Subgroups — C₇₁×#61994 #31882866

Order 18176.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3517	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×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3309	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3307	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3271	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3269	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#3250	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3219	C₂	1	2	yes	maximal, complemented
18	C₇₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₇₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#3035	C₂	1	2	yes	maximal, complemented
23	C₇₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₇₁	C₂²	1	2	yes	—
25	C₂×#135×C₇₁	C₂²	1	2	yes	—
26	C₂×#135×C₇₁	C₂²	1	2	yes	—
27	#559×C₇₁	—	2	1	no	—
28	#559×C₇₁	C₂²	1	1	yes	characteristic
29	#557×C₇₁	C₂²	1	1	yes	characteristic
30	#557×C₇₁	C₂²	1	1	yes	characteristic
31	#556×C₇₁	—	2	1	no	—
32	#556×C₇₁	C₂²	1	1	yes	characteristic
33	#553×C₇₁	—	2	2	no	—
34	#553×C₇₁	—	2	1	no	—
35	#553×C₇₁	—	2	2	no	—
36	#553×C₇₁	C₂²	1	2	yes	—
37	#550×C₇₁	—	2	1	no	—
38	#550×C₇₁	C₂²	1	1	yes	characteristic
39	#550×C₇₁	C₂²	1	2	yes	—
40	#550×C₇₁	C₂²	1	1	yes	characteristic
41	#550×C₇₁	C₂²	1	1	yes	characteristic
42	#548×C₇₁	C₂²	1	2	yes	—
43	#547×C₇₁	C₂²	1	1	yes	characteristic
44	#547×C₇₁	C₂²	1	2	yes	—
45	#540×C₇₁	—	2	2	no	—
46	#540×C₇₁	—	2	1	no	—
47	#532×C₇₁	—	2	1	no	—
48	#532×C₇₁	C₂²	1	1	yes	characteristic
49	#532×C₇₁	C₂²	1	2	yes	—
50	#532×C₇₁	C₂²	1	1	yes	characteristic
51	#529×C₇₁	—	2	2	no	—
52	#529×C₇₁	C₂²	1	1	yes	characteristic
53	#529×C₇₁	C₂²	1	2	yes	—
54	#529×C₇₁	C₂²	1	2	yes	—
55	#520×C₇₁	—	2	1	no	—
56	C₄×#41×C₇₁	—	2	1	no	—
57	C₄×#41×C₇₁	C₂²	1	2	yes	—
58	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
60	#497×C₇₁	C₂²	1	2	yes	—
61	#496×C₇₁	C₂²	1	2	yes	—
62	#493×C₇₁	C₂²	1	1	yes	characteristic
63	#492×C₇₁	C₂²	1	1	yes	characteristic
64	#491×C₇₁	C₂²	1	2	yes	—
65	#490×C₇₁	C₂²	1	2	yes	—
66	#487×C₇₁	C₂²	1	1	yes	characteristic
67	#486×C₇₁	C₂²	1	1	yes	characteristic
68	#485×C₇₁	C₂²	1	2	yes	—
69	#483×C₇₁	C₂²	1	1	yes	characteristic
70	#482×C₇₁	C₂²	1	2	yes	—
71	#480×C₇₁	C₂²	1	1	yes	characteristic
72	#479×C₇₁	C₂²	1	2	yes	—
73	#479×C₇₁	C₂²	1	1	yes	characteristic
74	#479×C₇₁	C₂²	1	1	yes	characteristic
75	#478×C₇₁	C₂²	1	2	yes	—
76	#478×C₇₁	C₂²	1	2	yes	—
77	#475×C₇₁	C₂²	1	1	yes	characteristic
78	#474×C₇₁	C₂²	1	1	yes	characteristic
79	#469×C₇₁	C₂²	1	2	yes	—
80	#468×C₇₁	C₂²	1	2	yes	—
81	#467×C₇₁	C₂²	1	2	yes	—
82	#466×C₇₁	C₂²	1	2	yes	—
83	#465×C₇₁	C₂²	1	2	yes	—
84	#465×C₇₁	C₂²	1	2	yes	—
85	#464×C₇₁	C₂²	1	1	yes	characteristic
86	#464×C₇₁	C₂²	1	1	yes	characteristic
87	#464×C₇₁	C₂²	1	2	yes	—
88	#464×C₇₁	C₂²	1	2	yes	—
89	#464×C₇₁	C₂²	1	2	yes	—
90	#463×C₇₁	C₂²	1	2	yes	—
91	#463×C₇₁	C₂²	1	2	yes	—
92	#463×C₇₁	C₂²	1	2	yes	—
93	#463×C₇₁	C₂²	1	2	yes	—
94	#462×C₇₁	C₂²	1	1	yes	characteristic
95	#462×C₇₁	C₂²	1	2	yes	—
96	#462×C₇₁	C₂²	1	1	yes	characteristic
97	#461×C₇₁	C₂²	1	2	yes	—
98	#460×C₇₁	C₂²	1	1	yes	characteristic
99	#460×C₇₁	C₂²	1	2	yes	—
100	#460×C₇₁	C₂²	1	1	yes	characteristic
101	#460×C₇₁	C₂²	1	1	yes	characteristic
102	#459×C₇₁	C₂²	1	2	yes	—
103	#459×C₇₁	C₂²	1	1	yes	characteristic
104	#452×C₇₁	C₂²	1	2	yes	—
105	#452×C₇₁	C₂²	1	2	yes	—
106	#452×C₇₁	C₂²	1	2	yes	—
107	#451×C₇₁	C₂²	1	1	yes	characteristic
108	#449×C₇₁	C₂²	1	2	yes	—
109	#449×C₇₁	C₂²	1	2	yes	—
110	#449×C₇₁	C₂²	1	2	yes	—
111	#449×C₇₁	C₂²	1	2	yes	—
112	#449×C₇₁	C₂²	1	2	yes	—
113	#448×C₇₁	C₂²	1	1	yes	characteristic
114	#446×C₇₁	C₂²	1	1	yes	characteristic
115	#446×C₇₁	C₂²	1	1	yes	characteristic
116	#442×C₇₁	C₂²	1	2	yes	—
117	#441×C₇₁	C₂²	1	2	yes	—
118	#440×C₇₁	C₂²	1	2	yes	—
119	#440×C₇₁	C₂²	1	2	yes	—
120	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
121	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
124	#435×C₇₁	C₂²	1	2	yes	—
125	#435×C₇₁	C₂²	1	2	yes	—
126	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
128	#432×C₇₁	C₂²	1	2	yes	—
129	#431×C₇₁	C₂²	1	1	yes	characteristic
130	#423×C₇₁	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
132	#417×C₇₁	C₂²	1	2	yes	—
133	#416×C₇₁	C₂²	1	2	yes	—
134	#416×C₇₁	C₂²	1	2	yes	—
135	C₂×#41×C₇₁	—	2	1	no	—
136	C₂×#41×C₇₁	—	2	1	no	—
137	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
138	C₂×#41×C₇₁	C₂³	1	2	yes	—
139	C₂×#41×C₇₁	C₂³	1	2	yes	—
140	C₂×#41×C₇₁	C₂³	1	2	yes	—
141	C₂×#41×C₇₁	C₂³	1	2	yes	—
142	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
143	#137×C₇₁	—	4	4	no	—
144	#135×C₇₁	—	4	4	no	—
145	#135×C₇₁	—	4	4	no	—
146	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
157	C₂×D₈×C₇₁	C₂³	1	2	yes	—
158	C₂×D₈×C₇₁	C₂³	1	2	yes	—
159	C₂×D₈×C₇₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₇₁	—	2	1	no	—
164	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
167	#127×C₇₁	—	2	1	no	—
168	#127×C₇₁	—	2	1	no	—
169	#127×C₇₁	—	2	2	no	—
170	#127×C₇₁	C₂³	1	2	yes	—
171	#127×C₇₁	C₂³	1	1	yes	characteristic
172	#127×C₇₁	C₂³	1	1	yes	characteristic
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	—	2	2	no	—
175	#126×C₇₁	—	2	2	no	—
176	#126×C₇₁	—	2	1	no	—
177	#126×C₇₁	—	2	2	no	—
178	#125×C₇₁	—	2	2	no	—
179	#125×C₇₁	—	2	1	no	—
180	#125×C₇₁	—	2	2	no	—
181	#125×C₇₁	C₂³	1	1	yes	characteristic
182	#125×C₇₁	C₂³	1	2	yes	—
183	#124×C₇₁	—	2	1	no	—
184	#124×C₇₁	—	2	1	no	—
185	#124×C₇₁	—	2	2	no	—
186	#124×C₇₁	—	2	1	no	—
187	#124×C₇₁	C₂³	1	2	yes	—
188	#124×C₇₁	C₂³	1	1	yes	characteristic
189	#124×C₇₁	C₂³	1	2	yes	—
190	#123×C₇₁	—	2	1	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	2	no	—
199	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
200	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
202	#121×C₇₁	—	2	2	no	—
203	#121×C₇₁	—	2	2	no	—
204	#121×C₇₁	—	2	1	no	—
205	#121×C₇₁	—	2	2	no	—
206	#121×C₇₁	—	2	1	no	—
207	#121×C₇₁	—	2	2	no	—
208	#121×C₇₁	—	2	1	no	—
209	#121×C₇₁	—	2	2	no	—
210	#121×C₇₁	—	2	1	no	—
211	#121×C₇₁	—	2	1	no	—
212	#121×C₇₁	—	2	2	no	—
213	#121×C₇₁	—	2	2	no	—
214	#121×C₇₁	—	2	2	no	—
215	#121×C₇₁	—	2	2	no	—
216	#121×C₇₁	—	2	2	no	—
217	#121×C₇₁	C₂³	1	1	yes	characteristic
218	#121×C₇₁	C₂³	1	2	yes	—
219	#121×C₇₁	C₂³	1	2	yes	—
220	#121×C₇₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₇₁	—	2	1	no	—
222	C₄×Q₈×C₇₁	—	2	1	no	—
223	C₄×Q₈×C₇₁	—	2	1	no	—
224	C₄×Q₈×C₇₁	—	2	1	no	—
225	C₄×Q₈×C₇₁	—	2	1	no	—
226	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
227	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
235	C₄×D₄×C₇₁	—	2	2	no	—
236	C₄×D₄×C₇₁	—	2	2	no	—
237	C₄×D₄×C₇₁	—	2	2	no	—
238	C₄×D₄×C₇₁	—	2	1	no	—
239	C₄×D₄×C₇₁	—	2	2	no	—
240	C₄×D₄×C₇₁	—	2	1	no	—
241	C₄×D₄×C₇₁	—	2	1	no	—
242	C₄×D₄×C₇₁	—	2	1	no	—
243	C₄×D₄×C₇₁	—	2	2	no	—
244	C₄×D₄×C₇₁	—	2	2	no	—
245	C₄×D₄×C₇₁	—	2	2	no	—
246	C₄×D₄×C₇₁	—	2	2	no	—
247	C₄×D₄×C₇₁	—	2	1	no	—
248	C₄×D₄×C₇₁	—	2	1	no	—
249	C₄×D₄×C₇₁	—	2	2	no	—
250	C₄×D₄×C₇₁	—	2	1	no	—
251	C₄×D₄×C₇₁	D₄	1	2	yes	—
252	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
253	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
258	C₄×D₄×C₇₁	C₂³	1	2	yes	—
259	#117×C₇₁	—	2	2	no	—
260	#117×C₇₁	—	2	2	no	—
261	#117×C₇₁	—	2	2	no	—
262	#117×C₇₁	—	2	1	no	—
263	#117×C₇₁	D₄	1	1	yes	characteristic
264	#117×C₇₁	D₄	1	2	yes	—
265	#117×C₇₁	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
269	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₇₁	—	2	1	no	—
271	C₂×C₄²×C₇₁	—	2	2	no	—
272	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
273	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
274	#107×C₇₁	C₂³	1	1	yes	characteristic
275	#107×C₇₁	C₂³	1	1	yes	characteristic
276	#107×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	2	yes	—
282	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
284	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
287	#103×C₇₁	C₂³	1	1	yes	characteristic
288	#103×C₇₁	C₂³	1	2	yes	—
289	#103×C₇₁	C₂³	1	2	yes	—
290	#103×C₇₁	C₂³	1	2	yes	—
291	#103×C₇₁	C₂³	1	2	yes	—
292	#103×C₇₁	C₂³	1	1	yes	characteristic
293	#103×C₇₁	C₂³	1	1	yes	characteristic
294	#103×C₇₁	C₂³	1	1	yes	characteristic
295	#103×C₇₁	C₂³	1	1	yes	characteristic
296	#103×C₇₁	C₂³	1	1	yes	characteristic
297	#103×C₇₁	C₂³	1	2	yes	—
298	#102×C₇₁	C₂³	1	1	yes	characteristic
299	#102×C₇₁	C₂³	1	2	yes	—
300	#102×C₇₁	C₂³	1	2	yes	—
301	#102×C₇₁	C₂³	1	2	yes	—
302	#102×C₇₁	C₂³	1	2	yes	—
303	#102×C₇₁	C₂³	1	1	yes	characteristic
304	#102×C₇₁	C₂³	1	2	yes	—
305	#102×C₇₁	C₂³	1	2	yes	—
306	#102×C₇₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
311	#97×C₇₁	C₂³	1	2	yes	—
312	#97×C₇₁	C₂³	1	2	yes	—
313	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
315	#41×C₇₁	—	2	4	no	—
316	#41×C₇₁	—	4	2	no	—
317	#41×C₇₁	—	4	2	no	—
318	#41×C₇₁	—	4	4	no	—
319	#41×C₇₁	—	4	2	no	—
320	#41×C₇₁	—	4	2	no	—
321	#41×C₇₁	—	4	2	no	—
322	#41×C₇₁	—	4	2	no	—
323	#41×C₇₁	—	4	2	no	—
324	#41×C₇₁	—	4	2	no	—
325	#41×C₇₁	—	4	4	no	—
326	C₂×Q₈×C₇₁	—	2	1	no	—
327	C₂×Q₈×C₇₁	—	2	1	no	—
328	C₂×Q₈×C₇₁	—	2	2	no	—
329	C₂×Q₈×C₇₁	—	4	1	no	—
330	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₇₁	—	2	2	no	—
336	C₂×D₄×C₇₁	—	2	2	no	—
337	C₂×D₄×C₇₁	—	2	2	no	—
338	C₂×D₄×C₇₁	—	2	2	no	—
339	C₂×D₄×C₇₁	—	2	1	no	—
340	C₂×D₄×C₇₁	—	2	2	no	—
341	C₂×D₄×C₇₁	—	2	2	no	—
342	C₂×D₄×C₇₁	—	2	2	no	—
343	C₂×D₄×C₇₁	—	2	2	no	—
344	C₂×D₄×C₇₁	—	2	1	no	—
345	C₂×D₄×C₇₁	—	2	1	no	—
346	C₂×D₄×C₇₁	—	2	2	no	—
347	C₂×D₄×C₇₁	—	2	1	no	—
348	C₂×D₄×C₇₁	—	2	1	no	—
349	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₇₁	—	2	1	no	—
355	C₂²×C₄×C₇₁	—	2	1	no	—
356	C₂²×C₄×C₇₁	—	2	2	no	—
357	C₂²×C₄×C₇₁	—	2	2	no	—
358	C₂²×C₄×C₇₁	—	2	2	no	—
359	C₂²×C₄×C₇₁	—	2	1	no	—
360	C₂²×C₄×C₇₁	—	2	2	no	—
361	C₂²×C₄×C₇₁	—	2	2	no	—
362	C₂²×C₄×C₇₁	—	2	2	no	—
363	C₂²×C₄×C₇₁	—	2	2	no	—
364	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₇₁	—	2	2	no	—
371	Q₁₆×C₇₁	—	2	4	no	—
372	Q₁₆×C₇₁	—	4	1	no	—
373	Q₁₆×C₇₁	—	4	2	no	—
374	SD₁₆×C₇₁	—	2	2	no	—
375	SD₁₆×C₇₁	—	2	4	no	—
376	SD₁₆×C₇₁	—	4	1	no	—
377	SD₁₆×C₇₁	—	4	2	no	—
378	SD₁₆×C₇₁	—	4	2	no	—
379	SD₁₆×C₇₁	—	4	2	no	—
380	SD₁₆×C₇₁	—	4	2	no	—
381	D₈×C₇₁	—	4	2	no	—
382	D₈×C₇₁	—	4	2	no	—
383	D₈×C₇₁	—	4	2	no	—
384	M₁₆×C₇₁	—	4	2	no	—
385	C₂×C₈×C₇₁	—	4	2	no	—
386	C₂×C₈×C₇₁	—	4	2	no	—
387	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
392	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
393	C₄⋊C₄×C₇₁	—	2	2	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	1	no	—
398	C₄⋊C₄×C₇₁	—	2	1	no	—
399	C₄⋊C₄×C₇₁	—	2	1	no	—
400	C₄⋊C₄×C₇₁	—	2	1	no	—
401	C₄⋊C₄×C₇₁	—	2	1	no	—
402	C₄⋊C₄×C₇₁	—	2	1	no	—
403	C₄⋊C₄×C₇₁	—	2	2	no	—
404	C₄⋊C₄×C₇₁	—	2	2	no	—
405	C₄⋊C₄×C₇₁	—	2	2	no	—
406	C₄⋊C₄×C₇₁	—	2	1	no	—
407	C₄⋊C₄×C₇₁	—	2	2	no	—
408	C₄⋊C₄×C₇₁	—	2	1	no	—
409	C₄⋊C₄×C₇₁	—	2	1	no	—
410	C₄⋊C₄×C₇₁	—	2	2	no	—
411	C₄⋊C₄×C₇₁	—	2	2	no	—
412	C₄⋊C₄×C₇₁	—	2	1	no	—
413	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₇₁	—	2	2	no	—
423	C₂²⋊C₄×C₇₁	—	2	2	no	—
424	C₂²⋊C₄×C₇₁	—	2	1	no	—
425	C₂²⋊C₄×C₇₁	—	2	2	no	—
426	C₂²⋊C₄×C₇₁	—	2	2	no	—
427	C₂²⋊C₄×C₇₁	—	2	1	no	—
428	C₂²⋊C₄×C₇₁	—	2	2	no	—
429	C₂²⋊C₄×C₇₁	—	2	1	no	—
430	C₂²⋊C₄×C₇₁	—	2	2	no	—
431	C₂²⋊C₄×C₇₁	—	2	2	no	—
432	C₂²⋊C₄×C₇₁	—	2	2	no	—
433	C₂²⋊C₄×C₇₁	—	2	2	no	—
434	C₂²⋊C₄×C₇₁	—	2	1	no	—
435	C₂²⋊C₄×C₇₁	—	2	2	no	—
436	C₂²⋊C₄×C₇₁	—	2	2	no	—
437	C₂²⋊C₄×C₇₁	—	2	2	no	—
438	C₂²⋊C₄×C₇₁	—	2	2	no	—
439	C₂²⋊C₄×C₇₁	—	2	1	no	—
440	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
443	C₄²×C₇₁	—	2	1	no	—
444	C₄²×C₇₁	—	2	1	no	—
445	C₄²×C₇₁	—	2	2	no	—
446	C₄²×C₇₁	—	2	2	no	—
447	C₄²×C₇₁	—	2	1	no	—
448	C₄²×C₇₁	—	2	1	no	—
449	C₄²×C₇₁	—	2	2	no	—
450	C₄²×C₇₁	—	2	1	no	—
451	C₄²×C₇₁	C₂×D₄	1	2	yes	—
452	C₄²×C₇₁	C₂×D₄	1	2	yes	—
453	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₇₁	C₂⁴	1	2	yes	—
457	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₇₁	—	2	2	no	—
459	C₂³×C₇₁	—	2	1	no	—
460	C₂³×C₇₁	—	2	2	no	—
461	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
462	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
463	Q₈×C₇₁	—	2	2	no	—
464	Q₈×C₇₁	—	2	1	no	—
465	Q₈×C₇₁	—	2	1	no	—
466	Q₈×C₇₁	—	2	1	no	—
467	Q₈×C₇₁	—	2	2	no	—
468	Q₈×C₇₁	—	2	1	no	—
469	Q₈×C₇₁	—	2	2	no	—
470	Q₈×C₇₁	—	2	1	no	—
471	Q₈×C₇₁	—	4	2	no	—
472	Q₈×C₇₁	—	4	2	no	—
473	Q₈×C₇₁	H(5,𝔽₂)	1	2	yes	—
474	D₄×C₇₁	—	2	2	no	—
475	D₄×C₇₁	—	2	1	no	—
476	D₄×C₇₁	—	2	2	no	—
477	D₄×C₇₁	—	2	2	no	—
478	D₄×C₇₁	—	2	2	no	—
479	D₄×C₇₁	—	2	2	no	—
480	D₄×C₇₁	—	2	1	no	—
481	D₄×C₇₁	—	4	2	no	—
482	D₄×C₇₁	—	4	4	no	—
483	D₄×C₇₁	—	4	4	no	—
484	D₄×C₇₁	—	4	4	no	—
485	D₄×C₇₁	—	4	2	no	—
486	D₄×C₇₁	—	4	2	no	—
487	D₄×C₇₁	—	8	2	no	—
488	D₄×C₇₁	—	8	1	no	—
489	D₄×C₇₁	—	8	1	no	—
490	D₄×C₇₁	—	8	2	no	—
491	D₄×C₇₁	—	8	1	no	—
492	D₄×C₇₁	—	8	2	no	—
493	D₄×C₇₁	—	8	2	no	—
494	D₄×C₇₁	—	8	2	no	—
495	D₄×C₇₁	—	8	2	no	—
496	C₂×C₄×C₇₁	—	2	1	no	—
497	C₂×C₄×C₇₁	—	2	2	no	—
498	C₂×C₄×C₇₁	—	2	2	no	—
499	C₂×C₄×C₇₁	—	2	1	no	—
500	C₂×C₄×C₇₁	—	2	1	no	—
501	C₂×C₄×C₇₁	—	2	2	no	—
502	C₂×C₄×C₇₁	—	2	1	no	—
503	C₂×C₄×C₇₁	—	2	1	no	—
504	C₂×C₄×C₇₁	—	2	1	no	—
505	C₂×C₄×C₇₁	—	2	2	no	—
506	C₂×C₄×C₇₁	—	2	1	no	—
507	C₂×C₄×C₇₁	—	2	1	no	—
508	C₂×C₄×C₇₁	—	2	2	no	—
509	C₂×C₄×C₇₁	—	2	1	no	—
510	C₂×C₄×C₇₁	—	4	2	no	—
511	C₂×C₄×C₇₁	—	4	1	no	—
512	C₂×C₄×C₇₁	—	4	2	no	—
513	C₂×C₄×C₇₁	—	4	4	no	—
514	C₂×C₄×C₇₁	—	4	2	no	—
515	C₂×C₄×C₇₁	—	4	4	no	—
516	C₂×C₄×C₇₁	—	4	4	no	—
517	C₂×C₄×C₇₁	—	4	2	no	—
518	C₂×C₄×C₇₁	—	8	2	no	—
519	C₂×C₄×C₇₁	—	8	2	no	—
520	C₂×C₄×C₇₁	—	8	2	no	—
521	C₂×C₄×C₇₁	—	8	2	no	—
522	C₂×C₄×C₇₁	—	8	1	no	—
523	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
532	C₈×C₇₁	—	2	1	no	—
533	C₈×C₇₁	—	2	1	no	—
534	C₈×C₇₁	—	2	2	no	—
535	C₈×C₇₁	—	2	2	no	—
536	C₈×C₇₁	—	2	1	no	—
537	C₈×C₇₁	—	2	1	no	—
538	C₂²×C₇₁	—	2	1	no	—
539	C₂²×C₇₁	—	2	2	no	—
540	C₂²×C₇₁	—	2	1	no	—
541	C₂²×C₇₁	—	2	2	no	—
542	C₂²×C₇₁	—	2	1	no	—
543	C₂²×C₇₁	—	2	2	no	—
544	C₂²×C₇₁	—	4	2	no	—
545	C₂²×C₇₁	—	4	1	no	—
546	C₂²×C₇₁	—	4	2	no	—
547	C₂²×C₇₁	—	4	2	no	—
548	C₂²×C₇₁	—	4	1	no	—
549	C₂²×C₇₁	—	4	2	no	—
550	C₂²×C₇₁	—	4	2	no	—
551	C₂²×C₇₁	—	4	2	no	—
552	C₂²×C₇₁	—	4	1	no	—
553	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
554	C₄×C₇₁	—	2	1	no	—
555	C₄×C₇₁	—	2	2	no	—
556	C₄×C₇₁	—	2	1	no	—
557	C₄×C₇₁	—	2	2	no	—
558	C₄×C₇₁	—	2	1	no	—
559	C₄×C₇₁	—	2	2	no	—
560	C₄×C₇₁	—	2	1	no	—
561	C₄×C₇₁	—	2	2	no	—
562	C₄×C₇₁	—	4	1	no	—
563	C₄×C₇₁	—	4	1	no	—
564	C₄×C₇₁	—	4	1	no	—
565	C₄×C₇₁	—	4	1	no	—
566	C₄×C₇₁	—	4	1	no	—
567	C₄×C₇₁	—	4	2	no	—
568	C₄×C₇₁	—	4	1	no	—
569	C₄×C₇₁	—	4	2	no	—
570	C₄×C₇₁	#575	1	2	yes	—
571	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
572	C₄×C₇₁	#585	1	1	yes	characteristic
573	#61994	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
574	C₂×C₇₁	—	4	1	no	—
575	C₂×C₇₁	—	4	2	no	—
576	C₂×C₇₁	—	8	2	no	—
577	C₂×C₇₁	—	8	1	no	—
578	C₂×C₇₁	—	8	2	no	—
579	C₂×C₇₁	#3488	1	1	yes	characteristic
580	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
581	C₂×C₇₁	#3584	1	1	yes	characteristic
582	#3517	C₂×C₇₁	1	1	yes	characteristic, complemented
583	#3480	C₂×C₇₁	1	1	yes	characteristic, complemented
584	#3400	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3399	C₂×C₇₁	1	1	yes	characteristic, complemented
586	#3374	C₂×C₇₁	1	1	yes	characteristic, complemented
587	#3368	C₂×C₇₁	1	1	yes	characteristic, complemented
588	#3309	C₂×C₇₁	1	2	yes	complemented
589	#3307	C₂×C₇₁	1	2	yes	complemented
590	#3304	C₂×C₇₁	1	1	yes	characteristic, complemented
591	#3302	C₂×C₇₁	1	1	yes	characteristic, complemented
592	#3287	C₂×C₇₁	1	1	yes	characteristic, complemented
593	#3284	C₂×C₇₁	1	1	yes	characteristic, complemented
594	#3271	C₂×C₇₁	1	2	yes	complemented
595	#3269	C₂×C₇₁	1	2	yes	complemented
596	#3251	C₂×C₇₁	1	1	yes	characteristic, complemented
597	#3250	C₂×C₇₁	1	2	yes	complemented
598	#3219	C₂×C₇₁	1	2	yes	complemented
599	#3207	C₂×C₇₁	1	1	yes	characteristic, complemented
600	#3111	C₂×C₇₁	1	2	yes	complemented
601	#3108	C₂×C₇₁	1	1	yes	characteristic, complemented
602	#3037	C₂×C₇₁	1	1	yes	characteristic, complemented
603	#3035	C₂×C₇₁	1	2	yes	complemented
604	#2990	C₂×C₇₁	1	1	yes	characteristic, complemented
605	C₇₁	#61994	1	1	yes	characteristic, direct product factor, Sylow
606	C₂×#137	C₂²×C₇₁	1	2	yes	—
607	C₂×#135	C₂²×C₇₁	1	2	yes	—
608	C₂×#135	C₂²×C₇₁	1	2	yes	—
609	#559	—	2	1	no	—
610	#559	C₂²×C₇₁	1	1	yes	characteristic
611	#557	C₂²×C₇₁	1	1	yes	characteristic
612	#557	C₂²×C₇₁	1	1	yes	characteristic
613	#556	—	2	1	no	—
614	#556	C₂²×C₇₁	1	1	yes	characteristic
615	#553	—	2	2	no	—
616	#553	—	2	1	no	—
617	#553	—	2	2	no	—
618	#553	C₂²×C₇₁	1	2	yes	—
619	#550	—	2	1	no	—
620	#550	C₂²×C₇₁	1	1	yes	characteristic
621	#550	C₂²×C₇₁	1	2	yes	—
622	#550	C₂²×C₇₁	1	1	yes	characteristic
623	#550	C₂²×C₇₁	1	1	yes	characteristic
624	#548	C₂²×C₇₁	1	2	yes	—
625	#547	C₂²×C₇₁	1	2	yes	—
626	#547	C₂²×C₇₁	1	1	yes	characteristic
627	#540	—	2	2	no	—
628	#540	—	2	1	no	—
629	#532	—	2	1	no	—
630	#532	C₂²×C₇₁	1	1	yes	characteristic
631	#532	C₂²×C₇₁	1	2	yes	—
632	#532	C₂²×C₇₁	1	1	yes	characteristic
633	#529	—	2	2	no	—
634	#529	C₂²×C₇₁	1	1	yes	characteristic
635	#529	C₂²×C₇₁	1	2	yes	—
636	#529	C₂²×C₇₁	1	2	yes	—
637	#520	—	2	1	no	—
638	C₄×#41	—	2	1	no	—
639	C₄×#41	C₂²×C₇₁	1	2	yes	—
640	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
641	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
642	#497	C₂²×C₇₁	1	2	yes	—
643	#496	C₂²×C₇₁	1	2	yes	—
644	#493	C₂²×C₇₁	1	1	yes	characteristic
645	#492	C₂²×C₇₁	1	1	yes	characteristic
646	#491	C₂²×C₇₁	1	2	yes	—
647	#490	C₂²×C₇₁	1	2	yes	—
648	#487	C₂²×C₇₁	1	1	yes	characteristic
649	#486	C₂²×C₇₁	1	1	yes	characteristic
650	#485	C₂²×C₇₁	1	2	yes	—
651	#483	C₂²×C₇₁	1	1	yes	characteristic
652	#482	C₂²×C₇₁	1	2	yes	—
653	#480	C₂²×C₇₁	1	1	yes	characteristic
654	#479	C₂²×C₇₁	1	1	yes	characteristic
655	#479	C₂²×C₇₁	1	1	yes	characteristic
656	#479	C₂²×C₇₁	1	2	yes	—
657	#478	C₂²×C₇₁	1	2	yes	—
658	#478	C₂²×C₇₁	1	2	yes	—
659	#475	C₂²×C₇₁	1	1	yes	characteristic
660	#474	C₂²×C₇₁	1	1	yes	characteristic
661	#469	C₂²×C₇₁	1	2	yes	—
662	#468	C₂²×C₇₁	1	2	yes	—
663	#467	C₂²×C₇₁	1	2	yes	—
664	#466	C₂²×C₇₁	1	2	yes	—
665	#465	C₂²×C₇₁	1	2	yes	—
666	#465	C₂²×C₇₁	1	2	yes	—
667	#464	C₂²×C₇₁	1	1	yes	characteristic
668	#464	C₂²×C₇₁	1	1	yes	characteristic
669	#464	C₂²×C₇₁	1	2	yes	—
670	#464	C₂²×C₇₁	1	2	yes	—
671	#464	C₂²×C₇₁	1	2	yes	—
672	#463	C₂²×C₇₁	1	2	yes	—
673	#463	C₂²×C₇₁	1	2	yes	—
674	#463	C₂²×C₇₁	1	2	yes	—
675	#463	C₂²×C₇₁	1	2	yes	—
676	#462	C₂²×C₇₁	1	2	yes	—
677	#462	C₂²×C₇₁	1	1	yes	characteristic
678	#462	C₂²×C₇₁	1	1	yes	characteristic
679	#461	C₂²×C₇₁	1	2	yes	—
680	#460	C₂²×C₇₁	1	2	yes	—
681	#460	C₂²×C₇₁	1	1	yes	characteristic
682	#460	C₂²×C₇₁	1	1	yes	characteristic
683	#460	C₂²×C₇₁	1	1	yes	characteristic
684	#459	C₂²×C₇₁	1	1	yes	characteristic
685	#459	C₂²×C₇₁	1	2	yes	—
686	#452	C₂²×C₇₁	1	2	yes	—
687	#452	C₂²×C₇₁	1	2	yes	—
688	#452	C₂²×C₇₁	1	2	yes	—
689	#451	C₂²×C₇₁	1	1	yes	characteristic
690	#449	C₂²×C₇₁	1	2	yes	—
691	#449	C₂²×C₇₁	1	2	yes	—
692	#449	C₂²×C₇₁	1	2	yes	—
693	#449	C₂²×C₇₁	1	2	yes	—
694	#449	C₂²×C₇₁	1	2	yes	—
695	#448	C₂²×C₇₁	1	1	yes	characteristic
696	#446	C₂²×C₇₁	1	1	yes	characteristic
697	#446	C₂²×C₇₁	1	1	yes	characteristic
698	#442	C₂²×C₇₁	1	2	yes	—
699	#441	C₂²×C₇₁	1	2	yes	—
700	#440	C₂²×C₇₁	1	2	yes	—
701	#440	C₂²×C₇₁	1	2	yes	—
702	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
703	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
704	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
705	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
706	#435	C₂²×C₇₁	1	2	yes	—
707	#435	C₂²×C₇₁	1	2	yes	—
708	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
709	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic
710	#432	C₂²×C₇₁	1	2	yes	—
711	#431	C₂²×C₇₁	1	1	yes	characteristic
712	#423	C₂²×C₇₁	1	1	yes	characteristic
713	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
714	#417	C₂²×C₇₁	1	2	yes	—
715	#416	C₂²×C₇₁	1	2	yes	—
716	#416	C₂²×C₇₁	1	2	yes	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
720	C₂×#41	C₂³×C₇₁	1	2	yes	—
721	C₂×#41	C₂³×C₇₁	1	2	yes	—
722	C₂×#41	C₂³×C₇₁	1	2	yes	—
723	C₂×#41	C₂³×C₇₁	1	2	yes	—
724	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
725	#137	—	4	4	no	—
726	#135	—	4	4	no	—
727	#135	—	4	4	no	—
728	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
729	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
739	C₂×D₈	C₂³×C₇₁	1	2	yes	—
740	C₂×D₈	C₂³×C₇₁	1	2	yes	—
741	C₂×D₈	C₂³×C₇₁	1	2	yes	—
742	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
743	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
744	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
747	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
749	#127	—	2	1	no	—
750	#127	—	2	1	no	—
751	#127	—	2	2	no	—
752	#127	C₂³×C₇₁	1	2	yes	—
753	#127	C₂³×C₇₁	1	1	yes	characteristic
754	#127	C₂³×C₇₁	1	1	yes	characteristic
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#126	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	—	2	2	no	—
763	#125	C₂³×C₇₁	1	1	yes	characteristic
764	#125	C₂³×C₇₁	1	2	yes	—
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	C₂³×C₇₁	1	1	yes	characteristic
770	#124	C₂³×C₇₁	1	2	yes	—
771	#124	C₂³×C₇₁	1	2	yes	—
772	#123	—	2	1	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
783	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	1	no	—
791	#121	—	2	2	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	C₂³×C₇₁	1	1	yes	characteristic
800	#121	C₂³×C₇₁	1	2	yes	—
801	#121	C₂³×C₇₁	1	2	yes	—
802	#121	C₂³×C₇₁	1	2	yes	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
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×Q₈	C₂³×C₇₁	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
816	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	D₄×C₇₁	1	2	yes	—
834	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₇₁	1	2	yes	—
836	C₄×D₄	C₂³×C₇₁	1	2	yes	—
837	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₇₁	1	2	yes	—
839	C₄×D₄	C₂³×C₇₁	1	2	yes	—
840	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
841	#117	—	2	2	no	—
842	#117	—	2	2	no	—
843	#117	—	2	2	no	—
844	#117	—	2	1	no	—
845	#117	D₄×C₇₁	1	1	yes	characteristic
846	#117	D₄×C₇₁	1	2	yes	—
847	#117	C₂³×C₇₁	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	2	no	—
851	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
852	C₂×C₄²	—	2	1	no	—
853	C₂×C₄²	—	2	2	no	—
854	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
855	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
856	#107	C₂³×C₇₁	1	1	yes	characteristic
857	#107	C₂³×C₇₁	1	1	yes	characteristic
858	#107	C₂³×C₇₁	1	2	yes	—
859	#106	C₂³×C₇₁	1	1	yes	characteristic
860	#106	C₂³×C₇₁	1	1	yes	characteristic
861	#106	C₂³×C₇₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
869	#103	C₂³×C₇₁	1	1	yes	characteristic
870	#103	C₂³×C₇₁	1	2	yes	—
871	#103	C₂³×C₇₁	1	2	yes	—
872	#103	C₂³×C₇₁	1	2	yes	—
873	#103	C₂³×C₇₁	1	2	yes	—
874	#103	C₂³×C₇₁	1	1	yes	characteristic
875	#103	C₂³×C₇₁	1	1	yes	characteristic
876	#103	C₂³×C₇₁	1	1	yes	characteristic
877	#103	C₂³×C₇₁	1	1	yes	characteristic
878	#103	C₂³×C₇₁	1	1	yes	characteristic
879	#103	C₂³×C₇₁	1	2	yes	—
880	#102	C₂³×C₇₁	1	1	yes	characteristic
881	#102	C₂³×C₇₁	1	2	yes	—
882	#102	C₂³×C₇₁	1	2	yes	—
883	#102	C₂³×C₇₁	1	2	yes	—
884	#102	C₂³×C₇₁	1	2	yes	—
885	#102	C₂³×C₇₁	1	1	yes	characteristic
886	#102	C₂³×C₇₁	1	2	yes	—
887	#102	C₂³×C₇₁	1	2	yes	—
888	#102	C₂³×C₇₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
893	#97	C₂³×C₇₁	1	2	yes	—
894	#97	C₂³×C₇₁	1	2	yes	—
895	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
897	#41	—	2	4	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	4	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	4	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	2	no	—
911	C₂×Q₈	—	4	1	no	—
912	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
933	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
947	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
948	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
949	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
950	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
952	Q₁₆	—	2	2	no	—
953	Q₁₆	—	2	4	no	—
954	Q₁₆	—	4	1	no	—
955	Q₁₆	—	4	2	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	2	4	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	2	no	—
966	M₁₆	—	4	2	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
974	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1035	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₇₁	1	2	yes	—
1039	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1044	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	H(5,𝔽₂)×C₇₁	1	2	yes	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	1	no	—
1077	D₄	—	8	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1107	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1113	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	#575×C₇₁	1	2	yes	—
1153	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
1154	C₄	#585×C₇₁	1	1	yes	characteristic
1155	C₂	—	4	1	no	—
1156	C₂	—	4	2	no	—
1157	C₂	—	8	2	no	—
1158	C₂	—	8	2	no	—
1159	C₂	—	8	1	no	—
1160	C₂	C₇₁×#3488	1	1	yes	characteristic
1161	C₂	C₂×#575×C₇₁	1	1	yes	characteristic
1162	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 ◁ C₄×#41×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3517	C₂	semidirect
2. C₇₁×#3480	C₂	semidirect
3. C₇₁×#3400	C₂	semidirect
4. C₇₁×#3399	C₂	semidirect
5. C₇₁×#3374	C₂	semidirect
6. C₇₁×#3368	C₂	semidirect
7. C₇₁×#3309	C₂	semidirect
8. C₇₁×#3307	C₂	semidirect
9. C₇₁×#3304	C₂	semidirect
10. C₇₁×#3302	C₂	semidirect
11. C₇₁×#3287	C₂	semidirect
12. C₇₁×#3284	C₂	semidirect
13. C₇₁×#3271	C₂	semidirect
14. C₇₁×#3269	C₂	semidirect
15. C₇₁×#3251	C₂	semidirect
16. C₇₁×#3250	C₂	semidirect
17. C₇₁×#3219	C₂	semidirect
18. C₇₁×#3207	C₂	semidirect
19. C₇₁×#3111	C₂	semidirect
20. C₇₁×#3108	C₂	semidirect
21. C₇₁×#3037	C₂	semidirect
22. C₇₁×#3035	C₂	semidirect
23. C₇₁×#2990	C₂	semidirect
573. #61994	C₇₁	direct (N × H)
582. #3517	C₂×C₇₁	semidirect
583. #3480	C₂×C₇₁	semidirect
584. #3400	C₂×C₇₁	semidirect
585. #3399	C₂×C₇₁	semidirect
586. #3374	C₂×C₇₁	semidirect
587. #3368	C₂×C₇₁	semidirect
588. #3309	C₂×C₇₁	semidirect
589. #3307	C₂×C₇₁	semidirect
590. #3304	C₂×C₇₁	semidirect
591. #3302	C₂×C₇₁	semidirect
592. #3287	C₂×C₇₁	semidirect
593. #3284	C₂×C₇₁	semidirect
594. #3271	C₂×C₇₁	semidirect
595. #3269	C₂×C₇₁	semidirect
596. #3251	C₂×C₇₁	semidirect
597. #3250	C₂×C₇₁	semidirect
598. #3219	C₂×C₇₁	semidirect
599. #3207	C₂×C₇₁	semidirect
600. #3111	C₂×C₇₁	semidirect
601. #3108	C₂×C₇₁	semidirect
602. #3037	C₂×C₇₁	semidirect
603. #3035	C₂×C₇₁	semidirect
604. #2990	C₂×C₇₁	semidirect
605. C₇₁	#61994	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₁×#3517	2
C₇₁×#3480	2
C₇₁×#3400	2
C₇₁×#3399	2
C₇₁×#3374	2
C₇₁×#3368	2
C₇₁×#3309	2
C₇₁×#3307	2
C₇₁×#3304	2
C₇₁×#3302	2
C₇₁×#3287	2
C₇₁×#3284	2
C₇₁×#3271	2
C₇₁×#3269	2
C₇₁×#3251	2
C₇₁×#3250	2
C₇₁×#3219	2
C₇₁×#3207	2
C₇₁×#3111	2
C₇₁×#3108	2
C₇₁×#3037	2
C₇₁×#3035	2
C₇₁×#2990	2
#61994	71

Subgroups — C71×#61994 #31882866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61994 #31882866