Subgroups — C₇₁×#61460 #31882332

Order 18176.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3350	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3313	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3269	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#3181	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3116	C₂	1	2	yes	maximal, complemented
18	C₇₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₇₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#2943	C₂	1	2	yes	maximal, 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	#557×C₇₁	C₂²	1	1	yes	characteristic
29	#557×C₇₁	C₂²	1	1	yes	characteristic
30	#556×C₇₁	—	2	1	no	—
31	#556×C₇₁	C₂²	1	1	yes	characteristic
32	#556×C₇₁	C₂²	1	1	yes	characteristic
33	#556×C₇₁	C₂²	1	2	yes	—
34	#553×C₇₁	—	2	2	no	—
35	#553×C₇₁	C₂²	1	2	yes	—
36	#552×C₇₁	—	2	1	no	—
37	#552×C₇₁	—	2	2	no	—
38	#550×C₇₁	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
40	#548×C₇₁	—	2	1	no	—
41	#548×C₇₁	C₂²	1	2	yes	—
42	#547×C₇₁	C₂²	1	1	yes	characteristic
43	#547×C₇₁	C₂²	1	2	yes	—
44	#533×C₇₁	C₂²	1	1	yes	characteristic
45	#533×C₇₁	C₂²	1	2	yes	—
46	#532×C₇₁	—	2	1	no	—
47	#532×C₇₁	C₂²	1	1	yes	characteristic
48	#529×C₇₁	—	2	2	no	—
49	#529×C₇₁	—	2	1	no	—
50	#529×C₇₁	—	2	2	no	—
51	#529×C₇₁	C₂²	1	2	yes	—
52	C₄×#41×C₇₁	—	2	1	no	—
53	C₄×#41×C₇₁	C₂²	1	2	yes	—
54	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₇₁	C₂²	1	2	yes	—
56	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₇₁	—	2	1	no	—
58	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
59	#501×C₇₁	C₂²	1	2	yes	—
60	#500×C₇₁	C₂²	1	1	yes	characteristic
61	#497×C₇₁	C₂²	1	2	yes	—
62	#492×C₇₁	C₂²	1	1	yes	characteristic
63	#491×C₇₁	C₂²	1	2	yes	—
64	#489×C₇₁	C₂²	1	2	yes	—
65	#487×C₇₁	C₂²	1	1	yes	characteristic
66	#486×C₇₁	C₂²	1	1	yes	characteristic
67	#485×C₇₁	C₂²	1	2	yes	—
68	#485×C₇₁	C₂²	1	2	yes	—
69	#485×C₇₁	C₂²	1	2	yes	—
70	#483×C₇₁	C₂²	1	2	yes	—
71	#482×C₇₁	C₂²	1	2	yes	—
72	#482×C₇₁	C₂²	1	2	yes	—
73	#479×C₇₁	C₂²	1	2	yes	—
74	#478×C₇₁	C₂²	1	2	yes	—
75	#477×C₇₁	C₂²	1	2	yes	—
76	#476×C₇₁	C₂²	1	2	yes	—
77	#475×C₇₁	C₂²	1	1	yes	characteristic
78	#475×C₇₁	C₂²	1	1	yes	characteristic
79	#475×C₇₁	C₂²	1	1	yes	characteristic
80	#474×C₇₁	C₂²	1	1	yes	characteristic
81	#468×C₇₁	C₂²	1	2	yes	—
82	#468×C₇₁	C₂²	1	2	yes	—
83	#467×C₇₁	C₂²	1	2	yes	—
84	#467×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	#462×C₇₁	C₂²	1	1	yes	characteristic
91	#462×C₇₁	C₂²	1	2	yes	—
92	#461×C₇₁	C₂²	1	2	yes	—
93	#460×C₇₁	C₂²	1	1	yes	characteristic
94	#459×C₇₁	C₂²	1	1	yes	characteristic
95	#452×C₇₁	C₂²	1	2	yes	—
96	#452×C₇₁	C₂²	1	2	yes	—
97	#452×C₇₁	C₂²	1	2	yes	—
98	#451×C₇₁	C₂²	1	2	yes	—
99	#449×C₇₁	C₂²	1	2	yes	—
100	#449×C₇₁	C₂²	1	2	yes	—
101	#446×C₇₁	C₂²	1	1	yes	characteristic
102	#446×C₇₁	C₂²	1	1	yes	characteristic
103	#442×C₇₁	C₂²	1	2	yes	—
104	#442×C₇₁	C₂²	1	2	yes	—
105	#441×C₇₁	C₂²	1	2	yes	—
106	#441×C₇₁	C₂²	1	2	yes	—
107	#441×C₇₁	C₂²	1	2	yes	—
108	#441×C₇₁	C₂²	1	1	yes	characteristic
109	#441×C₇₁	C₂²	1	1	yes	characteristic
110	#440×C₇₁	C₂²	1	2	yes	—
111	#440×C₇₁	C₂²	1	1	yes	characteristic
112	#440×C₇₁	C₂²	1	2	yes	—
113	#440×C₇₁	C₂²	1	2	yes	—
114	#440×C₇₁	C₂²	1	2	yes	—
115	#440×C₇₁	C₂²	1	2	yes	—
116	#440×C₇₁	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
121	#435×C₇₁	C₂²	1	2	yes	—
122	#435×C₇₁	C₂²	1	2	yes	—
123	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
125	#432×C₇₁	C₂²	1	2	yes	—
126	#432×C₇₁	C₂²	1	1	yes	characteristic
127	#428×C₇₁	C₂²	1	1	yes	characteristic
128	#427×C₇₁	C₂²	1	2	yes	—
129	#419×C₇₁	C₂²	1	1	yes	characteristic
130	#417×C₇₁	C₂²	1	1	yes	characteristic
131	#416×C₇₁	C₂²	1	2	yes	—
132	#416×C₇₁	C₂²	1	2	yes	—
133	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
134	C₂×#97×C₇₁	C₂²	1	2	yes	—
135	C₂×#41×C₇₁	—	2	1	no	—
136	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₇₁	C₂³	1	2	yes	—
138	C₂×#41×C₇₁	C₂³	1	2	yes	—
139	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₇₁	—	2	1	no	—
141	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
142	#137×C₇₁	—	2	4	no	—
143	#135×C₇₁	—	2	8	no	—
144	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
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×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₇₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₇₁	—	2	1	no	—
159	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
164	#127×C₇₁	—	2	1	no	—
165	#127×C₇₁	C₂³	1	1	yes	characteristic
166	#126×C₇₁	—	2	2	no	—
167	#126×C₇₁	—	2	2	no	—
168	#126×C₇₁	—	2	2	no	—
169	#126×C₇₁	—	2	2	no	—
170	#126×C₇₁	—	2	2	no	—
171	#126×C₇₁	—	2	2	no	—
172	#125×C₇₁	—	2	1	no	—
173	#125×C₇₁	—	2	2	no	—
174	#125×C₇₁	—	2	2	no	—
175	#125×C₇₁	—	2	2	no	—
176	#125×C₇₁	—	2	1	no	—
177	#125×C₇₁	C₂³	1	2	yes	—
178	#124×C₇₁	—	2	1	no	—
179	#124×C₇₁	—	2	1	no	—
180	#124×C₇₁	—	2	2	no	—
181	#124×C₇₁	—	2	1	no	—
182	#124×C₇₁	—	2	2	no	—
183	#124×C₇₁	—	2	1	no	—
184	#124×C₇₁	C₂³	1	2	yes	—
185	#123×C₇₁	—	2	2	no	—
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	C₂²⋊Q₈×C₇₁	—	2	1	no	—
192	C₂²⋊Q₈×C₇₁	—	2	2	no	—
193	C₂²⋊Q₈×C₇₁	—	2	2	no	—
194	C₂²⋊Q₈×C₇₁	—	2	1	no	—
195	C₂²⋊Q₈×C₇₁	—	2	2	no	—
196	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
200	#121×C₇₁	—	2	1	no	—
201	#121×C₇₁	—	2	2	no	—
202	#121×C₇₁	—	2	2	no	—
203	#121×C₇₁	—	2	2	no	—
204	#121×C₇₁	—	2	1	no	—
205	#121×C₇₁	—	2	2	no	—
206	#121×C₇₁	C₂³	1	2	yes	—
207	#121×C₇₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₇₁	—	2	1	no	—
209	C₄×Q₈×C₇₁	—	2	1	no	—
210	C₄×Q₈×C₇₁	—	2	2	no	—
211	C₄×Q₈×C₇₁	—	2	1	no	—
212	C₄×Q₈×C₇₁	—	2	1	no	—
213	C₄×Q₈×C₇₁	—	2	2	no	—
214	C₄×Q₈×C₇₁	—	2	1	no	—
215	C₄×Q₈×C₇₁	—	2	1	no	—
216	C₄×Q₈×C₇₁	—	2	1	no	—
217	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₇₁	—	2	1	no	—
229	C₄×D₄×C₇₁	—	2	2	no	—
230	C₄×D₄×C₇₁	—	2	2	no	—
231	C₄×D₄×C₇₁	—	2	1	no	—
232	C₄×D₄×C₇₁	—	2	2	no	—
233	C₄×D₄×C₇₁	—	2	2	no	—
234	C₄×D₄×C₇₁	—	2	2	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	2	no	—
239	C₄×D₄×C₇₁	—	2	1	no	—
240	C₄×D₄×C₇₁	D₄	1	2	yes	—
241	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
242	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₇₁	C₂³	1	2	yes	—
244	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₇₁	C₂³	1	2	yes	—
246	C₄×D₄×C₇₁	C₂³	1	2	yes	—
247	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₇₁	C₂³	1	2	yes	—
249	#117×C₇₁	—	2	1	no	—
250	#117×C₇₁	—	2	2	no	—
251	#117×C₇₁	—	2	2	no	—
252	#117×C₇₁	—	2	2	no	—
253	#117×C₇₁	—	2	1	no	—
254	#117×C₇₁	—	2	2	no	—
255	#117×C₇₁	D₄	1	1	yes	characteristic
256	#117×C₇₁	D₄	1	2	yes	—
257	#117×C₇₁	C₂³	1	2	yes	—
258	#117×C₇₁	C₂³	1	2	yes	—
259	#117×C₇₁	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
263	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₇₁	—	2	1	no	—
265	C₂×C₄²×C₇₁	—	2	2	no	—
266	C₂×C₄²×C₇₁	—	2	1	no	—
267	C₂×C₄²×C₇₁	—	2	2	no	—
268	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
270	#107×C₇₁	C₂³	1	1	yes	characteristic
271	#107×C₇₁	C₂³	1	2	yes	—
272	#107×C₇₁	C₂³	1	1	yes	characteristic
273	#107×C₇₁	C₂³	1	2	yes	—
274	#107×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	1	yes	characteristic
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	1	yes	characteristic
292	#103×C₇₁	C₂³	1	1	yes	characteristic
293	#103×C₇₁	C₂³	1	2	yes	—
294	#103×C₇₁	C₂³	1	2	yes	—
295	#103×C₇₁	C₂³	1	2	yes	—
296	#103×C₇₁	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
310	#97×C₇₁	C₂³	1	2	yes	—
311	#97×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	4	no	—
315	#41×C₇₁	—	2	4	no	—
316	#41×C₇₁	—	2	2	no	—
317	#41×C₇₁	—	4	2	no	—
318	#41×C₇₁	—	4	2	no	—
319	#41×C₇₁	—	4	2	no	—
320	#41×C₇₁	—	4	1	no	—
321	#41×C₇₁	—	4	4	no	—
322	C₂×Q₈×C₇₁	—	2	1	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	—	4	1	no	—
328	C₂×Q₈×C₇₁	—	4	4	no	—
329	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₇₁	—	2	2	no	—
335	C₂×D₄×C₇₁	—	2	2	no	—
336	C₂×D₄×C₇₁	—	2	1	no	—
337	C₂×D₄×C₇₁	—	2	2	no	—
338	C₂×D₄×C₇₁	—	2	2	no	—
339	C₂×D₄×C₇₁	—	2	1	no	—
340	C₂×D₄×C₇₁	—	2	1	no	—
341	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
344	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇₁	—	2	1	no	—
346	C₂²×C₄×C₇₁	—	2	1	no	—
347	C₂²×C₄×C₇₁	—	2	1	no	—
348	C₂²×C₄×C₇₁	—	2	2	no	—
349	C₂²×C₄×C₇₁	—	2	1	no	—
350	C₂²×C₄×C₇₁	—	2	2	no	—
351	C₂²×C₄×C₇₁	—	2	1	no	—
352	C₂²×C₄×C₇₁	—	2	2	no	—
353	C₂²×C₄×C₇₁	—	2	2	no	—
354	C₂²×C₄×C₇₁	—	2	2	no	—
355	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
361	Q₁₆×C₇₁	—	2	4	no	—
362	Q₁₆×C₇₁	—	2	2	no	—
363	Q₁₆×C₇₁	—	2	2	no	—
364	Q₁₆×C₇₁	—	4	2	no	—
365	SD₁₆×C₇₁	—	2	2	no	—
366	SD₁₆×C₇₁	—	2	4	no	—
367	SD₁₆×C₇₁	—	4	2	no	—
368	SD₁₆×C₇₁	—	4	2	no	—
369	SD₁₆×C₇₁	#41	1	4	yes	complemented
370	D₈×C₇₁	—	2	4	no	—
371	M₁₆×C₇₁	—	2	2	no	—
372	M₁₆×C₇₁	—	4	1	no	—
373	C₂×C₈×C₇₁	—	2	4	no	—
374	C₂×C₈×C₇₁	—	4	2	no	—
375	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
379	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₇₁	—	2	1	no	—
382	C₄⋊C₄×C₇₁	—	2	2	no	—
383	C₄⋊C₄×C₇₁	—	2	1	no	—
384	C₄⋊C₄×C₇₁	—	2	2	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	2	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	1	no	—
396	C₄⋊C₄×C₇₁	—	2	2	no	—
397	C₄⋊C₄×C₇₁	—	2	1	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	1	no	—
402	C₄⋊C₄×C₇₁	—	2	1	no	—
403	C₄⋊C₄×C₇₁	—	2	2	no	—
404	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
413	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
414	C₂²⋊C₄×C₇₁	—	2	2	no	—
415	C₂²⋊C₄×C₇₁	—	2	2	no	—
416	C₂²⋊C₄×C₇₁	—	2	2	no	—
417	C₂²⋊C₄×C₇₁	—	2	2	no	—
418	C₂²⋊C₄×C₇₁	—	2	2	no	—
419	C₂²⋊C₄×C₇₁	—	2	1	no	—
420	C₂²⋊C₄×C₇₁	—	2	2	no	—
421	C₂²⋊C₄×C₇₁	—	2	1	no	—
422	C₂²⋊C₄×C₇₁	—	2	2	no	—
423	C₂²⋊C₄×C₇₁	—	2	2	no	—
424	C₂²⋊C₄×C₇₁	—	2	2	no	—
425	C₂²⋊C₄×C₇₁	—	2	2	no	—
426	C₂²⋊C₄×C₇₁	—	2	2	no	—
427	C₂²⋊C₄×C₇₁	—	2	1	no	—
428	C₂²⋊C₄×C₇₁	—	2	2	no	—
429	C₂²⋊C₄×C₇₁	—	2	2	no	—
430	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
433	C₄²×C₇₁	—	2	1	no	—
434	C₄²×C₇₁	—	2	1	no	—
435	C₄²×C₇₁	—	2	2	no	—
436	C₄²×C₇₁	—	2	1	no	—
437	C₄²×C₇₁	—	2	2	no	—
438	C₄²×C₇₁	—	2	2	no	—
439	C₄²×C₇₁	—	2	1	no	—
440	C₄²×C₇₁	—	2	2	no	—
441	C₄²×C₇₁	—	2	1	no	—
442	C₄²×C₇₁	—	2	2	no	—
443	C₄²×C₇₁	—	2	1	no	—
444	C₄²×C₇₁	—	2	1	no	—
445	C₄²×C₇₁	C₂×D₄	1	2	yes	—
446	C₄²×C₇₁	C₂×D₄	1	2	yes	—
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	2	no	—
454	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
455	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
456	Q₈×C₇₁	—	2	2	no	—
457	Q₈×C₇₁	—	2	1	no	—
458	Q₈×C₇₁	—	2	1	no	—
459	Q₈×C₇₁	—	2	2	no	—
460	Q₈×C₇₁	—	2	1	no	—
461	Q₈×C₇₁	—	2	1	no	—
462	Q₈×C₇₁	—	2	2	no	—
463	Q₈×C₇₁	—	2	1	no	—
464	Q₈×C₇₁	—	4	2	no	—
465	Q₈×C₇₁	—	4	4	no	—
466	Q₈×C₇₁	—	4	2	no	—
467	Q₈×C₇₁	—	4	2	no	—
468	Q₈×C₇₁	C₂×#41	1	2	yes	—
469	D₄×C₇₁	—	2	2	no	—
470	D₄×C₇₁	—	2	2	no	—
471	D₄×C₇₁	—	2	1	no	—
472	D₄×C₇₁	—	2	2	no	—
473	D₄×C₇₁	—	4	2	no	—
474	D₄×C₇₁	—	4	4	no	—
475	D₄×C₇₁	—	4	2	no	—
476	D₄×C₇₁	—	4	4	no	—
477	D₄×C₇₁	—	4	4	no	—
478	D₄×C₇₁	—	4	2	no	—
479	D₄×C₇₁	—	8	1	no	—
480	D₄×C₇₁	—	8	2	no	—
481	D₄×C₇₁	C₂×#41	1	2	yes	—
482	C₂×C₄×C₇₁	—	2	1	no	—
483	C₂×C₄×C₇₁	—	2	2	no	—
484	C₂×C₄×C₇₁	—	2	2	no	—
485	C₂×C₄×C₇₁	—	2	1	no	—
486	C₂×C₄×C₇₁	—	2	2	no	—
487	C₂×C₄×C₇₁	—	2	1	no	—
488	C₂×C₄×C₇₁	—	2	1	no	—
489	C₂×C₄×C₇₁	—	2	1	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	2	no	—
495	C₂×C₄×C₇₁	—	2	1	no	—
496	C₂×C₄×C₇₁	—	2	1	no	—
497	C₂×C₄×C₇₁	—	4	2	no	—
498	C₂×C₄×C₇₁	—	4	1	no	—
499	C₂×C₄×C₇₁	—	4	2	no	—
500	C₂×C₄×C₇₁	—	4	4	no	—
501	C₂×C₄×C₇₁	—	4	2	no	—
502	C₂×C₄×C₇₁	—	4	4	no	—
503	C₂×C₄×C₇₁	—	4	2	no	—
504	C₂×C₄×C₇₁	—	4	2	no	—
505	C₂×C₄×C₇₁	—	4	4	no	—
506	C₂×C₄×C₇₁	—	4	4	no	—
507	C₂×C₄×C₇₁	—	4	2	no	—
508	C₂×C₄×C₇₁	—	8	2	no	—
509	C₂×C₄×C₇₁	—	8	1	no	—
510	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₇₁	—	2	2	no	—
520	C₈×C₇₁	—	2	1	no	—
521	C₈×C₇₁	—	2	1	no	—
522	C₈×C₇₁	—	2	2	no	—
523	C₈×C₇₁	—	2	1	no	—
524	C₈×C₇₁	C₂×#41	1	2	yes	—
525	C₂²×C₇₁	—	2	1	no	—
526	C₂²×C₇₁	—	2	2	no	—
527	C₂²×C₇₁	—	2	1	no	—
528	C₂²×C₇₁	—	2	2	no	—
529	C₂²×C₇₁	—	2	2	no	—
530	C₂²×C₇₁	—	2	1	no	—
531	C₂²×C₇₁	—	2	2	no	—
532	C₂²×C₇₁	—	4	1	no	—
533	C₂²×C₇₁	—	4	1	no	—
534	C₂²×C₇₁	—	4	2	no	—
535	C₂²×C₇₁	—	4	2	no	—
536	C₂²×C₇₁	—	4	2	no	—
537	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
538	C₄×C₇₁	—	2	1	no	—
539	C₄×C₇₁	—	2	2	no	—
540	C₄×C₇₁	—	2	1	no	—
541	C₄×C₇₁	—	2	2	no	—
542	C₄×C₇₁	—	2	1	no	—
543	C₄×C₇₁	—	2	2	no	—
544	C₄×C₇₁	—	2	1	no	—
545	C₄×C₇₁	—	2	2	no	—
546	C₄×C₇₁	—	4	1	no	—
547	C₄×C₇₁	—	4	1	no	—
548	C₄×C₇₁	—	4	1	no	—
549	C₄×C₇₁	—	4	2	no	—
550	C₄×C₇₁	—	4	1	no	—
551	C₄×C₇₁	—	4	1	no	—
552	C₄×C₇₁	—	4	2	no	—
553	C₄×C₇₁	—	4	2	no	—
554	C₄×C₇₁	—	4	1	no	—
555	C₄×C₇₁	#575	1	2	yes	—
556	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
557	C₄×C₇₁	#585	1	1	yes	characteristic
558	#61460	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
559	C₂×C₇₁	—	4	1	no	—
560	C₂×C₇₁	—	4	2	no	—
561	C₂×C₇₁	—	4	2	no	—
562	C₂×C₇₁	—	8	2	no	—
563	C₂×C₇₁	D₄×#41	1	1	yes	characteristic
564	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
565	C₂×C₇₁	#3586	1	1	yes	characteristic
566	#3482	C₂×C₇₁	1	1	yes	characteristic, complemented
567	#3480	C₂×C₇₁	1	1	yes	characteristic, complemented
568	#3400	C₂×C₇₁	1	1	yes	characteristic, complemented
569	#3386	C₂×C₇₁	1	1	yes	characteristic, complemented
570	#3374	C₂×C₇₁	1	1	yes	characteristic, complemented
571	#3373	C₂×C₇₁	1	1	yes	characteristic, complemented
572	#3350	C₂×C₇₁	1	2	yes	complemented
573	#3342	C₂×C₇₁	1	1	yes	characteristic, complemented
574	#3313	C₂×C₇₁	1	2	yes	complemented
575	#3307	C₂×C₇₁	1	2	yes	complemented
576	#3304	C₂×C₇₁	1	1	yes	characteristic, complemented
577	#3302	C₂×C₇₁	1	1	yes	characteristic, complemented
578	#3284	C₂×C₇₁	1	1	yes	characteristic, complemented
579	#3269	C₂×C₇₁	1	2	yes	complemented
580	#3182	C₂×C₇₁	1	1	yes	characteristic, complemented
581	#3181	C₂×C₇₁	1	2	yes	complemented
582	#3116	C₂×C₇₁	1	2	yes	complemented
583	#3115	C₂×C₇₁	1	1	yes	characteristic, complemented
584	#3113	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3111	C₂×C₇₁	1	2	yes	complemented
586	#2970	C₂×C₇₁	1	1	yes	characteristic, complemented
587	C₄×#137	C₂×C₇₁	1	1	yes	characteristic, complemented
588	#2943	C₂×C₇₁	1	2	yes	complemented
589	C₇₁	#61460	1	1	yes	characteristic, direct product factor, Sylow
590	C₂×#137	C₂²×C₇₁	1	1	yes	characteristic
591	C₂×#135	C₂²×C₇₁	1	2	yes	—
592	#559	—	2	1	no	—
593	#559	C₂²×C₇₁	1	1	yes	characteristic
594	#557	C₂²×C₇₁	1	1	yes	characteristic
595	#557	C₂²×C₇₁	1	1	yes	characteristic
596	#556	—	2	1	no	—
597	#556	C₂²×C₇₁	1	1	yes	characteristic
598	#556	C₂²×C₇₁	1	1	yes	characteristic
599	#556	C₂²×C₇₁	1	2	yes	—
600	#553	—	2	2	no	—
601	#553	C₂²×C₇₁	1	2	yes	—
602	#552	—	2	1	no	—
603	#552	—	2	2	no	—
604	#550	C₂²×C₇₁	1	1	yes	characteristic
605	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
606	#548	—	2	1	no	—
607	#548	C₂²×C₇₁	1	2	yes	—
608	#547	C₂²×C₇₁	1	2	yes	—
609	#547	C₂²×C₇₁	1	1	yes	characteristic
610	#533	C₂²×C₇₁	1	1	yes	characteristic
611	#533	C₂²×C₇₁	1	2	yes	—
612	#532	—	2	1	no	—
613	#532	C₂²×C₇₁	1	1	yes	characteristic
614	#529	—	2	2	no	—
615	#529	—	2	1	no	—
616	#529	—	2	2	no	—
617	#529	C₂²×C₇₁	1	2	yes	—
618	C₄×#41	—	2	1	no	—
619	C₄×#41	C₂²×C₇₁	1	2	yes	—
620	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
621	C₄×#41	C₂²×C₇₁	1	2	yes	—
622	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
623	C₂×C₄×Q₈	—	2	1	no	—
624	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
625	#501	C₂²×C₇₁	1	2	yes	—
626	#500	C₂²×C₇₁	1	1	yes	characteristic
627	#497	C₂²×C₇₁	1	2	yes	—
628	#492	C₂²×C₇₁	1	1	yes	characteristic
629	#491	C₂²×C₇₁	1	2	yes	—
630	#489	C₂²×C₇₁	1	2	yes	—
631	#487	C₂²×C₇₁	1	1	yes	characteristic
632	#486	C₂²×C₇₁	1	1	yes	characteristic
633	#485	C₂²×C₇₁	1	2	yes	—
634	#485	C₂²×C₇₁	1	2	yes	—
635	#485	C₂²×C₇₁	1	2	yes	—
636	#483	C₂²×C₇₁	1	2	yes	—
637	#482	C₂²×C₇₁	1	2	yes	—
638	#482	C₂²×C₇₁	1	2	yes	—
639	#479	C₂²×C₇₁	1	2	yes	—
640	#478	C₂²×C₇₁	1	2	yes	—
641	#477	C₂²×C₇₁	1	2	yes	—
642	#476	C₂²×C₇₁	1	2	yes	—
643	#475	C₂²×C₇₁	1	1	yes	characteristic
644	#475	C₂²×C₇₁	1	1	yes	characteristic
645	#475	C₂²×C₇₁	1	1	yes	characteristic
646	#474	C₂²×C₇₁	1	1	yes	characteristic
647	#468	C₂²×C₇₁	1	2	yes	—
648	#468	C₂²×C₇₁	1	2	yes	—
649	#467	C₂²×C₇₁	1	2	yes	—
650	#467	C₂²×C₇₁	1	2	yes	—
651	#465	C₂²×C₇₁	1	2	yes	—
652	#465	C₂²×C₇₁	1	2	yes	—
653	#464	C₂²×C₇₁	1	2	yes	—
654	#463	C₂²×C₇₁	1	2	yes	—
655	#462	C₂²×C₇₁	1	1	yes	characteristic
656	#462	C₂²×C₇₁	1	1	yes	characteristic
657	#462	C₂²×C₇₁	1	2	yes	—
658	#461	C₂²×C₇₁	1	2	yes	—
659	#460	C₂²×C₇₁	1	1	yes	characteristic
660	#459	C₂²×C₇₁	1	1	yes	characteristic
661	#452	C₂²×C₇₁	1	2	yes	—
662	#452	C₂²×C₇₁	1	2	yes	—
663	#452	C₂²×C₇₁	1	2	yes	—
664	#451	C₂²×C₇₁	1	2	yes	—
665	#449	C₂²×C₇₁	1	2	yes	—
666	#449	C₂²×C₇₁	1	2	yes	—
667	#446	C₂²×C₇₁	1	1	yes	characteristic
668	#446	C₂²×C₇₁	1	1	yes	characteristic
669	#442	C₂²×C₇₁	1	2	yes	—
670	#442	C₂²×C₇₁	1	2	yes	—
671	#441	C₂²×C₇₁	1	2	yes	—
672	#441	C₂²×C₇₁	1	2	yes	—
673	#441	C₂²×C₇₁	1	1	yes	characteristic
674	#441	C₂²×C₇₁	1	2	yes	—
675	#441	C₂²×C₇₁	1	1	yes	characteristic
676	#440	C₂²×C₇₁	1	2	yes	—
677	#440	C₂²×C₇₁	1	1	yes	characteristic
678	#440	C₂²×C₇₁	1	2	yes	—
679	#440	C₂²×C₇₁	1	2	yes	—
680	#440	C₂²×C₇₁	1	2	yes	—
681	#440	C₂²×C₇₁	1	2	yes	—
682	#440	C₂²×C₇₁	1	1	yes	characteristic
683	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
684	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
686	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
687	#435	C₂²×C₇₁	1	2	yes	—
688	#435	C₂²×C₇₁	1	2	yes	—
689	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
690	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
691	#432	C₂²×C₇₁	1	2	yes	—
692	#432	C₂²×C₇₁	1	1	yes	characteristic
693	#428	C₂²×C₇₁	1	1	yes	characteristic
694	#427	C₂²×C₇₁	1	2	yes	—
695	#419	C₂²×C₇₁	1	1	yes	characteristic
696	#417	C₂²×C₇₁	1	1	yes	characteristic
697	#416	C₂²×C₇₁	1	2	yes	—
698	#416	C₂²×C₇₁	1	2	yes	—
699	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
700	C₂×#97	C₂²×C₇₁	1	2	yes	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
703	C₂×#41	C₂³×C₇₁	1	2	yes	—
704	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
705	C₂×#41	C₂³×C₇₁	1	2	yes	—
706	C₂²×Q₈	—	2	1	no	—
707	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
708	#137	—	2	4	no	—
709	#135	—	2	8	no	—
710	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
712	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
713	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
719	C₂×D₈	C₂³×C₇₁	1	2	yes	—
720	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
721	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
722	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
723	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
726	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
730	#127	—	2	1	no	—
731	#127	C₂³×C₇₁	1	1	yes	characteristic
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	—	2	2	no	—
740	#125	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	—	2	1	no	—
743	#125	C₂³×C₇₁	1	2	yes	—
744	#124	—	2	1	no	—
745	#124	—	2	1	no	—
746	#124	—	2	2	no	—
747	#124	—	2	1	no	—
748	#124	—	2	2	no	—
749	#124	—	2	1	no	—
750	#124	C₂³×C₇₁	1	2	yes	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	C₂³×C₇₁	1	2	yes	—
773	#121	C₂³×C₇₁	1	2	yes	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
791	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	D₄×C₇₁	1	2	yes	—
807	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₇₁	1	2	yes	—
810	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₇₁	1	2	yes	—
812	C₄×D₄	C₂³×C₇₁	1	2	yes	—
813	C₄×D₄	C₂³×C₇₁	1	2	yes	—
814	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	—	2	2	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	D₄×C₇₁	1	1	yes	characteristic
822	#117	D₄×C₇₁	1	2	yes	—
823	#117	C₂³×C₇₁	1	2	yes	—
824	#117	C₂³×C₇₁	1	2	yes	—
825	#117	C₂³×C₇₁	1	1	yes	characteristic
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	—	2	2	no	—
829	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	—	2	2	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	2	2	no	—
834	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
835	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
836	#107	C₂³×C₇₁	1	1	yes	characteristic
837	#107	C₂³×C₇₁	1	2	yes	—
838	#107	C₂³×C₇₁	1	1	yes	characteristic
839	#107	C₂³×C₇₁	1	2	yes	—
840	#107	C₂³×C₇₁	1	2	yes	—
841	#106	C₂³×C₇₁	1	2	yes	—
842	#106	C₂³×C₇₁	1	2	yes	—
843	#106	C₂³×C₇₁	1	1	yes	characteristic
844	#106	C₂³×C₇₁	1	1	yes	characteristic
845	#106	C₂³×C₇₁	1	2	yes	—
846	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
850	#103	C₂³×C₇₁	1	1	yes	characteristic
851	#103	C₂³×C₇₁	1	2	yes	—
852	#103	C₂³×C₇₁	1	2	yes	—
853	#103	C₂³×C₇₁	1	2	yes	—
854	#103	C₂³×C₇₁	1	1	yes	characteristic
855	#103	C₂³×C₇₁	1	1	yes	characteristic
856	#103	C₂³×C₇₁	1	1	yes	characteristic
857	#103	C₂³×C₇₁	1	1	yes	characteristic
858	#103	C₂³×C₇₁	1	1	yes	characteristic
859	#103	C₂³×C₇₁	1	2	yes	—
860	#103	C₂³×C₇₁	1	2	yes	—
861	#103	C₂³×C₇₁	1	2	yes	—
862	#103	C₂³×C₇₁	1	2	yes	—
863	#102	C₂³×C₇₁	1	1	yes	characteristic
864	#102	C₂³×C₇₁	1	2	yes	—
865	#102	C₂³×C₇₁	1	2	yes	—
866	#102	C₂³×C₇₁	1	2	yes	—
867	#102	C₂³×C₇₁	1	1	yes	characteristic
868	#102	C₂³×C₇₁	1	2	yes	—
869	#102	C₂³×C₇₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
873	#97	C₂³×C₇₁	1	1	yes	characteristic
874	#97	C₂³×C₇₁	1	2	yes	—
875	#97	C₂³×C₇₁	1	2	yes	—
876	#97	C₂³×C₇₁	1	2	yes	—
877	#97	C₂³×C₇₁	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
880	#41	—	2	4	no	—
881	#41	—	2	4	no	—
882	#41	—	2	2	no	—
883	#41	—	4	2	no	—
884	#41	—	4	2	no	—
885	#41	—	4	2	no	—
886	#41	—	4	1	no	—
887	#41	—	4	4	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	4	1	no	—
894	C₂×Q₈	—	4	4	no	—
895	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
908	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
909	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
910	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
922	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
923	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
924	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
927	Q₁₆	—	2	4	no	—
928	Q₁₆	—	2	2	no	—
929	Q₁₆	—	2	2	no	—
930	Q₁₆	—	4	2	no	—
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	2	4	no	—
933	SD₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	#41×C₇₁	1	4	yes	complemented
936	D₈	—	2	4	no	—
937	M₁₆	—	2	2	no	—
938	M₁₆	—	4	1	no	—
939	C₂×C₈	—	2	4	no	—
940	C₂×C₈	—	4	2	no	—
941	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
945	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
946	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1012	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1013	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1014	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₇₁	1	2	yes	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1021	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	4	4	no	—
1032	Q₈	—	4	2	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	C₂×#41×C₇₁	1	2	yes	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	1	no	—
1046	D₄	—	8	2	no	—
1047	D₄	C₂×#41×C₇₁	1	2	yes	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1084	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	2	no	—
1089	C₈	—	2	1	no	—
1090	C₈	C₂×#41×C₇₁	1	2	yes	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	#575×C₇₁	1	2	yes	—
1122	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
1123	C₄	#585×C₇₁	1	1	yes	characteristic
1124	C₂	—	4	1	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	8	2	no	—
1128	C₂	D₄×#41×C₇₁	1	1	yes	characteristic
1129	C₂	C₂×#575×C₇₁	1	1	yes	characteristic
1130	C₂	C₇₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₄×#41×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3482	C₂	semidirect
2. C₇₁×#3480	C₂	semidirect
3. C₇₁×#3400	C₂	semidirect
4. C₇₁×#3386	C₂	semidirect
5. C₇₁×#3374	C₂	semidirect
6. C₇₁×#3373	C₂	semidirect
7. C₇₁×#3350	C₂	semidirect
8. C₇₁×#3342	C₂	semidirect
9. C₇₁×#3313	C₂	semidirect
10. C₇₁×#3307	C₂	semidirect
11. C₇₁×#3304	C₂	semidirect
12. C₇₁×#3302	C₂	semidirect
13. C₇₁×#3284	C₂	semidirect
14. C₇₁×#3269	C₂	semidirect
15. C₇₁×#3182	C₂	semidirect
16. C₇₁×#3181	C₂	semidirect
17. C₇₁×#3116	C₂	semidirect
18. C₇₁×#3115	C₂	semidirect
19. C₇₁×#3113	C₂	semidirect
20. C₇₁×#3111	C₂	semidirect
21. C₇₁×#2970	C₂	semidirect
22. C₄×#137×C₇₁	C₂	semidirect
23. C₇₁×#2943	C₂	semidirect
369. SD₁₆×C₇₁	#41	semidirect
558. #61460	C₇₁	direct (N × H)
566. #3482	C₂×C₇₁	semidirect
567. #3480	C₂×C₇₁	semidirect
568. #3400	C₂×C₇₁	semidirect
569. #3386	C₂×C₇₁	semidirect
570. #3374	C₂×C₇₁	semidirect
571. #3373	C₂×C₇₁	semidirect
572. #3350	C₂×C₇₁	semidirect
573. #3342	C₂×C₇₁	semidirect
574. #3313	C₂×C₇₁	semidirect
575. #3307	C₂×C₇₁	semidirect
576. #3304	C₂×C₇₁	semidirect
577. #3302	C₂×C₇₁	semidirect
578. #3284	C₂×C₇₁	semidirect
579. #3269	C₂×C₇₁	semidirect
580. #3182	C₂×C₇₁	semidirect
581. #3181	C₂×C₇₁	semidirect
582. #3116	C₂×C₇₁	semidirect
583. #3115	C₂×C₇₁	semidirect
584. #3113	C₂×C₇₁	semidirect
585. #3111	C₂×C₇₁	semidirect
586. #2970	C₂×C₇₁	semidirect
587. C₄×#137	C₂×C₇₁	semidirect
588. #2943	C₂×C₇₁	semidirect
589. C₇₁	#61460	direct (N × H)
935. SD₁₆	#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×#3482	2
C₇₁×#3480	2
C₇₁×#3400	2
C₇₁×#3386	2
C₇₁×#3374	2
C₇₁×#3373	2
C₇₁×#3350	2
C₇₁×#3342	2
C₇₁×#3313	2
C₇₁×#3307	2
C₇₁×#3304	2
C₇₁×#3302	2
C₇₁×#3284	2
C₇₁×#3269	2
C₇₁×#3182	2
C₇₁×#3181	2
C₇₁×#3116	2
C₇₁×#3115	2
C₇₁×#3113	2
C₇₁×#3111	2
C₇₁×#2970	2
C₄×#137×C₇₁	2
C₇₁×#2943	2
#61460	71

Subgroups — C71×#61460 #31882332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61460 #31882332