Subgroups — C₇₁×#60875 #31881747

Order 18176.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3494	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#3458	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3244	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3243	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3241	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3241	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3240	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3235	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3233	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3228	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#482×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#555×C₇₁	—	2	1	no	—
25	#553×C₇₁	—	2	1	no	—
26	#553×C₇₁	—	2	1	no	—
27	#551×C₇₁	—	2	2	no	—
28	#547×C₇₁	—	2	1	no	—
29	#546×C₇₁	—	2	2	no	—
30	#544×C₇₁	—	2	1	no	—
31	#544×C₇₁	—	2	1	no	—
32	#544×C₇₁	C₂²	1	1	yes	characteristic
33	#544×C₇₁	C₂²	1	1	yes	characteristic
34	#544×C₇₁	C₂²	1	1	yes	characteristic
35	#544×C₇₁	C₂²	1	1	yes	characteristic
36	#544×C₇₁	C₂²	1	1	yes	characteristic
37	#544×C₇₁	C₂²	1	2	yes	complemented
38	#544×C₇₁	C₂²	1	2	yes	complemented
39	#543×C₇₁	—	2	2	no	—
40	#542×C₇₁	C₂²	1	2	yes	—
41	#540×C₇₁	C₂²	1	2	yes	—
42	#535×C₇₁	C₂²	1	1	yes	characteristic
43	#533×C₇₁	—	2	2	no	—
44	#533×C₇₁	—	2	1	no	—
45	#533×C₇₁	—	2	1	no	—
46	#533×C₇₁	C₂²	1	2	yes	complemented
47	#533×C₇₁	C₂²	1	2	yes	complemented
48	#532×C₇₁	C₂²	1	2	yes	—
49	#529×C₇₁	C₂²	1	2	yes	—
50	#525×C₇₁	C₂²	1	1	yes	characteristic
51	C₂×#121×C₇₁	C₂²	1	1	yes	characteristic
52	#520×C₇₁	C₂²	1	1	yes	characteristic
53	#518×C₇₁	C₂²	1	1	yes	characteristic
54	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
55	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
56	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
57	#501×C₇₁	C₂²	1	2	yes	complemented
58	#501×C₇₁	C₂²	1	2	yes	complemented
59	#501×C₇₁	C₂²	1	2	yes	complemented
60	#501×C₇₁	C₂²	1	2	yes	complemented
61	#500×C₇₁	C₂²	1	2	yes	complemented
62	#499×C₇₁	C₂²	1	2	yes	complemented
63	#499×C₇₁	C₂²	1	2	yes	complemented
64	#498×C₇₁	C₂²	1	2	yes	complemented
65	#490×C₇₁	C₂²	1	2	yes	complemented
66	#490×C₇₁	C₂²	1	2	yes	complemented
67	#489×C₇₁	C₂²	1	2	yes	complemented
68	#489×C₇₁	C₂²	1	2	yes	complemented
69	#488×C₇₁	C₂²	1	2	yes	complemented
70	#488×C₇₁	C₂²	1	2	yes	complemented
71	#486×C₇₁	C₂²	1	2	yes	complemented
72	#486×C₇₁	C₂²	1	2	yes	complemented
73	#485×C₇₁	C₂²	1	1	yes	characteristic, complemented
74	#485×C₇₁	C₂²	1	1	yes	characteristic, complemented
75	#485×C₇₁	C₂²	1	2	yes	complemented
76	#485×C₇₁	C₂²	1	2	yes	complemented
77	#484×C₇₁	C₂²	1	1	yes	characteristic, complemented
78	#483×C₇₁	C₂²	1	1	yes	characteristic, complemented
79	#482×C₇₁	C₂²	1	2	yes	—
80	#482×C₇₁	C₂²	1	2	yes	—
81	#482×C₇₁	C₂²	1	2	yes	—
82	#482×C₇₁	C₂²	1	2	yes	—
83	#482×C₇₁	C₂²	1	2	yes	—
84	#482×C₇₁	C₂²	1	2	yes	—
85	#482×C₇₁	C₂²	1	1	yes	characteristic, complemented
86	#482×C₇₁	C₂²	1	1	yes	characteristic, complemented
87	#482×C₇₁	C₂²	1	2	yes	complemented
88	#482×C₇₁	C₂²	1	2	yes	complemented
89	#481×C₇₁	C₂²	1	2	yes	—
90	#481×C₇₁	C₂²	1	1	yes	characteristic, complemented
91	#480×C₇₁	C₂²	1	2	yes	—
92	#480×C₇₁	C₂²	1	1	yes	characteristic, complemented
93	#479×C₇₁	C₂²	1	2	yes	complemented
94	#479×C₇₁	C₂²	1	2	yes	complemented
95	#478×C₇₁	C₂²	1	2	yes	complemented
96	#478×C₇₁	C₂²	1	2	yes	complemented
97	#478×C₇₁	C₂²	1	2	yes	complemented
98	#478×C₇₁	C₂²	1	2	yes	complemented
99	#478×C₇₁	C₂²	1	2	yes	complemented
100	#478×C₇₁	C₂²	1	2	yes	complemented
101	#477×C₇₁	C₂²	1	2	yes	complemented
102	#476×C₇₁	C₂²	1	2	yes	complemented
103	#476×C₇₁	C₂²	1	2	yes	complemented
104	#476×C₇₁	C₂²	1	2	yes	complemented
105	#475×C₇₁	C₂²	1	2	yes	complemented
106	#474×C₇₁	C₂²	1	2	yes	complemented
107	#474×C₇₁	C₂²	1	2	yes	complemented
108	#474×C₇₁	C₂²	1	2	yes	complemented
109	#433×C₇₁	C₂²	1	2	yes	complemented
110	#433×C₇₁	C₂²	1	2	yes	complemented
111	#432×C₇₁	C₂²	1	2	yes	complemented
112	#431×C₇₁	C₂²	1	2	yes	complemented
113	#428×C₇₁	C₂²	1	1	yes	characteristic
114	#428×C₇₁	C₂²	1	1	yes	characteristic
115	#428×C₇₁	C₂²	1	1	yes	characteristic
116	#428×C₇₁	C₂²	1	1	yes	characteristic
117	#427×C₇₁	C₂²	1	1	yes	characteristic
118	#427×C₇₁	C₂²	1	1	yes	characteristic
119	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
120	C₂×#106×C₇₁	C₂²	1	1	yes	characteristic
121	#424×C₇₁	C₂²	1	1	yes	characteristic
122	#424×C₇₁	C₂²	1	1	yes	characteristic
123	#418×C₇₁	C₂²	1	1	yes	characteristic
124	#418×C₇₁	C₂²	1	1	yes	characteristic
125	#417×C₇₁	C₂²	1	1	yes	characteristic
126	#417×C₇₁	C₂²	1	1	yes	characteristic
127	#416×C₇₁	C₂²	1	1	yes	characteristic
128	#416×C₇₁	C₂²	1	1	yes	characteristic
129	C₂×#102×C₇₁	C₂²	1	1	yes	characteristic
130	C₂×#102×C₇₁	C₂²	1	1	yes	characteristic
131	#407×C₇₁	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
133	#405×C₇₁	C₂²	1	1	yes	characteristic
134	#405×C₇₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₇₁	—	2	2	no	—
136	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₇₁	—	2	1	no	—
138	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₇₁	—	2	1	no	—
145	C₄⋊Q₈×C₇₁	—	2	1	no	—
146	C₄⋊Q₈×C₇₁	—	2	1	no	—
147	C₄⋊Q₈×C₇₁	—	2	1	no	—
148	C₄⋊Q₈×C₇₁	—	2	2	no	—
149	C₄⋊Q₈×C₇₁	—	2	2	no	—
150	C₄⋊Q₈×C₇₁	—	2	1	no	—
151	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
156	#127×C₇₁	C₂³	1	2	yes	—
157	#126×C₇₁	—	2	2	no	—
158	#126×C₇₁	—	2	2	no	—
159	#125×C₇₁	—	2	1	no	—
160	#125×C₇₁	—	2	1	no	—
161	#125×C₇₁	—	2	1	no	—
162	#125×C₇₁	—	2	1	no	—
163	#125×C₇₁	—	2	2	no	—
164	#125×C₇₁	—	2	2	no	—
165	#125×C₇₁	—	2	1	no	—
166	#125×C₇₁	C₂³	1	2	yes	—
167	#125×C₇₁	C₂³	1	2	yes	—
168	#125×C₇₁	C₂³	1	2	yes	—
169	#125×C₇₁	C₂³	1	2	yes	—
170	#125×C₇₁	C₂³	1	2	yes	—
171	#124×C₇₁	—	2	2	no	—
172	#124×C₇₁	—	2	2	no	—
173	#124×C₇₁	C₂³	1	2	yes	—
174	#123×C₇₁	—	2	1	no	—
175	#123×C₇₁	—	2	2	no	—
176	#123×C₇₁	—	2	2	no	—
177	#123×C₇₁	—	2	2	no	—
178	#123×C₇₁	—	2	2	no	—
179	C₂²⋊Q₈×C₇₁	—	2	2	no	—
180	C₂²⋊Q₈×C₇₁	—	2	2	no	—
181	C₂²⋊Q₈×C₇₁	—	2	2	no	—
182	C₂²⋊Q₈×C₇₁	—	2	2	no	—
183	C₂²⋊Q₈×C₇₁	—	2	2	no	—
184	C₂²⋊Q₈×C₇₁	—	2	2	no	—
185	C₂²⋊Q₈×C₇₁	—	2	2	no	—
186	C₂²⋊Q₈×C₇₁	—	2	2	no	—
187	C₂²⋊Q₈×C₇₁	—	2	2	no	—
188	C₂²⋊Q₈×C₇₁	—	2	2	no	—
189	C₂²⋊Q₈×C₇₁	—	2	2	no	—
190	C₂²⋊Q₈×C₇₁	—	2	2	no	—
191	C₂²⋊Q₈×C₇₁	—	2	2	no	—
192	C₂²⋊Q₈×C₇₁	—	2	2	no	—
193	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
195	#121×C₇₁	—	2	1	no	—
196	#121×C₇₁	—	2	1	no	—
197	#121×C₇₁	—	2	2	no	—
198	#121×C₇₁	—	2	1	no	—
199	#121×C₇₁	—	2	1	no	—
200	#121×C₇₁	—	2	2	no	—
201	#121×C₇₁	—	2	2	no	—
202	#121×C₇₁	C₂³	1	2	yes	—
203	#121×C₇₁	C₂³	1	1	yes	characteristic
204	#121×C₇₁	C₂³	1	2	yes	—
205	#121×C₇₁	C₂³	1	1	yes	characteristic
206	#120×C₇₁	—	2	1	no	—
207	#120×C₇₁	—	2	2	no	—
208	C₄×Q₈×C₇₁	—	2	2	no	—
209	C₄×Q₈×C₇₁	—	2	2	no	—
210	C₄×Q₈×C₇₁	—	2	2	no	—
211	C₄×Q₈×C₇₁	—	2	2	no	—
212	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
213	C₄×D₄×C₇₁	—	2	1	no	—
214	C₄×D₄×C₇₁	—	2	1	no	—
215	C₄×D₄×C₇₁	—	2	2	no	—
216	C₄×D₄×C₇₁	—	2	1	no	—
217	C₄×D₄×C₇₁	—	2	1	no	—
218	C₄×D₄×C₇₁	—	2	2	no	—
219	C₄×D₄×C₇₁	—	2	2	no	—
220	C₄×D₄×C₇₁	C₂³	1	2	yes	—
221	C₄×D₄×C₇₁	C₂³	1	2	yes	—
222	C₄×D₄×C₇₁	C₂³	1	2	yes	—
223	#117×C₇₁	—	2	1	no	—
224	#117×C₇₁	—	2	1	no	—
225	#117×C₇₁	—	2	1	no	—
226	#117×C₇₁	—	2	1	no	—
227	#117×C₇₁	—	2	1	no	—
228	#117×C₇₁	—	2	2	no	—
229	#117×C₇₁	D₄	1	2	yes	—
230	#117×C₇₁	D₄	1	1	yes	characteristic
231	#117×C₇₁	D₄	1	1	yes	characteristic
232	#117×C₇₁	C₂³	1	1	yes	characteristic
233	#117×C₇₁	C₂³	1	1	yes	characteristic
234	#117×C₇₁	C₂³	1	1	yes	characteristic
235	#117×C₇₁	C₂³	1	2	yes	—
236	#117×C₇₁	C₂³	1	1	yes	characteristic
237	#117×C₇₁	C₂³	1	1	yes	characteristic
238	#117×C₇₁	C₂³	1	2	yes	—
239	#117×C₇₁	C₂³	1	1	yes	characteristic
240	#117×C₇₁	C₂³	1	1	yes	characteristic
241	#117×C₇₁	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
243	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
251	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
252	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
254	C₂×C₂²⋊C₄×C₇₁	D₄	1	2	yes	—
255	C₂×C₄²×C₇₁	—	2	1	no	—
256	C₂×C₄²×C₇₁	—	2	1	no	—
257	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
258	#107×C₇₁	C₂³	1	2	yes	—
259	#107×C₇₁	C₂³	1	2	yes	—
260	#107×C₇₁	C₂³	1	1	yes	characteristic
261	#107×C₇₁	C₂³	1	1	yes	characteristic
262	#107×C₇₁	C₂³	1	1	yes	characteristic
263	#107×C₇₁	C₂³	1	1	yes	characteristic
264	#107×C₇₁	C₂³	1	2	yes	—
265	#107×C₇₁	C₂³	1	2	yes	—
266	#107×C₇₁	C₂³	1	2	yes	—
267	#107×C₇₁	C₂³	1	2	yes	—
268	#106×C₇₁	C₂³	1	2	yes	—
269	#106×C₇₁	C₂³	1	2	yes	—
270	#106×C₇₁	C₂³	1	1	yes	characteristic
271	#106×C₇₁	C₂³	1	1	yes	characteristic
272	#106×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
278	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
279	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
282	#103×C₇₁	C₂³	1	1	yes	characteristic
283	#103×C₇₁	C₂³	1	1	yes	characteristic
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	#102×C₇₁	C₂³	1	2	yes	—
289	#102×C₇₁	C₂³	1	2	yes	—
290	#102×C₇₁	C₂³	1	2	yes	—
291	#102×C₇₁	C₂³	1	2	yes	—
292	#102×C₇₁	C₂³	1	1	yes	characteristic
293	#102×C₇₁	C₂³	1	1	yes	characteristic
294	#102×C₇₁	C₂³	1	1	yes	characteristic
295	#102×C₇₁	C₂³	1	1	yes	characteristic
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	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
308	#97×C₇₁	C₂³	1	2	yes	—
309	#97×C₇₁	C₂³	1	2	yes	—
310	C₄×C₈×C₇₁	C₂³	1	2	yes	—
311	C₄×C₈×C₇₁	C₂³	1	2	yes	—
312	C₂⁴×C₇₁	—	2	1	no	—
313	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
314	#41×C₇₁	—	2	2	no	—
315	#41×C₇₁	—	2	2	no	—
316	#41×C₇₁	—	8	4	no	—
317	C₂×Q₈×C₇₁	—	2	2	no	—
318	C₂×Q₈×C₇₁	—	2	2	no	—
319	C₂×Q₈×C₇₁	—	2	2	no	—
320	C₂×Q₈×C₇₁	—	2	2	no	—
321	C₂×Q₈×C₇₁	—	2	2	no	—
322	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₇₁	—	2	1	no	—
324	C₂×D₄×C₇₁	—	2	1	no	—
325	C₂×D₄×C₇₁	—	2	2	no	—
326	C₂×D₄×C₇₁	—	2	1	no	—
327	C₂×D₄×C₇₁	—	2	2	no	—
328	C₂×D₄×C₇₁	—	2	1	no	—
329	C₂×D₄×C₇₁	—	2	2	no	—
330	C₂×D₄×C₇₁	—	2	2	no	—
331	C₂×D₄×C₇₁	—	2	2	no	—
332	C₂×D₄×C₇₁	—	2	2	no	—
333	C₂×D₄×C₇₁	—	8	2	no	—
334	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
335	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇₁	—	2	2	no	—
337	C₂²×C₄×C₇₁	—	2	2	no	—
338	C₂²×C₄×C₇₁	—	2	1	no	—
339	C₂²×C₄×C₇₁	—	2	1	no	—
340	C₂²×C₄×C₇₁	—	2	1	no	—
341	C₂²×C₄×C₇₁	—	2	1	no	—
342	C₂²×C₄×C₇₁	—	2	1	no	—
343	C₂²×C₄×C₇₁	—	2	1	no	—
344	C₂²×C₄×C₇₁	—	2	2	no	—
345	C₂²×C₄×C₇₁	—	2	2	no	—
346	C₂²×C₄×C₇₁	—	2	2	no	—
347	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
352	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
355	M₁₆×C₇₁	—	2	2	no	—
356	M₁₆×C₇₁	—	2	2	no	—
357	C₂×C₈×C₇₁	—	2	2	no	—
358	C₂×C₈×C₇₁	—	2	2	no	—
359	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₇₁	—	2	1	no	—
366	C₄⋊C₄×C₇₁	—	2	2	no	—
367	C₄⋊C₄×C₇₁	—	2	1	no	—
368	C₄⋊C₄×C₇₁	—	2	1	no	—
369	C₄⋊C₄×C₇₁	—	2	1	no	—
370	C₄⋊C₄×C₇₁	—	2	1	no	—
371	C₄⋊C₄×C₇₁	—	2	1	no	—
372	C₄⋊C₄×C₇₁	—	2	2	no	—
373	C₄⋊C₄×C₇₁	—	2	2	no	—
374	C₄⋊C₄×C₇₁	—	2	2	no	—
375	C₄⋊C₄×C₇₁	—	2	1	no	—
376	C₄⋊C₄×C₇₁	—	2	2	no	—
377	C₄⋊C₄×C₇₁	—	2	2	no	—
378	C₄⋊C₄×C₇₁	—	2	2	no	—
379	C₄⋊C₄×C₇₁	—	2	2	no	—
380	C₄⋊C₄×C₇₁	—	2	2	no	—
381	C₄⋊C₄×C₇₁	—	2	2	no	—
382	C₄⋊C₄×C₇₁	—	2	2	no	—
383	C₄⋊C₄×C₇₁	—	2	2	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	2	no	—
388	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₇₁	—	2	1	no	—
404	C₂²⋊C₄×C₇₁	—	2	2	no	—
405	C₂²⋊C₄×C₇₁	—	2	1	no	—
406	C₂²⋊C₄×C₇₁	—	2	1	no	—
407	C₂²⋊C₄×C₇₁	—	2	2	no	—
408	C₂²⋊C₄×C₇₁	—	2	1	no	—
409	C₂²⋊C₄×C₇₁	—	2	1	no	—
410	C₂²⋊C₄×C₇₁	—	2	1	no	—
411	C₂²⋊C₄×C₇₁	—	2	1	no	—
412	C₂²⋊C₄×C₇₁	—	2	2	no	—
413	C₂²⋊C₄×C₇₁	—	2	2	no	—
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	1	no	—
419	C₂²⋊C₄×C₇₁	—	2	2	no	—
420	C₂²⋊C₄×C₇₁	—	2	1	no	—
421	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
425	C₄²×C₇₁	—	2	2	no	—
426	C₄²×C₇₁	—	2	1	no	—
427	C₄²×C₇₁	—	2	1	no	—
428	C₄²×C₇₁	—	2	2	no	—
429	C₄²×C₇₁	—	2	1	no	—
430	C₄²×C₇₁	—	2	1	no	—
431	C₄²×C₇₁	—	2	2	no	—
432	C₄²×C₇₁	—	2	1	no	—
433	C₄²×C₇₁	C₂×D₄	1	2	yes	—
434	C₄²×C₇₁	C₂×D₄	1	2	yes	—
435	C₄²×C₇₁	C₂⁴	1	2	yes	—
436	C₄²×C₇₁	C₂⁴	1	2	yes	—
437	C₂³×C₇₁	—	2	2	no	—
438	C₂³×C₇₁	—	2	2	no	—
439	C₂³×C₇₁	—	2	1	no	—
440	C₂³×C₇₁	—	4	1	no	—
441	C₂³×C₇₁	—	4	1	no	—
442	C₂³×C₇₁	—	4	2	no	—
443	C₂³×C₇₁	—	8	1	no	—
444	C₂³×C₇₁	—	8	1	no	—
445	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
446	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₇₁	—	2	1	no	—
449	Q₈×C₇₁	—	2	1	no	—
450	Q₈×C₇₁	—	8	2	no	—
451	Q₈×C₇₁	—	8	2	no	—
452	Q₈×C₇₁	—	8	2	no	—
453	Q₈×C₇₁	—	8	2	no	—
454	Q₈×C₇₁	—	8	2	no	—
455	D₄×C₇₁	—	2	2	no	—
456	D₄×C₇₁	—	2	2	no	—
457	D₄×C₇₁	—	2	1	no	—
458	D₄×C₇₁	—	2	1	no	—
459	D₄×C₇₁	—	4	4	no	—
460	D₄×C₇₁	—	4	2	no	—
461	D₄×C₇₁	—	4	2	no	—
462	D₄×C₇₁	—	4	2	no	—
463	D₄×C₇₁	—	8	2	no	—
464	D₄×C₇₁	—	8	2	no	—
465	D₄×C₇₁	—	8	1	no	—
466	D₄×C₇₁	—	8	2	no	—
467	C₂×C₄×C₇₁	—	2	2	no	—
468	C₂×C₄×C₇₁	—	2	2	no	—
469	C₂×C₄×C₇₁	—	2	2	no	—
470	C₂×C₄×C₇₁	—	2	1	no	—
471	C₂×C₄×C₇₁	—	2	1	no	—
472	C₂×C₄×C₇₁	—	2	1	no	—
473	C₂×C₄×C₇₁	—	2	1	no	—
474	C₂×C₄×C₇₁	—	2	1	no	—
475	C₂×C₄×C₇₁	—	2	2	no	—
476	C₂×C₄×C₇₁	—	2	1	no	—
477	C₂×C₄×C₇₁	—	2	1	no	—
478	C₂×C₄×C₇₁	—	2	2	no	—
479	C₂×C₄×C₇₁	—	2	1	no	—
480	C₂×C₄×C₇₁	—	2	1	no	—
481	C₂×C₄×C₇₁	—	2	1	no	—
482	C₂×C₄×C₇₁	—	2	1	no	—
483	C₂×C₄×C₇₁	—	2	2	no	—
484	C₂×C₄×C₇₁	—	4	2	no	—
485	C₂×C₄×C₇₁	—	4	2	no	—
486	C₂×C₄×C₇₁	—	4	2	no	—
487	C₂×C₄×C₇₁	—	8	2	no	—
488	C₂×C₄×C₇₁	—	8	2	no	—
489	C₂×C₄×C₇₁	—	8	2	no	—
490	C₂×C₄×C₇₁	—	8	1	no	—
491	C₂×C₄×C₇₁	—	8	1	no	—
492	C₂×C₄×C₇₁	—	8	1	no	—
493	C₂×C₄×C₇₁	—	8	1	no	—
494	C₂×C₄×C₇₁	—	8	1	no	—
495	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
503	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
504	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
505	C₈×C₇₁	—	2	1	no	—
506	C₈×C₇₁	—	2	1	no	—
507	C₈×C₇₁	—	2	1	no	—
508	C₈×C₇₁	—	2	1	no	—
509	C₈×C₇₁	—	2	2	no	—
510	C₈×C₇₁	—	2	2	no	—
511	C₂²×C₇₁	—	2	1	no	—
512	C₂²×C₇₁	—	2	1	no	—
513	C₂²×C₇₁	—	2	1	no	—
514	C₂²×C₇₁	—	2	1	no	—
515	C₂²×C₇₁	—	2	1	no	—
516	C₂²×C₇₁	—	2	1	no	—
517	C₂²×C₇₁	—	2	1	no	—
518	C₂²×C₇₁	—	2	1	no	—
519	C₂²×C₇₁	—	4	2	no	—
520	C₂²×C₇₁	—	4	1	no	—
521	C₂²×C₇₁	—	4	1	no	—
522	C₂²×C₇₁	—	4	2	no	—
523	C₂²×C₇₁	—	4	1	no	—
524	C₂²×C₇₁	—	4	2	no	—
525	C₂²×C₇₁	—	8	2	no	—
526	C₂²×C₇₁	—	16	2	no	—
527	C₂²×C₇₁	#536	1	2	yes	—
528	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₇₁	—	2	2	no	—
530	C₄×C₇₁	—	2	2	no	—
531	C₄×C₇₁	—	2	2	no	—
532	C₄×C₇₁	—	2	2	no	—
533	C₄×C₇₁	—	2	1	no	—
534	C₄×C₇₁	—	2	1	no	—
535	C₄×C₇₁	—	4	1	no	—
536	C₄×C₇₁	—	4	2	no	—
537	C₄×C₇₁	—	4	1	no	—
538	C₄×C₇₁	—	4	1	no	—
539	C₄×C₇₁	—	4	2	no	—
540	C₄×C₇₁	—	4	1	no	—
541	C₄×C₇₁	—	4	2	no	—
542	C₄×C₇₁	—	4	1	no	—
543	C₄×C₇₁	—	4	1	no	—
544	C₄×C₇₁	—	4	1	no	—
545	C₄×C₇₁	#536	1	2	yes	—
546	C₄×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₄×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	#60875	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
549	C₂×C₇₁	—	2	2	no	—
550	C₂×C₇₁	—	4	1	no	—
551	C₂×C₇₁	—	4	1	no	—
552	C₂×C₇₁	—	8	1	no	—
553	C₂×C₇₁	—	8	2	no	—
554	C₂×C₇₁	C₂×#536	1	1	yes	characteristic
555	C₂×C₇₁	#3584	1	1	yes	characteristic
556	C₂×C₇₁	#3585	1	1	yes	characteristic
557	#3494	C₂×C₇₁	1	1	yes	characteristic
558	#3458	C₂×C₇₁	1	1	yes	characteristic, complemented
559	#3244	C₂×C₇₁	1	2	yes	complemented
560	#3243	C₂×C₇₁	1	2	yes	complemented
561	#3241	C₂×C₇₁	1	2	yes	complemented
562	#3241	C₂×C₇₁	1	2	yes	complemented
563	#3240	C₂×C₇₁	1	2	yes	complemented
564	#3235	C₂×C₇₁	1	2	yes	complemented
565	#3233	C₂×C₇₁	1	2	yes	complemented
566	#3228	C₂×C₇₁	1	2	yes	complemented
567	#3164	C₂×C₇₁	1	1	yes	characteristic, complemented
568	#3163	C₂×C₇₁	1	1	yes	characteristic, complemented
569	#3136	C₂×C₇₁	1	1	yes	characteristic, complemented
570	#3136	C₂×C₇₁	1	1	yes	characteristic, complemented
571	#3094	C₂×C₇₁	1	1	yes	characteristic, complemented
572	#3093	C₂×C₇₁	1	1	yes	characteristic, complemented
573	#3091	C₂×C₇₁	1	1	yes	characteristic, complemented
574	C₂×#482	C₂×C₇₁	1	1	yes	characteristic, complemented
575	#3084	C₂×C₇₁	1	1	yes	characteristic, complemented
576	#3083	C₂×C₇₁	1	1	yes	characteristic, complemented
577	#3081	C₂×C₇₁	1	1	yes	characteristic, complemented
578	#3081	C₂×C₇₁	1	1	yes	characteristic, complemented
579	#2924	C₂×C₇₁	1	1	yes	characteristic, complemented
580	C₇₁	#60875	1	1	yes	characteristic, direct product factor, Sylow
581	#555	—	2	1	no	—
582	#553	—	2	1	no	—
583	#553	—	2	1	no	—
584	#551	—	2	2	no	—
585	#547	—	2	1	no	—
586	#546	—	2	2	no	—
587	#544	—	2	1	no	—
588	#544	—	2	1	no	—
589	#544	C₂²×C₇₁	1	1	yes	characteristic
590	#544	C₂²×C₇₁	1	1	yes	characteristic
591	#544	C₂²×C₇₁	1	1	yes	characteristic
592	#544	C₂²×C₇₁	1	1	yes	characteristic
593	#544	C₂²×C₇₁	1	1	yes	characteristic
594	#544	C₂²×C₇₁	1	2	yes	complemented
595	#544	C₂²×C₇₁	1	2	yes	complemented
596	#543	—	2	2	no	—
597	#542	C₂²×C₇₁	1	2	yes	—
598	#540	C₂²×C₇₁	1	2	yes	—
599	#535	C₂²×C₇₁	1	1	yes	characteristic
600	#533	—	2	2	no	—
601	#533	—	2	1	no	—
602	#533	—	2	1	no	—
603	#533	C₂²×C₇₁	1	2	yes	complemented
604	#533	C₂²×C₇₁	1	2	yes	complemented
605	#532	C₂²×C₇₁	1	2	yes	—
606	#529	C₂²×C₇₁	1	2	yes	—
607	#525	C₂²×C₇₁	1	1	yes	characteristic
608	C₂×#121	C₂²×C₇₁	1	1	yes	characteristic
609	#520	C₂²×C₇₁	1	1	yes	characteristic
610	#518	C₂²×C₇₁	1	1	yes	characteristic
611	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
612	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
613	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
614	#501	C₂²×C₇₁	1	2	yes	complemented
615	#501	C₂²×C₇₁	1	2	yes	complemented
616	#501	C₂²×C₇₁	1	2	yes	complemented
617	#501	C₂²×C₇₁	1	2	yes	complemented
618	#500	C₂²×C₇₁	1	2	yes	complemented
619	#499	C₂²×C₇₁	1	2	yes	complemented
620	#499	C₂²×C₇₁	1	2	yes	complemented
621	#498	C₂²×C₇₁	1	2	yes	complemented
622	#490	C₂²×C₇₁	1	2	yes	complemented
623	#490	C₂²×C₇₁	1	2	yes	complemented
624	#489	C₂²×C₇₁	1	2	yes	complemented
625	#489	C₂²×C₇₁	1	2	yes	complemented
626	#488	C₂²×C₇₁	1	2	yes	complemented
627	#488	C₂²×C₇₁	1	2	yes	complemented
628	#486	C₂²×C₇₁	1	2	yes	complemented
629	#486	C₂²×C₇₁	1	2	yes	complemented
630	#485	C₂²×C₇₁	1	1	yes	characteristic, complemented
631	#485	C₂²×C₇₁	1	1	yes	characteristic, complemented
632	#485	C₂²×C₇₁	1	2	yes	complemented
633	#485	C₂²×C₇₁	1	2	yes	complemented
634	#484	C₂²×C₇₁	1	1	yes	characteristic, complemented
635	#483	C₂²×C₇₁	1	1	yes	characteristic, complemented
636	#482	C₂²×C₇₁	1	2	yes	—
637	#482	C₂²×C₇₁	1	2	yes	—
638	#482	C₂²×C₇₁	1	2	yes	—
639	#482	C₂²×C₇₁	1	2	yes	—
640	#482	C₂²×C₇₁	1	2	yes	—
641	#482	C₂²×C₇₁	1	2	yes	—
642	#482	C₂²×C₇₁	1	1	yes	characteristic, complemented
643	#482	C₂²×C₇₁	1	1	yes	characteristic, complemented
644	#482	C₂²×C₇₁	1	2	yes	complemented
645	#482	C₂²×C₇₁	1	2	yes	complemented
646	#481	C₂²×C₇₁	1	2	yes	—
647	#481	C₂²×C₇₁	1	1	yes	characteristic, complemented
648	#480	C₂²×C₇₁	1	2	yes	—
649	#480	C₂²×C₇₁	1	1	yes	characteristic, complemented
650	#479	C₂²×C₇₁	1	2	yes	complemented
651	#479	C₂²×C₇₁	1	2	yes	complemented
652	#478	C₂²×C₇₁	1	2	yes	complemented
653	#478	C₂²×C₇₁	1	2	yes	complemented
654	#478	C₂²×C₇₁	1	2	yes	complemented
655	#478	C₂²×C₇₁	1	2	yes	complemented
656	#478	C₂²×C₇₁	1	2	yes	complemented
657	#478	C₂²×C₇₁	1	2	yes	complemented
658	#477	C₂²×C₇₁	1	2	yes	complemented
659	#476	C₂²×C₇₁	1	2	yes	complemented
660	#476	C₂²×C₇₁	1	2	yes	complemented
661	#476	C₂²×C₇₁	1	2	yes	complemented
662	#475	C₂²×C₇₁	1	2	yes	complemented
663	#474	C₂²×C₇₁	1	2	yes	complemented
664	#474	C₂²×C₇₁	1	2	yes	complemented
665	#474	C₂²×C₇₁	1	2	yes	complemented
666	#433	C₂²×C₇₁	1	2	yes	complemented
667	#433	C₂²×C₇₁	1	2	yes	complemented
668	#432	C₂²×C₇₁	1	2	yes	complemented
669	#431	C₂²×C₇₁	1	2	yes	complemented
670	#428	C₂²×C₇₁	1	1	yes	characteristic
671	#428	C₂²×C₇₁	1	1	yes	characteristic
672	#428	C₂²×C₇₁	1	1	yes	characteristic
673	#428	C₂²×C₇₁	1	1	yes	characteristic
674	#427	C₂²×C₇₁	1	1	yes	characteristic
675	#427	C₂²×C₇₁	1	1	yes	characteristic
676	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
677	C₂×#106	C₂²×C₇₁	1	1	yes	characteristic
678	#424	C₂²×C₇₁	1	1	yes	characteristic
679	#424	C₂²×C₇₁	1	1	yes	characteristic
680	#418	C₂²×C₇₁	1	1	yes	characteristic
681	#418	C₂²×C₇₁	1	1	yes	characteristic
682	#417	C₂²×C₇₁	1	1	yes	characteristic
683	#417	C₂²×C₇₁	1	1	yes	characteristic
684	#416	C₂²×C₇₁	1	1	yes	characteristic
685	#416	C₂²×C₇₁	1	1	yes	characteristic
686	C₂×#102	C₂²×C₇₁	1	1	yes	characteristic
687	C₂×#102	C₂²×C₇₁	1	1	yes	characteristic
688	#407	C₂²×C₇₁	1	1	yes	characteristic
689	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
690	#405	C₂²×C₇₁	1	1	yes	characteristic
691	#405	C₂²×C₇₁	1	1	yes	characteristic
692	C₂×#41	—	2	2	no	—
693	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
694	C₂²×D₄	—	2	1	no	—
695	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
697	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
698	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
699	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
700	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	1	no	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	—	2	2	no	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
709	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
710	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
711	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
712	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
713	#127	C₂³×C₇₁	1	2	yes	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	1	no	—
718	#125	—	2	1	no	—
719	#125	—	2	1	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	C₂³×C₇₁	1	2	yes	—
724	#125	C₂³×C₇₁	1	2	yes	—
725	#125	C₂³×C₇₁	1	2	yes	—
726	#125	C₂³×C₇₁	1	2	yes	—
727	#125	C₂³×C₇₁	1	2	yes	—
728	#124	—	2	2	no	—
729	#124	—	2	2	no	—
730	#124	C₂³×C₇₁	1	2	yes	—
731	#123	—	2	1	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
751	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
752	#121	—	2	1	no	—
753	#121	—	2	1	no	—
754	#121	—	2	2	no	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	C₂³×C₇₁	1	2	yes	—
760	#121	C₂³×C₇₁	1	2	yes	—
761	#121	C₂³×C₇₁	1	1	yes	characteristic
762	#121	C₂³×C₇₁	1	1	yes	characteristic
763	#120	—	2	1	no	—
764	#120	—	2	2	no	—
765	C₄×Q₈	—	2	2	no	—
766	C₄×Q₈	—	2	2	no	—
767	C₄×Q₈	—	2	2	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	C₂³×C₇₁	1	2	yes	—
778	C₄×D₄	C₂³×C₇₁	1	2	yes	—
779	C₄×D₄	C₂³×C₇₁	1	2	yes	—
780	#117	—	2	1	no	—
781	#117	—	2	1	no	—
782	#117	—	2	1	no	—
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	—	2	2	no	—
786	#117	D₄×C₇₁	1	2	yes	—
787	#117	D₄×C₇₁	1	1	yes	characteristic
788	#117	D₄×C₇₁	1	1	yes	characteristic
789	#117	C₂³×C₇₁	1	2	yes	—
790	#117	C₂³×C₇₁	1	1	yes	characteristic
791	#117	C₂³×C₇₁	1	1	yes	characteristic
792	#117	C₂³×C₇₁	1	1	yes	characteristic
793	#117	C₂³×C₇₁	1	1	yes	characteristic
794	#117	C₂³×C₇₁	1	2	yes	—
795	#117	C₂³×C₇₁	1	1	yes	characteristic
796	#117	C₂³×C₇₁	1	1	yes	characteristic
797	#117	C₂³×C₇₁	1	1	yes	characteristic
798	#117	C₂³×C₇₁	1	2	yes	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
801	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
803	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
804	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
805	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
806	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	—	2	1	no	—
808	C₂×C₂²⋊C₄	—	2	1	no	—
809	C₂×C₂²⋊C₄	—	2	1	no	—
810	C₂×C₂²⋊C₄	—	2	2	no	—
811	C₂×C₂²⋊C₄	D₄×C₇₁	1	2	yes	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	—	2	1	no	—
814	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
815	#107	C₂³×C₇₁	1	2	yes	—
816	#107	C₂³×C₇₁	1	2	yes	—
817	#107	C₂³×C₇₁	1	1	yes	characteristic
818	#107	C₂³×C₇₁	1	1	yes	characteristic
819	#107	C₂³×C₇₁	1	1	yes	characteristic
820	#107	C₂³×C₇₁	1	1	yes	characteristic
821	#107	C₂³×C₇₁	1	2	yes	—
822	#107	C₂³×C₇₁	1	2	yes	—
823	#107	C₂³×C₇₁	1	2	yes	—
824	#107	C₂³×C₇₁	1	2	yes	—
825	#106	C₂³×C₇₁	1	2	yes	—
826	#106	C₂³×C₇₁	1	2	yes	—
827	#106	C₂³×C₇₁	1	1	yes	characteristic
828	#106	C₂³×C₇₁	1	1	yes	characteristic
829	#106	C₂³×C₇₁	1	1	yes	characteristic
830	#106	C₂³×C₇₁	1	1	yes	characteristic
831	#106	C₂³×C₇₁	1	2	yes	—
832	#106	C₂³×C₇₁	1	2	yes	—
833	#106	C₂³×C₇₁	1	2	yes	—
834	#106	C₂³×C₇₁	1	2	yes	—
835	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
836	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
839	#103	C₂³×C₇₁	1	1	yes	characteristic
840	#103	C₂³×C₇₁	1	1	yes	characteristic
841	#103	C₂³×C₇₁	1	1	yes	characteristic
842	#103	C₂³×C₇₁	1	1	yes	characteristic
843	#103	C₂³×C₇₁	1	2	yes	—
844	#103	C₂³×C₇₁	1	2	yes	—
845	#102	C₂³×C₇₁	1	2	yes	—
846	#102	C₂³×C₇₁	1	2	yes	—
847	#102	C₂³×C₇₁	1	2	yes	—
848	#102	C₂³×C₇₁	1	2	yes	—
849	#102	C₂³×C₇₁	1	1	yes	characteristic
850	#102	C₂³×C₇₁	1	1	yes	characteristic
851	#102	C₂³×C₇₁	1	1	yes	characteristic
852	#102	C₂³×C₇₁	1	1	yes	characteristic
853	#102	C₂³×C₇₁	1	2	yes	—
854	#102	C₂³×C₇₁	1	2	yes	—
855	#102	C₂³×C₇₁	1	2	yes	—
856	#102	C₂³×C₇₁	1	2	yes	—
857	#102	C₂³×C₇₁	1	2	yes	—
858	#102	C₂³×C₇₁	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
860	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
865	#97	C₂³×C₇₁	1	2	yes	—
866	#97	C₂³×C₇₁	1	2	yes	—
867	C₄×C₈	C₂³×C₇₁	1	2	yes	—
868	C₄×C₈	C₂³×C₇₁	1	2	yes	—
869	C₂⁴	—	2	1	no	—
870	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	—	8	4	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	8	2	no	—
891	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
892	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
905	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
908	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
912	M₁₆	—	2	2	no	—
913	M₁₆	—	2	2	no	—
914	C₂×C₈	—	2	2	no	—
915	C₂×C₈	—	2	2	no	—
916	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
919	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
920	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
946	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
950	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
979	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	C₂×D₄×C₇₁	1	2	yes	—
991	C₄²	C₂×D₄×C₇₁	1	2	yes	—
992	C₄²	C₂⁴×C₇₁	1	2	yes	—
993	C₄²	C₂⁴×C₇₁	1	2	yes	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	4	1	no	—
998	C₂³	—	4	1	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1003	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1004	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	8	2	no	—
1008	Q₈	—	8	2	no	—
1009	Q₈	—	8	2	no	—
1010	Q₈	—	8	2	no	—
1011	Q₈	—	8	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	2	1	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	2	no	—
1022	D₄	—	8	2	no	—
1023	D₄	—	8	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	8	2	no	—
1047	C₂×C₄	—	8	1	no	—
1048	C₂×C₄	—	8	1	no	—
1049	C₂×C₄	—	8	1	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	—	8	1	no	—
1052	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1055	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1059	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
1060	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
1061	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1062	C₈	—	2	1	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	8	2	no	—
1083	C₂²	—	16	2	no	—
1084	C₂²	#536×C₇₁	1	2	yes	—
1085	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	#536×C₇₁	1	2	yes	—
1103	C₄	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
1104	C₄	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
1105	C₂	—	2	2	no	—
1106	C₂	—	4	1	no	—
1107	C₂	—	4	1	no	—
1108	C₂	—	8	2	no	—
1109	C₂	—	8	1	no	—
1110	C₂	C₂×#536×C₇₁	1	1	yes	characteristic
1111	C₂	C₇₁×#3584	1	1	yes	characteristic
1112	C₂	C₇₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₇₁×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂×#117×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₁×#3458	C₂	semidirect
3. C₇₁×#3244	C₂	semidirect
4. C₇₁×#3243	C₂	semidirect
5. C₇₁×#3241	C₂	semidirect
6. C₇₁×#3241	C₂	semidirect
7. C₇₁×#3240	C₂	semidirect
8. C₇₁×#3235	C₂	semidirect
9. C₇₁×#3233	C₂	semidirect
10. C₇₁×#3228	C₂	semidirect
11. C₇₁×#3164	C₂	semidirect
12. C₇₁×#3163	C₂	semidirect
13. C₇₁×#3136	C₂	semidirect
14. C₇₁×#3136	C₂	semidirect
15. C₇₁×#3094	C₂	semidirect
16. C₇₁×#3093	C₂	semidirect
17. C₇₁×#3091	C₂	semidirect
18. C₂×#482×C₇₁	C₂	semidirect
19. C₇₁×#3084	C₂	semidirect
20. C₇₁×#3083	C₂	semidirect
21. C₇₁×#3081	C₂	semidirect
22. C₇₁×#3081	C₂	semidirect
23. C₇₁×#2924	C₂	semidirect
37. #544×C₇₁	C₂²	semidirect
38. #544×C₇₁	C₂²	semidirect
46. #533×C₇₁	C₂²	semidirect
47. #533×C₇₁	C₂²	semidirect
57. #501×C₇₁	C₂²	semidirect
58. #501×C₇₁	C₂²	semidirect
59. #501×C₇₁	C₂²	semidirect
60. #501×C₇₁	C₂²	semidirect
61. #500×C₇₁	C₂²	semidirect
62. #499×C₇₁	C₂²	semidirect
63. #499×C₇₁	C₂²	semidirect
64. #498×C₇₁	C₂²	semidirect
65. #490×C₇₁	C₂²	semidirect
66. #490×C₇₁	C₂²	semidirect
67. #489×C₇₁	C₂²	semidirect
68. #489×C₇₁	C₂²	semidirect
69. #488×C₇₁	C₂²	semidirect
70. #488×C₇₁	C₂²	semidirect
71. #486×C₇₁	C₂²	semidirect
72. #486×C₇₁	C₂²	semidirect
73. #485×C₇₁	C₂²	semidirect
74. #485×C₇₁	C₂²	semidirect
75. #485×C₇₁	C₂²	semidirect
76. #485×C₇₁	C₂²	semidirect
77. #484×C₇₁	C₂²	semidirect
78. #483×C₇₁	C₂²	semidirect
85. #482×C₇₁	C₂²	semidirect
86. #482×C₇₁	C₂²	semidirect
87. #482×C₇₁	C₂²	semidirect
88. #482×C₇₁	C₂²	semidirect
90. #481×C₇₁	C₂²	semidirect
92. #480×C₇₁	C₂²	semidirect
93. #479×C₇₁	C₂²	semidirect
94. #479×C₇₁	C₂²	semidirect
95. #478×C₇₁	C₂²	semidirect
96. #478×C₇₁	C₂²	semidirect
97. #478×C₇₁	C₂²	semidirect
98. #478×C₇₁	C₂²	semidirect
99. #478×C₇₁	C₂²	semidirect
100. #478×C₇₁	C₂²	semidirect
101. #477×C₇₁	C₂²	semidirect
102. #476×C₇₁	C₂²	semidirect
103. #476×C₇₁	C₂²	semidirect
104. #476×C₇₁	C₂²	semidirect
105. #475×C₇₁	C₂²	semidirect
106. #474×C₇₁	C₂²	semidirect
107. #474×C₇₁	C₂²	semidirect
108. #474×C₇₁	C₂²	semidirect
109. #433×C₇₁	C₂²	semidirect
110. #433×C₇₁	C₂²	semidirect
111. #432×C₇₁	C₂²	semidirect
112. #431×C₇₁	C₂²	semidirect
548. #60875	C₇₁	direct (N × H)
558. #3458	C₂×C₇₁	semidirect
559. #3244	C₂×C₇₁	semidirect
560. #3243	C₂×C₇₁	semidirect
561. #3241	C₂×C₇₁	semidirect
562. #3241	C₂×C₇₁	semidirect
563. #3240	C₂×C₇₁	semidirect
564. #3235	C₂×C₇₁	semidirect
565. #3233	C₂×C₇₁	semidirect
566. #3228	C₂×C₇₁	semidirect
567. #3164	C₂×C₇₁	semidirect
568. #3163	C₂×C₇₁	semidirect
569. #3136	C₂×C₇₁	semidirect
570. #3136	C₂×C₇₁	semidirect
571. #3094	C₂×C₇₁	semidirect
572. #3093	C₂×C₇₁	semidirect
573. #3091	C₂×C₇₁	semidirect
574. C₂×#482	C₂×C₇₁	semidirect
575. #3084	C₂×C₇₁	semidirect
576. #3083	C₂×C₇₁	semidirect
577. #3081	C₂×C₇₁	semidirect
578. #3081	C₂×C₇₁	semidirect
579. #2924	C₂×C₇₁	semidirect
580. C₇₁	#60875	direct (N × H)
594. #544	C₂²×C₇₁	semidirect
595. #544	C₂²×C₇₁	semidirect
603. #533	C₂²×C₇₁	semidirect
604. #533	C₂²×C₇₁	semidirect
614. #501	C₂²×C₇₁	semidirect
615. #501	C₂²×C₇₁	semidirect
616. #501	C₂²×C₇₁	semidirect
617. #501	C₂²×C₇₁	semidirect
618. #500	C₂²×C₇₁	semidirect
619. #499	C₂²×C₇₁	semidirect
620. #499	C₂²×C₇₁	semidirect
621. #498	C₂²×C₇₁	semidirect
622. #490	C₂²×C₇₁	semidirect
623. #490	C₂²×C₇₁	semidirect
624. #489	C₂²×C₇₁	semidirect
625. #489	C₂²×C₇₁	semidirect
626. #488	C₂²×C₇₁	semidirect
627. #488	C₂²×C₇₁	semidirect
628. #486	C₂²×C₇₁	semidirect
629. #486	C₂²×C₇₁	semidirect
630. #485	C₂²×C₇₁	semidirect
631. #485	C₂²×C₇₁	semidirect
632. #485	C₂²×C₇₁	semidirect
633. #485	C₂²×C₇₁	semidirect
634. #484	C₂²×C₇₁	semidirect
635. #483	C₂²×C₇₁	semidirect
642. #482	C₂²×C₇₁	semidirect
643. #482	C₂²×C₇₁	semidirect
644. #482	C₂²×C₇₁	semidirect
645. #482	C₂²×C₇₁	semidirect
647. #481	C₂²×C₇₁	semidirect
649. #480	C₂²×C₇₁	semidirect
650. #479	C₂²×C₇₁	semidirect
651. #479	C₂²×C₇₁	semidirect
652. #478	C₂²×C₇₁	semidirect
653. #478	C₂²×C₇₁	semidirect
654. #478	C₂²×C₇₁	semidirect
655. #478	C₂²×C₇₁	semidirect
656. #478	C₂²×C₇₁	semidirect
657. #478	C₂²×C₇₁	semidirect
658. #477	C₂²×C₇₁	semidirect
659. #476	C₂²×C₇₁	semidirect
660. #476	C₂²×C₇₁	semidirect
661. #476	C₂²×C₇₁	semidirect
662. #475	C₂²×C₇₁	semidirect
663. #474	C₂²×C₇₁	semidirect
664. #474	C₂²×C₇₁	semidirect
665. #474	C₂²×C₇₁	semidirect
666. #433	C₂²×C₇₁	semidirect
667. #433	C₂²×C₇₁	semidirect
668. #432	C₂²×C₇₁	semidirect
669. #431	C₂²×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#3494	2
C₇₁×#3458	2
C₇₁×#3244	2
C₇₁×#3243	2
C₇₁×#3241	2
C₇₁×#3240	2
C₇₁×#3235	2
C₇₁×#3233	2
C₇₁×#3228	2
C₇₁×#3164	2
C₇₁×#3163	2
C₇₁×#3136	2
C₇₁×#3094	2
C₇₁×#3093	2
C₇₁×#3091	2
C₂×#482×C₇₁	2
C₇₁×#3084	2
C₇₁×#3083	2
C₇₁×#3081	2
C₇₁×#2924	2
#60875	71

Subgroups — C71×#60875 #31881747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#60875 #31881747