Subgroups — C₇₁×#34326 #31855198

Order 18176.

2128 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#2373	C₂	1	2	yes	maximal, complemented
3	C₇₁×#2373	C₂	1	2	yes	maximal, complemented
4	C₇₁×#2368	C₂	1	2	yes	maximal, complemented
5	C₇₁×#2367	C₂	1	1	yes	maximal, characteristic
6	C₇₁×#2367	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#2357	C₂	1	1	yes	maximal, characteristic
9	C₇₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#2343	C₂	1	2	yes	maximal, complemented
13	C₇₁×#2334	C₂	1	2	yes	maximal, complemented
14	C₇₁×#2332	C₂	1	2	yes	maximal, complemented
15	C₇₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#2326	C₂	1	1	yes	maximal, characteristic
17	C₄×#126×C₇₁	C₂	1	2	yes	maximal, complemented
18	C₄×#124×C₇₁	C₂	1	1	yes	maximal, characteristic
19	C₇₁×#2298	C₂	1	2	yes	maximal, complemented
20	C₇₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#2275	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₇₁	C₄	1	16	yes	complemented
25	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
26	C₂×#126×C₇₁	C₂²	1	2	yes	—
27	C₂×#126×C₇₁	C₂²	1	2	yes	—
28	C₂×#124×C₇₁	C₂²	1	1	yes	characteristic
29	C₂×#124×C₇₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
41	C₂×#117×C₇₁	C₂²	1	2	yes	—
42	#391×C₇₁	C₂²	1	1	yes	characteristic
43	#391×C₇₁	C₂²	1	1	yes	characteristic
44	#391×C₇₁	C₂²	1	1	yes	characteristic
45	#391×C₇₁	C₂²	1	1	yes	characteristic
46	#391×C₇₁	C₂²	1	1	yes	characteristic
47	#391×C₇₁	C₂²	1	1	yes	characteristic
48	#391×C₇₁	C₂²	1	2	yes	—
49	#390×C₇₁	C₂²	1	1	yes	characteristic
50	#390×C₇₁	C₂²	1	1	yes	characteristic
51	#389×C₇₁	C₂²	1	1	yes	characteristic
52	#389×C₇₁	C₂²	1	1	yes	characteristic
53	#389×C₇₁	C₂²	1	2	yes	—
54	#388×C₇₁	C₂²	1	2	yes	—
55	#388×C₇₁	C₂²	1	2	yes	—
56	#388×C₇₁	C₂²	1	2	yes	—
57	#388×C₇₁	C₂²	1	2	yes	—
58	#388×C₇₁	C₂²	1	2	yes	—
59	#388×C₇₁	C₂²	1	2	yes	—
60	#388×C₇₁	C₂²	1	2	yes	—
61	#388×C₇₁	C₂²	1	2	yes	—
62	#388×C₇₁	C₂²	1	2	yes	—
63	#388×C₇₁	C₂²	1	2	yes	—
64	#387×C₇₁	C₂²	1	1	yes	characteristic
65	#387×C₇₁	C₂²	1	1	yes	characteristic
66	#387×C₇₁	C₂²	1	1	yes	characteristic
67	#387×C₇₁	C₂²	1	1	yes	characteristic
68	#387×C₇₁	C₂²	1	2	yes	—
69	#387×C₇₁	C₂²	1	2	yes	—
70	#387×C₇₁	C₂²	1	2	yes	—
71	#387×C₇₁	C₂²	1	2	yes	—
72	#387×C₇₁	C₂²	1	2	yes	—
73	#387×C₇₁	C₂²	1	2	yes	—
74	#387×C₇₁	C₂²	1	2	yes	—
75	#387×C₇₁	C₂²	1	2	yes	—
76	#387×C₇₁	C₂²	1	2	yes	—
77	#387×C₇₁	C₂²	1	2	yes	—
78	#387×C₇₁	C₂²	1	2	yes	—
79	#387×C₇₁	C₂²	1	2	yes	—
80	#385×C₇₁	C₂²	1	2	yes	—
81	#385×C₇₁	C₂²	1	2	yes	—
82	#385×C₇₁	C₂²	1	2	yes	—
83	#385×C₇₁	C₂²	1	2	yes	—
84	#384×C₇₁	C₂²	1	1	yes	characteristic
85	#383×C₇₁	C₂²	1	2	yes	—
86	#382×C₇₁	C₂²	1	1	yes	characteristic
87	#382×C₇₁	C₂²	1	1	yes	characteristic
88	#382×C₇₁	C₂²	1	2	yes	—
89	#381×C₇₁	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
117	#376×C₇₁	C₂²	1	1	yes	characteristic
118	#376×C₇₁	C₂²	1	1	yes	characteristic
119	#376×C₇₁	C₂²	1	2	yes	—
120	#376×C₇₁	C₂²	1	2	yes	—
121	C₂×#95×C₇₁	C₂²	1	2	yes	—
122	C₄³×C₇₁	C₂²	1	1	yes	characteristic
123	C₄³×C₇₁	C₂²	1	2	yes	—
124	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₇₁	C₂×C₄	1	8	yes	complemented
132	#126×C₇₁	C₂×C₄	1	16	yes	complemented
133	#126×C₇₁	C₂×C₄	1	16	yes	complemented
134	#124×C₇₁	C₂×C₄	1	8	yes	—
135	#124×C₇₁	C₂×C₄	1	8	yes	—
136	C₂²⋊Q₈×C₇₁	C₂×C₄	1	16	yes	complemented
137	C₄×Q₈×C₇₁	—	2	4	no	—
138	C₄×Q₈×C₇₁	—	2	4	no	—
139	C₄×Q₈×C₇₁	—	2	4	no	—
140	C₄×Q₈×C₇₁	—	2	4	no	—
141	C₄×Q₈×C₇₁	C₂×C₄	1	8	yes	complemented
142	C₄×Q₈×C₇₁	C₂×C₄	1	8	yes	complemented
143	C₄×Q₈×C₇₁	C₂×C₄	1	8	yes	complemented
144	C₄×D₄×C₇₁	—	2	4	no	—
145	C₄×D₄×C₇₁	—	2	4	no	—
146	C₄×D₄×C₇₁	C₂×C₄	1	8	yes	—
147	#117×C₇₁	C₂×C₄	1	16	yes	complemented
148	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
183	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
185	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
189	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
192	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
195	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
196	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
207	#95×C₇₁	C₂³	1	1	yes	characteristic
208	#95×C₇₁	C₂³	1	2	yes	—
209	#95×C₇₁	C₂³	1	2	yes	—
210	#95×C₇₁	C₂³	1	2	yes	—
211	#95×C₇₁	C₂³	1	1	yes	characteristic
212	#95×C₇₁	C₂³	1	1	yes	characteristic
213	#95×C₇₁	C₂³	1	1	yes	characteristic
214	#95×C₇₁	C₂³	1	1	yes	characteristic
215	#95×C₇₁	C₂³	1	1	yes	characteristic
216	#95×C₇₁	C₂³	1	2	yes	—
217	#95×C₇₁	C₂³	1	2	yes	—
218	#95×C₇₁	C₂³	1	1	yes	characteristic
219	#95×C₇₁	C₂³	1	2	yes	—
220	#95×C₇₁	C₂³	1	1	yes	characteristic
221	#95×C₇₁	C₂³	1	1	yes	characteristic
222	#95×C₇₁	C₂³	1	2	yes	—
223	#95×C₇₁	C₂³	1	2	yes	—
224	#95×C₇₁	C₂³	1	1	yes	characteristic
225	#95×C₇₁	C₂³	1	1	yes	characteristic
226	#95×C₇₁	C₂³	1	1	yes	characteristic
227	#95×C₇₁	C₂³	1	2	yes	—
228	#95×C₇₁	C₂³	1	2	yes	—
229	#95×C₇₁	C₂³	1	2	yes	—
230	#95×C₇₁	C₂³	1	2	yes	—
231	#95×C₇₁	C₂³	1	2	yes	—
232	#95×C₇₁	C₂³	1	2	yes	—
233	#95×C₇₁	C₂³	1	2	yes	—
234	#95×C₇₁	C₂³	1	2	yes	—
235	#95×C₇₁	C₂³	1	1	yes	characteristic
236	#95×C₇₁	C₂³	1	2	yes	—
237	#95×C₇₁	C₂³	1	2	yes	—
238	#95×C₇₁	C₂³	1	1	yes	characteristic
239	#95×C₇₁	C₂³	1	2	yes	—
240	C₂⁴×C₇₁	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₇₁	—	2	2	no	—
242	C₂×Q₈×C₇₁	—	2	2	no	—
243	C₂×Q₈×C₇₁	—	2	2	no	—
244	C₂×Q₈×C₇₁	—	2	2	no	—
245	C₂×Q₈×C₇₁	—	4	1	no	—
246	C₂×Q₈×C₇₁	—	4	1	no	—
247	C₂×Q₈×C₇₁	C₂²×C₄	1	4	yes	—
248	C₂×Q₈×C₇₁	C₂²×C₄	1	4	yes	—
249	C₂×Q₈×C₇₁	C₂²×C₄	1	4	yes	—
250	C₂×D₄×C₇₁	—	2	2	no	—
251	C₂×D₄×C₇₁	—	2	2	no	—
252	C₂×D₄×C₇₁	C₂²×C₄	1	4	yes	—
253	C₂²×C₄×C₇₁	—	2	4	no	—
254	C₂²×C₄×C₇₁	—	2	4	no	—
255	C₂²×C₄×C₇₁	—	4	2	no	—
256	C₂²×C₄×C₇₁	—	4	2	no	—
257	C₂²×C₄×C₇₁	—	4	2	no	—
258	C₂²×C₄×C₇₁	—	4	2	no	—
259	C₂²×C₄×C₇₁	—	4	2	no	—
260	C₂²×C₄×C₇₁	—	4	2	no	—
261	C₂²×C₄×C₇₁	C₂²×C₄	1	8	yes	—
262	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₇₁	—	2	2	no	—
285	C₄⋊C₄×C₇₁	—	2	4	no	—
286	C₄⋊C₄×C₇₁	—	2	4	no	—
287	C₄⋊C₄×C₇₁	—	2	4	no	—
288	C₄⋊C₄×C₇₁	—	2	4	no	—
289	C₄⋊C₄×C₇₁	—	2	2	no	—
290	C₄⋊C₄×C₇₁	—	2	2	no	—
291	C₄⋊C₄×C₇₁	—	2	2	no	—
292	C₄⋊C₄×C₇₁	—	2	2	no	—
293	C₄⋊C₄×C₇₁	—	4	1	no	—
294	C₄⋊C₄×C₇₁	—	4	1	no	—
295	C₄⋊C₄×C₇₁	—	4	1	no	—
296	C₄⋊C₄×C₇₁	—	4	2	no	—
297	C₄⋊C₄×C₇₁	—	4	1	no	—
298	C₄⋊C₄×C₇₁	—	4	2	no	—
299	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
300	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
301	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
302	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
303	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
304	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
305	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
306	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
307	C₄⋊C₄×C₇₁	#41	1	4	yes	—
308	C₂²⋊C₄×C₇₁	—	2	4	no	—
309	C₂²⋊C₄×C₇₁	—	2	4	no	—
310	C₂²⋊C₄×C₇₁	—	2	4	no	—
311	C₂²⋊C₄×C₇₁	—	4	2	no	—
312	C₂²⋊C₄×C₇₁	—	4	2	no	—
313	C₂²⋊C₄×C₇₁	—	4	2	no	—
314	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
315	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
316	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
317	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
318	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
319	C₄²×C₇₁	—	2	2	no	—
320	C₄²×C₇₁	—	2	4	no	—
321	C₄²×C₇₁	—	2	2	no	—
322	C₄²×C₇₁	—	2	4	no	—
323	C₄²×C₇₁	—	2	4	no	—
324	C₄²×C₇₁	—	2	4	no	—
325	C₄²×C₇₁	—	2	2	no	—
326	C₄²×C₇₁	—	2	2	no	—
327	C₄²×C₇₁	—	4	2	no	—
328	C₄²×C₇₁	—	4	2	no	—
329	C₄²×C₇₁	—	4	2	no	—
330	C₄²×C₇₁	—	4	1	no	—
331	C₄²×C₇₁	—	4	1	no	—
332	C₄²×C₇₁	—	4	1	no	—
333	C₄²×C₇₁	—	4	2	no	—
334	C₄²×C₇₁	—	4	2	no	—
335	C₄²×C₇₁	—	4	2	no	—
336	C₄²×C₇₁	—	4	2	no	—
337	C₄²×C₇₁	C₂²×C₄	1	8	yes	—
338	C₄²×C₇₁	C₂²×C₄	1	8	yes	—
339	C₄²×C₇₁	C₂²×C₄	1	4	yes	—
340	C₄²×C₇₁	C₂²×C₄	1	4	yes	—
341	C₄²×C₇₁	C₂²×C₄	1	4	yes	—
342	C₄²×C₇₁	#41	1	4	yes	—
343	C₂³×C₇₁	—	2	2	no	—
344	C₂³×C₇₁	—	2	2	no	—
345	C₂³×C₇₁	—	2	2	no	—
346	C₂³×C₇₁	—	2	2	no	—
347	C₂³×C₇₁	—	2	2	no	—
348	C₂³×C₇₁	—	2	2	no	—
349	C₂³×C₇₁	C₂³×C₄	1	4	yes	—
350	C₂³×C₇₁	C₂⁵	1	1	yes	characteristic
351	Q₈×C₇₁	—	2	8	no	—
352	Q₈×C₇₁	—	2	8	no	—
353	Q₈×C₇₁	—	4	4	no	—
354	D₄×C₇₁	—	2	8	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	2	no	—
359	C₂×C₄×C₇₁	—	2	2	no	—
360	C₂×C₄×C₇₁	—	2	1	no	—
361	C₂×C₄×C₇₁	—	2	1	no	—
362	C₂×C₄×C₇₁	—	2	1	no	—
363	C₂×C₄×C₇₁	—	2	1	no	—
364	C₂×C₄×C₇₁	—	2	1	no	—
365	C₂×C₄×C₇₁	—	2	1	no	—
366	C₂×C₄×C₇₁	—	2	1	no	—
367	C₂×C₄×C₇₁	—	2	1	no	—
368	C₂×C₄×C₇₁	—	2	2	no	—
369	C₂×C₄×C₇₁	—	2	2	no	—
370	C₂×C₄×C₇₁	—	2	2	no	—
371	C₂×C₄×C₇₁	—	2	2	no	—
372	C₂×C₄×C₇₁	—	2	1	no	—
373	C₂×C₄×C₇₁	—	2	1	no	—
374	C₂×C₄×C₇₁	—	2	1	no	—
375	C₂×C₄×C₇₁	—	2	1	no	—
376	C₂×C₄×C₇₁	—	2	1	no	—
377	C₂×C₄×C₇₁	—	2	1	no	—
378	C₂×C₄×C₇₁	—	2	1	no	—
379	C₂×C₄×C₇₁	—	2	1	no	—
380	C₂×C₄×C₇₁	—	2	1	no	—
381	C₂×C₄×C₇₁	—	2	1	no	—
382	C₂×C₄×C₇₁	—	2	1	no	—
383	C₂×C₄×C₇₁	—	2	2	no	—
384	C₂×C₄×C₇₁	—	2	2	no	—
385	C₂×C₄×C₇₁	—	2	1	no	—
386	C₂×C₄×C₇₁	—	2	1	no	—
387	C₂×C₄×C₇₁	—	2	1	no	—
388	C₂×C₄×C₇₁	—	2	2	no	—
389	C₂×C₄×C₇₁	—	2	2	no	—
390	C₂×C₄×C₇₁	—	2	1	no	—
391	C₂×C₄×C₇₁	—	2	1	no	—
392	C₂×C₄×C₇₁	—	2	2	no	—
393	C₂×C₄×C₇₁	—	2	1	no	—
394	C₂×C₄×C₇₁	—	2	1	no	—
395	C₂×C₄×C₇₁	—	2	1	no	—
396	C₂×C₄×C₇₁	—	2	2	no	—
397	C₂×C₄×C₇₁	—	2	2	no	—
398	C₂×C₄×C₇₁	—	2	1	no	—
399	C₂×C₄×C₇₁	—	2	2	no	—
400	C₂×C₄×C₇₁	—	2	2	no	—
401	C₂×C₄×C₇₁	—	2	1	no	—
402	C₂×C₄×C₇₁	—	2	1	no	—
403	C₂×C₄×C₇₁	—	2	1	no	—
404	C₂×C₄×C₇₁	—	2	1	no	—
405	C₂×C₄×C₇₁	—	4	8	no	—
406	C₂×C₄×C₇₁	—	8	4	no	—
407	C₂×C₄×C₇₁	—	8	4	no	—
408	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
409	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
410	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
411	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
412	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
414	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
417	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
418	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
419	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
420	C₂×C₄×C₇₁	C₂×#41	1	4	yes	—
421	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
422	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
423	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
424	C₂²×C₇₁	—	2	4	no	—
425	C₂²×C₇₁	—	2	4	no	—
426	C₂²×C₇₁	—	2	4	no	—
427	C₂²×C₇₁	—	4	2	no	—
428	C₂²×C₇₁	—	4	2	no	—
429	C₂²×C₇₁	—	4	2	no	—
430	C₂²×C₇₁	—	4	2	no	—
431	C₂²×C₇₁	C₂⁴×C₄	1	1	yes	characteristic
432	C₂²×C₇₁	C₂²×#41	1	1	yes	characteristic
433	C₂²×C₇₁	C₂²×#41	1	1	yes	characteristic
434	C₂²×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
435	C₂²×C₇₁	#585	1	1	yes	characteristic
436	C₂²×C₇₁	#585	1	1	yes	characteristic
437	C₂²×C₇₁	#585	1	1	yes	characteristic
438	C₄×C₇₁	—	2	4	no	—
439	C₄×C₇₁	—	2	4	no	—
440	C₄×C₇₁	—	2	2	no	—
441	C₄×C₇₁	—	2	4	no	—
442	C₄×C₇₁	—	2	2	no	—
443	C₄×C₇₁	—	2	2	no	—
444	C₄×C₇₁	—	2	2	no	—
445	C₄×C₇₁	—	2	2	no	—
446	C₄×C₇₁	—	2	2	no	—
447	C₄×C₇₁	—	2	2	no	—
448	C₄×C₇₁	—	2	2	no	—
449	C₄×C₇₁	—	2	2	no	—
450	C₄×C₇₁	—	2	4	no	—
451	C₄×C₇₁	—	4	2	no	—
452	C₄×C₇₁	—	4	2	no	—
453	C₄×C₇₁	—	4	2	no	—
454	C₄×C₇₁	—	4	1	no	—
455	C₄×C₇₁	—	4	1	no	—
456	C₄×C₇₁	—	4	1	no	—
457	C₄×C₇₁	—	4	1	no	—
458	C₄×C₇₁	—	4	1	no	—
459	C₄×C₇₁	C₄×#41	1	4	yes	—
460	#34326	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂×C₇₁	—	4	4	no	—
462	C₂×C₇₁	C₂×C₄×#41	1	1	yes	characteristic
463	C₂×C₇₁	#3428	1	1	yes	characteristic
464	C₂×C₇₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
465	C₂×C₇₁	#3507	1	1	yes	characteristic
466	C₂×C₇₁	#3510	1	1	yes	characteristic
467	C₂×C₇₁	#3516	1	1	yes	characteristic
468	C₂×C₇₁	#3521	1	1	yes	characteristic
469	C₂×#556	C₂×C₇₁	1	1	yes	characteristic
470	#2373	C₂×C₇₁	1	2	yes	complemented
471	#2373	C₂×C₇₁	1	2	yes	complemented
472	#2368	C₂×C₇₁	1	2	yes	complemented
473	#2367	C₂×C₇₁	1	1	yes	characteristic
474	#2367	C₂×C₇₁	1	1	yes	characteristic
475	#2365	C₂×C₇₁	1	1	yes	characteristic, complemented
476	#2357	C₂×C₇₁	1	1	yes	characteristic
477	#2356	C₂×C₇₁	1	1	yes	characteristic, complemented
478	#2355	C₂×C₇₁	1	1	yes	characteristic, complemented
479	#2355	C₂×C₇₁	1	1	yes	characteristic, complemented
480	#2343	C₂×C₇₁	1	2	yes	complemented
481	#2334	C₂×C₇₁	1	2	yes	complemented
482	#2332	C₂×C₇₁	1	2	yes	complemented
483	#2327	C₂×C₇₁	1	1	yes	characteristic, complemented
484	#2326	C₂×C₇₁	1	1	yes	characteristic
485	C₄×#126	C₂×C₇₁	1	2	yes	complemented
486	C₄×#124	C₂×C₇₁	1	1	yes	characteristic
487	#2298	C₂×C₇₁	1	2	yes	complemented
488	#2295	C₂×C₇₁	1	1	yes	characteristic, complemented
489	#2276	C₂×C₇₁	1	1	yes	characteristic, complemented
490	#2275	C₂×C₇₁	1	1	yes	characteristic
491	C₄²×Q₈	C₂×C₇₁	1	1	yes	characteristic, complemented
492	C₇₁	#34326	1	1	yes	characteristic, direct product factor, Sylow
493	#556	C₄×C₇₁	1	16	yes	complemented
494	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
495	C₂×#126	C₂²×C₇₁	1	2	yes	—
496	C₂×#126	C₂²×C₇₁	1	2	yes	—
497	C₂×#124	C₂²×C₇₁	1	1	yes	characteristic
498	C₂×#124	C₂²×C₇₁	1	1	yes	characteristic
499	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	2	yes	—
500	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
501	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
502	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
503	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
504	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
505	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
506	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
510	C₂×#117	C₂²×C₇₁	1	2	yes	—
511	#391	C₂²×C₇₁	1	1	yes	characteristic
512	#391	C₂²×C₇₁	1	1	yes	characteristic
513	#391	C₂²×C₇₁	1	1	yes	characteristic
514	#391	C₂²×C₇₁	1	1	yes	characteristic
515	#391	C₂²×C₇₁	1	2	yes	—
516	#391	C₂²×C₇₁	1	1	yes	characteristic
517	#391	C₂²×C₇₁	1	1	yes	characteristic
518	#390	C₂²×C₇₁	1	1	yes	characteristic
519	#390	C₂²×C₇₁	1	1	yes	characteristic
520	#389	C₂²×C₇₁	1	1	yes	characteristic
521	#389	C₂²×C₇₁	1	2	yes	—
522	#389	C₂²×C₇₁	1	1	yes	characteristic
523	#388	C₂²×C₇₁	1	2	yes	—
524	#388	C₂²×C₇₁	1	2	yes	—
525	#388	C₂²×C₇₁	1	2	yes	—
526	#388	C₂²×C₇₁	1	2	yes	—
527	#388	C₂²×C₇₁	1	2	yes	—
528	#388	C₂²×C₇₁	1	2	yes	—
529	#388	C₂²×C₇₁	1	2	yes	—
530	#388	C₂²×C₇₁	1	2	yes	—
531	#388	C₂²×C₇₁	1	2	yes	—
532	#388	C₂²×C₇₁	1	2	yes	—
533	#387	C₂²×C₇₁	1	1	yes	characteristic
534	#387	C₂²×C₇₁	1	2	yes	—
535	#387	C₂²×C₇₁	1	2	yes	—
536	#387	C₂²×C₇₁	1	2	yes	—
537	#387	C₂²×C₇₁	1	2	yes	—
538	#387	C₂²×C₇₁	1	2	yes	—
539	#387	C₂²×C₇₁	1	2	yes	—
540	#387	C₂²×C₇₁	1	2	yes	—
541	#387	C₂²×C₇₁	1	2	yes	—
542	#387	C₂²×C₇₁	1	2	yes	—
543	#387	C₂²×C₇₁	1	2	yes	—
544	#387	C₂²×C₇₁	1	1	yes	characteristic
545	#387	C₂²×C₇₁	1	2	yes	—
546	#387	C₂²×C₇₁	1	2	yes	—
547	#387	C₂²×C₇₁	1	1	yes	characteristic
548	#387	C₂²×C₇₁	1	1	yes	characteristic
549	#385	C₂²×C₇₁	1	2	yes	—
550	#385	C₂²×C₇₁	1	2	yes	—
551	#385	C₂²×C₇₁	1	2	yes	—
552	#385	C₂²×C₇₁	1	2	yes	—
553	#384	C₂²×C₇₁	1	1	yes	characteristic
554	#383	C₂²×C₇₁	1	2	yes	—
555	#382	C₂²×C₇₁	1	1	yes	characteristic
556	#382	C₂²×C₇₁	1	2	yes	—
557	#382	C₂²×C₇₁	1	1	yes	characteristic
558	#381	C₂²×C₇₁	1	2	yes	—
559	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
561	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
562	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
565	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
580	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
584	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
585	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
586	#376	C₂²×C₇₁	1	1	yes	characteristic
587	#376	C₂²×C₇₁	1	1	yes	characteristic
588	#376	C₂²×C₇₁	1	2	yes	—
589	#376	C₂²×C₇₁	1	2	yes	—
590	C₂×#95	C₂²×C₇₁	1	2	yes	—
591	C₄³	C₂²×C₇₁	1	2	yes	—
592	C₄³	C₂²×C₇₁	1	1	yes	characteristic
593	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
595	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
598	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
599	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
600	C₄⋊Q₈	C₂×C₄×C₇₁	1	8	yes	complemented
601	#126	C₂×C₄×C₇₁	1	16	yes	complemented
602	#126	C₂×C₄×C₇₁	1	16	yes	complemented
603	#124	C₂×C₄×C₇₁	1	8	yes	—
604	#124	C₂×C₄×C₇₁	1	8	yes	—
605	C₂²⋊Q₈	C₂×C₄×C₇₁	1	16	yes	complemented
606	C₄×Q₈	—	2	4	no	—
607	C₄×Q₈	—	2	4	no	—
608	C₄×Q₈	—	2	4	no	—
609	C₄×Q₈	—	2	4	no	—
610	C₄×Q₈	C₂×C₄×C₇₁	1	8	yes	complemented
611	C₄×Q₈	C₂×C₄×C₇₁	1	8	yes	complemented
612	C₄×Q₈	C₂×C₄×C₇₁	1	8	yes	complemented
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	C₂×C₄×C₇₁	1	8	yes	—
616	#117	C₂×C₄×C₇₁	1	16	yes	complemented
617	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
652	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
654	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
656	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
657	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
658	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
661	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
664	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
665	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
667	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
668	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
669	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
670	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
671	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
672	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
676	#95	C₂³×C₇₁	1	1	yes	characteristic
677	#95	C₂³×C₇₁	1	2	yes	—
678	#95	C₂³×C₇₁	1	2	yes	—
679	#95	C₂³×C₇₁	1	2	yes	—
680	#95	C₂³×C₇₁	1	1	yes	characteristic
681	#95	C₂³×C₇₁	1	1	yes	characteristic
682	#95	C₂³×C₇₁	1	1	yes	characteristic
683	#95	C₂³×C₇₁	1	1	yes	characteristic
684	#95	C₂³×C₇₁	1	1	yes	characteristic
685	#95	C₂³×C₇₁	1	2	yes	—
686	#95	C₂³×C₇₁	1	2	yes	—
687	#95	C₂³×C₇₁	1	1	yes	characteristic
688	#95	C₂³×C₇₁	1	2	yes	—
689	#95	C₂³×C₇₁	1	1	yes	characteristic
690	#95	C₂³×C₇₁	1	1	yes	characteristic
691	#95	C₂³×C₇₁	1	2	yes	—
692	#95	C₂³×C₇₁	1	2	yes	—
693	#95	C₂³×C₇₁	1	1	yes	characteristic
694	#95	C₂³×C₇₁	1	1	yes	characteristic
695	#95	C₂³×C₇₁	1	1	yes	characteristic
696	#95	C₂³×C₇₁	1	2	yes	—
697	#95	C₂³×C₇₁	1	2	yes	—
698	#95	C₂³×C₇₁	1	2	yes	—
699	#95	C₂³×C₇₁	1	2	yes	—
700	#95	C₂³×C₇₁	1	2	yes	—
701	#95	C₂³×C₇₁	1	2	yes	—
702	#95	C₂³×C₇₁	1	2	yes	—
703	#95	C₂³×C₇₁	1	2	yes	—
704	#95	C₂³×C₇₁	1	1	yes	characteristic
705	#95	C₂³×C₇₁	1	2	yes	—
706	#95	C₂³×C₇₁	1	2	yes	—
707	#95	C₂³×C₇₁	1	1	yes	characteristic
708	#95	C₂³×C₇₁	1	2	yes	—
709	C₂⁴	C₂⁴×C₇₁	1	2	yes	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	4	1	no	—
715	C₂×Q₈	—	4	1	no	—
716	C₂×Q₈	C₂²×C₄×C₇₁	1	4	yes	—
717	C₂×Q₈	C₂²×C₄×C₇₁	1	4	yes	—
718	C₂×Q₈	C₂²×C₄×C₇₁	1	4	yes	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	C₂²×C₄×C₇₁	1	4	yes	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	C₂²×C₄×C₇₁	1	8	yes	—
731	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
769	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
770	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
771	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
772	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
773	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
774	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
775	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
776	C₄⋊C₄	#41×C₇₁	1	4	yes	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
784	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
785	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
786	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
787	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	4	2	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	1	no	—
800	C₄²	—	4	1	no	—
801	C₄²	—	4	1	no	—
802	C₄²	—	4	2	no	—
803	C₄²	—	4	2	no	—
804	C₄²	—	4	2	no	—
805	C₄²	—	4	2	no	—
806	C₄²	C₂²×C₄×C₇₁	1	8	yes	—
807	C₄²	C₂²×C₄×C₇₁	1	8	yes	—
808	C₄²	C₂²×C₄×C₇₁	1	4	yes	—
809	C₄²	C₂²×C₄×C₇₁	1	4	yes	—
810	C₄²	C₂²×C₄×C₇₁	1	4	yes	—
811	C₄²	#41×C₇₁	1	4	yes	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	C₂³×C₄×C₇₁	1	4	yes	—
819	C₂³	C₂⁵×C₇₁	1	1	yes	characteristic
820	Q₈	—	2	8	no	—
821	Q₈	—	2	8	no	—
822	Q₈	—	4	4	no	—
823	D₄	—	2	8	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	4	8	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	—	8	4	no	—
877	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
878	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
879	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
880	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
881	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
882	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
883	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
884	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
887	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
888	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
889	C₂×C₄	C₂×#41×C₇₁	1	4	yes	—
890	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
891	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
892	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂⁴×C₄×C₇₁	1	1	yes	characteristic
901	C₂²	C₂²×#41×C₇₁	1	1	yes	characteristic
902	C₂²	C₂²×#41×C₇₁	1	1	yes	characteristic
903	C₂²	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
904	C₂²	#585×C₇₁	1	1	yes	characteristic
905	C₂²	#585×C₇₁	1	1	yes	characteristic
906	C₂²	#585×C₇₁	1	1	yes	characteristic
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	C₄×#41×C₇₁	1	4	yes	—
929	C₂	—	4	4	no	—
930	C₂	C₂×C₄×#41×C₇₁	1	1	yes	characteristic
931	C₂	C₇₁×#3428	1	1	yes	characteristic
932	C₂	C₄×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
933	C₂	C₇₁×#3507	1	1	yes	characteristic
934	C₂	C₇₁×#3510	1	1	yes	characteristic
935	C₂	C₇₁×#3516	1	1	yes	characteristic
936	C₂	C₇₁×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇₁
Frattini, cosocle	C₂³	C₂⁵×C₇₁
prime radical	C₂²×D₄×C₇₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₁×#2373	C₂	semidirect
3. C₇₁×#2373	C₂	semidirect
4. C₇₁×#2368	C₂	semidirect
7. C₇₁×#2365	C₂	semidirect
9. C₇₁×#2356	C₂	semidirect
10. C₇₁×#2355	C₂	semidirect
11. C₇₁×#2355	C₂	semidirect
12. C₇₁×#2343	C₂	semidirect
13. C₇₁×#2334	C₂	semidirect
14. C₇₁×#2332	C₂	semidirect
15. C₇₁×#2327	C₂	semidirect
17. C₄×#126×C₇₁	C₂	semidirect
19. C₇₁×#2298	C₂	semidirect
20. C₇₁×#2295	C₂	semidirect
21. C₇₁×#2276	C₂	semidirect
23. C₄²×Q₈×C₇₁	C₂	semidirect
24. #556×C₇₁	C₄	semidirect
131. C₄⋊Q₈×C₇₁	C₂×C₄	semidirect
132. #126×C₇₁	C₂×C₄	semidirect
133. #126×C₇₁	C₂×C₄	semidirect
136. C₂²⋊Q₈×C₇₁	C₂×C₄	semidirect
141. C₄×Q₈×C₇₁	C₂×C₄	semidirect
142. C₄×Q₈×C₇₁	C₂×C₄	semidirect
143. C₄×Q₈×C₇₁	C₂×C₄	semidirect
147. #117×C₇₁	C₂×C₄	semidirect
460. #34326	C₇₁	direct (N × H)
470. #2373	C₂×C₇₁	semidirect
471. #2373	C₂×C₇₁	semidirect
472. #2368	C₂×C₇₁	semidirect
475. #2365	C₂×C₇₁	semidirect
477. #2356	C₂×C₇₁	semidirect
478. #2355	C₂×C₇₁	semidirect
479. #2355	C₂×C₇₁	semidirect
480. #2343	C₂×C₇₁	semidirect
481. #2334	C₂×C₇₁	semidirect
482. #2332	C₂×C₇₁	semidirect
483. #2327	C₂×C₇₁	semidirect
485. C₄×#126	C₂×C₇₁	semidirect
487. #2298	C₂×C₇₁	semidirect
488. #2295	C₂×C₇₁	semidirect
489. #2276	C₂×C₇₁	semidirect
491. C₄²×Q₈	C₂×C₇₁	semidirect
492. C₇₁	#34326	direct (N × H)
493. #556	C₄×C₇₁	semidirect
600. C₄⋊Q₈	C₂×C₄×C₇₁	semidirect
601. #126	C₂×C₄×C₇₁	semidirect
602. #126	C₂×C₄×C₇₁	semidirect
605. C₂²⋊Q₈	C₂×C₄×C₇₁	semidirect
610. C₄×Q₈	C₂×C₄×C₇₁	semidirect
611. C₄×Q₈	C₂×C₄×C₇₁	semidirect
612. C₄×Q₈	C₂×C₄×C₇₁	semidirect
616. #117	C₂×C₄×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₇₁	2
C₇₁×#2373	2
C₇₁×#2368	2
C₇₁×#2367	2
C₇₁×#2365	2
C₇₁×#2357	2
C₇₁×#2356	2
C₇₁×#2355	2
C₇₁×#2343	2
C₇₁×#2334	2
C₇₁×#2332	2
C₇₁×#2327	2
C₇₁×#2326	2
C₄×#126×C₇₁	2
C₄×#124×C₇₁	2
C₇₁×#2298	2
C₇₁×#2295	2
C₇₁×#2276	2
C₇₁×#2275	2
C₄²×Q₈×C₇₁	2
#34326	71

Subgroups — C71×#34326 #31855198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#34326 #31855198