Subgroups — C₇₁×#60874 #31881746

Order 18176.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×#544×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3243	C₂	1	4	yes	maximal, complemented
4	C₇₁×#3242	C₂	1	4	yes	maximal, complemented
5	C₇₁×#3239	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3236	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3232	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3230	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3164	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3137	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3092	C₂	1	1	yes	maximal, characteristic
13	C₇₁×#3091	C₂	1	1	yes	maximal, characteristic
14	C₂×#484×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3083	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3082	C₂	1	2	yes	maximal, complemented
17	C₇₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	#556×C₇₁	—	2	1	no	—
19	#554×C₇₁	—	2	1	no	—
20	#552×C₇₁	—	2	2	no	—
21	#552×C₇₁	—	2	1	no	—
22	#552×C₇₁	—	2	1	no	—
23	#551×C₇₁	—	2	2	no	—
24	#544×C₇₁	—	2	2	no	—
25	#544×C₇₁	—	2	1	no	—
26	#544×C₇₁	—	2	1	no	—
27	#544×C₇₁	C₂²	1	2	yes	—
28	#544×C₇₁	C₂²	1	2	yes	—
29	#544×C₇₁	C₂²	1	1	yes	characteristic
30	#544×C₇₁	C₂²	1	4	yes	—
31	#542×C₇₁	C₂²	1	2	yes	—
32	#541×C₇₁	C₂²	1	2	yes	—
33	#536×C₇₁	C₂²	1	1	yes	characteristic
34	#533×C₇₁	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₇₁	—	2	1	no	—
36	C₂×C₄⋊Q₈×C₇₁	C₂²	1	2	yes	—
37	#529×C₇₁	C₂²	1	2	yes	—
38	C₂×#125×C₇₁	—	2	1	no	—
39	C₂×#125×C₇₁	C₂²	1	2	yes	—
40	#525×C₇₁	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₇₁	—	2	2	no	—
42	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
43	#520×C₇₁	C₂²	1	1	yes	characteristic
44	#519×C₇₁	C₂²	1	1	yes	characteristic
45	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
46	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
48	#501×C₇₁	C₂²	1	4	yes	complemented
49	#501×C₇₁	C₂²	1	4	yes	complemented
50	#500×C₇₁	C₂²	1	4	yes	complemented
51	#499×C₇₁	C₂²	1	4	yes	complemented
52	#491×C₇₁	C₂²	1	4	yes	complemented
53	#489×C₇₁	C₂²	1	4	yes	complemented
54	#488×C₇₁	C₂²	1	4	yes	complemented
55	#487×C₇₁	C₂²	1	4	yes	complemented
56	#485×C₇₁	C₂²	1	2	yes	—
57	#485×C₇₁	C₂²	1	4	yes	—
58	#484×C₇₁	C₂²	1	2	yes	—
59	#484×C₇₁	C₂²	1	2	yes	—
60	#484×C₇₁	C₂²	1	4	yes	—
61	#484×C₇₁	C₂²	1	1	yes	characteristic
62	#484×C₇₁	C₂²	1	2	yes	—
63	#484×C₇₁	C₂²	1	2	yes	—
64	#483×C₇₁	C₂²	1	1	yes	characteristic
65	#483×C₇₁	C₂²	1	2	yes	—
66	#483×C₇₁	C₂²	1	2	yes	—
67	#482×C₇₁	C₂²	1	2	yes	—
68	#481×C₇₁	C₂²	1	1	yes	characteristic
69	#481×C₇₁	C₂²	1	2	yes	—
70	#480×C₇₁	C₂²	1	1	yes	characteristic
71	#480×C₇₁	C₂²	1	2	yes	—
72	#479×C₇₁	C₂²	1	4	yes	complemented
73	#479×C₇₁	C₂²	1	4	yes	complemented
74	#479×C₇₁	C₂²	1	4	yes	complemented
75	#478×C₇₁	C₂²	1	4	yes	complemented
76	#477×C₇₁	C₂²	1	4	yes	complemented
77	#477×C₇₁	C₂²	1	4	yes	complemented
78	#475×C₇₁	C₂²	1	4	yes	complemented
79	#474×C₇₁	C₂²	1	4	yes	complemented
80	#433×C₇₁	C₂²	1	4	yes	—
81	#432×C₇₁	C₂²	1	2	yes	—
82	#431×C₇₁	C₂²	1	2	yes	—
83	#428×C₇₁	C₂²	1	2	yes	—
84	#428×C₇₁	C₂²	1	2	yes	—
85	#427×C₇₁	C₂²	1	2	yes	—
86	C₂×#107×C₇₁	C₂²	1	2	yes	—
87	#424×C₇₁	C₂²	1	2	yes	—
88	#419×C₇₁	C₂²	1	2	yes	—
89	#417×C₇₁	C₂²	1	2	yes	—
90	#416×C₇₁	C₂²	1	2	yes	—
91	C₂×#103×C₇₁	C₂²	1	2	yes	—
92	#407×C₇₁	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
94	#405×C₇₁	C₂²	1	2	yes	—
95	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₇₁	—	2	2	no	—
97	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇₁	—	2	1	no	—
99	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₇₁	—	2	2	no	—
103	C₄⋊Q₈×C₇₁	—	2	4	no	—
104	C₄⋊Q₈×C₇₁	—	2	2	no	—
105	C₄⋊Q₈×C₇₁	—	2	1	no	—
106	C₄⋊Q₈×C₇₁	—	2	2	no	—
107	C₄⋊Q₈×C₇₁	—	2	2	no	—
108	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
111	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
112	#126×C₇₁	—	2	2	no	—
113	#126×C₇₁	—	2	2	no	—
114	#126×C₇₁	—	2	2	no	—
115	#126×C₇₁	—	2	2	no	—
116	#125×C₇₁	—	2	2	no	—
117	#125×C₇₁	—	2	2	no	—
118	#125×C₇₁	—	2	4	no	—
119	#125×C₇₁	—	2	2	no	—
120	#125×C₇₁	—	2	2	no	—
121	#125×C₇₁	—	2	1	no	—
122	#125×C₇₁	—	2	2	no	—
123	#125×C₇₁	—	2	2	no	—
124	#125×C₇₁	—	2	2	no	—
125	#125×C₇₁	C₂³	1	4	yes	—
126	#125×C₇₁	C₂³	1	4	yes	—
127	#125×C₇₁	C₂³	1	2	yes	—
128	#124×C₇₁	—	2	2	no	—
129	#124×C₇₁	C₂³	1	2	yes	—
130	#123×C₇₁	—	2	1	no	—
131	#123×C₇₁	—	2	2	no	—
132	#123×C₇₁	—	2	2	no	—
133	#123×C₇₁	—	2	2	no	—
134	C₂²⋊Q₈×C₇₁	—	2	1	no	—
135	C₂²⋊Q₈×C₇₁	—	2	1	no	—
136	C₂²⋊Q₈×C₇₁	—	2	2	no	—
137	C₂²⋊Q₈×C₇₁	—	2	1	no	—
138	C₂²⋊Q₈×C₇₁	—	2	1	no	—
139	C₂²⋊Q₈×C₇₁	—	2	2	no	—
140	C₂²⋊Q₈×C₇₁	—	2	4	no	—
141	C₂²⋊Q₈×C₇₁	—	2	4	no	—
142	C₂²⋊Q₈×C₇₁	—	2	4	no	—
143	C₂²⋊Q₈×C₇₁	—	2	4	no	—
144	C₂²⋊Q₈×C₇₁	—	2	2	no	—
145	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
146	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
148	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
149	#121×C₇₁	C₂³	1	1	yes	characteristic
150	#121×C₇₁	C₂³	1	1	yes	characteristic
151	#120×C₇₁	—	2	1	no	—
152	C₄×Q₈×C₇₁	—	2	1	no	—
153	C₄×Q₈×C₇₁	—	2	1	no	—
154	C₄×Q₈×C₇₁	—	2	2	no	—
155	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
158	C₄×D₄×C₇₁	—	2	1	no	—
159	C₄×D₄×C₇₁	—	2	1	no	—
160	C₄×D₄×C₇₁	—	2	2	no	—
161	C₄×D₄×C₇₁	—	2	2	no	—
162	C₄×D₄×C₇₁	C₂³	1	2	yes	—
163	#117×C₇₁	—	2	1	no	—
164	#117×C₇₁	—	2	1	no	—
165	#117×C₇₁	—	2	2	no	—
166	#117×C₇₁	—	2	1	no	—
167	#117×C₇₁	—	2	2	no	—
168	#117×C₇₁	—	2	2	no	—
169	#117×C₇₁	D₄	1	1	yes	characteristic
170	#117×C₇₁	D₄	1	2	yes	—
171	#117×C₇₁	D₄	1	1	yes	characteristic
172	#117×C₇₁	C₂³	1	2	yes	—
173	#117×C₇₁	C₂³	1	1	yes	characteristic
174	#117×C₇₁	C₂³	1	2	yes	—
175	#117×C₇₁	C₂³	1	1	yes	characteristic
176	#117×C₇₁	C₂³	1	1	yes	characteristic
177	#117×C₇₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
181	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
182	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
183	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
184	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
185	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
186	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₇₁	D₄	1	2	yes	—
197	C₂×C₄²×C₇₁	—	2	1	no	—
198	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
199	#107×C₇₁	C₂³	1	4	yes	—
200	#107×C₇₁	C₂³	1	4	yes	—
201	#107×C₇₁	C₂³	1	2	yes	—
202	#107×C₇₁	C₂³	1	2	yes	—
203	#107×C₇₁	C₂³	1	4	yes	—
204	#107×C₇₁	C₂³	1	4	yes	—
205	#106×C₇₁	C₂³	1	2	yes	—
206	#106×C₇₁	C₂³	1	2	yes	—
207	#106×C₇₁	C₂³	1	4	yes	—
208	#106×C₇₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
210	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
211	#103×C₇₁	C₂³	1	4	yes	—
212	#103×C₇₁	C₂³	1	4	yes	—
213	#103×C₇₁	C₂³	1	2	yes	—
214	#103×C₇₁	C₂³	1	2	yes	—
215	#103×C₇₁	C₂³	1	4	yes	—
216	#103×C₇₁	C₂³	1	4	yes	—
217	#103×C₇₁	C₂³	1	4	yes	—
218	#102×C₇₁	C₂³	1	2	yes	—
219	#102×C₇₁	C₂³	1	2	yes	—
220	#102×C₇₁	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
226	#97×C₇₁	C₂³	1	4	yes	—
227	C₄×C₈×C₇₁	C₂³	1	4	yes	—
228	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
229	#41×C₇₁	—	2	4	no	—
230	C₂×Q₈×C₇₁	—	2	1	no	—
231	C₂×Q₈×C₇₁	—	2	2	no	—
232	C₂×Q₈×C₇₁	—	2	4	no	—
233	C₂×Q₈×C₇₁	—	2	4	no	—
234	C₂×Q₈×C₇₁	—	2	4	no	—
235	C₂×Q₈×C₇₁	—	8	4	no	—
236	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
238	C₂×D₄×C₇₁	—	2	1	no	—
239	C₂×D₄×C₇₁	—	2	1	no	—
240	C₂×D₄×C₇₁	—	2	1	no	—
241	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₇₁	—	2	4	no	—
243	C₂²×C₄×C₇₁	—	2	1	no	—
244	C₂²×C₄×C₇₁	—	2	1	no	—
245	C₂²×C₄×C₇₁	—	2	1	no	—
246	C₂²×C₄×C₇₁	—	2	2	no	—
247	C₂²×C₄×C₇₁	—	2	1	no	—
248	C₂²×C₄×C₇₁	—	2	2	no	—
249	C₂²×C₄×C₇₁	—	2	2	no	—
250	C₂²×C₄×C₇₁	—	2	1	no	—
251	C₂²×C₄×C₇₁	—	2	2	no	—
252	C₂²×C₄×C₇₁	—	8	2	no	—
253	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
261	M₁₆×C₇₁	—	2	4	no	—
262	C₂×C₈×C₇₁	—	2	4	no	—
263	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
264	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
265	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₇₁	—	2	2	no	—
267	C₄⋊C₄×C₇₁	—	2	2	no	—
268	C₄⋊C₄×C₇₁	—	2	2	no	—
269	C₄⋊C₄×C₇₁	—	2	1	no	—
270	C₄⋊C₄×C₇₁	—	2	2	no	—
271	C₄⋊C₄×C₇₁	—	2	2	no	—
272	C₄⋊C₄×C₇₁	—	2	2	no	—
273	C₄⋊C₄×C₇₁	—	2	4	no	—
274	C₄⋊C₄×C₇₁	—	2	4	no	—
275	C₄⋊C₄×C₇₁	—	2	4	no	—
276	C₄⋊C₄×C₇₁	—	2	4	no	—
277	C₄⋊C₄×C₇₁	—	2	4	no	—
278	C₄⋊C₄×C₇₁	—	2	4	no	—
279	C₄⋊C₄×C₇₁	—	2	1	no	—
280	C₄⋊C₄×C₇₁	—	2	1	no	—
281	C₄⋊C₄×C₇₁	—	2	2	no	—
282	C₄⋊C₄×C₇₁	—	2	2	no	—
283	C₄⋊C₄×C₇₁	—	2	2	no	—
284	C₄⋊C₄×C₇₁	—	2	2	no	—
285	C₄⋊C₄×C₇₁	—	2	2	no	—
286	C₄⋊C₄×C₇₁	—	2	1	no	—
287	C₄⋊C₄×C₇₁	—	2	2	no	—
288	C₄⋊C₄×C₇₁	—	2	1	no	—
289	C₄⋊C₄×C₇₁	—	2	2	no	—
290	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
291	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
292	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₇₁	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
302	C₂²⋊C₄×C₇₁	—	2	2	no	—
303	C₂²⋊C₄×C₇₁	—	2	2	no	—
304	C₂²⋊C₄×C₇₁	—	2	2	no	—
305	C₂²⋊C₄×C₇₁	—	2	2	no	—
306	C₂²⋊C₄×C₇₁	—	2	1	no	—
307	C₂²⋊C₄×C₇₁	—	2	1	no	—
308	C₂²⋊C₄×C₇₁	—	2	1	no	—
309	C₂²⋊C₄×C₇₁	—	2	1	no	—
310	C₂²⋊C₄×C₇₁	—	2	2	no	—
311	C₂²⋊C₄×C₇₁	—	2	2	no	—
312	C₂²⋊C₄×C₇₁	—	2	1	no	—
313	C₂²⋊C₄×C₇₁	—	2	2	no	—
314	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
317	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
318	C₄²×C₇₁	—	2	2	no	—
319	C₄²×C₇₁	—	2	2	no	—
320	C₄²×C₇₁	—	2	2	no	—
321	C₄²×C₇₁	—	2	2	no	—
322	C₄²×C₇₁	—	2	2	no	—
323	C₄²×C₇₁	—	2	1	no	—
324	C₄²×C₇₁	C₂×D₄	1	2	yes	—
325	C₄²×C₇₁	C₂×D₄	1	2	yes	—
326	C₄²×C₇₁	C₂⁴	1	2	yes	—
327	C₄²×C₇₁	C₂⁴	1	2	yes	—
328	C₂³×C₇₁	—	2	2	no	—
329	C₂³×C₇₁	—	2	2	no	—
330	C₂³×C₇₁	—	2	1	no	—
331	C₂³×C₇₁	—	4	1	no	—
332	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
333	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
334	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₇₁	—	2	4	no	—
336	Q₈×C₇₁	—	2	2	no	—
337	Q₈×C₇₁	—	4	2	no	—
338	Q₈×C₇₁	—	8	2	no	—
339	Q₈×C₇₁	—	8	4	no	—
340	Q₈×C₇₁	—	8	4	no	—
341	D₄×C₇₁	—	2	2	no	—
342	D₄×C₇₁	—	4	2	no	—
343	D₄×C₇₁	—	4	2	no	—
344	D₄×C₇₁	—	8	1	no	—
345	C₂×C₄×C₇₁	—	2	2	no	—
346	C₂×C₄×C₇₁	—	2	4	no	—
347	C₂×C₄×C₇₁	—	2	2	no	—
348	C₂×C₄×C₇₁	—	2	2	no	—
349	C₂×C₄×C₇₁	—	2	2	no	—
350	C₂×C₄×C₇₁	—	2	2	no	—
351	C₂×C₄×C₇₁	—	2	1	no	—
352	C₂×C₄×C₇₁	—	2	1	no	—
353	C₂×C₄×C₇₁	—	2	2	no	—
354	C₂×C₄×C₇₁	—	2	2	no	—
355	C₂×C₄×C₇₁	—	2	1	no	—
356	C₂×C₄×C₇₁	—	2	2	no	—
357	C₂×C₄×C₇₁	—	2	2	no	—
358	C₂×C₄×C₇₁	—	2	4	no	—
359	C₂×C₄×C₇₁	—	4	2	no	—
360	C₂×C₄×C₇₁	—	4	4	no	—
361	C₂×C₄×C₇₁	—	4	2	no	—
362	C₂×C₄×C₇₁	—	4	2	no	—
363	C₂×C₄×C₇₁	—	4	2	no	—
364	C₂×C₄×C₇₁	—	4	2	no	—
365	C₂×C₄×C₇₁	—	8	2	no	—
366	C₂×C₄×C₇₁	—	8	1	no	—
367	C₂×C₄×C₇₁	—	8	2	no	—
368	C₂×C₄×C₇₁	—	8	2	no	—
369	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₇₁	2₋¹⁺⁴	1	4	yes	—
377	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
378	C₈×C₇₁	—	2	2	no	—
379	C₈×C₇₁	—	2	2	no	—
380	C₈×C₇₁	—	2	4	no	—
381	C₂²×C₇₁	—	2	1	no	—
382	C₂²×C₇₁	—	2	1	no	—
383	C₂²×C₇₁	—	2	1	no	—
384	C₂²×C₇₁	—	2	1	no	—
385	C₂²×C₇₁	—	2	1	no	—
386	C₂²×C₇₁	—	2	1	no	—
387	C₂²×C₇₁	—	2	1	no	—
388	C₂²×C₇₁	—	4	4	no	—
389	C₂²×C₇₁	—	4	1	no	—
390	C₂²×C₇₁	—	4	1	no	—
391	C₂²×C₇₁	—	4	1	no	—
392	C₂²×C₇₁	#536	1	2	yes	—
393	C₂²×C₇₁	#578	1	2	yes	—
394	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₇₁	—	2	2	no	—
396	C₄×C₇₁	—	2	2	no	—
397	C₄×C₇₁	—	2	1	no	—
398	C₄×C₇₁	—	2	1	no	—
399	C₄×C₇₁	—	2	2	no	—
400	C₄×C₇₁	—	2	2	no	—
401	C₄×C₇₁	—	4	4	no	—
402	C₄×C₇₁	—	4	2	no	—
403	C₄×C₇₁	—	4	2	no	—
404	C₄×C₇₁	—	4	1	no	—
405	C₄×C₇₁	—	4	1	no	—
406	C₄×C₇₁	—	4	2	no	—
407	C₄×C₇₁	—	4	2	no	—
408	C₄×C₇₁	—	4	1	no	—
409	C₄×C₇₁	#536	1	2	yes	—
410	C₄×C₇₁	C₂×2₋¹⁺⁴	1	2	yes	—
411	#60874	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂×C₇₁	—	2	2	no	—
413	C₂×C₇₁	—	2	2	no	—
414	C₂×C₇₁	—	4	1	no	—
415	C₂×C₇₁	—	8	1	no	—
416	C₂×C₇₁	C₂×#536	1	1	yes	characteristic
417	C₂×C₇₁	C₂×#578	1	1	yes	characteristic
418	C₂×C₇₁	#3585	1	1	yes	characteristic
419	#3495	C₂×C₇₁	1	1	yes	characteristic
420	C₂×#544	C₂×C₇₁	1	1	yes	characteristic, complemented
421	#3243	C₂×C₇₁	1	4	yes	complemented
422	#3242	C₂×C₇₁	1	4	yes	complemented
423	#3239	C₂×C₇₁	1	2	yes	complemented
424	#3236	C₂×C₇₁	1	2	yes	complemented
425	#3232	C₂×C₇₁	1	2	yes	complemented
426	#3230	C₂×C₇₁	1	2	yes	complemented
427	#3164	C₂×C₇₁	1	2	yes	complemented
428	#3137	C₂×C₇₁	1	2	yes	complemented
429	#3095	C₂×C₇₁	1	1	yes	characteristic, complemented
430	#3092	C₂×C₇₁	1	1	yes	characteristic
431	#3091	C₂×C₇₁	1	1	yes	characteristic
432	C₂×#484	C₂×C₇₁	1	1	yes	characteristic, complemented
433	#3083	C₂×C₇₁	1	2	yes	complemented
434	#3082	C₂×C₇₁	1	2	yes	complemented
435	#2924	C₂×C₇₁	1	1	yes	characteristic, complemented
436	C₇₁	#60874	1	1	yes	characteristic, direct product factor, Sylow
437	#556	—	2	1	no	—
438	#554	—	2	1	no	—
439	#552	—	2	2	no	—
440	#552	—	2	1	no	—
441	#552	—	2	1	no	—
442	#551	—	2	2	no	—
443	#544	—	2	2	no	—
444	#544	—	2	1	no	—
445	#544	—	2	1	no	—
446	#544	C₂²×C₇₁	1	2	yes	—
447	#544	C₂²×C₇₁	1	2	yes	—
448	#544	C₂²×C₇₁	1	1	yes	characteristic
449	#544	C₂²×C₇₁	1	4	yes	—
450	#542	C₂²×C₇₁	1	2	yes	—
451	#541	C₂²×C₇₁	1	2	yes	—
452	#536	C₂²×C₇₁	1	1	yes	characteristic
453	#533	C₂²×C₇₁	1	2	yes	—
454	C₂×C₄⋊Q₈	—	2	1	no	—
455	C₂×C₄⋊Q₈	C₂²×C₇₁	1	2	yes	—
456	#529	C₂²×C₇₁	1	2	yes	—
457	C₂×#125	—	2	1	no	—
458	C₂×#125	C₂²×C₇₁	1	2	yes	—
459	#525	C₂²×C₇₁	1	1	yes	characteristic
460	C₂×C₂²⋊Q₈	—	2	2	no	—
461	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
462	#520	C₂²×C₇₁	1	1	yes	characteristic
463	#519	C₂²×C₇₁	1	1	yes	characteristic
464	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
465	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
466	C₂²×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
467	#501	C₂²×C₇₁	1	4	yes	complemented
468	#501	C₂²×C₇₁	1	4	yes	complemented
469	#500	C₂²×C₇₁	1	4	yes	complemented
470	#499	C₂²×C₇₁	1	4	yes	complemented
471	#491	C₂²×C₇₁	1	4	yes	complemented
472	#489	C₂²×C₇₁	1	4	yes	complemented
473	#488	C₂²×C₇₁	1	4	yes	complemented
474	#487	C₂²×C₇₁	1	4	yes	complemented
475	#485	C₂²×C₇₁	1	2	yes	—
476	#485	C₂²×C₇₁	1	4	yes	—
477	#484	C₂²×C₇₁	1	2	yes	—
478	#484	C₂²×C₇₁	1	2	yes	—
479	#484	C₂²×C₇₁	1	4	yes	—
480	#484	C₂²×C₇₁	1	1	yes	characteristic
481	#484	C₂²×C₇₁	1	2	yes	—
482	#484	C₂²×C₇₁	1	2	yes	—
483	#483	C₂²×C₇₁	1	1	yes	characteristic
484	#483	C₂²×C₇₁	1	2	yes	—
485	#483	C₂²×C₇₁	1	2	yes	—
486	#482	C₂²×C₇₁	1	2	yes	—
487	#481	C₂²×C₇₁	1	1	yes	characteristic
488	#481	C₂²×C₇₁	1	2	yes	—
489	#480	C₂²×C₇₁	1	1	yes	characteristic
490	#480	C₂²×C₇₁	1	2	yes	—
491	#479	C₂²×C₇₁	1	4	yes	complemented
492	#479	C₂²×C₇₁	1	4	yes	complemented
493	#479	C₂²×C₇₁	1	4	yes	complemented
494	#478	C₂²×C₇₁	1	4	yes	complemented
495	#477	C₂²×C₇₁	1	4	yes	complemented
496	#477	C₂²×C₇₁	1	4	yes	complemented
497	#475	C₂²×C₇₁	1	4	yes	complemented
498	#474	C₂²×C₇₁	1	4	yes	complemented
499	#433	C₂²×C₇₁	1	4	yes	—
500	#432	C₂²×C₇₁	1	2	yes	—
501	#431	C₂²×C₇₁	1	2	yes	—
502	#428	C₂²×C₇₁	1	2	yes	—
503	#428	C₂²×C₇₁	1	2	yes	—
504	#427	C₂²×C₇₁	1	2	yes	—
505	C₂×#107	C₂²×C₇₁	1	2	yes	—
506	#424	C₂²×C₇₁	1	2	yes	—
507	#419	C₂²×C₇₁	1	2	yes	—
508	#417	C₂²×C₇₁	1	2	yes	—
509	#416	C₂²×C₇₁	1	2	yes	—
510	C₂×#103	C₂²×C₇₁	1	2	yes	—
511	#407	C₂²×C₇₁	1	1	yes	characteristic
512	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
513	#405	C₂²×C₇₁	1	2	yes	—
514	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
515	C₂²×Q₈	—	2	2	no	—
516	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
519	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
520	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
521	C₄⋊Q₈	—	2	2	no	—
522	C₄⋊Q₈	—	2	4	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
529	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
530	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
531	#126	—	2	2	no	—
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	2	4	no	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	—	2	1	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	C₂³×C₇₁	1	4	yes	—
545	#125	C₂³×C₇₁	1	4	yes	—
546	#125	C₂³×C₇₁	1	2	yes	—
547	#124	—	2	2	no	—
548	#124	C₂³×C₇₁	1	2	yes	—
549	#123	—	2	1	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	2	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
565	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
566	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
567	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
568	#121	C₂³×C₇₁	1	1	yes	characteristic
569	#121	C₂³×C₇₁	1	1	yes	characteristic
570	#120	—	2	1	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
575	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
576	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	C₂³×C₇₁	1	2	yes	—
582	#117	—	2	1	no	—
583	#117	—	2	1	no	—
584	#117	—	2	2	no	—
585	#117	—	2	1	no	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	D₄×C₇₁	1	1	yes	characteristic
589	#117	D₄×C₇₁	1	2	yes	—
590	#117	D₄×C₇₁	1	1	yes	characteristic
591	#117	C₂³×C₇₁	1	2	yes	—
592	#117	C₂³×C₇₁	1	2	yes	—
593	#117	C₂³×C₇₁	1	1	yes	characteristic
594	#117	C₂³×C₇₁	1	1	yes	characteristic
595	#117	C₂³×C₇₁	1	1	yes	characteristic
596	#117	C₂³×C₇₁	1	2	yes	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
606	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	D₄×C₇₁	1	2	yes	—
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
618	#107	C₂³×C₇₁	1	4	yes	—
619	#107	C₂³×C₇₁	1	4	yes	—
620	#107	C₂³×C₇₁	1	2	yes	—
621	#107	C₂³×C₇₁	1	2	yes	—
622	#107	C₂³×C₇₁	1	4	yes	—
623	#107	C₂³×C₇₁	1	4	yes	—
624	#106	C₂³×C₇₁	1	2	yes	—
625	#106	C₂³×C₇₁	1	2	yes	—
626	#106	C₂³×C₇₁	1	4	yes	—
627	#106	C₂³×C₇₁	1	4	yes	—
628	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
629	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
630	#103	C₂³×C₇₁	1	4	yes	—
631	#103	C₂³×C₇₁	1	4	yes	—
632	#103	C₂³×C₇₁	1	2	yes	—
633	#103	C₂³×C₇₁	1	2	yes	—
634	#103	C₂³×C₇₁	1	4	yes	—
635	#103	C₂³×C₇₁	1	4	yes	—
636	#103	C₂³×C₇₁	1	4	yes	—
637	#102	C₂³×C₇₁	1	2	yes	—
638	#102	C₂³×C₇₁	1	2	yes	—
639	#102	C₂³×C₇₁	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
641	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
642	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
643	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
644	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
645	#97	C₂³×C₇₁	1	4	yes	—
646	C₄×C₈	C₂³×C₇₁	1	4	yes	—
647	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
648	#41	—	2	4	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	8	4	no	—
655	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
656	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	8	2	no	—
672	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
674	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
680	M₁₆	—	2	4	no	—
681	C₂×C₈	—	2	4	no	—
682	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
683	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
684	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
710	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
711	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₇₁	1	4	yes	—
717	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
719	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
734	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	1	no	—
743	C₄²	C₂×D₄×C₇₁	1	2	yes	—
744	C₄²	C₂×D₄×C₇₁	1	2	yes	—
745	C₄²	C₂⁴×C₇₁	1	2	yes	—
746	C₄²	C₂⁴×C₇₁	1	2	yes	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
752	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
753	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	8	4	no	—
758	Q₈	—	8	4	no	—
759	Q₈	—	8	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	8	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	8	2	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	1	no	—
788	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
795	C₂×C₄	2₋¹⁺⁴×C₇₁	1	4	yes	—
796	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
797	C₈	—	2	2	no	—
798	C₈	—	2	2	no	—
799	C₈	—	2	4	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	#536×C₇₁	1	2	yes	—
812	C₂²	#578×C₇₁	1	2	yes	—
813	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	4	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	2	no	—
828	C₄	#536×C₇₁	1	2	yes	—
829	C₄	C₂×2₋¹⁺⁴×C₇₁	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₂×#536×C₇₁	1	1	yes	characteristic
835	C₂	C₂×#578×C₇₁	1	1	yes	characteristic
836	C₂	C₇₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	#525×C₇₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂×#117×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#544×C₇₁	C₂	semidirect
3. C₇₁×#3243	C₂	semidirect
4. C₇₁×#3242	C₂	semidirect
5. C₇₁×#3239	C₂	semidirect
6. C₇₁×#3236	C₂	semidirect
7. C₇₁×#3232	C₂	semidirect
8. C₇₁×#3230	C₂	semidirect
9. C₇₁×#3164	C₂	semidirect
10. C₇₁×#3137	C₂	semidirect
11. C₇₁×#3095	C₂	semidirect
14. C₂×#484×C₇₁	C₂	semidirect
15. C₇₁×#3083	C₂	semidirect
16. C₇₁×#3082	C₂	semidirect
17. C₇₁×#2924	C₂	semidirect
48. #501×C₇₁	C₂²	semidirect
49. #501×C₇₁	C₂²	semidirect
50. #500×C₇₁	C₂²	semidirect
51. #499×C₇₁	C₂²	semidirect
52. #491×C₇₁	C₂²	semidirect
53. #489×C₇₁	C₂²	semidirect
54. #488×C₇₁	C₂²	semidirect
55. #487×C₇₁	C₂²	semidirect
72. #479×C₇₁	C₂²	semidirect
73. #479×C₇₁	C₂²	semidirect
74. #479×C₇₁	C₂²	semidirect
75. #478×C₇₁	C₂²	semidirect
76. #477×C₇₁	C₂²	semidirect
77. #477×C₇₁	C₂²	semidirect
78. #475×C₇₁	C₂²	semidirect
79. #474×C₇₁	C₂²	semidirect
411. #60874	C₇₁	direct (N × H)
420. C₂×#544	C₂×C₇₁	semidirect
421. #3243	C₂×C₇₁	semidirect
422. #3242	C₂×C₇₁	semidirect
423. #3239	C₂×C₇₁	semidirect
424. #3236	C₂×C₇₁	semidirect
425. #3232	C₂×C₇₁	semidirect
426. #3230	C₂×C₇₁	semidirect
427. #3164	C₂×C₇₁	semidirect
428. #3137	C₂×C₇₁	semidirect
429. #3095	C₂×C₇₁	semidirect
432. C₂×#484	C₂×C₇₁	semidirect
433. #3083	C₂×C₇₁	semidirect
434. #3082	C₂×C₇₁	semidirect
435. #2924	C₂×C₇₁	semidirect
436. C₇₁	#60874	direct (N × H)
467. #501	C₂²×C₇₁	semidirect
468. #501	C₂²×C₇₁	semidirect
469. #500	C₂²×C₇₁	semidirect
470. #499	C₂²×C₇₁	semidirect
471. #491	C₂²×C₇₁	semidirect
472. #489	C₂²×C₇₁	semidirect
473. #488	C₂²×C₇₁	semidirect
474. #487	C₂²×C₇₁	semidirect
491. #479	C₂²×C₇₁	semidirect
492. #479	C₂²×C₇₁	semidirect
493. #479	C₂²×C₇₁	semidirect
494. #478	C₂²×C₇₁	semidirect
495. #477	C₂²×C₇₁	semidirect
496. #477	C₂²×C₇₁	semidirect
497. #475	C₂²×C₇₁	semidirect
498. #474	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×#3495	2
C₂×#544×C₇₁	2
C₇₁×#3243	2
C₇₁×#3242	2
C₇₁×#3239	2
C₇₁×#3236	2
C₇₁×#3232	2
C₇₁×#3230	2
C₇₁×#3164	2
C₇₁×#3137	2
C₇₁×#3095	2
C₇₁×#3092	2
C₇₁×#3091	2
C₂×#484×C₇₁	2
C₇₁×#3083	2
C₇₁×#3082	2
C₇₁×#2924	2
#60874	71

Subgroups — C71×#60874 #31881746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#60874 #31881746