₂	semidirect
15. C₇₁×#3184	C₂	semidirect
16. C₇₁×#3179	C₂	semidirect
17. C₇₁×#3125	C₂	semidirect
18. C₇₁×#3119	C₂	semidirect
19. C₇₁×#3106	C₂	semidirect
20. C₇₁×#3103	C₂	semidirect
21. C₇₁×#2969	C₂	semidirect
22. C₇₁×#2952	C₂	semidirect
23. C₄×#137×C₇₁	C₂	semidirect
372. Q₁₆×C₇₁	#41	semidirect
570. #61546	C₇₁	direct (N × H)
579. #3522	C₂×C₇₁	semidirect
580. #3517	C₂×C₇₁	semidirect
581. #3399	C₂×C₇₁	semidirect
582. #3387	C₂×C₇₁	semidirect
583. #3365	C₂×C₇₁	semidirect
584. #3362	C₂×C₇₁	semidirect
585. #3345	C₂×C₇₁	semidirect
586. #3335	C₂×C₇₁	semidirect
587. #3333	C₂×C₇₁	semidirect
588. #3332	C₂×C₇₁	semidirect
589. #3332	C₂×C₇₁	semidirect
590. #3326	C₂×C₇₁	semidirect
591. #3287	C₂×C₇₁	semidirect
592. #3271	C₂×C₇₁	semidirect
593. #3184	C₂×C₇₁	semidirect
594. #3179	C₂×C₇₁	semidirect
595. #3125	C₂×C₇₁	semidirect
596. #3119	C₂×C₇₁	semidirect
597. #3106	C₂×C₇₁	semidirect
598. #3103	C₂×C₇₁	semidirect
599. #2969	C₂×C₇₁	semidirect
600. #2952	C₂×C₇₁	semidirect
601. C₄×#137	C₂×C₇₁	semidirect
602. C₇₁	#61546	direct (N × H)
951. Q₁₆	#41×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#3522	2
C₇₁×#3517	2
C₇₁×#3399	2
C₇₁×#3387	2
C₇₁×#3365	2
C₇₁×#3362	2
C₇₁×#3345	2
C₇₁×#3335	2
C₇₁×#3333	2
C₇₁×#3332	2
C₇₁×#3326	2
C₇₁×#3287	2
C₇₁×#3271	2
C₇₁×#3184	2
C₇₁×#3179	2
C₇₁×#3125	2
C₇₁×#3119	2
C₇₁×#3106	2
C₇₁×#3103	2
C₇₁×#2969	2
C₇₁×#2952	2
C₄×#137×C₇₁	2
#61546	71

Subgroups — C71×#61546 #31882418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61546 #31882418