Subgroups — C₇₁×#61495 #31882367

Order 18176.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#3350	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3304	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3301	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3271	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₁×#3126	C₂	1	2	yes	maximal, complemented
18	C₇₁×#3125	C₂	1	2	yes	maximal, complemented
19	C₇₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#2947	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₇₁	C₂²	1	2	yes	—
25	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
26	Q₈²×C₇₁	C₂²	1	1	yes	characteristic
27	#557×C₇₁	C₂²	1	1	yes	characteristic
28	#556×C₇₁	—	2	2	no	—
29	#556×C₇₁	—	2	1	no	—
30	#556×C₇₁	C₂²	1	1	yes	characteristic
31	#556×C₇₁	C₂²	1	2	yes	—
32	#555×C₇₁	—	2	1	no	—
33	#555×C₇₁	C₂²	1	1	yes	characteristic
34	#553×C₇₁	—	2	2	no	—
35	#553×C₇₁	C₂²	1	2	yes	—
36	#550×C₇₁	—	2	1	no	—
37	#550×C₇₁	C₂²	1	2	yes	—
38	#550×C₇₁	C₂²	1	1	yes	characteristic
39	#550×C₇₁	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
41	#548×C₇₁	C₂²	1	2	yes	—
42	#547×C₇₁	—	2	1	no	—
43	#547×C₇₁	C₂²	1	1	yes	characteristic
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	#533×C₇₁	—	2	1	no	—
49	#533×C₇₁	C₂²	1	1	yes	characteristic
50	#532×C₇₁	—	2	1	no	—
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	#519×C₇₁	C₂²	1	2	yes	—
57	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
58	C₄×#41×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	#492×C₇₁	C₂²	1	1	yes	characteristic
63	#488×C₇₁	C₂²	1	2	yes	—
64	#487×C₇₁	C₂²	1	1	yes	characteristic
65	#486×C₇₁	C₂²	1	2	yes	—
66	#486×C₇₁	C₂²	1	1	yes	characteristic
67	#485×C₇₁	C₂²	1	2	yes	—
68	#483×C₇₁	C₂²	1	2	yes	—
69	#482×C₇₁	C₂²	1	2	yes	—
70	#482×C₇₁	C₂²	1	2	yes	—
71	#482×C₇₁	C₂²	1	2	yes	—
72	#481×C₇₁	C₂²	1	2	yes	—
73	#479×C₇₁	C₂²	1	2	yes	—
74	#479×C₇₁	C₂²	1	2	yes	—
75	#477×C₇₁	C₂²	1	1	yes	characteristic
76	#476×C₇₁	C₂²	1	2	yes	—
77	#476×C₇₁	C₂²	1	1	yes	characteristic
78	#475×C₇₁	C₂²	1	1	yes	characteristic
79	#475×C₇₁	C₂²	1	2	yes	—
80	#474×C₇₁	C₂²	1	1	yes	characteristic
81	#469×C₇₁	C₂²	1	2	yes	—
82	#468×C₇₁	C₂²	1	2	yes	—
83	#466×C₇₁	C₂²	1	2	yes	—
84	#465×C₇₁	C₂²	1	2	yes	—
85	#465×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	#462×C₇₁	C₂²	1	1	yes	characteristic
90	#461×C₇₁	C₂²	1	1	yes	characteristic
91	#460×C₇₁	C₂²	1	2	yes	—
92	#460×C₇₁	C₂²	1	1	yes	characteristic
93	#460×C₇₁	C₂²	1	2	yes	—
94	#459×C₇₁	C₂²	1	1	yes	characteristic
95	#452×C₇₁	C₂²	1	2	yes	—
96	#452×C₇₁	C₂²	1	2	yes	—
97	#449×C₇₁	C₂²	1	2	yes	—
98	#449×C₇₁	C₂²	1	2	yes	—
99	#448×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	#441×C₇₁	C₂²	1	2	yes	—
105	#441×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	—
109	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	—
110	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×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	1	yes	characteristic
116	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
119	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
121	#436×C₇₁	C₂²	1	1	yes	characteristic
122	#435×C₇₁	C₂²	1	2	yes	—
123	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₇₁	C₂²	1	2	yes	—
125	#433×C₇₁	C₂²	1	2	yes	—
126	#432×C₇₁	C₂²	1	1	yes	characteristic
127	#428×C₇₁	C₂²	1	2	yes	—
128	#427×C₇₁	C₂²	1	1	yes	characteristic
129	#416×C₇₁	C₂²	1	1	yes	characteristic
130	#416×C₇₁	C₂²	1	1	yes	characteristic
131	#416×C₇₁	C₂²	1	2	yes	—
132	C₂×#103×C₇₁	C₂²	1	2	yes	—
133	#405×C₇₁	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₇₁	—	2	1	no	—
136	C₂×#41×C₇₁	—	2	1	no	—
137	C₂×#41×C₇₁	—	2	1	no	—
138	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
139	C₂×#41×C₇₁	C₂³	1	2	yes	—
140	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
142	#137×C₇₁	—	2	8	no	—
143	#135×C₇₁	—	2	4	no	—
144	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×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	2	yes	—
151	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
152	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₇₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₇₁	—	2	1	no	—
159	C₄⋊Q₈×C₇₁	—	2	1	no	—
160	C₄⋊Q₈×C₇₁	—	2	1	no	—
161	C₄⋊Q₈×C₇₁	—	2	2	no	—
162	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
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	2	no	—
168	#127×C₇₁	C₂³	1	1	yes	characteristic
169	#127×C₇₁	C₂³	1	2	yes	—
170	#126×C₇₁	—	2	2	no	—
171	#126×C₇₁	—	2	2	no	—
172	#126×C₇₁	—	2	2	no	—
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	—	2	2	no	—
175	#126×C₇₁	D₄	1	2	yes	—
176	#125×C₇₁	—	2	2	no	—
177	#125×C₇₁	—	2	1	no	—
178	#125×C₇₁	D₄	1	1	yes	characteristic
179	#125×C₇₁	C₂³	1	2	yes	—
180	#124×C₇₁	—	2	2	no	—
181	#124×C₇₁	—	2	2	no	—
182	#124×C₇₁	—	2	2	no	—
183	#124×C₇₁	—	2	2	no	—
184	#124×C₇₁	—	2	1	no	—
185	#124×C₇₁	D₄	1	1	yes	characteristic
186	#124×C₇₁	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
193	C₂²⋊Q₈×C₇₁	—	2	1	no	—
194	C₂²⋊Q₈×C₇₁	—	2	1	no	—
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	D₄	1	1	yes	characteristic
200	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
202	#121×C₇₁	—	2	1	no	—
203	#121×C₇₁	—	2	2	no	—
204	#121×C₇₁	—	2	2	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	D₄	1	1	yes	characteristic
214	#121×C₇₁	C₂³	1	2	yes	—
215	#121×C₇₁	C₂³	1	2	yes	—
216	#121×C₇₁	C₂³	1	2	yes	—
217	#121×C₇₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₇₁	—	2	1	no	—
219	C₄×Q₈×C₇₁	—	2	2	no	—
220	C₄×Q₈×C₇₁	—	2	2	no	—
221	C₄×Q₈×C₇₁	—	2	1	no	—
222	C₄×Q₈×C₇₁	—	2	2	no	—
223	C₄×Q₈×C₇₁	—	2	1	no	—
224	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
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	2	yes	—
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	1	no	—
238	C₄×D₄×C₇₁	—	2	1	no	—
239	C₄×D₄×C₇₁	—	2	2	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	1	no	—
245	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
252	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
253	#117×C₇₁	—	2	1	no	—
254	#117×C₇₁	—	2	2	no	—
255	#117×C₇₁	—	2	1	no	—
256	#117×C₇₁	—	2	1	no	—
257	#117×C₇₁	—	2	2	no	—
258	#117×C₇₁	—	2	2	no	—
259	#117×C₇₁	—	2	1	no	—
260	#117×C₇₁	—	2	1	no	—
261	#117×C₇₁	C₂³	1	1	yes	characteristic
262	#117×C₇₁	C₂³	1	1	yes	characteristic
263	#117×C₇₁	C₂³	1	2	yes	—
264	#117×C₇₁	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
266	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
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	#107×C₇₁	C₂³	1	2	yes	—
274	#106×C₇₁	C₂³	1	1	yes	characteristic
275	#106×C₇₁	C₂³	1	1	yes	characteristic
276	#106×C₇₁	C₂³	1	2	yes	—
277	#106×C₇₁	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
292	#103×C₇₁	C₂³	1	2	yes	—
293	#103×C₇₁	C₂³	1	2	yes	—
294	#102×C₇₁	C₂³	1	1	yes	characteristic
295	#102×C₇₁	C₂³	1	1	yes	characteristic
296	#102×C₇₁	C₂³	1	1	yes	characteristic
297	#102×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
308	#97×C₇₁	C₂³	1	2	yes	—
309	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₁	C₂³	1	2	yes	—
311	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
314	#41×C₇₁	—	2	2	no	—
315	#41×C₇₁	—	2	2	no	—
316	#41×C₇₁	—	2	4	no	—
317	#41×C₇₁	—	4	2	no	—
318	#41×C₇₁	—	4	1	no	—
319	#41×C₇₁	—	4	1	no	—
320	#41×C₇₁	—	8	2	no	—
321	#41×C₇₁	—	8	2	no	—
322	#41×C₇₁	—	8	2	no	—
323	C₂×Q₈×C₇₁	—	2	2	no	—
324	C₂×Q₈×C₇₁	—	2	1	no	—
325	C₂×Q₈×C₇₁	—	2	1	no	—
326	C₂×Q₈×C₇₁	—	2	2	no	—
327	C₂×Q₈×C₇₁	—	2	4	no	—
328	C₂×Q₈×C₇₁	—	4	2	no	—
329	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₇₁	—	2	1	no	—
334	C₂×D₄×C₇₁	—	2	1	no	—
335	C₂×D₄×C₇₁	—	2	2	no	—
336	C₂×D₄×C₇₁	—	2	2	no	—
337	C₂×D₄×C₇₁	—	2	2	no	—
338	C₂×D₄×C₇₁	—	2	2	no	—
339	C₂×D₄×C₇₁	—	2	2	no	—
340	C₂×D₄×C₇₁	—	2	1	no	—
341	C₂×D₄×C₇₁	—	2	1	no	—
342	C₂×D₄×C₇₁	—	2	2	no	—
343	C₂×D₄×C₇₁	—	2	2	no	—
344	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₇₁	—	2	2	no	—
350	C₂²×C₄×C₇₁	—	2	2	no	—
351	C₂²×C₄×C₇₁	—	2	1	no	—
352	C₂²×C₄×C₇₁	—	2	1	no	—
353	C₂²×C₄×C₇₁	—	2	1	no	—
354	C₂²×C₄×C₇₁	—	2	1	no	—
355	C₂²×C₄×C₇₁	—	2	2	no	—
356	C₂²×C₄×C₇₁	—	2	1	no	—
357	C₂²×C₄×C₇₁	—	2	1	no	—
358	C₂²×C₄×C₇₁	—	2	2	no	—
359	C₂²×C₄×C₇₁	—	2	2	no	—
360	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
364	Q₁₆×C₇₁	—	2	4	no	—
365	Q₁₆×C₇₁	#41	1	4	yes	complemented
366	SD₁₆×C₇₁	—	2	2	no	—
367	SD₁₆×C₇₁	—	2	2	no	—
368	SD₁₆×C₇₁	—	2	4	no	—
369	SD₁₆×C₇₁	—	2	4	no	—
370	SD₁₆×C₇₁	—	4	2	no	—
371	SD₁₆×C₇₁	—	4	2	no	—
372	D₈×C₇₁	—	2	2	no	—
373	D₈×C₇₁	—	4	2	no	—
374	M₁₆×C₇₁	—	2	4	no	—
375	C₂×C₈×C₇₁	—	2	2	no	—
376	C₂×C₈×C₇₁	—	4	2	no	—
377	C₂×C₈×C₇₁	—	4	1	no	—
378	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
382	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
383	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₇₁	—	2	1	no	—
385	C₄⋊C₄×C₇₁	—	2	2	no	—
386	C₄⋊C₄×C₇₁	—	2	2	no	—
387	C₄⋊C₄×C₇₁	—	2	1	no	—
388	C₄⋊C₄×C₇₁	—	2	1	no	—
389	C₄⋊C₄×C₇₁	—	2	1	no	—
390	C₄⋊C₄×C₇₁	—	2	1	no	—
391	C₄⋊C₄×C₇₁	—	2	1	no	—
392	C₄⋊C₄×C₇₁	—	2	2	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	1	no	—
397	C₄⋊C₄×C₇₁	—	2	2	no	—
398	C₄⋊C₄×C₇₁	—	2	2	no	—
399	C₄⋊C₄×C₇₁	—	2	1	no	—
400	C₄⋊C₄×C₇₁	—	2	2	no	—
401	C₄⋊C₄×C₇₁	—	2	2	no	—
402	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₇₁	—	2	2	no	—
415	C₂²⋊C₄×C₇₁	—	2	2	no	—
416	C₂²⋊C₄×C₇₁	—	2	1	no	—
417	C₂²⋊C₄×C₇₁	—	2	1	no	—
418	C₂²⋊C₄×C₇₁	—	2	2	no	—
419	C₂²⋊C₄×C₇₁	—	2	2	no	—
420	C₂²⋊C₄×C₇₁	—	2	1	no	—
421	C₂²⋊C₄×C₇₁	—	2	1	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	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
436	C₄²×C₇₁	—	2	1	no	—
437	C₄²×C₇₁	—	2	1	no	—
438	C₄²×C₇₁	—	2	1	no	—
439	C₄²×C₇₁	—	2	1	no	—
440	C₄²×C₇₁	—	2	1	no	—
441	C₄²×C₇₁	—	2	1	no	—
442	C₄²×C₇₁	—	2	2	no	—
443	C₄²×C₇₁	—	2	2	no	—
444	C₄²×C₇₁	—	2	2	no	—
445	C₄²×C₇₁	—	2	2	no	—
446	C₄²×C₇₁	—	2	2	no	—
447	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₇₁	C₂⁴	1	2	yes	—
452	C₂³×C₇₁	—	2	1	no	—
453	C₂³×C₇₁	—	2	1	no	—
454	C₂³×C₇₁	—	2	2	no	—
455	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
456	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
457	Q₈×C₇₁	—	2	2	no	—
458	Q₈×C₇₁	—	2	1	no	—
459	Q₈×C₇₁	—	2	1	no	—
460	Q₈×C₇₁	—	2	2	no	—
461	Q₈×C₇₁	—	2	2	no	—
462	Q₈×C₇₁	—	4	4	no	—
463	Q₈×C₇₁	—	4	2	no	—
464	Q₈×C₇₁	—	8	1	no	—
465	Q₈×C₇₁	—	8	2	no	—
466	Q₈×C₇₁	C₂×#41	1	2	yes	—
467	Q₈×C₇₁	C₂×#41	1	2	yes	—
468	D₄×C₇₁	—	2	2	no	—
469	D₄×C₇₁	—	2	1	no	—
470	D₄×C₇₁	—	2	1	no	—
471	D₄×C₇₁	—	2	2	no	—
472	D₄×C₇₁	—	2	1	no	—
473	D₄×C₇₁	—	2	2	no	—
474	D₄×C₇₁	—	2	1	no	—
475	D₄×C₇₁	—	4	2	no	—
476	D₄×C₇₁	—	4	4	no	—
477	D₄×C₇₁	—	4	2	no	—
478	D₄×C₇₁	—	4	2	no	—
479	D₄×C₇₁	—	4	2	no	—
480	D₄×C₇₁	—	8	1	no	—
481	D₄×C₇₁	—	8	2	no	—
482	D₄×C₇₁	—	8	2	no	—
483	D₄×C₇₁	—	8	2	no	—
484	D₄×C₇₁	—	8	2	no	—
485	D₄×C₇₁	—	8	2	no	—
486	D₄×C₇₁	—	8	2	no	—
487	C₂×C₄×C₇₁	—	2	1	no	—
488	C₂×C₄×C₇₁	—	2	1	no	—
489	C₂×C₄×C₇₁	—	2	2	no	—
490	C₂×C₄×C₇₁	—	2	1	no	—
491	C₂×C₄×C₇₁	—	2	2	no	—
492	C₂×C₄×C₇₁	—	2	2	no	—
493	C₂×C₄×C₇₁	—	2	1	no	—
494	C₂×C₄×C₇₁	—	2	1	no	—
495	C₂×C₄×C₇₁	—	2	2	no	—
496	C₂×C₄×C₇₁	—	2	2	no	—
497	C₂×C₄×C₇₁	—	2	1	no	—
498	C₂×C₄×C₇₁	—	2	1	no	—
499	C₂×C₄×C₇₁	—	2	1	no	—
500	C₂×C₄×C₇₁	—	2	2	no	—
501	C₂×C₄×C₇₁	—	4	1	no	—
502	C₂×C₄×C₇₁	—	4	2	no	—
503	C₂×C₄×C₇₁	—	4	2	no	—
504	C₂×C₄×C₇₁	—	4	4	no	—
505	C₂×C₄×C₇₁	—	4	4	no	—
506	C₂×C₄×C₇₁	—	4	2	no	—
507	C₂×C₄×C₇₁	—	4	2	no	—
508	C₂×C₄×C₇₁	—	8	1	no	—
509	C₂×C₄×C₇₁	—	8	1	no	—
510	C₂×C₄×C₇₁	—	8	2	no	—
511	C₂×C₄×C₇₁	—	8	2	no	—
512	C₂×C₄×C₇₁	—	8	2	no	—
513	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
522	C₈×C₇₁	—	2	1	no	—
523	C₈×C₇₁	—	2	2	no	—
524	C₈×C₇₁	—	2	1	no	—
525	C₈×C₇₁	—	2	2	no	—
526	C₈×C₇₁	—	2	1	no	—
527	C₈×C₇₁	C₂×#41	1	2	yes	—
528	C₂²×C₇₁	—	2	1	no	—
529	C₂²×C₇₁	—	2	2	no	—
530	C₂²×C₇₁	—	2	2	no	—
531	C₂²×C₇₁	—	2	1	no	—
532	C₂²×C₇₁	—	2	1	no	—
533	C₂²×C₇₁	—	2	2	no	—
534	C₂²×C₇₁	—	4	1	no	—
535	C₂²×C₇₁	—	4	1	no	—
536	C₂²×C₇₁	—	4	2	no	—
537	C₂²×C₇₁	—	4	1	no	—
538	C₂²×C₇₁	—	4	1	no	—
539	C₂²×C₇₁	—	4	2	no	—
540	C₂²×C₇₁	—	4	1	no	—
541	C₂²×C₇₁	—	4	1	no	—
542	C₂²×C₇₁	—	4	2	no	—
543	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₇₁	—	2	1	no	—
545	C₄×C₇₁	—	2	1	no	—
546	C₄×C₇₁	—	2	2	no	—
547	C₄×C₇₁	—	2	1	no	—
548	C₄×C₇₁	—	2	2	no	—
549	C₄×C₇₁	—	2	2	no	—
550	C₄×C₇₁	—	2	2	no	—
551	C₄×C₇₁	—	2	1	no	—
552	C₄×C₇₁	—	2	2	no	—
553	C₄×C₇₁	—	4	1	no	—
554	C₄×C₇₁	—	4	1	no	—
555	C₄×C₇₁	—	4	2	no	—
556	C₄×C₇₁	—	4	2	no	—
557	C₄×C₇₁	—	4	1	no	—
558	C₄×C₇₁	—	4	1	no	—
559	C₄×C₇₁	—	4	2	no	—
560	C₄×C₇₁	#577	1	2	yes	—
561	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
562	C₄×C₇₁	#585	1	1	yes	characteristic
563	#61495	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
564	C₂×C₇₁	—	4	1	no	—
565	C₂×C₇₁	—	4	2	no	—
566	C₂×C₇₁	—	8	1	no	—
567	C₂×C₇₁	—	8	1	no	—
568	C₂×C₇₁	—	8	2	no	—
569	C₂×C₇₁	D₄×#41	1	1	yes	characteristic
570	C₂×C₇₁	C₂×#577	1	1	yes	characteristic
571	C₂×C₇₁	#3584	1	1	yes	characteristic
572	#3518	C₂×C₇₁	1	1	yes	characteristic, complemented
573	#3517	C₂×C₇₁	1	1	yes	characteristic, complemented
574	#3397	C₂×C₇₁	1	1	yes	characteristic, complemented
575	#3387	C₂×C₇₁	1	1	yes	characteristic, complemented
576	#3364	C₂×C₇₁	1	1	yes	characteristic, complemented
577	#3362	C₂×C₇₁	1	1	yes	characteristic, complemented
578	#3354	C₂×C₇₁	1	1	yes	characteristic, complemented
579	#3350	C₂×C₇₁	1	2	yes	complemented
580	#3305	C₂×C₇₁	1	1	yes	characteristic, complemented
581	#3304	C₂×C₇₁	1	2	yes	complemented
582	#3301	C₂×C₇₁	1	2	yes	complemented
583	#3298	C₂×C₇₁	1	1	yes	characteristic, complemented
584	#3278	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3271	C₂×C₇₁	1	2	yes	complemented
586	#3179	C₂×C₇₁	1	2	yes	complemented
587	#3167	C₂×C₇₁	1	1	yes	characteristic, complemented
588	#3126	C₂×C₇₁	1	2	yes	complemented
589	#3125	C₂×C₇₁	1	2	yes	complemented
590	#3116	C₂×C₇₁	1	1	yes	characteristic, complemented
591	#3115	C₂×C₇₁	1	1	yes	characteristic, complemented
592	#2966	C₂×C₇₁	1	1	yes	characteristic, complemented
593	#2947	C₂×C₇₁	1	2	yes	complemented
594	C₄×#135	C₂×C₇₁	1	1	yes	characteristic, complemented
595	C₇₁	#61495	1	1	yes	characteristic, direct product factor, Sylow
596	C₂×#137	C₂²×C₇₁	1	2	yes	—
597	C₂×#135	C₂²×C₇₁	1	1	yes	characteristic
598	Q₈²	C₂²×C₇₁	1	1	yes	characteristic
599	#557	C₂²×C₇₁	1	1	yes	characteristic
600	#556	—	2	2	no	—
601	#556	—	2	1	no	—
602	#556	C₂²×C₇₁	1	1	yes	characteristic
603	#556	C₂²×C₇₁	1	2	yes	—
604	#555	—	2	1	no	—
605	#555	C₂²×C₇₁	1	1	yes	characteristic
606	#553	—	2	2	no	—
607	#553	C₂²×C₇₁	1	2	yes	—
608	#550	—	2	1	no	—
609	#550	C₂²×C₇₁	1	2	yes	—
610	#550	C₂²×C₇₁	1	1	yes	characteristic
611	#550	C₂²×C₇₁	1	1	yes	characteristic
612	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
613	#548	C₂²×C₇₁	1	2	yes	—
614	#547	—	2	1	no	—
615	#547	C₂²×C₇₁	1	1	yes	characteristic
616	#542	—	2	2	no	—
617	#542	C₂²×C₇₁	1	2	yes	—
618	#540	—	2	2	no	—
619	#540	C₂²×C₇₁	1	2	yes	—
620	#533	—	2	1	no	—
621	#533	C₂²×C₇₁	1	1	yes	characteristic
622	#532	—	2	1	no	—
623	#532	C₂²×C₇₁	1	1	yes	characteristic
624	#529	—	2	1	no	—
625	#529	—	2	1	no	—
626	#529	C₂²×C₇₁	1	1	yes	characteristic
627	#520	C₂²×C₇₁	1	2	yes	—
628	#519	C₂²×C₇₁	1	2	yes	—
629	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
630	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
631	#501	C₂²×C₇₁	1	2	yes	—
632	#498	C₂²×C₇₁	1	1	yes	characteristic
633	#496	C₂²×C₇₁	1	2	yes	—
634	#492	C₂²×C₇₁	1	1	yes	characteristic
635	#488	C₂²×C₇₁	1	2	yes	—
636	#487	C₂²×C₇₁	1	1	yes	characteristic
637	#486	C₂²×C₇₁	1	1	yes	characteristic
638	#486	C₂²×C₇₁	1	2	yes	—
639	#485	C₂²×C₇₁	1	2	yes	—
640	#483	C₂²×C₇₁	1	2	yes	—
641	#482	C₂²×C₇₁	1	2	yes	—
642	#482	C₂²×C₇₁	1	2	yes	—
643	#482	C₂²×C₇₁	1	2	yes	—
644	#481	C₂²×C₇₁	1	2	yes	—
645	#479	C₂²×C₇₁	1	2	yes	—
646	#479	C₂²×C₇₁	1	2	yes	—
647	#477	C₂²×C₇₁	1	1	yes	characteristic
648	#476	C₂²×C₇₁	1	2	yes	—
649	#476	C₂²×C₇₁	1	1	yes	characteristic
650	#475	C₂²×C₇₁	1	1	yes	characteristic
651	#475	C₂²×C₇₁	1	2	yes	—
652	#474	C₂²×C₇₁	1	1	yes	characteristic
653	#469	C₂²×C₇₁	1	2	yes	—
654	#468	C₂²×C₇₁	1	2	yes	—
655	#466	C₂²×C₇₁	1	2	yes	—
656	#465	C₂²×C₇₁	1	2	yes	—
657	#465	C₂²×C₇₁	1	2	yes	—
658	#465	C₂²×C₇₁	1	2	yes	—
659	#464	C₂²×C₇₁	1	2	yes	—
660	#463	C₂²×C₇₁	1	2	yes	—
661	#462	C₂²×C₇₁	1	1	yes	characteristic
662	#461	C₂²×C₇₁	1	1	yes	characteristic
663	#460	C₂²×C₇₁	1	1	yes	characteristic
664	#460	C₂²×C₇₁	1	2	yes	—
665	#460	C₂²×C₇₁	1	2	yes	—
666	#459	C₂²×C₇₁	1	1	yes	characteristic
667	#452	C₂²×C₇₁	1	2	yes	—
668	#452	C₂²×C₇₁	1	2	yes	—
669	#449	C₂²×C₇₁	1	2	yes	—
670	#449	C₂²×C₇₁	1	2	yes	—
671	#448	C₂²×C₇₁	1	2	yes	—
672	#448	C₂²×C₇₁	1	2	yes	—
673	#446	C₂²×C₇₁	1	1	yes	characteristic
674	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic
675	#442	C₂²×C₇₁	1	2	yes	—
676	#441	C₂²×C₇₁	1	2	yes	—
677	#441	C₂²×C₇₁	1	2	yes	—
678	#440	C₂²×C₇₁	1	2	yes	—
679	#440	C₂²×C₇₁	1	2	yes	—
680	#440	C₂²×C₇₁	1	2	yes	—
681	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	—
682	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
683	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
691	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
693	#436	C₂²×C₇₁	1	1	yes	characteristic
694	#435	C₂²×C₇₁	1	2	yes	—
695	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
696	C₈×D₄	C₂²×C₇₁	1	2	yes	—
697	#433	C₂²×C₇₁	1	2	yes	—
698	#432	C₂²×C₇₁	1	1	yes	characteristic
699	#428	C₂²×C₇₁	1	2	yes	—
700	#427	C₂²×C₇₁	1	1	yes	characteristic
701	#416	C₂²×C₇₁	1	1	yes	characteristic
702	#416	C₂²×C₇₁	1	1	yes	characteristic
703	#416	C₂²×C₇₁	1	2	yes	—
704	C₂×#103	C₂²×C₇₁	1	2	yes	—
705	#405	C₂²×C₇₁	1	2	yes	—
706	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
711	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
712	C₂×#41	C₂³×C₇₁	1	2	yes	—
713	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
714	#137	—	2	8	no	—
715	#135	—	2	4	no	—
716	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
718	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
724	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₇₁	1	2	yes	—
726	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
727	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
738	#127	—	2	1	no	—
739	#127	—	2	2	no	—
740	#127	C₂³×C₇₁	1	1	yes	characteristic
741	#127	C₂³×C₇₁	1	2	yes	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	D₄×C₇₁	1	2	yes	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	D₄×C₇₁	1	1	yes	characteristic
751	#125	C₂³×C₇₁	1	2	yes	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	D₄×C₇₁	1	1	yes	characteristic
758	#124	C₂³×C₇₁	1	2	yes	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	D₄×C₇₁	1	2	yes	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
772	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	D₄×C₇₁	1	1	yes	characteristic
786	#121	C₂³×C₇₁	1	2	yes	—
787	#121	C₂³×C₇₁	1	2	yes	—
788	#121	C₂³×C₇₁	1	2	yes	—
789	#121	C₂³×C₇₁	1	2	yes	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
802	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
803	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₇₁	1	2	yes	—
822	C₄×D₄	C₂³×C₇₁	1	2	yes	—
823	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₇₁	1	2	yes	—
825	#117	—	2	1	no	—
826	#117	—	2	2	no	—
827	#117	—	2	1	no	—
828	#117	—	2	1	no	—
829	#117	—	2	2	no	—
830	#117	—	2	2	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	C₂³×C₇₁	1	1	yes	characteristic
834	#117	C₂³×C₇₁	1	1	yes	characteristic
835	#117	C₂³×C₇₁	1	2	yes	—
836	#117	C₂³×C₇₁	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
839	C₂×C₄²	—	2	1	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
842	#107	C₂³×C₇₁	1	1	yes	characteristic
843	#107	C₂³×C₇₁	1	1	yes	characteristic
844	#107	C₂³×C₇₁	1	2	yes	—
845	#107	C₂³×C₇₁	1	2	yes	—
846	#106	C₂³×C₇₁	1	1	yes	characteristic
847	#106	C₂³×C₇₁	1	1	yes	characteristic
848	#106	C₂³×C₇₁	1	2	yes	—
849	#106	C₂³×C₇₁	1	2	yes	—
850	#106	C₂³×C₇₁	1	2	yes	—
851	#106	C₂³×C₇₁	1	2	yes	—
852	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
855	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
856	#103	C₂³×C₇₁	1	1	yes	characteristic
857	#103	C₂³×C₇₁	1	2	yes	—
858	#103	C₂³×C₇₁	1	2	yes	—
859	#103	C₂³×C₇₁	1	2	yes	—
860	#103	C₂³×C₇₁	1	1	yes	characteristic
861	#103	C₂³×C₇₁	1	1	yes	characteristic
862	#103	C₂³×C₇₁	1	1	yes	characteristic
863	#103	C₂³×C₇₁	1	2	yes	—
864	#103	C₂³×C₇₁	1	2	yes	—
865	#103	C₂³×C₇₁	1	2	yes	—
866	#102	C₂³×C₇₁	1	1	yes	characteristic
867	#102	C₂³×C₇₁	1	1	yes	characteristic
868	#102	C₂³×C₇₁	1	1	yes	characteristic
869	#102	C₂³×C₇₁	1	1	yes	characteristic
870	#102	C₂³×C₇₁	1	2	yes	—
871	#102	C₂³×C₇₁	1	2	yes	—
872	#102	C₂³×C₇₁	1	2	yes	—
873	#102	C₂³×C₇₁	1	2	yes	—
874	#102	C₂³×C₇₁	1	2	yes	—
875	#102	C₂³×C₇₁	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
879	#97	C₂³×C₇₁	1	2	yes	—
880	#97	C₂³×C₇₁	1	2	yes	—
881	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₇₁	1	2	yes	—
886	#41	—	2	2	no	—
887	#41	—	2	2	no	—
888	#41	—	2	4	no	—
889	#41	—	4	2	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	8	2	no	—
893	#41	—	8	2	no	—
894	#41	—	8	2	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	4	no	—
900	C₂×Q₈	—	4	2	no	—
901	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
917	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
918	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
936	Q₁₆	—	2	4	no	—
937	Q₁₆	#41×C₇₁	1	4	yes	complemented
938	SD₁₆	—	2	2	no	—
939	SD₁₆	—	2	2	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	2	4	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	D₈	—	2	2	no	—
945	D₈	—	4	2	no	—
946	M₁₆	—	2	4	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	4	2	no	—
949	C₂×C₈	—	4	1	no	—
950	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
954	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
955	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1020	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₇₁	1	2	yes	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1028	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	4	4	no	—
1035	Q₈	—	4	2	no	—
1036	Q₈	—	8	1	no	—
1037	Q₈	—	8	2	no	—
1038	Q₈	C₂×#41×C₇₁	1	2	yes	—
1039	Q₈	C₂×#41×C₇₁	1	2	yes	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	4	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	1	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	1	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1093	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1094	C₈	—	2	1	no	—
1095	C₈	—	2	2	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	2	no	—
1098	C₈	—	2	1	no	—
1099	C₈	C₂×#41×C₇₁	1	2	yes	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	#577×C₇₁	1	2	yes	—
1133	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
1134	C₄	#585×C₇₁	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	8	1	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	2	no	—
1140	C₂	D₄×#41×C₇₁	1	1	yes	characteristic
1141	C₂	C₂×#577×C₇₁	1	1	yes	characteristic
1142	C₂	C₇₁×#3584	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×#3518	C₂	semidirect
2. C₇₁×#3517	C₂	semidirect
3. C₇₁×#3397	C₂	semidirect
4. C₇₁×#3387	C₂	semidirect
5. C₇₁×#3364	C₂	semidirect
6. C₇₁×#3362	C₂	semidirect
7. C₇₁×#3354	C₂	semidirect
8. C₇₁×#3350	C₂	semidirect
9. C₇₁×#3305	C₂	semidirect
10. C₇₁×#3304	C₂	semidirect
11. C₇₁×#3301	C₂	semidirect
12. C₇₁×#3298	C₂	semidirect
13. C₇₁×#3278	C₂	semidirect
14. C₇₁×#3271	C₂	semidirect
15. C₇₁×#3179	C₂	semidirect
16. C₇₁×#3167	C₂	semidirect
17. C₇₁×#3126	C₂	semidirect
18. C₇₁×#3125	C₂	semidirect
19. C₇₁×#3116	C₂	semidirect
20. C₇₁×#3115	C₂	semidirect
21. C₇₁×#2966	C₂	semidirect
22. C₇₁×#2947	C₂	semidirect
23. C₄×#135×C₇₁	C₂	semidirect
365. Q₁₆×C₇₁	#41	semidirect
563. #61495	C₇₁	direct (N × H)
572. #3518	C₂×C₇₁	semidirect
573. #3517	C₂×C₇₁	semidirect
574. #3397	C₂×C₇₁	semidirect
575. #3387	C₂×C₇₁	semidirect
576. #3364	C₂×C₇₁	semidirect
577. #3362	C₂×C₇₁	semidirect
578. #3354	C₂×C₇₁	semidirect
579. #3350	C₂×C₇₁	semidirect
580. #3305	C₂×C₇₁	semidirect
581. #3304	C₂×C₇₁	semidirect
582. #3301	C₂×C₇₁	semidirect
583. #3298	C₂×C₇₁	semidirect
584. #3278	C₂×C₇₁	semidirect
585. #3271	C₂×C₇₁	semidirect
586. #3179	C₂×C₇₁	semidirect
587. #3167	C₂×C₇₁	semidirect
588. #3126	C₂×C₇₁	semidirect
589. #3125	C₂×C₇₁	semidirect
590. #3116	C₂×C₇₁	semidirect
591. #3115	C₂×C₇₁	semidirect
592. #2966	C₂×C₇₁	semidirect
593. #2947	C₂×C₇₁	semidirect
594. C₄×#135	C₂×C₇₁	semidirect
595. C₇₁	#61495	direct (N × H)
937. 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×#3518	2
C₇₁×#3517	2
C₇₁×#3397	2
C₇₁×#3387	2
C₇₁×#3364	2
C₇₁×#3362	2
C₇₁×#3354	2
C₇₁×#3350	2
C₇₁×#3305	2
C₇₁×#3304	2
C₇₁×#3301	2
C₇₁×#3298	2
C₇₁×#3278	2
C₇₁×#3271	2
C₇₁×#3179	2
C₇₁×#3167	2
C₇₁×#3126	2
C₇₁×#3125	2
C₇₁×#3116	2
C₇₁×#3115	2
C₇₁×#2966	2
C₇₁×#2947	2
C₄×#135×C₇₁	2
#61495	71

Subgroups — C71×#61495 #31882367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61495 #31882367