Subgroups — C₇₁×#61920 #31882792

Order 18176.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1168 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×#3508	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×#3399	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3366	C₂	1	2	yes	maximal, complemented
13	C₇₁×#3365	C₂	1	1	yes	maximal, characteristic, 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×#3217	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₇₁×#3118	C₂	1	2	yes	maximal, complemented
21	C₇₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	#562×C₇₁	—	2	2	no	—
25	#559×C₇₁	C₂²	1	1	yes	characteristic
26	#559×C₇₁	C₂²	1	2	yes	—
27	#559×C₇₁	C₂²	1	1	yes	characteristic
28	#559×C₇₁	C₂²	1	1	yes	characteristic, complemented
29	#559×C₇₁	C₂²	1	2	yes	complemented
30	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
31	#554×C₇₁	C₂²	1	2	yes	complemented
32	#550×C₇₁	C₂²	1	1	yes	characteristic
33	#550×C₇₁	C₂²	1	2	yes	—
34	#550×C₇₁	C₂²	1	1	yes	characteristic
35	#550×C₇₁	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
37	#548×C₇₁	—	2	1	no	—
38	#547×C₇₁	—	2	1	no	—
39	#546×C₇₁	—	2	1	no	—
40	#546×C₇₁	—	2	1	no	—
41	#546×C₇₁	—	2	2	no	—
42	#542×C₇₁	—	2	1	no	—
43	#542×C₇₁	C₂²	1	2	yes	—
44	#540×C₇₁	—	2	2	no	—
45	#540×C₇₁	C₂²	1	2	yes	—
46	#539×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	—	2	1	no	—
51	#532×C₇₁	—	2	1	no	—
52	#532×C₇₁	C₂²	1	1	yes	characteristic
53	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic
54	#529×C₇₁	C₂²	1	1	yes	characteristic
55	#518×C₇₁	C₂²	1	2	yes	—
56	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
57	#496×C₇₁	C₂²	1	2	yes	—
58	#496×C₇₁	C₂²	1	2	yes	complemented
59	#496×C₇₁	C₂²	1	2	yes	complemented
60	#495×C₇₁	C₂²	1	2	yes	complemented
61	#493×C₇₁	C₂²	1	1	yes	characteristic
62	#493×C₇₁	C₂²	1	1	yes	characteristic
63	#493×C₇₁	C₂²	1	2	yes	complemented
64	#490×C₇₁	C₂²	1	2	yes	—
65	#490×C₇₁	C₂²	1	2	yes	complemented
66	#489×C₇₁	C₂²	1	2	yes	complemented
67	#488×C₇₁	C₂²	1	2	yes	complemented
68	#486×C₇₁	C₂²	1	1	yes	characteristic
69	#486×C₇₁	C₂²	1	1	yes	characteristic
70	#486×C₇₁	C₂²	1	2	yes	complemented
71	#485×C₇₁	C₂²	1	1	yes	characteristic
72	#482×C₇₁	C₂²	1	1	yes	characteristic
73	#482×C₇₁	C₂²	1	2	yes	—
74	#479×C₇₁	C₂²	1	1	yes	characteristic, complemented
75	#478×C₇₁	C₂²	1	1	yes	characteristic, complemented
76	#478×C₇₁	C₂²	1	2	yes	complemented
77	#478×C₇₁	C₂²	1	2	yes	complemented
78	#476×C₇₁	C₂²	1	2	yes	complemented
79	#475×C₇₁	C₂²	1	1	yes	characteristic, complemented
80	#474×C₇₁	C₂²	1	1	yes	characteristic, complemented
81	#474×C₇₁	C₂²	1	2	yes	complemented
82	#464×C₇₁	C₂²	1	1	yes	characteristic, complemented
83	#464×C₇₁	C₂²	1	2	yes	complemented
84	#463×C₇₁	C₂²	1	1	yes	characteristic, complemented
85	#463×C₇₁	C₂²	1	2	yes	complemented
86	#463×C₇₁	C₂²	1	2	yes	complemented
87	#463×C₇₁	C₂²	1	2	yes	complemented
88	#463×C₇₁	C₂²	1	2	yes	complemented
89	#463×C₇₁	C₂²	1	2	yes	complemented
90	#460×C₇₁	C₂²	1	1	yes	characteristic
91	#460×C₇₁	C₂²	1	1	yes	characteristic
92	#460×C₇₁	C₂²	1	2	yes	complemented
93	#460×C₇₁	C₂²	1	1	yes	characteristic, complemented
94	#459×C₇₁	C₂²	1	1	yes	characteristic
95	#459×C₇₁	C₂²	1	2	yes	—
96	#459×C₇₁	C₂²	1	2	yes	—
97	#459×C₇₁	C₂²	1	1	yes	characteristic
98	#459×C₇₁	C₂²	1	2	yes	complemented
99	#459×C₇₁	C₂²	1	2	yes	complemented
100	#459×C₇₁	C₂²	1	2	yes	complemented
101	#459×C₇₁	C₂²	1	1	yes	characteristic, complemented
102	#459×C₇₁	C₂²	1	2	yes	complemented
103	#459×C₇₁	C₂²	1	2	yes	complemented
104	#452×C₇₁	C₂²	1	1	yes	characteristic
105	#450×C₇₁	C₂²	1	2	yes	—
106	#449×C₇₁	C₂²	1	1	yes	characteristic
107	#449×C₇₁	C₂²	1	2	yes	—
108	#447×C₇₁	C₂²	1	2	yes	—
109	#447×C₇₁	C₂²	1	2	yes	—
110	#447×C₇₁	C₂²	1	2	yes	—
111	#446×C₇₁	C₂²	1	2	yes	complemented
112	#446×C₇₁	C₂²	1	1	yes	characteristic, complemented
113	#446×C₇₁	C₂²	1	2	yes	complemented
114	#446×C₇₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
117	#442×C₇₁	C₂²	1	2	yes	complemented
118	#442×C₇₁	C₂²	1	2	yes	complemented
119	#442×C₇₁	C₂²	1	2	yes	complemented
120	#442×C₇₁	C₂²	1	2	yes	complemented
121	#440×C₇₁	C₂²	1	2	yes	complemented
122	#440×C₇₁	C₂²	1	2	yes	complemented
123	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
124	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
127	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₇₁	C₂²	1	2	yes	complemented
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	#432×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	2	no	—
138	C₂×#41×C₇₁	—	2	1	no	—
139	C₂×#41×C₇₁	—	2	1	no	—
140	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₇₁	—	2	1	no	—
142	C₂²×D₄×C₇₁	—	2	1	no	—
143	C₂²×D₄×C₇₁	—	2	1	no	—
144	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
151	C₂×D₈×C₇₁	C₂³	1	2	yes	—
152	C₂×D₈×C₇₁	C₂³	1	2	yes	—
153	C₂×D₈×C₇₁	C₂³	1	2	yes	—
154	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₇₁	C₂³	1	2	yes	—
156	C₂×D₈×C₇₁	C₂³	1	2	yes	—
157	C₂×D₈×C₇₁	C₂³	1	2	yes	—
158	C₂×D₈×C₇₁	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₇₁	—	2	1	no	—
160	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
161	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
162	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
164	#127×C₇₁	—	2	1	no	—
165	#127×C₇₁	—	2	1	no	—
166	#127×C₇₁	C₂³	1	2	yes	—
167	#127×C₇₁	C₂³	1	1	yes	characteristic
168	#127×C₇₁	C₂³	1	1	yes	characteristic
169	#127×C₇₁	C₂³	1	2	yes	—
170	#127×C₇₁	C₂³	1	2	yes	—
171	#127×C₇₁	C₂³	1	2	yes	—
172	#127×C₇₁	C₂³	1	1	yes	characteristic
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	—	2	1	no	—
175	#125×C₇₁	—	2	2	no	—
176	#125×C₇₁	D₄	1	2	yes	—
177	#125×C₇₁	C₂³	1	2	yes	—
178	#125×C₇₁	C₂³	1	1	yes	characteristic
179	#124×C₇₁	—	2	1	no	—
180	#124×C₇₁	—	2	1	no	—
181	#124×C₇₁	—	2	2	no	—
182	#124×C₇₁	—	2	1	no	—
183	#124×C₇₁	—	2	2	no	—
184	#124×C₇₁	—	2	2	no	—
185	#124×C₇₁	—	2	1	no	—
186	#124×C₇₁	C₂³	1	2	yes	—
187	#124×C₇₁	C₂³	1	2	yes	—
188	#124×C₇₁	C₂³	1	2	yes	—
189	#124×C₇₁	C₂³	1	1	yes	characteristic
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	#123×C₇₁	—	2	2	no	—
199	#123×C₇₁	—	2	2	no	—
200	#123×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	2	no	—
206	C₂²⋊Q₈×C₇₁	—	2	1	no	—
207	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
210	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
211	#121×C₇₁	—	2	1	no	—
212	#121×C₇₁	—	2	2	no	—
213	#121×C₇₁	—	2	2	no	—
214	#121×C₇₁	—	2	1	no	—
215	#121×C₇₁	—	2	1	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	2	no	—
221	#121×C₇₁	—	2	2	no	—
222	#121×C₇₁	—	2	1	no	—
223	#121×C₇₁	—	2	2	no	—
224	#121×C₇₁	—	2	2	no	—
225	#121×C₇₁	C₂³	1	1	yes	characteristic
226	#121×C₇₁	C₂³	1	2	yes	—
227	#120×C₇₁	—	2	2	no	—
228	#120×C₇₁	—	2	2	no	—
229	C₄×Q₈×C₇₁	—	2	1	no	—
230	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
237	C₄×D₄×C₇₁	—	2	1	no	—
238	C₄×D₄×C₇₁	—	2	1	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	2	no	—
245	C₄×D₄×C₇₁	—	2	2	no	—
246	C₄×D₄×C₇₁	—	2	1	no	—
247	C₄×D₄×C₇₁	—	2	1	no	—
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	2	yes	—
252	C₄×D₄×C₇₁	C₂³	1	2	yes	—
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	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
259	#117×C₇₁	—	2	1	no	—
260	#117×C₇₁	—	2	1	no	—
261	#117×C₇₁	C₂³	1	1	yes	characteristic
262	#117×C₇₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
266	C₂×C₄²×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	1	yes	characteristic
270	#107×C₇₁	C₂³	1	2	yes	—
271	#106×C₇₁	C₂³	1	2	yes	—
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	1	yes	characteristic
285	#103×C₇₁	C₂³	1	1	yes	characteristic
286	#103×C₇₁	C₂³	1	2	yes	—
287	#102×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
293	#102×C₇₁	C₂³	1	1	yes	characteristic
294	#102×C₇₁	C₂³	1	1	yes	characteristic
295	#102×C₇₁	C₂³	1	2	yes	—
296	#102×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
305	#97×C₇₁	C₂³	1	2	yes	—
306	#97×C₇₁	C₂³	1	2	yes	—
307	#97×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	2	no	—
313	#41×C₇₁	—	4	1	no	—
314	#41×C₇₁	—	4	1	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	#41×C₇₁	—	8	4	no	—
320	C₂×Q₈×C₇₁	—	2	1	no	—
321	C₂×Q₈×C₇₁	—	2	2	no	—
322	C₂×Q₈×C₇₁	—	8	2	no	—
323	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₇₁	—	2	1	no	—
329	C₂×D₄×C₇₁	—	2	1	no	—
330	C₂×D₄×C₇₁	—	2	2	no	—
331	C₂×D₄×C₇₁	—	2	2	no	—
332	C₂×D₄×C₇₁	—	2	1	no	—
333	C₂×D₄×C₇₁	—	2	2	no	—
334	C₂×D₄×C₇₁	—	2	1	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	—	2	2	no	—
342	C₂×D₄×C₇₁	—	2	2	no	—
343	C₂×D₄×C₇₁	—	2	1	no	—
344	C₂×D₄×C₇₁	—	2	1	no	—
345	C₂×D₄×C₇₁	—	2	2	no	—
346	C₂×D₄×C₇₁	—	4	2	no	—
347	C₂×D₄×C₇₁	—	4	2	no	—
348	C₂×D₄×C₇₁	—	8	2	no	—
349	C₂×D₄×C₇₁	—	8	2	no	—
350	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
351	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₇₁	—	2	1	no	—
356	C₂²×C₄×C₇₁	—	2	1	no	—
357	C₂²×C₄×C₇₁	—	2	1	no	—
358	C₂²×C₄×C₇₁	—	2	1	no	—
359	C₂²×C₄×C₇₁	—	2	2	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	—	2	2	no	—
365	C₂²×C₄×C₇₁	—	2	2	no	—
366	C₂²×C₄×C₇₁	—	2	2	no	—
367	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
370	Q₁₆×C₇₁	—	4	1	no	—
371	SD₁₆×C₇₁	—	4	1	no	—
372	SD₁₆×C₇₁	—	4	2	no	—
373	SD₁₆×C₇₁	—	4	1	no	—
374	SD₁₆×C₇₁	—	4	2	no	—
375	SD₁₆×C₇₁	—	4	2	no	—
376	D₈×C₇₁	—	4	1	no	—
377	D₈×C₇₁	—	4	2	no	—
378	D₈×C₇₁	—	4	2	no	—
379	D₈×C₇₁	—	4	2	no	—
380	D₈×C₇₁	—	4	2	no	—
381	D₈×C₇₁	—	4	2	no	—
382	D₈×C₇₁	—	4	2	no	—
383	D₈×C₇₁	—	4	2	no	—
384	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₇₁	—	2	1	no	—
391	C₄⋊C₄×C₇₁	—	2	2	no	—
392	C₄⋊C₄×C₇₁	—	2	2	no	—
393	C₄⋊C₄×C₇₁	—	2	1	no	—
394	C₄⋊C₄×C₇₁	—	2	1	no	—
395	C₄⋊C₄×C₇₁	—	2	1	no	—
396	C₄⋊C₄×C₇₁	—	2	1	no	—
397	C₄⋊C₄×C₇₁	—	2	1	no	—
398	C₄⋊C₄×C₇₁	—	2	2	no	—
399	C₄⋊C₄×C₇₁	—	2	2	no	—
400	C₄⋊C₄×C₇₁	—	2	1	no	—
401	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄×C₇₁	—	2	1	no	—
416	C₂²⋊C₄×C₇₁	—	2	1	no	—
417	C₂²⋊C₄×C₇₁	—	2	2	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	1	no	—
422	C₂²⋊C₄×C₇₁	—	2	1	no	—
423	C₂²⋊C₄×C₇₁	—	2	1	no	—
424	C₂²⋊C₄×C₇₁	—	2	1	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	2	no	—
433	C₂²⋊C₄×C₇₁	—	2	1	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	—	2	2	no	—
438	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
440	C₄²×C₇₁	—	2	1	no	—
441	C₄²×C₇₁	—	2	1	no	—
442	C₄²×C₇₁	—	2	1	no	—
443	C₄²×C₇₁	—	2	1	no	—
444	C₄²×C₇₁	—	2	2	no	—
445	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₇₁	C₂⁴	1	2	yes	—
449	C₄²×C₇₁	C₂⁴	1	2	yes	—
450	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
451	C₂³×C₇₁	—	2	2	no	—
452	C₂³×C₇₁	—	2	1	no	—
453	C₂³×C₇₁	—	2	2	no	—
454	C₂³×C₇₁	—	2	2	no	—
455	C₂³×C₇₁	—	2	1	no	—
456	C₂³×C₇₁	—	4	4	no	—
457	C₂³×C₇₁	—	8	2	no	—
458	C₂³×C₇₁	—	8	2	no	—
459	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₇₁	—	2	2	no	—
461	Q₈×C₇₁	—	2	2	no	—
462	Q₈×C₇₁	—	2	1	no	—
463	Q₈×C₇₁	—	2	1	no	—
464	Q₈×C₇₁	—	2	1	no	—
465	Q₈×C₇₁	—	2	1	no	—
466	Q₈×C₇₁	—	4	2	no	—
467	Q₈×C₇₁	—	4	2	no	—
468	Q₈×C₇₁	—	8	2	no	—
469	D₄×C₇₁	—	2	1	no	—
470	D₄×C₇₁	—	2	2	no	—
471	D₄×C₇₁	—	2	2	no	—
472	D₄×C₇₁	—	2	1	no	—
473	D₄×C₇₁	—	2	2	no	—
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	1	no	—
479	D₄×C₇₁	—	4	4	no	—
480	D₄×C₇₁	—	4	4	no	—
481	D₄×C₇₁	—	4	2	no	—
482	D₄×C₇₁	—	4	2	no	—
483	D₄×C₇₁	—	4	2	no	—
484	D₄×C₇₁	—	4	2	no	—
485	D₄×C₇₁	—	8	1	no	—
486	D₄×C₇₁	—	8	2	no	—
487	D₄×C₇₁	—	8	1	no	—
488	D₄×C₇₁	—	8	1	no	—
489	D₄×C₇₁	—	8	2	no	—
490	D₄×C₇₁	—	8	2	no	—
491	D₄×C₇₁	—	8	2	no	—
492	D₄×C₇₁	—	8	2	no	—
493	D₄×C₇₁	—	8	2	no	—
494	D₄×C₇₁	—	8	2	no	—
495	D₄×C₇₁	—	8	1	no	—
496	D₄×C₇₁	—	8	2	no	—
497	C₂×C₄×C₇₁	—	2	2	no	—
498	C₂×C₄×C₇₁	—	2	1	no	—
499	C₂×C₄×C₇₁	—	2	1	no	—
500	C₂×C₄×C₇₁	—	2	1	no	—
501	C₂×C₄×C₇₁	—	2	1	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	—	4	1	no	—
508	C₂×C₄×C₇₁	—	4	2	no	—
509	C₂×C₄×C₇₁	—	4	2	no	—
510	C₂×C₄×C₇₁	—	4	2	no	—
511	C₂×C₄×C₇₁	—	4	2	no	—
512	C₂×C₄×C₇₁	—	8	2	no	—
513	C₂×C₄×C₇₁	—	8	2	no	—
514	C₂×C₄×C₇₁	—	8	2	no	—
515	C₂×C₄×C₇₁	—	8	2	no	—
516	C₂×C₄×C₇₁	—	8	2	no	—
517	C₂×C₄×C₇₁	—	8	2	no	—
518	C₂×C₄×C₇₁	—	8	2	no	—
519	C₂×C₄×C₇₁	—	8	2	no	—
520	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
528	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
530	C₈×C₇₁	—	2	1	no	—
531	C₈×C₇₁	—	2	1	no	—
532	C₈×C₇₁	—	2	1	no	—
533	C₈×C₇₁	—	2	2	no	—
534	C₈×C₇₁	—	2	1	no	—
535	C₈×C₇₁	—	2	2	no	—
536	C₂²×C₇₁	—	2	1	no	—
537	C₂²×C₇₁	—	2	1	no	—
538	C₂²×C₇₁	—	2	1	no	—
539	C₂²×C₇₁	—	4	1	no	—
540	C₂²×C₇₁	—	4	2	no	—
541	C₂²×C₇₁	—	4	2	no	—
542	C₂²×C₇₁	—	4	2	no	—
543	C₂²×C₇₁	—	4	1	no	—
544	C₂²×C₇₁	—	4	1	no	—
545	C₂²×C₇₁	—	4	2	no	—
546	C₂²×C₇₁	—	4	2	no	—
547	C₂²×C₇₁	—	4	2	no	—
548	C₂²×C₇₁	—	4	1	no	—
549	C₂²×C₇₁	—	4	1	no	—
550	C₂²×C₇₁	—	4	1	no	—
551	C₂²×C₇₁	—	4	2	no	—
552	C₂²×C₇₁	—	4	2	no	—
553	C₂²×C₇₁	—	4	2	no	—
554	C₂²×C₇₁	—	16	4	no	—
555	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
556	C₄×C₇₁	—	2	1	no	—
557	C₄×C₇₁	—	2	1	no	—
558	C₄×C₇₁	—	2	2	no	—
559	C₄×C₇₁	—	2	2	no	—
560	C₄×C₇₁	—	2	1	no	—
561	C₄×C₇₁	—	2	1	no	—
562	C₄×C₇₁	—	2	2	no	—
563	C₄×C₇₁	—	2	2	no	—
564	C₄×C₇₁	—	4	1	no	—
565	C₄×C₇₁	—	4	1	no	—
566	C₄×C₇₁	—	4	1	no	—
567	C₄×C₇₁	—	4	1	no	—
568	C₄×C₇₁	—	4	1	no	—
569	C₄×C₇₁	—	4	1	no	—
570	C₄×C₇₁	—	4	2	no	—
571	C₄×C₇₁	#576	1	2	yes	—
572	C₄×C₇₁	#585	1	1	yes	characteristic
573	C₄×C₇₁	#585	1	1	yes	characteristic
574	#61920	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
575	C₂×C₇₁	—	4	1	no	—
576	C₂×C₇₁	—	8	1	no	—
577	C₂×C₇₁	—	8	2	no	—
578	C₂×C₇₁	—	8	1	no	—
579	C₂×C₇₁	—	8	2	no	—
580	C₂×C₇₁	—	8	2	no	—
581	C₂×C₇₁	#3487	1	1	yes	characteristic
582	C₂×C₇₁	C₂×#576	1	1	yes	characteristic
583	C₂×C₇₁	#3585	1	1	yes	characteristic
584	#3554	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3508	C₂×C₇₁	1	1	yes	characteristic, complemented
586	#3403	C₂×C₇₁	1	2	yes	complemented
587	#3399	C₂×C₇₁	1	2	yes	complemented
588	#3399	C₂×C₇₁	1	1	yes	characteristic, complemented
589	#3399	C₂×C₇₁	1	1	yes	characteristic, complemented
590	#3396	C₂×C₇₁	1	1	yes	characteristic, complemented
591	#3391	C₂×C₇₁	1	1	yes	characteristic, complemented
592	#3373	C₂×C₇₁	1	1	yes	characteristic, complemented
593	#3370	C₂×C₇₁	1	2	yes	complemented
594	#3368	C₂×C₇₁	1	1	yes	characteristic, complemented
595	#3366	C₂×C₇₁	1	2	yes	complemented
596	#3365	C₂×C₇₁	1	1	yes	characteristic, complemented
597	#3358	C₂×C₇₁	1	1	yes	characteristic, complemented
598	#3224	C₂×C₇₁	1	2	yes	complemented
599	#3220	C₂×C₇₁	1	2	yes	complemented
600	#3217	C₂×C₇₁	1	1	yes	characteristic, complemented
601	#3205	C₂×C₇₁	1	1	yes	characteristic, complemented
602	#3122	C₂×C₇₁	1	2	yes	complemented
603	#3118	C₂×C₇₁	1	2	yes	complemented
604	#3115	C₂×C₇₁	1	1	yes	characteristic, complemented
605	#3102	C₂×C₇₁	1	1	yes	characteristic, complemented
606	#2985	C₂×C₇₁	1	1	yes	characteristic, complemented
607	C₇₁	#61920	1	1	yes	characteristic, direct product factor, Sylow
608	#562	—	2	2	no	—
609	#559	C₂²×C₇₁	1	1	yes	characteristic
610	#559	C₂²×C₇₁	1	2	yes	—
611	#559	C₂²×C₇₁	1	1	yes	characteristic
612	#559	C₂²×C₇₁	1	1	yes	characteristic, complemented
613	#559	C₂²×C₇₁	1	2	yes	complemented
614	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
615	#554	C₂²×C₇₁	1	2	yes	complemented
616	#550	C₂²×C₇₁	1	1	yes	characteristic
617	#550	C₂²×C₇₁	1	2	yes	—
618	#550	C₂²×C₇₁	1	1	yes	characteristic
619	#550	C₂²×C₇₁	1	1	yes	characteristic, complemented
620	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
621	#548	—	2	1	no	—
622	#547	—	2	1	no	—
623	#546	—	2	1	no	—
624	#546	—	2	1	no	—
625	#546	—	2	2	no	—
626	#542	—	2	1	no	—
627	#542	C₂²×C₇₁	1	2	yes	—
628	#540	—	2	2	no	—
629	#540	C₂²×C₇₁	1	2	yes	—
630	#539	—	2	2	no	—
631	#536	—	2	1	no	—
632	#535	C₂²×C₇₁	1	2	yes	—
633	#533	C₂²×C₇₁	1	1	yes	characteristic
634	#532	—	2	1	no	—
635	#532	—	2	1	no	—
636	#532	C₂²×C₇₁	1	1	yes	characteristic
637	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
638	#529	C₂²×C₇₁	1	1	yes	characteristic
639	#518	C₂²×C₇₁	1	2	yes	—
640	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
641	#496	C₂²×C₇₁	1	2	yes	—
642	#496	C₂²×C₇₁	1	2	yes	complemented
643	#496	C₂²×C₇₁	1	2	yes	complemented
644	#495	C₂²×C₇₁	1	2	yes	complemented
645	#493	C₂²×C₇₁	1	1	yes	characteristic
646	#493	C₂²×C₇₁	1	1	yes	characteristic
647	#493	C₂²×C₇₁	1	2	yes	complemented
648	#490	C₂²×C₇₁	1	2	yes	—
649	#490	C₂²×C₇₁	1	2	yes	complemented
650	#489	C₂²×C₇₁	1	2	yes	complemented
651	#488	C₂²×C₇₁	1	2	yes	complemented
652	#486	C₂²×C₇₁	1	1	yes	characteristic
653	#486	C₂²×C₇₁	1	1	yes	characteristic
654	#486	C₂²×C₇₁	1	2	yes	complemented
655	#485	C₂²×C₇₁	1	1	yes	characteristic
656	#482	C₂²×C₇₁	1	1	yes	characteristic
657	#482	C₂²×C₇₁	1	2	yes	—
658	#479	C₂²×C₇₁	1	1	yes	characteristic, complemented
659	#478	C₂²×C₇₁	1	1	yes	characteristic, complemented
660	#478	C₂²×C₇₁	1	2	yes	complemented
661	#478	C₂²×C₇₁	1	2	yes	complemented
662	#476	C₂²×C₇₁	1	2	yes	complemented
663	#475	C₂²×C₇₁	1	1	yes	characteristic, complemented
664	#474	C₂²×C₇₁	1	1	yes	characteristic, complemented
665	#474	C₂²×C₇₁	1	2	yes	complemented
666	#464	C₂²×C₇₁	1	1	yes	characteristic, complemented
667	#464	C₂²×C₇₁	1	2	yes	complemented
668	#463	C₂²×C₇₁	1	1	yes	characteristic, complemented
669	#463	C₂²×C₇₁	1	2	yes	complemented
670	#463	C₂²×C₇₁	1	2	yes	complemented
671	#463	C₂²×C₇₁	1	2	yes	complemented
672	#463	C₂²×C₇₁	1	2	yes	complemented
673	#463	C₂²×C₇₁	1	2	yes	complemented
674	#460	C₂²×C₇₁	1	1	yes	characteristic
675	#460	C₂²×C₇₁	1	1	yes	characteristic
676	#460	C₂²×C₇₁	1	2	yes	complemented
677	#460	C₂²×C₇₁	1	1	yes	characteristic, complemented
678	#459	C₂²×C₇₁	1	1	yes	characteristic
679	#459	C₂²×C₇₁	1	2	yes	—
680	#459	C₂²×C₇₁	1	2	yes	—
681	#459	C₂²×C₇₁	1	1	yes	characteristic
682	#459	C₂²×C₇₁	1	2	yes	complemented
683	#459	C₂²×C₇₁	1	2	yes	complemented
684	#459	C₂²×C₇₁	1	2	yes	complemented
685	#459	C₂²×C₇₁	1	1	yes	characteristic, complemented
686	#459	C₂²×C₇₁	1	2	yes	complemented
687	#459	C₂²×C₇₁	1	2	yes	complemented
688	#452	C₂²×C₇₁	1	1	yes	characteristic
689	#450	C₂²×C₇₁	1	2	yes	—
690	#449	C₂²×C₇₁	1	1	yes	characteristic
691	#449	C₂²×C₇₁	1	2	yes	—
692	#447	C₂²×C₇₁	1	2	yes	—
693	#447	C₂²×C₇₁	1	2	yes	—
694	#447	C₂²×C₇₁	1	2	yes	—
695	#446	C₂²×C₇₁	1	2	yes	complemented
696	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
697	#446	C₂²×C₇₁	1	2	yes	complemented
698	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
699	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
700	C₈×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
701	#442	C₂²×C₇₁	1	2	yes	complemented
702	#442	C₂²×C₇₁	1	2	yes	complemented
703	#442	C₂²×C₇₁	1	2	yes	complemented
704	#442	C₂²×C₇₁	1	2	yes	complemented
705	#440	C₂²×C₇₁	1	2	yes	complemented
706	#440	C₂²×C₇₁	1	2	yes	complemented
707	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
709	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
711	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
712	C₄×D₈	C₂²×C₇₁	1	2	yes	complemented
713	C₄×D₈	C₂²×C₇₁	1	2	yes	complemented
714	C₄×D₈	C₂²×C₇₁	1	2	yes	complemented
715	#433	C₂²×C₇₁	1	2	yes	—
716	#433	C₂²×C₇₁	1	2	yes	—
717	#432	C₂²×C₇₁	1	1	yes	characteristic
718	#431	C₂²×C₇₁	1	1	yes	characteristic
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	2	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
725	C₂²×Q₈	—	2	1	no	—
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
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×D₈	C₂³×C₇₁	1	2	yes	—
736	C₂×D₈	C₂³×C₇₁	1	2	yes	—
737	C₂×D₈	C₂³×C₇₁	1	2	yes	—
738	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
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×D₈	C₂³×C₇₁	1	2	yes	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
745	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
748	#127	—	2	1	no	—
749	#127	—	2	1	no	—
750	#127	C₂³×C₇₁	1	2	yes	—
751	#127	C₂³×C₇₁	1	1	yes	characteristic
752	#127	C₂³×C₇₁	1	1	yes	characteristic
753	#127	C₂³×C₇₁	1	1	yes	characteristic
754	#127	C₂³×C₇₁	1	2	yes	—
755	#127	C₂³×C₇₁	1	2	yes	—
756	#127	C₂³×C₇₁	1	2	yes	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#125	—	2	2	no	—
760	#125	D₄×C₇₁	1	2	yes	—
761	#125	C₂³×C₇₁	1	1	yes	characteristic
762	#125	C₂³×C₇₁	1	2	yes	—
763	#124	—	2	1	no	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	—	2	1	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	1	no	—
770	#124	C₂³×C₇₁	1	1	yes	characteristic
771	#124	C₂³×C₇₁	1	2	yes	—
772	#124	C₂³×C₇₁	1	2	yes	—
773	#124	C₂³×C₇₁	1	2	yes	—
774	#123	—	2	1	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	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
792	C₂²⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
793	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	C₂³×C₇₁	1	1	yes	characteristic
810	#121	C₂³×C₇₁	1	2	yes	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
818	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
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	C₄×D₄	C₂³×C₇₁	1	2	yes	—
838	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₇₁	1	2	yes	—
840	C₄×D₄	C₂³×C₇₁	1	2	yes	—
841	C₄×D₄	C₂³×C₇₁	1	2	yes	—
842	C₄×D₄	C₂³×C₇₁	1	2	yes	—
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	C₂³×C₇₁	1	1	yes	characteristic
846	#117	C₂³×C₇₁	1	2	yes	—
847	C₂×C₄⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	—	2	1	no	—
851	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
852	#107	C₂³×C₇₁	1	1	yes	characteristic
853	#107	C₂³×C₇₁	1	1	yes	characteristic
854	#107	C₂³×C₇₁	1	2	yes	—
855	#106	C₂³×C₇₁	1	2	yes	—
856	#106	C₂³×C₇₁	1	1	yes	characteristic
857	#106	C₂³×C₇₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
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	#103	C₂³×C₇₁	1	1	yes	characteristic
867	#103	C₂³×C₇₁	1	1	yes	characteristic
868	#103	C₂³×C₇₁	1	1	yes	characteristic
869	#103	C₂³×C₇₁	1	1	yes	characteristic
870	#103	C₂³×C₇₁	1	2	yes	—
871	#102	C₂³×C₇₁	1	1	yes	characteristic
872	#102	C₂³×C₇₁	1	2	yes	—
873	#102	C₂³×C₇₁	1	2	yes	—
874	#102	C₂³×C₇₁	1	2	yes	—
875	#102	C₂³×C₇₁	1	2	yes	—
876	#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	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	2	yes	—
886	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
889	#97	C₂³×C₇₁	1	2	yes	—
890	#97	C₂³×C₇₁	1	2	yes	—
891	#97	C₂³×C₇₁	1	2	yes	—
892	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₇₁	1	2	yes	—
895	C₄×C₈	C₂³×C₇₁	1	2	yes	—
896	C₂⁴	—	2	2	no	—
897	#41	—	4	1	no	—
898	#41	—	4	1	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	#41	—	8	4	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	8	2	no	—
907	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
908	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
909	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	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	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	2	no	—
932	C₂×D₄	—	8	2	no	—
933	C₂×D₄	—	8	2	no	—
934	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
954	Q₁₆	—	4	1	no	—
955	SD₁₆	—	4	1	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	1	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	2	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	2	no	—
966	D₈	—	4	2	no	—
967	D₈	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
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	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	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	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	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₇₁	1	2	yes	—
1033	C₄²	C₂⁴×C₇₁	1	2	yes	—
1034	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	4	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	8	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	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	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	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	C₂²×D₄×C₇₁	1	1	yes	characteristic
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	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
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	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	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	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	16	4	no	—
1139	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	#576×C₇₁	1	2	yes	—
1156	C₄	#585×C₇₁	1	1	yes	characteristic
1157	C₄	#585×C₇₁	1	1	yes	characteristic
1158	C₂	—	4	1	no	—
1159	C₂	—	8	2	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	1	no	—
1162	C₂	—	8	1	no	—
1163	C₂	—	8	2	no	—
1164	C₂	C₇₁×#3487	1	1	yes	characteristic
1165	C₂	C₂×#576×C₇₁	1	1	yes	characteristic
1166	C₂	C₇₁×#3585	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×#3508	C₂	semidirect
3. C₇₁×#3403	C₂	semidirect
4. C₇₁×#3399	C₂	semidirect
5. C₇₁×#3399	C₂	semidirect
6. C₇₁×#3399	C₂	semidirect
7. C₇₁×#3396	C₂	semidirect
8. C₇₁×#3391	C₂	semidirect
9. C₇₁×#3373	C₂	semidirect
10. C₇₁×#3370	C₂	semidirect
11. C₇₁×#3368	C₂	semidirect
12. C₇₁×#3366	C₂	semidirect
13. C₇₁×#3365	C₂	semidirect
14. C₇₁×#3358	C₂	semidirect
15. C₇₁×#3224	C₂	semidirect
16. C₇₁×#3220	C₂	semidirect
17. C₇₁×#3217	C₂	semidirect
18. C₇₁×#3205	C₂	semidirect
19. C₇₁×#3122	C₂	semidirect
20. C₇₁×#3118	C₂	semidirect
21. C₇₁×#3115	C₂	semidirect
22. C₇₁×#3102	C₂	semidirect
23. C₇₁×#2985	C₂	semidirect
28. #559×C₇₁	C₂²	semidirect
29. #559×C₇₁	C₂²	semidirect
30. #557×C₇₁	C₂²	semidirect
31. #554×C₇₁	C₂²	semidirect
35. #550×C₇₁	C₂²	semidirect
36. D₄×Q₈×C₇₁	C₂²	semidirect
58. #496×C₇₁	C₂²	semidirect
59. #496×C₇₁	C₂²	semidirect
60. #495×C₇₁	C₂²	semidirect
63. #493×C₇₁	C₂²	semidirect
65. #490×C₇₁	C₂²	semidirect
66. #489×C₇₁	C₂²	semidirect
67. #488×C₇₁	C₂²	semidirect
70. #486×C₇₁	C₂²	semidirect
74. #479×C₇₁	C₂²	semidirect
75. #478×C₇₁	C₂²	semidirect
76. #478×C₇₁	C₂²	semidirect
77. #478×C₇₁	C₂²	semidirect
78. #476×C₇₁	C₂²	semidirect
79. #475×C₇₁	C₂²	semidirect
80. #474×C₇₁	C₂²	semidirect
81. #474×C₇₁	C₂²	semidirect
82. #464×C₇₁	C₂²	semidirect
83. #464×C₇₁	C₂²	semidirect
84. #463×C₇₁	C₂²	semidirect
85. #463×C₇₁	C₂²	semidirect
86. #463×C₇₁	C₂²	semidirect
87. #463×C₇₁	C₂²	semidirect
88. #463×C₇₁	C₂²	semidirect
89. #463×C₇₁	C₂²	semidirect
92. #460×C₇₁	C₂²	semidirect
93. #460×C₇₁	C₂²	semidirect
98. #459×C₇₁	C₂²	semidirect
99. #459×C₇₁	C₂²	semidirect
100. #459×C₇₁	C₂²	semidirect
101. #459×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. #446×C₇₁	C₂²	semidirect
115. C₈×Q₈×C₇₁	C₂²	semidirect
116. C₈×Q₈×C₇₁	C₂²	semidirect
117. #442×C₇₁	C₂²	semidirect
118. #442×C₇₁	C₂²	semidirect
119. #442×C₇₁	C₂²	semidirect
120. #442×C₇₁	C₂²	semidirect
121. #440×C₇₁	C₂²	semidirect
122. #440×C₇₁	C₂²	semidirect
123. C₄×Q₁₆×C₇₁	C₂²	semidirect
124. C₄×SD₁₆×C₇₁	C₂²	semidirect
125. C₄×SD₁₆×C₇₁	C₂²	semidirect
126. C₄×SD₁₆×C₇₁	C₂²	semidirect
127. C₄×D₈×C₇₁	C₂²	semidirect
128. C₄×D₈×C₇₁	C₂²	semidirect
129. C₄×D₈×C₇₁	C₂²	semidirect
130. C₄×D₈×C₇₁	C₂²	semidirect
574. #61920	C₇₁	direct (N × H)
584. #3554	C₂×C₇₁	semidirect
585. #3508	C₂×C₇₁	semidirect
586. #3403	C₂×C₇₁	semidirect
587. #3399	C₂×C₇₁	semidirect
588. #3399	C₂×C₇₁	semidirect
589. #3399	C₂×C₇₁	semidirect
590. #3396	C₂×C₇₁	semidirect
591. #3391	C₂×C₇₁	semidirect
592. #3373	C₂×C₇₁	semidirect
593. #3370	C₂×C₇₁	semidirect
594. #3368	C₂×C₇₁	semidirect
595. #3366	C₂×C₇₁	semidirect
596. #3365	C₂×C₇₁	semidirect
597. #3358	C₂×C₇₁	semidirect
598. #3224	C₂×C₇₁	semidirect
599. #3220	C₂×C₇₁	semidirect
600. #3217	C₂×C₇₁	semidirect
601. #3205	C₂×C₇₁	semidirect
602. #3122	C₂×C₇₁	semidirect
603. #3118	C₂×C₇₁	semidirect
604. #3115	C₂×C₇₁	semidirect
605. #3102	C₂×C₇₁	semidirect
606. #2985	C₂×C₇₁	semidirect
607. C₇₁	#61920	direct (N × H)
612. #559	C₂²×C₇₁	semidirect
613. #559	C₂²×C₇₁	semidirect
614. #557	C₂²×C₇₁	semidirect
615. #554	C₂²×C₇₁	semidirect
619. #550	C₂²×C₇₁	semidirect
620. D₄×Q₈	C₂²×C₇₁	semidirect
642. #496	C₂²×C₇₁	semidirect
643. #496	C₂²×C₇₁	semidirect
644. #495	C₂²×C₇₁	semidirect
647. #493	C₂²×C₇₁	semidirect
649. #490	C₂²×C₇₁	semidirect
650. #489	C₂²×C₇₁	semidirect
651. #488	C₂²×C₇₁	semidirect
654. #486	C₂²×C₇₁	semidirect
658. #479	C₂²×C₇₁	semidirect
659. #478	C₂²×C₇₁	semidirect
660. #478	C₂²×C₇₁	semidirect
661. #478	C₂²×C₇₁	semidirect
662. #476	C₂²×C₇₁	semidirect
663. #475	C₂²×C₇₁	semidirect
664. #474	C₂²×C₇₁	semidirect
665. #474	C₂²×C₇₁	semidirect
666. #464	C₂²×C₇₁	semidirect
667. #464	C₂²×C₇₁	semidirect
668. #463	C₂²×C₇₁	semidirect
669. #463	C₂²×C₇₁	semidirect
670. #463	C₂²×C₇₁	semidirect
671. #463	C₂²×C₇₁	semidirect
672. #463	C₂²×C₇₁	semidirect
673. #463	C₂²×C₇₁	semidirect
676. #460	C₂²×C₇₁	semidirect
677. #460	C₂²×C₇₁	semidirect
682. #459	C₂²×C₇₁	semidirect
683. #459	C₂²×C₇₁	semidirect
684. #459	C₂²×C₇₁	semidirect
685. #459	C₂²×C₇₁	semidirect
686. #459	C₂²×C₇₁	semidirect
687. #459	C₂²×C₇₁	semidirect
695. #446	C₂²×C₇₁	semidirect
696. #446	C₂²×C₇₁	semidirect
697. #446	C₂²×C₇₁	semidirect
698. #446	C₂²×C₇₁	semidirect
699. C₈×Q₈	C₂²×C₇₁	semidirect
700. C₈×Q₈	C₂²×C₇₁	semidirect
701. #442	C₂²×C₇₁	semidirect
702. #442	C₂²×C₇₁	semidirect
703. #442	C₂²×C₇₁	semidirect
704. #442	C₂²×C₇₁	semidirect
705. #440	C₂²×C₇₁	semidirect
706. #440	C₂²×C₇₁	semidirect
707. C₄×Q₁₆	C₂²×C₇₁	semidirect
708. C₄×SD₁₆	C₂²×C₇₁	semidirect
709. C₄×SD₁₆	C₂²×C₇₁	semidirect
710. C₄×SD₁₆	C₂²×C₇₁	semidirect
711. C₄×D₈	C₂²×C₇₁	semidirect
712. C₄×D₈	C₂²×C₇₁	semidirect
713. C₄×D₈	C₂²×C₇₁	semidirect
714. 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×#3508	2
C₇₁×#3403	2
C₇₁×#3399	2
C₇₁×#3396	2
C₇₁×#3391	2
C₇₁×#3373	2
C₇₁×#3370	2
C₇₁×#3368	2
C₇₁×#3366	2
C₇₁×#3365	2
C₇₁×#3358	2
C₇₁×#3224	2
C₇₁×#3220	2
C₇₁×#3217	2
C₇₁×#3205	2
C₇₁×#3122	2
C₇₁×#3118	2
C₇₁×#3115	2
C₇₁×#3102	2
C₇₁×#2985	2
#61920	71

Subgroups — C71×#61920 #31882792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61920 #31882792