Subgroups — C₇₁×#61926 #31882798

Order 18176.

1774 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3396	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3370	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3361	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3220	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3124	C₂	1	2	yes	maximal, complemented
20	C₇₁×#3119	C₂	1	2	yes	maximal, complemented
21	C₇₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	#562×C₇₁	—	2	2	no	—
25	#559×C₇₁	C₂²	1	2	yes	—
26	#559×C₇₁	C₂²	1	2	yes	—
27	#559×C₇₁	C₂²	1	1	yes	characteristic, complemented
28	#559×C₇₁	C₂²	1	2	yes	complemented
29	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
30	#556×C₇₁	C₂²	1	1	yes	characteristic
31	#556×C₇₁	C₂²	1	1	yes	characteristic
32	#555×C₇₁	—	2	1	no	—
33	#554×C₇₁	C₂²	1	2	yes	complemented
34	#553×C₇₁	—	2	2	no	—
35	#550×C₇₁	C₂²	1	1	yes	characteristic
36	#550×C₇₁	C₂²	1	1	yes	characteristic
37	#550×C₇₁	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
39	#548×C₇₁	—	2	1	no	—
40	#547×C₇₁	—	2	1	no	—
41	#547×C₇₁	—	2	1	no	—
42	#542×C₇₁	—	2	1	no	—
43	#542×C₇₁	C₂²	1	2	yes	—
44	#540×C₇₁	C₂²	1	2	yes	—
45	#539×C₇₁	—	2	2	no	—
46	#538×C₇₁	—	2	2	no	—
47	#536×C₇₁	—	2	1	no	—
48	#535×C₇₁	C₂²	1	2	yes	—
49	#533×C₇₁	C₂²	1	1	yes	characteristic
50	#532×C₇₁	C₂²	1	1	yes	characteristic
51	#532×C₇₁	C₂²	1	1	yes	characteristic
52	#529×C₇₁	C₂²	1	1	yes	characteristic
53	#525×C₇₁	—	2	1	no	—
54	#525×C₇₁	—	2	1	no	—
55	#520×C₇₁	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
57	#496×C₇₁	C₂²	1	2	yes	—
58	#496×C₇₁	C₂²	1	2	yes	—
59	#495×C₇₁	C₂²	1	2	yes	—
60	#495×C₇₁	C₂²	1	2	yes	complemented
61	#493×C₇₁	C₂²	1	2	yes	—
62	#493×C₇₁	C₂²	1	1	yes	characteristic, complemented
63	#492×C₇₁	C₂²	1	1	yes	characteristic, complemented
64	#490×C₇₁	C₂²	1	2	yes	—
65	#489×C₇₁	C₂²	1	2	yes	—
66	#488×C₇₁	C₂²	1	2	yes	—
67	#488×C₇₁	C₂²	1	2	yes	complemented
68	#487×C₇₁	C₂²	1	1	yes	characteristic, complemented
69	#486×C₇₁	C₂²	1	2	yes	—
70	#486×C₇₁	C₂²	1	1	yes	characteristic, complemented
71	#484×C₇₁	C₂²	1	1	yes	characteristic
72	#481×C₇₁	C₂²	1	1	yes	characteristic
73	#480×C₇₁	C₂²	1	2	yes	—
74	#479×C₇₁	C₂²	1	2	yes	complemented
75	#478×C₇₁	C₂²	1	1	yes	characteristic
76	#478×C₇₁	C₂²	1	1	yes	characteristic
77	#478×C₇₁	C₂²	1	2	yes	complemented
78	#477×C₇₁	C₂²	1	2	yes	complemented
79	#474×C₇₁	C₂²	1	1	yes	characteristic
80	#474×C₇₁	C₂²	1	1	yes	characteristic
81	#474×C₇₁	C₂²	1	2	yes	complemented
82	#464×C₇₁	C₂²	1	2	yes	—
83	#464×C₇₁	C₂²	1	2	yes	complemented
84	#463×C₇₁	C₂²	1	1	yes	characteristic
85	#463×C₇₁	C₂²	1	1	yes	characteristic
86	#463×C₇₁	C₂²	1	2	yes	—
87	#463×C₇₁	C₂²	1	2	yes	—
88	#463×C₇₁	C₂²	1	2	yes	—
89	#463×C₇₁	C₂²	1	2	yes	complemented
90	#463×C₇₁	C₂²	1	2	yes	complemented
91	#463×C₇₁	C₂²	1	2	yes	complemented
92	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
93	#461×C₇₁	C₂²	1	1	yes	characteristic, complemented
94	#460×C₇₁	C₂²	1	2	yes	—
95	#460×C₇₁	C₂²	1	1	yes	characteristic, complemented
96	#460×C₇₁	C₂²	1	2	yes	complemented
97	#459×C₇₁	C₂²	1	1	yes	characteristic
98	#459×C₇₁	C₂²	1	1	yes	characteristic
99	#459×C₇₁	C₂²	1	2	yes	—
100	#459×C₇₁	C₂²	1	2	yes	—
101	#459×C₇₁	C₂²	1	2	yes	—
102	#459×C₇₁	C₂²	1	1	yes	characteristic, complemented
103	#459×C₇₁	C₂²	1	2	yes	complemented
104	#452×C₇₁	C₂²	1	2	yes	—
105	#450×C₇₁	C₂²	1	1	yes	characteristic
106	#449×C₇₁	C₂²	1	2	yes	—
107	#449×C₇₁	C₂²	1	2	yes	—
108	#449×C₇₁	C₂²	1	2	yes	—
109	#447×C₇₁	C₂²	1	2	yes	—
110	#447×C₇₁	C₂²	1	1	yes	characteristic
111	#446×C₇₁	C₂²	1	1	yes	characteristic, complemented
112	#446×C₇₁	C₂²	1	1	yes	characteristic, complemented
113	#446×C₇₁	C₂²	1	2	yes	complemented
114	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
116	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
117	#442×C₇₁	C₂²	1	2	yes	complemented
118	#440×C₇₁	C₂²	1	2	yes	complemented
119	#440×C₇₁	C₂²	1	2	yes	complemented
120	#440×C₇₁	C₂²	1	2	yes	complemented
121	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
125	C₄×D₈×C₇₁	C₂²	1	2	yes	—
126	C₄×D₈×C₇₁	C₂²	1	2	yes	—
127	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
128	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₇₁	C₂²	1	2	yes	complemented
130	C₄×D₈×C₇₁	C₂²	1	2	yes	complemented
131	#433×C₇₁	C₂²	1	2	yes	—
132	#433×C₇₁	C₂²	1	2	yes	—
133	#431×C₇₁	C₂²	1	1	yes	characteristic
134	#431×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	—	2	1	no	—
139	C₂×#41×C₇₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₇₁	—	2	1	no	—
141	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇₁	—	2	1	no	—
143	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
150	C₂×D₈×C₇₁	C₂³	1	2	yes	—
151	C₂×D₈×C₇₁	C₂³	1	2	yes	—
152	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₇₁	C₂³	1	2	yes	—
155	C₂×D₈×C₇₁	C₂³	1	2	yes	—
156	C₂×D₈×C₇₁	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₇₁	—	2	1	no	—
158	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
159	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
160	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
163	#127×C₇₁	C₂³	1	2	yes	—
164	#127×C₇₁	C₂³	1	1	yes	characteristic
165	#127×C₇₁	C₂³	1	2	yes	—
166	#127×C₇₁	C₂³	1	1	yes	characteristic
167	#127×C₇₁	C₂³	1	2	yes	—
168	#126×C₇₁	—	2	2	no	—
169	#126×C₇₁	—	2	2	no	—
170	#126×C₇₁	—	2	2	no	—
171	#126×C₇₁	—	2	1	no	—
172	#125×C₇₁	—	2	2	no	—
173	#125×C₇₁	D₄	1	2	yes	—
174	#125×C₇₁	C₂³	1	1	yes	characteristic
175	#125×C₇₁	C₂³	1	2	yes	—
176	#124×C₇₁	—	2	1	no	—
177	#124×C₇₁	—	2	2	no	—
178	#124×C₇₁	—	2	2	no	—
179	#124×C₇₁	—	2	2	no	—
180	#124×C₇₁	—	2	2	no	—
181	#124×C₇₁	—	2	1	no	—
182	#124×C₇₁	C₂³	1	2	yes	—
183	#124×C₇₁	C₂³	1	1	yes	characteristic
184	#124×C₇₁	C₂³	1	2	yes	—
185	#124×C₇₁	C₂³	1	2	yes	—
186	#124×C₇₁	C₂³	1	2	yes	—
187	#123×C₇₁	—	2	1	no	—
188	#123×C₇₁	—	2	2	no	—
189	#123×C₇₁	—	2	2	no	—
190	#123×C₇₁	—	2	2	no	—
191	#123×C₇₁	—	2	2	no	—
192	#123×C₇₁	—	2	2	no	—
193	#123×C₇₁	—	2	2	no	—
194	#123×C₇₁	—	2	2	no	—
195	#123×C₇₁	—	2	2	no	—
196	#123×C₇₁	—	2	2	no	—
197	#123×C₇₁	—	2	2	no	—
198	C₂²⋊Q₈×C₇₁	—	2	1	no	—
199	C₂²⋊Q₈×C₇₁	—	2	1	no	—
200	C₂²⋊Q₈×C₇₁	—	2	2	no	—
201	C₂²⋊Q₈×C₇₁	—	2	2	no	—
202	C₂²⋊Q₈×C₇₁	—	2	2	no	—
203	C₂²⋊Q₈×C₇₁	—	2	2	no	—
204	C₂²⋊Q₈×C₇₁	—	2	2	no	—
205	C₂²⋊Q₈×C₇₁	—	2	1	no	—
206	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
209	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
210	#121×C₇₁	—	2	1	no	—
211	#121×C₇₁	—	2	1	no	—
212	#121×C₇₁	—	2	1	no	—
213	#121×C₇₁	—	2	1	no	—
214	#121×C₇₁	—	2	1	no	—
215	#121×C₇₁	—	2	2	no	—
216	#121×C₇₁	—	2	2	no	—
217	#121×C₇₁	—	2	2	no	—
218	#121×C₇₁	—	2	2	no	—
219	#121×C₇₁	—	2	2	no	—
220	#121×C₇₁	—	2	1	no	—
221	#121×C₇₁	—	2	2	no	—
222	#121×C₇₁	—	2	2	no	—
223	#121×C₇₁	C₂³	1	2	yes	—
224	#121×C₇₁	C₂³	1	1	yes	characteristic
225	#120×C₇₁	—	2	2	no	—
226	#120×C₇₁	—	2	2	no	—
227	C₄×Q₈×C₇₁	—	2	1	no	—
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×Q₈×C₇₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
235	C₄×D₄×C₇₁	—	2	1	no	—
236	C₄×D₄×C₇₁	—	2	2	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	—	2	2	no	—
241	C₄×D₄×C₇₁	—	2	2	no	—
242	C₄×D₄×C₇₁	—	2	1	no	—
243	C₄×D₄×C₇₁	—	2	1	no	—
244	C₄×D₄×C₇₁	—	2	1	no	—
245	C₄×D₄×C₇₁	—	2	1	no	—
246	C₄×D₄×C₇₁	—	2	1	no	—
247	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₇₁	C₂³	1	2	yes	—
251	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₇₁	C₂³	1	2	yes	—
254	C₄×D₄×C₇₁	C₂³	1	2	yes	—
255	C₄×D₄×C₇₁	C₂³	1	2	yes	—
256	C₄×D₄×C₇₁	C₂³	1	2	yes	—
257	C₄×D₄×C₇₁	C₂³	1	2	yes	—
258	#117×C₇₁	—	2	2	no	—
259	#117×C₇₁	—	2	1	no	—
260	#117×C₇₁	—	2	1	no	—
261	#117×C₇₁	—	2	1	no	—
262	#117×C₇₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
264	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
265	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
267	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
268	#107×C₇₁	C₂³	1	1	yes	characteristic
269	#107×C₇₁	C₂³	1	2	yes	—
270	#107×C₇₁	C₂³	1	2	yes	—
271	#107×C₇₁	C₂³	1	1	yes	characteristic
272	#106×C₇₁	C₂³	1	1	yes	characteristic
273	#106×C₇₁	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
285	#103×C₇₁	C₂³	1	2	yes	—
286	#103×C₇₁	C₂³	1	2	yes	—
287	#103×C₇₁	C₂³	1	2	yes	—
288	#102×C₇₁	C₂³	1	1	yes	characteristic
289	#102×C₇₁	C₂³	1	2	yes	—
290	#102×C₇₁	C₂³	1	1	yes	characteristic
291	#102×C₇₁	C₂³	1	2	yes	—
292	#102×C₇₁	C₂³	1	2	yes	—
293	#102×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	2	yes	—
297	#102×C₇₁	C₂³	1	2	yes	—
298	#102×C₇₁	C₂³	1	1	yes	characteristic
299	#102×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
304	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
305	#97×C₇₁	C₂³	1	2	yes	—
306	#97×C₇₁	C₂³	1	2	yes	—
307	C₄×C₈×C₇₁	C₂³	1	2	yes	—
308	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₁	C₂³	1	2	yes	—
311	C₄×C₈×C₇₁	C₂³	1	2	yes	—
312	C₂⁴×C₇₁	—	2	1	no	—
313	#41×C₇₁	—	4	2	no	—
314	#41×C₇₁	—	4	2	no	—
315	#41×C₇₁	—	8	2	no	—
316	#41×C₇₁	—	8	2	no	—
317	#41×C₇₁	—	8	2	no	—
318	#41×C₇₁	—	8	2	no	—
319	C₂×Q₈×C₇₁	—	2	1	no	—
320	C₂×Q₈×C₇₁	—	2	2	no	—
321	C₂×Q₈×C₇₁	—	8	2	no	—
322	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
331	C₂×D₄×C₇₁	—	2	1	no	—
332	C₂×D₄×C₇₁	—	2	1	no	—
333	C₂×D₄×C₇₁	—	2	2	no	—
334	C₂×D₄×C₇₁	—	2	2	no	—
335	C₂×D₄×C₇₁	—	2	1	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	2	no	—
340	C₂×D₄×C₇₁	—	2	2	no	—
341	C₂×D₄×C₇₁	—	4	1	no	—
342	C₂×D₄×C₇₁	—	4	1	no	—
343	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
346	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₇₁	—	2	1	no	—
349	C₂²×C₄×C₇₁	—	2	2	no	—
350	C₂²×C₄×C₇₁	—	2	1	no	—
351	C₂²×C₄×C₇₁	—	2	1	no	—
352	C₂²×C₄×C₇₁	—	2	1	no	—
353	C₂²×C₄×C₇₁	—	2	2	no	—
354	C₂²×C₄×C₇₁	—	2	2	no	—
355	C₂²×C₄×C₇₁	—	2	2	no	—
356	C₂²×C₄×C₇₁	—	2	2	no	—
357	C₂²×C₄×C₇₁	—	2	2	no	—
358	C₂²×C₄×C₇₁	—	2	1	no	—
359	C₂²×C₄×C₇₁	—	2	1	no	—
360	C₂²×C₄×C₇₁	—	2	2	no	—
361	C₂²×C₄×C₇₁	—	8	2	no	—
362	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₇₁	—	4	2	no	—
366	SD₁₆×C₇₁	—	4	1	no	—
367	SD₁₆×C₇₁	—	4	2	no	—
368	SD₁₆×C₇₁	—	4	2	no	—
369	SD₁₆×C₇₁	—	4	2	no	—
370	SD₁₆×C₇₁	—	4	2	no	—
371	SD₁₆×C₇₁	—	4	1	no	—
372	D₈×C₇₁	—	4	2	no	—
373	D₈×C₇₁	—	4	1	no	—
374	D₈×C₇₁	—	4	2	no	—
375	D₈×C₇₁	—	4	2	no	—
376	D₈×C₇₁	—	4	2	no	—
377	D₈×C₇₁	—	4	1	no	—
378	D₈×C₇₁	—	4	2	no	—
379	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
381	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
383	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₇₁	—	2	1	no	—
386	C₄⋊C₄×C₇₁	—	2	1	no	—
387	C₄⋊C₄×C₇₁	—	2	2	no	—
388	C₄⋊C₄×C₇₁	—	2	2	no	—
389	C₄⋊C₄×C₇₁	—	2	2	no	—
390	C₄⋊C₄×C₇₁	—	2	2	no	—
391	C₄⋊C₄×C₇₁	—	2	1	no	—
392	C₄⋊C₄×C₇₁	—	2	1	no	—
393	C₄⋊C₄×C₇₁	—	2	1	no	—
394	C₄⋊C₄×C₇₁	—	2	1	no	—
395	C₄⋊C₄×C₇₁	—	2	1	no	—
396	C₄⋊C₄×C₇₁	—	2	2	no	—
397	C₄⋊C₄×C₇₁	—	2	2	no	—
398	C₄⋊C₄×C₇₁	—	2	1	no	—
399	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
410	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
413	C₂²⋊C₄×C₇₁	—	2	1	no	—
414	C₂²⋊C₄×C₇₁	—	2	1	no	—
415	C₂²⋊C₄×C₇₁	—	2	1	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	2	no	—
421	C₂²⋊C₄×C₇₁	—	2	2	no	—
422	C₂²⋊C₄×C₇₁	—	2	1	no	—
423	C₂²⋊C₄×C₇₁	—	2	1	no	—
424	C₂²⋊C₄×C₇₁	—	2	2	no	—
425	C₂²⋊C₄×C₇₁	—	2	1	no	—
426	C₂²⋊C₄×C₇₁	—	2	2	no	—
427	C₂²⋊C₄×C₇₁	—	2	2	no	—
428	C₂²⋊C₄×C₇₁	—	2	2	no	—
429	C₂²⋊C₄×C₇₁	—	2	2	no	—
430	C₂²⋊C₄×C₇₁	—	2	2	no	—
431	C₂²⋊C₄×C₇₁	—	2	2	no	—
432	C₂²⋊C₄×C₇₁	—	2	1	no	—
433	C₂²⋊C₄×C₇₁	—	2	2	no	—
434	C₂²⋊C₄×C₇₁	—	2	2	no	—
435	C₂²⋊C₄×C₇₁	—	2	2	no	—
436	C₂²⋊C₄×C₇₁	—	2	2	no	—
437	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
439	C₄²×C₇₁	—	2	2	no	—
440	C₄²×C₇₁	—	2	2	no	—
441	C₄²×C₇₁	—	2	1	no	—
442	C₄²×C₇₁	—	2	2	no	—
443	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
446	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
447	C₄²×C₇₁	C₂⁴	1	2	yes	—
448	C₄²×C₇₁	C₂⁴	1	2	yes	—
449	C₂³×C₇₁	—	2	2	no	—
450	C₂³×C₇₁	—	2	1	no	—
451	C₂³×C₇₁	—	2	1	no	—
452	C₂³×C₇₁	—	2	1	no	—
453	C₂³×C₇₁	—	2	2	no	—
454	C₂³×C₇₁	—	4	2	no	—
455	C₂³×C₇₁	—	8	1	no	—
456	C₂³×C₇₁	—	8	1	no	—
457	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₇₁	—	2	2	no	—
459	Q₈×C₇₁	—	2	2	no	—
460	Q₈×C₇₁	—	2	1	no	—
461	Q₈×C₇₁	—	2	2	no	—
462	Q₈×C₇₁	—	2	1	no	—
463	Q₈×C₇₁	—	2	2	no	—
464	Q₈×C₇₁	—	4	2	no	—
465	Q₈×C₇₁	—	4	2	no	—
466	Q₈×C₇₁	—	8	2	no	—
467	D₄×C₇₁	—	2	1	no	—
468	D₄×C₇₁	—	2	2	no	—
469	D₄×C₇₁	—	2	2	no	—
470	D₄×C₇₁	—	2	1	no	—
471	D₄×C₇₁	—	2	1	no	—
472	D₄×C₇₁	—	2	2	no	—
473	D₄×C₇₁	—	2	1	no	—
474	D₄×C₇₁	—	2	1	no	—
475	D₄×C₇₁	—	2	1	no	—
476	D₄×C₇₁	—	2	2	no	—
477	D₄×C₇₁	—	4	2	no	—
478	D₄×C₇₁	—	4	4	no	—
479	D₄×C₇₁	—	4	2	no	—
480	D₄×C₇₁	—	4	2	no	—
481	D₄×C₇₁	—	8	1	no	—
482	D₄×C₇₁	—	8	1	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	D₄×C₇₁	—	8	2	no	—
488	D₄×C₇₁	—	8	2	no	—
489	D₄×C₇₁	—	8	1	no	—
490	D₄×C₇₁	—	8	2	no	—
491	C₂×C₄×C₇₁	—	2	2	no	—
492	C₂×C₄×C₇₁	—	2	1	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	1	no	—
497	C₂×C₄×C₇₁	—	2	1	no	—
498	C₂×C₄×C₇₁	—	2	1	no	—
499	C₂×C₄×C₇₁	—	2	2	no	—
500	C₂×C₄×C₇₁	—	2	1	no	—
501	C₂×C₄×C₇₁	—	4	1	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	2	no	—
506	C₂×C₄×C₇₁	—	8	2	no	—
507	C₂×C₄×C₇₁	—	8	1	no	—
508	C₂×C₄×C₇₁	—	8	1	no	—
509	C₂×C₄×C₇₁	—	8	2	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	—	8	2	no	—
514	C₂×C₄×C₇₁	—	8	1	no	—
515	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
525	C₈×C₇₁	—	2	1	no	—
526	C₈×C₇₁	—	2	1	no	—
527	C₈×C₇₁	—	2	2	no	—
528	C₈×C₇₁	—	2	2	no	—
529	C₈×C₇₁	—	2	1	no	—
530	C₈×C₇₁	—	2	1	no	—
531	C₂²×C₇₁	—	2	1	no	—
532	C₂²×C₇₁	—	2	1	no	—
533	C₂²×C₇₁	—	2	1	no	—
534	C₂²×C₇₁	—	4	2	no	—
535	C₂²×C₇₁	—	4	2	no	—
536	C₂²×C₇₁	—	4	1	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	1	no	—
543	C₂²×C₇₁	—	4	2	no	—
544	C₂²×C₇₁	—	4	1	no	—
545	C₂²×C₇₁	—	4	1	no	—
546	C₂²×C₇₁	—	4	1	no	—
547	C₂²×C₇₁	—	4	2	no	—
548	C₂²×C₇₁	—	4	2	no	—
549	C₂²×C₇₁	—	8	4	no	—
550	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₇₁	—	2	1	no	—
552	C₄×C₇₁	—	2	1	no	—
553	C₄×C₇₁	—	2	2	no	—
554	C₄×C₇₁	—	2	2	no	—
555	C₄×C₇₁	—	2	1	no	—
556	C₄×C₇₁	—	2	1	no	—
557	C₄×C₇₁	—	2	2	no	—
558	C₄×C₇₁	—	2	2	no	—
559	C₄×C₇₁	—	4	1	no	—
560	C₄×C₇₁	—	4	2	no	—
561	C₄×C₇₁	—	4	1	no	—
562	C₄×C₇₁	—	4	1	no	—
563	C₄×C₇₁	—	4	1	no	—
564	C₄×C₇₁	—	4	1	no	—
565	C₄×C₇₁	—	4	2	no	—
566	C₄×C₇₁	#576	1	2	yes	—
567	C₄×C₇₁	#585	1	1	yes	characteristic
568	C₄×C₇₁	#585	1	1	yes	characteristic
569	#61926	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
570	C₂×C₇₁	—	4	1	no	—
571	C₂×C₇₁	—	8	2	no	—
572	C₂×C₇₁	—	8	2	no	—
573	C₂×C₇₁	—	8	1	no	—
574	C₂×C₇₁	—	8	1	no	—
575	C₂×C₇₁	—	8	1	no	—
576	C₂×C₇₁	#3487	1	1	yes	characteristic
577	C₂×C₇₁	C₂×#576	1	1	yes	characteristic
578	C₂×C₇₁	#3584	1	1	yes	characteristic
579	#3554	C₂×C₇₁	1	1	yes	characteristic, complemented
580	#3506	C₂×C₇₁	1	1	yes	characteristic, complemented
581	#3403	C₂×C₇₁	1	2	yes	complemented
582	#3399	C₂×C₇₁	1	1	yes	characteristic, complemented
583	#3397	C₂×C₇₁	1	1	yes	characteristic, complemented
584	#3396	C₂×C₇₁	1	2	yes	complemented
585	#3394	C₂×C₇₁	1	1	yes	characteristic, complemented
586	#3391	C₂×C₇₁	1	1	yes	characteristic, complemented
587	#3370	C₂×C₇₁	1	2	yes	complemented
588	#3368	C₂×C₇₁	1	1	yes	characteristic, complemented
589	#3367	C₂×C₇₁	1	1	yes	characteristic, complemented
590	#3364	C₂×C₇₁	1	1	yes	characteristic, complemented
591	#3361	C₂×C₇₁	1	2	yes	complemented
592	#3358	C₂×C₇₁	1	1	yes	characteristic, complemented
593	#3224	C₂×C₇₁	1	2	yes	complemented
594	#3220	C₂×C₇₁	1	2	yes	complemented
595	#3212	C₂×C₇₁	1	1	yes	characteristic, complemented
596	#3207	C₂×C₇₁	1	1	yes	characteristic, complemented
597	#3124	C₂×C₇₁	1	2	yes	complemented
598	#3119	C₂×C₇₁	1	2	yes	complemented
599	#3105	C₂×C₇₁	1	1	yes	characteristic, complemented
600	#3100	C₂×C₇₁	1	1	yes	characteristic, complemented
601	#2986	C₂×C₇₁	1	1	yes	characteristic, complemented
602	C₇₁	#61926	1	1	yes	characteristic, direct product factor, Sylow
603	#562	—	2	2	no	—
604	#559	C₂²×C₇₁	1	2	yes	—
605	#559	C₂²×C₇₁	1	2	yes	—
606	#559	C₂²×C₇₁	1	1	yes	characteristic, complemented
607	#559	C₂²×C₇₁	1	2	yes	complemented
608	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
609	#556	C₂²×C₇₁	1	1	yes	characteristic
610	#556	C₂²×C₇₁	1	1	yes	characteristic
611	#555	—	2	1	no	—
612	#554	C₂²×C₇₁	1	2	yes	complemented
613	#553	—	2	2	no	—
614	#550	C₂²×C₇₁	1	1	yes	characteristic
615	#550	C₂²×C₇₁	1	1	yes	characteristic
616	#550	C₂²×C₇₁	1	1	yes	characteristic, complemented
617	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
618	#548	—	2	1	no	—
619	#547	—	2	1	no	—
620	#547	—	2	1	no	—
621	#542	—	2	1	no	—
622	#542	C₂²×C₇₁	1	2	yes	—
623	#540	C₂²×C₇₁	1	2	yes	—
624	#539	—	2	2	no	—
625	#538	—	2	2	no	—
626	#536	—	2	1	no	—
627	#535	C₂²×C₇₁	1	2	yes	—
628	#533	C₂²×C₇₁	1	1	yes	characteristic
629	#532	C₂²×C₇₁	1	1	yes	characteristic
630	#532	C₂²×C₇₁	1	1	yes	characteristic
631	#529	C₂²×C₇₁	1	1	yes	characteristic
632	#525	—	2	1	no	—
633	#525	—	2	1	no	—
634	#520	C₂²×C₇₁	1	2	yes	—
635	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
636	#496	C₂²×C₇₁	1	2	yes	—
637	#496	C₂²×C₇₁	1	2	yes	—
638	#495	C₂²×C₇₁	1	2	yes	—
639	#495	C₂²×C₇₁	1	2	yes	complemented
640	#493	C₂²×C₇₁	1	2	yes	—
641	#493	C₂²×C₇₁	1	1	yes	characteristic, complemented
642	#492	C₂²×C₇₁	1	1	yes	characteristic, complemented
643	#490	C₂²×C₇₁	1	2	yes	—
644	#489	C₂²×C₇₁	1	2	yes	—
645	#488	C₂²×C₇₁	1	2	yes	—
646	#488	C₂²×C₇₁	1	2	yes	complemented
647	#487	C₂²×C₇₁	1	1	yes	characteristic, complemented
648	#486	C₂²×C₇₁	1	2	yes	—
649	#486	C₂²×C₇₁	1	1	yes	characteristic, complemented
650	#484	C₂²×C₇₁	1	1	yes	characteristic
651	#481	C₂²×C₇₁	1	1	yes	characteristic
652	#480	C₂²×C₇₁	1	2	yes	—
653	#479	C₂²×C₇₁	1	2	yes	complemented
654	#478	C₂²×C₇₁	1	1	yes	characteristic
655	#478	C₂²×C₇₁	1	1	yes	characteristic
656	#478	C₂²×C₇₁	1	2	yes	complemented
657	#477	C₂²×C₇₁	1	2	yes	complemented
658	#474	C₂²×C₇₁	1	1	yes	characteristic
659	#474	C₂²×C₇₁	1	1	yes	characteristic
660	#474	C₂²×C₇₁	1	2	yes	complemented
661	#464	C₂²×C₇₁	1	2	yes	—
662	#464	C₂²×C₇₁	1	2	yes	complemented
663	#463	C₂²×C₇₁	1	1	yes	characteristic
664	#463	C₂²×C₇₁	1	1	yes	characteristic
665	#463	C₂²×C₇₁	1	2	yes	—
666	#463	C₂²×C₇₁	1	2	yes	—
667	#463	C₂²×C₇₁	1	2	yes	—
668	#463	C₂²×C₇₁	1	2	yes	complemented
669	#463	C₂²×C₇₁	1	2	yes	complemented
670	#463	C₂²×C₇₁	1	2	yes	complemented
671	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
672	#461	C₂²×C₇₁	1	1	yes	characteristic, complemented
673	#460	C₂²×C₇₁	1	2	yes	—
674	#460	C₂²×C₇₁	1	1	yes	characteristic, complemented
675	#460	C₂²×C₇₁	1	2	yes	complemented
676	#459	C₂²×C₇₁	1	1	yes	characteristic
677	#459	C₂²×C₇₁	1	1	yes	characteristic
678	#459	C₂²×C₇₁	1	2	yes	—
679	#459	C₂²×C₇₁	1	2	yes	—
680	#459	C₂²×C₇₁	1	2	yes	—
681	#459	C₂²×C₇₁	1	1	yes	characteristic, complemented
682	#459	C₂²×C₇₁	1	2	yes	complemented
683	#452	C₂²×C₇₁	1	2	yes	—
684	#450	C₂²×C₇₁	1	1	yes	characteristic
685	#449	C₂²×C₇₁	1	2	yes	—
686	#449	C₂²×C₇₁	1	2	yes	—
687	#449	C₂²×C₇₁	1	2	yes	—
688	#447	C₂²×C₇₁	1	2	yes	—
689	#447	C₂²×C₇₁	1	1	yes	characteristic
690	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
691	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
692	#446	C₂²×C₇₁	1	2	yes	complemented
693	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
694	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
695	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
696	#442	C₂²×C₇₁	1	2	yes	complemented
697	#440	C₂²×C₇₁	1	2	yes	complemented
698	#440	C₂²×C₇₁	1	2	yes	complemented
699	#440	C₂²×C₇₁	1	2	yes	complemented
700	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
704	C₄×D₈	C₂²×C₇₁	1	2	yes	—
705	C₄×D₈	C₂²×C₇₁	1	2	yes	—
706	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
707	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
708	C₄×D₈	C₂²×C₇₁	1	2	yes	complemented
709	C₄×D₈	C₂²×C₇₁	1	2	yes	complemented
710	#433	C₂²×C₇₁	1	2	yes	—
711	#433	C₂²×C₇₁	1	2	yes	—
712	#431	C₂²×C₇₁	1	1	yes	characteristic
713	#431	C₂²×C₇₁	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	C₂³×C₇₁	1	2	yes	—
719	C₂²×Q₈	—	2	1	no	—
720	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
721	C₂³×C₄	—	2	1	no	—
722	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
729	C₂×D₈	C₂³×C₇₁	1	2	yes	—
730	C₂×D₈	C₂³×C₇₁	1	2	yes	—
731	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
733	C₂×D₈	C₂³×C₇₁	1	2	yes	—
734	C₂×D₈	C₂³×C₇₁	1	2	yes	—
735	C₂×D₈	C₂³×C₇₁	1	2	yes	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
738	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
742	#127	C₂³×C₇₁	1	1	yes	characteristic
743	#127	C₂³×C₇₁	1	1	yes	characteristic
744	#127	C₂³×C₇₁	1	2	yes	—
745	#127	C₂³×C₇₁	1	2	yes	—
746	#127	C₂³×C₇₁	1	2	yes	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	1	no	—
751	#125	—	2	2	no	—
752	#125	D₄×C₇₁	1	2	yes	—
753	#125	C₂³×C₇₁	1	1	yes	characteristic
754	#125	C₂³×C₇₁	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	1	no	—
761	#124	C₂³×C₇₁	1	1	yes	characteristic
762	#124	C₂³×C₇₁	1	2	yes	—
763	#124	C₂³×C₇₁	1	2	yes	—
764	#124	C₂³×C₇₁	1	2	yes	—
765	#124	C₂³×C₇₁	1	2	yes	—
766	#123	—	2	1	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
786	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
787	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	C₂³×C₇₁	1	1	yes	characteristic
803	#121	C₂³×C₇₁	1	2	yes	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
811	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₇₁	1	2	yes	—
831	C₄×D₄	C₂³×C₇₁	1	2	yes	—
832	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₇₁	1	2	yes	—
834	C₄×D₄	C₂³×C₇₁	1	2	yes	—
835	C₄×D₄	C₂³×C₇₁	1	2	yes	—
836	C₄×D₄	C₂³×C₇₁	1	2	yes	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	C₂³×C₇₁	1	2	yes	—
842	C₂×C₄⋊C₄	—	2	2	no	—
843	C₂×C₄⋊C₄	—	2	2	no	—
844	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
845	C₂×C₂²⋊C₄	—	2	1	no	—
846	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
847	#107	C₂³×C₇₁	1	1	yes	characteristic
848	#107	C₂³×C₇₁	1	2	yes	—
849	#107	C₂³×C₇₁	1	2	yes	—
850	#107	C₂³×C₇₁	1	1	yes	characteristic
851	#106	C₂³×C₇₁	1	1	yes	characteristic
852	#106	C₂³×C₇₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
858	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
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	#103	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	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	1	yes	characteristic
874	#102	C₂³×C₇₁	1	1	yes	characteristic
875	#102	C₂³×C₇₁	1	2	yes	—
876	#102	C₂³×C₇₁	1	2	yes	—
877	#102	C₂³×C₇₁	1	1	yes	characteristic
878	#102	C₂³×C₇₁	1	1	yes	characteristic
879	#102	C₂³×C₇₁	1	2	yes	—
880	#102	C₂³×C₇₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
884	#97	C₂³×C₇₁	1	2	yes	—
885	#97	C₂³×C₇₁	1	2	yes	—
886	C₄×C₈	C₂³×C₇₁	1	2	yes	—
887	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₇₁	1	2	yes	—
890	C₄×C₈	C₂³×C₇₁	1	2	yes	—
891	C₂⁴	—	2	1	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	8	2	no	—
895	#41	—	8	2	no	—
896	#41	—	8	2	no	—
897	#41	—	8	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	8	2	no	—
901	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
902	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
903	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	4	1	no	—
921	C₂×D₄	—	4	1	no	—
922	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
925	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	8	2	no	—
941	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	4	1	no	—
946	SD₁₆	—	4	2	no	—
947	SD₁₆	—	4	2	no	—
948	SD₁₆	—	4	2	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	1	no	—
951	D₈	—	4	2	no	—
952	D₈	—	4	1	no	—
953	D₈	—	4	2	no	—
954	D₈	—	4	2	no	—
955	D₈	—	4	2	no	—
956	D₈	—	4	1	no	—
957	D₈	—	4	2	no	—
958	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
960	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
962	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
981	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	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	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1023	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₇₁	1	2	yes	—
1027	C₄²	C₂⁴×C₇₁	1	2	yes	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	4	2	no	—
1034	C₂³	—	8	1	no	—
1035	C₂³	—	8	1	no	—
1036	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	2	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	8	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	8	1	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	4	1	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	8	1	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1103	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1104	C₈	—	2	1	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	2	no	—
1107	C₈	—	2	2	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	8	4	no	—
1129	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	#576×C₇₁	1	2	yes	—
1146	C₄	#585×C₇₁	1	1	yes	characteristic
1147	C₄	#585×C₇₁	1	1	yes	characteristic
1148	C₂	—	4	1	no	—
1149	C₂	—	8	1	no	—
1150	C₂	—	8	1	no	—
1151	C₂	—	8	1	no	—
1152	C₂	—	8	2	no	—
1153	C₂	—	8	2	no	—
1154	C₂	C₇₁×#3487	1	1	yes	characteristic
1155	C₂	C₂×#576×C₇₁	1	1	yes	characteristic
1156	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 ◁ #533×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3554	C₂	semidirect
2. C₇₁×#3506	C₂	semidirect
3. C₇₁×#3403	C₂	semidirect
4. C₇₁×#3399	C₂	semidirect
5. C₇₁×#3397	C₂	semidirect
6. C₇₁×#3396	C₂	semidirect
7. C₇₁×#3394	C₂	semidirect
8. C₇₁×#3391	C₂	semidirect
9. C₇₁×#3370	C₂	semidirect
10. C₇₁×#3368	C₂	semidirect
11. C₇₁×#3367	C₂	semidirect
12. C₇₁×#3364	C₂	semidirect
13. C₇₁×#3361	C₂	semidirect
14. C₇₁×#3358	C₂	semidirect
15. C₇₁×#3224	C₂	semidirect
16. C₇₁×#3220	C₂	semidirect
17. C₇₁×#3212	C₂	semidirect
18. C₇₁×#3207	C₂	semidirect
19. C₇₁×#3124	C₂	semidirect
20. C₇₁×#3119	C₂	semidirect
21. C₇₁×#3105	C₂	semidirect
22. C₇₁×#3100	C₂	semidirect
23. C₇₁×#2986	C₂	semidirect
27. #559×C₇₁	C₂²	semidirect
28. #559×C₇₁	C₂²	semidirect
29. #557×C₇₁	C₂²	semidirect
33. #554×C₇₁	C₂²	semidirect
37. #550×C₇₁	C₂²	semidirect
38. D₄×Q₈×C₇₁	C₂²	semidirect
60. #495×C₇₁	C₂²	semidirect
62. #493×C₇₁	C₂²	semidirect
63. #492×C₇₁	C₂²	semidirect
67. #488×C₇₁	C₂²	semidirect
68. #487×C₇₁	C₂²	semidirect
70. #486×C₇₁	C₂²	semidirect
74. #479×C₇₁	C₂²	semidirect
77. #478×C₇₁	C₂²	semidirect
78. #477×C₇₁	C₂²	semidirect
81. #474×C₇₁	C₂²	semidirect
83. #464×C₇₁	C₂²	semidirect
89. #463×C₇₁	C₂²	semidirect
90. #463×C₇₁	C₂²	semidirect
91. #463×C₇₁	C₂²	semidirect
92. #462×C₇₁	C₂²	semidirect
93. #461×C₇₁	C₂²	semidirect
95. #460×C₇₁	C₂²	semidirect
96. #460×C₇₁	C₂²	semidirect
102. #459×C₇₁	C₂²	semidirect
103. #459×C₇₁	C₂²	semidirect
111. #446×C₇₁	C₂²	semidirect
112. #446×C₇₁	C₂²	semidirect
113. #446×C₇₁	C₂²	semidirect
114. C₈×Q₈×C₇₁	C₂²	semidirect
115. C₈×Q₈×C₇₁	C₂²	semidirect
116. C₈×Q₈×C₇₁	C₂²	semidirect
117. #442×C₇₁	C₂²	semidirect
118. #440×C₇₁	C₂²	semidirect
119. #440×C₇₁	C₂²	semidirect
120. #440×C₇₁	C₂²	semidirect
121. C₄×Q₁₆×C₇₁	C₂²	semidirect
124. C₄×SD₁₆×C₇₁	C₂²	semidirect
129. C₄×D₈×C₇₁	C₂²	semidirect
130. C₄×D₈×C₇₁	C₂²	semidirect
569. #61926	C₇₁	direct (N × H)
579. #3554	C₂×C₇₁	semidirect
580. #3506	C₂×C₇₁	semidirect
581. #3403	C₂×C₇₁	semidirect
582. #3399	C₂×C₇₁	semidirect
583. #3397	C₂×C₇₁	semidirect
584. #3396	C₂×C₇₁	semidirect
585. #3394	C₂×C₇₁	semidirect
586. #3391	C₂×C₇₁	semidirect
587. #3370	C₂×C₇₁	semidirect
588. #3368	C₂×C₇₁	semidirect
589. #3367	C₂×C₇₁	semidirect
590. #3364	C₂×C₇₁	semidirect
591. #3361	C₂×C₇₁	semidirect
592. #3358	C₂×C₇₁	semidirect
593. #3224	C₂×C₇₁	semidirect
594. #3220	C₂×C₇₁	semidirect
595. #3212	C₂×C₇₁	semidirect
596. #3207	C₂×C₇₁	semidirect
597. #3124	C₂×C₇₁	semidirect
598. #3119	C₂×C₇₁	semidirect
599. #3105	C₂×C₇₁	semidirect
600. #3100	C₂×C₇₁	semidirect
601. #2986	C₂×C₇₁	semidirect
602. C₇₁	#61926	direct (N × H)
606. #559	C₂²×C₇₁	semidirect
607. #559	C₂²×C₇₁	semidirect
608. #557	C₂²×C₇₁	semidirect
612. #554	C₂²×C₇₁	semidirect
616. #550	C₂²×C₇₁	semidirect
617. D₄×Q₈	C₂²×C₇₁	semidirect
639. #495	C₂²×C₇₁	semidirect
641. #493	C₂²×C₇₁	semidirect
642. #492	C₂²×C₇₁	semidirect
646. #488	C₂²×C₇₁	semidirect
647. #487	C₂²×C₇₁	semidirect
649. #486	C₂²×C₇₁	semidirect
653. #479	C₂²×C₇₁	semidirect
656. #478	C₂²×C₇₁	semidirect
657. #477	C₂²×C₇₁	semidirect
660. #474	C₂²×C₇₁	semidirect
662. #464	C₂²×C₇₁	semidirect
668. #463	C₂²×C₇₁	semidirect
669. #463	C₂²×C₇₁	semidirect
670. #463	C₂²×C₇₁	semidirect
671. #462	C₂²×C₇₁	semidirect
672. #461	C₂²×C₇₁	semidirect
674. #460	C₂²×C₇₁	semidirect
675. #460	C₂²×C₇₁	semidirect
681. #459	C₂²×C₇₁	semidirect
682. #459	C₂²×C₇₁	semidirect
690. #446	C₂²×C₇₁	semidirect
691. #446	C₂²×C₇₁	semidirect
692. #446	C₂²×C₇₁	semidirect
693. C₈×Q₈	C₂²×C₇₁	semidirect
694. C₈×Q₈	C₂²×C₇₁	semidirect
695. C₈×Q₈	C₂²×C₇₁	semidirect
696. #442	C₂²×C₇₁	semidirect
697. #440	C₂²×C₇₁	semidirect
698. #440	C₂²×C₇₁	semidirect
699. #440	C₂²×C₇₁	semidirect
700. C₄×Q₁₆	C₂²×C₇₁	semidirect
703. C₄×SD₁₆	C₂²×C₇₁	semidirect
708. C₄×D₈	C₂²×C₇₁	semidirect
709. C₄×D₈	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×#3554	2
C₇₁×#3506	2
C₇₁×#3403	2
C₇₁×#3399	2
C₇₁×#3397	2
C₇₁×#3396	2
C₇₁×#3394	2
C₇₁×#3391	2
C₇₁×#3370	2
C₇₁×#3368	2
C₇₁×#3367	2
C₇₁×#3364	2
C₇₁×#3361	2
C₇₁×#3358	2
C₇₁×#3224	2
C₇₁×#3220	2
C₇₁×#3212	2
C₇₁×#3207	2
C₇₁×#3124	2
C₇₁×#3119	2
C₇₁×#3105	2
C₇₁×#3100	2
C₇₁×#2986	2
#61926	71

Subgroups — C71×#61926 #31882798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61926 #31882798