Subgroups — C₇₁×#61980 #31882852

Order 18176.

1894 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3481	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3372	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3320	C₂	1	4	yes	maximal, complemented
6	C₇₁×#3299	C₂	1	2	yes	maximal, complemented
7	D₄×SD₁₆×C₇₁	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₇₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3248	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3218	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3110	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#461×C₇₁	C₂	1	2	yes	maximal, complemented
17	C₇₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₇₁	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₇₁	C₂²	1	4	yes	—
20	#559×C₇₁	C₂²	1	1	yes	characteristic
21	Q₈²×C₇₁	—	2	1	no	—
22	#557×C₇₁	C₂²	1	2	yes	complemented
23	#554×C₇₁	—	2	1	no	—
24	#554×C₇₁	—	2	2	no	—
25	#554×C₇₁	C₂²	1	1	yes	characteristic
26	#554×C₇₁	C₂²	1	1	yes	characteristic
27	#553×C₇₁	—	2	1	no	—
28	#553×C₇₁	C₂²	1	2	yes	—
29	#551×C₇₁	—	2	2	no	—
30	D₄×Q₈×C₇₁	C₂²	1	2	yes	—
31	D₄×Q₈×C₇₁	C₂²	1	4	yes	complemented
32	#546×C₇₁	—	2	1	no	—
33	#546×C₇₁	C₂²	1	2	yes	—
34	D₄²×C₇₁	C₂²	1	1	yes	characteristic
35	#544×C₇₁	—	2	2	no	—
36	#544×C₇₁	—	2	1	no	—
37	#533×C₇₁	C₂²	1	1	yes	characteristic, complemented
38	#533×C₇₁	C₂²	1	2	yes	complemented
39	#532×C₇₁	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊Q₈×C₇₁	C₂²	1	2	yes	complemented
42	#529×C₇₁	—	2	1	no	—
43	#529×C₇₁	C₂²	1	2	yes	—
44	#525×C₇₁	—	2	2	no	—
45	#520×C₇₁	—	2	1	no	—
46	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₁	—	2	1	no	—
49	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
50	#497×C₇₁	C₂²	1	4	yes	complemented
51	#492×C₇₁	C₂²	1	2	yes	—
52	#491×C₇₁	C₂²	1	4	yes	complemented
53	#487×C₇₁	C₂²	1	2	yes	complemented
54	#485×C₇₁	C₂²	1	2	yes	complemented
55	#484×C₇₁	C₂²	1	4	yes	complemented
56	#479×C₇₁	C₂²	1	4	yes	complemented
57	#477×C₇₁	C₂²	1	2	yes	complemented
58	#475×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	#474×C₇₁	C₂²	1	1	yes	characteristic
60	#474×C₇₁	C₂²	1	2	yes	complemented
61	#468×C₇₁	C₂²	1	4	yes	complemented
62	#467×C₇₁	C₂²	1	4	yes	complemented
63	#465×C₇₁	C₂²	1	4	yes	—
64	#464×C₇₁	C₂²	1	4	yes	complemented
65	#462×C₇₁	C₂²	1	2	yes	complemented
66	#462×C₇₁	C₂²	1	2	yes	complemented
67	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
68	#461×C₇₁	C₂²	1	2	yes	—
69	#461×C₇₁	C₂²	1	2	yes	—
70	#461×C₇₁	C₂²	1	1	yes	characteristic
71	#461×C₇₁	C₂²	1	4	yes	—
72	#461×C₇₁	C₂²	1	4	yes	complemented
73	#461×C₇₁	C₂²	1	2	yes	complemented
74	#461×C₇₁	C₂²	1	2	yes	complemented
75	#461×C₇₁	C₂²	1	2	yes	complemented
76	#460×C₇₁	C₂²	1	2	yes	—
77	#452×C₇₁	C₂²	1	2	yes	—
78	#451×C₇₁	C₂²	1	4	yes	complemented
79	#450×C₇₁	C₂²	1	4	yes	—
80	#448×C₇₁	C₂²	1	4	yes	—
81	#448×C₇₁	C₂²	1	4	yes	complemented
82	#446×C₇₁	C₂²	1	2	yes	complemented
83	#440×C₇₁	C₂²	1	4	yes	—
84	#440×C₇₁	C₂²	1	4	yes	complemented
85	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
87	#435×C₇₁	C₂²	1	4	yes	complemented
88	C₈×D₄×C₇₁	C₂²	1	2	yes	—
89	#432×C₇₁	C₂²	1	2	yes	complemented
90	#431×C₇₁	C₂²	1	1	yes	characteristic, complemented
91	#423×C₇₁	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	complemented
93	#419×C₇₁	C₂²	1	2	yes	complemented
94	C₂×#103×C₇₁	C₂²	1	4	yes	complemented
95	C₂×#41×C₇₁	—	2	1	no	—
96	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₇₁	C₂³	1	4	yes	—
99	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₇₁	—	2	1	no	—
101	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
102	C₂³×C₄×C₇₁	—	2	2	no	—
103	#137×C₇₁	—	4	4	no	—
104	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₇₁	—	4	8	no	—
107	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
112	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
113	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₇₁	—	2	2	no	—
115	C₄⋊Q₈×C₇₁	—	2	4	no	—
116	C₄⋊Q₈×C₇₁	—	2	1	no	—
117	C₄⋊Q₈×C₇₁	—	2	2	no	—
118	C₄⋊Q₈×C₇₁	—	2	1	no	—
119	C₄⋊Q₈×C₇₁	—	2	2	no	—
120	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
123	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
126	#127×C₇₁	C₂³	1	1	yes	characteristic
127	#126×C₇₁	—	2	2	no	—
128	#126×C₇₁	—	2	2	no	—
129	#125×C₇₁	—	2	1	no	—
130	#125×C₇₁	—	2	2	no	—
131	#125×C₇₁	—	2	4	no	—
132	#125×C₇₁	—	2	1	no	—
133	#125×C₇₁	—	2	2	no	—
134	#125×C₇₁	C₂³	1	2	yes	—
135	#124×C₇₁	—	2	1	no	—
136	#124×C₇₁	—	2	1	no	—
137	#124×C₇₁	C₂³	1	2	yes	—
138	#123×C₇₁	—	2	2	no	—
139	#123×C₇₁	—	2	2	no	—
140	#123×C₇₁	—	2	2	no	—
141	#123×C₇₁	—	2	2	no	—
142	C₂²⋊Q₈×C₇₁	—	2	1	no	—
143	C₂²⋊Q₈×C₇₁	—	2	2	no	—
144	C₂²⋊Q₈×C₇₁	—	2	1	no	—
145	C₂²⋊Q₈×C₇₁	—	2	2	no	—
146	C₂²⋊Q₈×C₇₁	—	2	2	no	—
147	C₂²⋊Q₈×C₇₁	—	2	4	no	—
148	C₂²⋊Q₈×C₇₁	—	2	4	no	—
149	C₂²⋊Q₈×C₇₁	—	2	4	no	—
150	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
153	#121×C₇₁	—	2	2	no	—
154	#121×C₇₁	—	2	1	no	—
155	#121×C₇₁	—	2	1	no	—
156	#121×C₇₁	—	2	2	no	—
157	#121×C₇₁	C₂³	1	2	yes	—
158	#121×C₇₁	C₂³	1	2	yes	—
159	#120×C₇₁	—	2	2	no	—
160	#120×C₇₁	—	2	2	no	—
161	C₄×Q₈×C₇₁	—	2	2	no	—
162	C₄×Q₈×C₇₁	—	2	1	no	—
163	C₄×Q₈×C₇₁	—	2	2	no	—
164	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
168	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₇₁	—	2	1	no	—
171	C₄×D₄×C₇₁	—	2	2	no	—
172	C₄×D₄×C₇₁	—	2	4	no	—
173	C₄×D₄×C₇₁	—	2	2	no	—
174	C₄×D₄×C₇₁	—	2	1	no	—
175	C₄×D₄×C₇₁	—	2	1	no	—
176	C₄×D₄×C₇₁	—	2	1	no	—
177	C₄×D₄×C₇₁	—	2	2	no	—
178	C₄×D₄×C₇₁	—	2	1	no	—
179	C₄×D₄×C₇₁	—	2	2	no	—
180	C₄×D₄×C₇₁	—	2	2	no	—
181	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
182	C₄×D₄×C₇₁	D₄	1	2	yes	—
183	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₇₁	C₂³	1	2	yes	—
185	C₄×D₄×C₇₁	C₂³	1	2	yes	—
186	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₇₁	C₂³	1	2	yes	—
188	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₇₁	C₂³	1	2	yes	—
190	#117×C₇₁	—	2	2	no	—
191	#117×C₇₁	—	2	1	no	—
192	#117×C₇₁	—	2	1	no	—
193	#117×C₇₁	—	2	2	no	—
194	#117×C₇₁	D₄	1	2	yes	—
195	#117×C₇₁	D₄	1	1	yes	characteristic
196	#117×C₇₁	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
200	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
205	C₂×C₄²×C₇₁	—	2	1	no	—
206	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
208	#107×C₇₁	C₂³	1	2	yes	—
209	#107×C₇₁	C₂³	1	4	yes	—
210	#106×C₇₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
214	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
215	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
216	#103×C₇₁	C₂³	1	2	yes	—
217	#103×C₇₁	C₂³	1	4	yes	—
218	#103×C₇₁	C₂³	1	4	yes	—
219	#103×C₇₁	C₂³	1	4	yes	—
220	#103×C₇₁	C₂³	1	4	yes	—
221	#103×C₇₁	C₂³	1	2	yes	—
222	#103×C₇₁	C₂³	1	2	yes	—
223	#103×C₇₁	C₂³	1	4	yes	—
224	#102×C₇₁	C₂³	1	2	yes	—
225	#102×C₇₁	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
228	#97×C₇₁	C₂³	1	4	yes	—
229	C₄×C₈×C₇₁	C₂³	1	2	yes	—
230	C₂⁴×C₇₁	—	2	2	no	—
231	#41×C₇₁	—	2	4	no	—
232	#41×C₇₁	—	2	2	no	—
233	#41×C₇₁	—	4	1	no	—
234	#41×C₇₁	—	8	2	no	—
235	C₂×Q₈×C₇₁	—	2	1	no	—
236	C₂×Q₈×C₇₁	—	2	1	no	—
237	C₂×Q₈×C₇₁	—	2	2	no	—
238	C₂×Q₈×C₇₁	—	2	4	no	—
239	C₂×Q₈×C₇₁	—	4	4	no	—
240	C₂×Q₈×C₇₁	—	4	2	no	—
241	C₂×Q₈×C₇₁	—	4	4	no	—
242	C₂×Q₈×C₇₁	—	4	2	no	—
243	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₇₁	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₇₁	—	2	4	no	—
248	C₂×D₄×C₇₁	—	2	1	no	—
249	C₂×D₄×C₇₁	—	2	2	no	—
250	C₂×D₄×C₇₁	—	2	2	no	—
251	C₂×D₄×C₇₁	—	2	2	no	—
252	C₂×D₄×C₇₁	—	2	1	no	—
253	C₂×D₄×C₇₁	—	2	1	no	—
254	C₂×D₄×C₇₁	—	4	2	no	—
255	C₂×D₄×C₇₁	—	4	4	no	—
256	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
259	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇₁	—	2	2	no	—
261	C₂²×C₄×C₇₁	—	2	2	no	—
262	C₂²×C₄×C₇₁	—	2	4	no	—
263	C₂²×C₄×C₇₁	—	2	1	no	—
264	C₂²×C₄×C₇₁	—	2	1	no	—
265	C₂²×C₄×C₇₁	—	2	1	no	—
266	C₂²×C₄×C₇₁	—	2	2	no	—
267	C₂²×C₄×C₇₁	—	2	2	no	—
268	C₂²×C₄×C₇₁	—	2	2	no	—
269	C₂²×C₄×C₇₁	—	8	4	no	—
270	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
276	Q₁₆×C₇₁	—	4	2	no	—
277	Q₁₆×C₇₁	—	4	4	no	—
278	SD₁₆×C₇₁	—	2	4	no	—
279	SD₁₆×C₇₁	—	2	8	no	—
280	SD₁₆×C₇₁	—	4	4	no	—
281	SD₁₆×C₇₁	—	4	4	no	—
282	SD₁₆×C₇₁	—	4	4	no	—
283	M₁₆×C₇₁	—	4	2	no	—
284	C₂×C₈×C₇₁	—	4	4	no	—
285	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₇₁	—	2	1	no	—
289	C₄⋊C₄×C₇₁	—	2	2	no	—
290	C₄⋊C₄×C₇₁	—	2	1	no	—
291	C₄⋊C₄×C₇₁	—	2	2	no	—
292	C₄⋊C₄×C₇₁	—	2	1	no	—
293	C₄⋊C₄×C₇₁	—	2	2	no	—
294	C₄⋊C₄×C₇₁	—	2	4	no	—
295	C₄⋊C₄×C₇₁	—	2	2	no	—
296	C₄⋊C₄×C₇₁	—	2	4	no	—
297	C₄⋊C₄×C₇₁	—	2	2	no	—
298	C₄⋊C₄×C₇₁	—	2	2	no	—
299	C₄⋊C₄×C₇₁	—	2	1	no	—
300	C₄⋊C₄×C₇₁	—	2	1	no	—
301	C₄⋊C₄×C₇₁	—	2	1	no	—
302	C₄⋊C₄×C₇₁	—	2	2	no	—
303	C₄⋊C₄×C₇₁	—	2	2	no	—
304	C₄⋊C₄×C₇₁	—	2	2	no	—
305	C₄⋊C₄×C₇₁	—	2	4	no	—
306	C₄⋊C₄×C₇₁	—	2	4	no	—
307	C₄⋊C₄×C₇₁	—	2	2	no	—
308	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
316	C₂²⋊C₄×C₇₁	—	2	2	no	—
317	C₂²⋊C₄×C₇₁	—	2	2	no	—
318	C₂²⋊C₄×C₇₁	—	2	4	no	—
319	C₂²⋊C₄×C₇₁	—	2	1	no	—
320	C₂²⋊C₄×C₇₁	—	2	1	no	—
321	C₂²⋊C₄×C₇₁	—	2	2	no	—
322	C₂²⋊C₄×C₇₁	—	2	2	no	—
323	C₂²⋊C₄×C₇₁	—	2	2	no	—
324	C₂²⋊C₄×C₇₁	—	2	2	no	—
325	C₂²⋊C₄×C₇₁	—	2	2	no	—
326	C₂²⋊C₄×C₇₁	—	2	1	no	—
327	C₂²⋊C₄×C₇₁	—	2	2	no	—
328	C₂²⋊C₄×C₇₁	—	2	2	no	—
329	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
332	C₄²×C₇₁	—	2	1	no	—
333	C₄²×C₇₁	—	2	1	no	—
334	C₄²×C₇₁	—	2	1	no	—
335	C₄²×C₇₁	—	2	4	no	—
336	C₄²×C₇₁	—	2	2	no	—
337	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇₁	C₂×D₄	1	2	yes	—
340	C₄²×C₇₁	C₂×D₄	1	2	yes	—
341	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
342	C₄²×C₇₁	C₂⁴	1	2	yes	—
343	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
344	C₂³×C₇₁	—	2	1	no	—
345	C₂³×C₇₁	—	2	2	no	—
346	C₂³×C₇₁	—	4	4	no	—
347	C₂³×C₇₁	—	4	4	no	—
348	C₂³×C₇₁	—	8	2	no	—
349	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
350	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
351	Q₈×C₇₁	—	2	2	no	—
352	Q₈×C₇₁	—	2	2	no	—
353	Q₈×C₇₁	—	2	4	no	—
354	Q₈×C₇₁	—	2	1	no	—
355	Q₈×C₇₁	—	2	4	no	—
356	Q₈×C₇₁	—	2	1	no	—
357	Q₈×C₇₁	—	2	2	no	—
358	Q₈×C₇₁	—	4	2	no	—
359	Q₈×C₇₁	—	8	2	no	—
360	Q₈×C₇₁	—	8	4	no	—
361	Q₈×C₇₁	—	8	1	no	—
362	D₄×C₇₁	—	2	4	no	—
363	D₄×C₇₁	—	2	2	no	—
364	D₄×C₇₁	—	2	1	no	—
365	D₄×C₇₁	—	2	2	no	—
366	D₄×C₇₁	—	4	4	no	—
367	D₄×C₇₁	—	4	2	no	—
368	D₄×C₇₁	—	4	4	no	—
369	D₄×C₇₁	—	4	2	no	—
370	D₄×C₇₁	—	8	1	no	—
371	D₄×C₇₁	—	8	2	no	—
372	D₄×C₇₁	#137	1	4	yes	complemented
373	D₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
374	C₂×C₄×C₇₁	—	2	4	no	—
375	C₂×C₄×C₇₁	—	2	2	no	—
376	C₂×C₄×C₇₁	—	2	4	no	—
377	C₂×C₄×C₇₁	—	2	2	no	—
378	C₂×C₄×C₇₁	—	2	2	no	—
379	C₂×C₄×C₇₁	—	2	1	no	—
380	C₂×C₄×C₇₁	—	2	2	no	—
381	C₂×C₄×C₇₁	—	2	1	no	—
382	C₂×C₄×C₇₁	—	2	2	no	—
383	C₂×C₄×C₇₁	—	2	1	no	—
384	C₂×C₄×C₇₁	—	2	1	no	—
385	C₂×C₄×C₇₁	—	2	1	no	—
386	C₂×C₄×C₇₁	—	2	2	no	—
387	C₂×C₄×C₇₁	—	2	4	no	—
388	C₂×C₄×C₇₁	—	2	2	no	—
389	C₂×C₄×C₇₁	—	4	2	no	—
390	C₂×C₄×C₇₁	—	4	2	no	—
391	C₂×C₄×C₇₁	—	4	2	no	—
392	C₂×C₄×C₇₁	—	4	4	no	—
393	C₂×C₄×C₇₁	—	8	2	no	—
394	C₂×C₄×C₇₁	—	8	2	no	—
395	C₂×C₄×C₇₁	—	8	2	no	—
396	C₂×C₄×C₇₁	—	8	4	no	—
397	C₂×C₄×C₇₁	—	8	2	no	—
398	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
407	C₈×C₇₁	—	2	2	no	—
408	C₈×C₇₁	—	2	4	no	—
409	C₈×C₇₁	—	2	2	no	—
410	C₂²×C₇₁	—	2	2	no	—
411	C₂²×C₇₁	—	2	2	no	—
412	C₂²×C₇₁	—	2	1	no	—
413	C₂²×C₇₁	—	2	2	no	—
414	C₂²×C₇₁	—	2	1	no	—
415	C₂²×C₇₁	—	2	1	no	—
416	C₂²×C₇₁	—	4	1	no	—
417	C₂²×C₇₁	—	4	1	no	—
418	C₂²×C₇₁	—	4	2	no	—
419	C₂²×C₇₁	—	4	2	no	—
420	C₂²×C₇₁	—	4	2	no	—
421	C₂²×C₇₁	—	8	8	no	—
422	C₂²×C₇₁	C₂×#137	1	4	yes	—
423	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₇₁	—	2	1	no	—
425	C₄×C₇₁	—	2	2	no	—
426	C₄×C₇₁	—	2	1	no	—
427	C₄×C₇₁	—	2	2	no	—
428	C₄×C₇₁	—	2	2	no	—
429	C₄×C₇₁	—	2	1	no	—
430	C₄×C₇₁	—	4	1	no	—
431	C₄×C₇₁	—	4	2	no	—
432	C₄×C₇₁	—	4	4	no	—
433	C₄×C₇₁	—	4	1	no	—
434	C₄×C₇₁	—	4	1	no	—
435	C₄×C₇₁	—	4	2	no	—
436	C₄×C₇₁	—	4	2	no	—
437	C₄×C₇₁	C₂×#137	1	2	yes	—
438	C₄×C₇₁	#577	1	2	yes	—
439	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₄×C₇₁	#585	1	1	yes	characteristic
441	#61980	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂×C₇₁	—	2	4	no	—
443	C₂×C₇₁	—	4	1	no	—
444	C₂×C₇₁	—	4	2	no	—
445	C₂×C₇₁	—	8	2	no	—
446	C₂×C₇₁	#3488	1	1	yes	characteristic
447	C₂×C₇₁	C₂²×#137	1	1	yes	characteristic
448	C₂×C₇₁	C₂×#577	1	1	yes	characteristic
449	#3503	C₂×C₇₁	1	1	yes	characteristic, complemented
450	#3481	C₂×C₇₁	1	1	yes	characteristic
451	#3400	C₂×C₇₁	1	2	yes	complemented
452	#3372	C₂×C₇₁	1	2	yes	complemented
453	#3320	C₂×C₇₁	1	4	yes	complemented
454	#3299	C₂×C₇₁	1	2	yes	complemented
455	D₄×SD₁₆	C₂×C₇₁	1	2	yes	complemented
456	#3266	C₂×C₇₁	1	4	yes	complemented
457	#3254	C₂×C₇₁	1	1	yes	characteristic, complemented
458	#3248	C₂×C₇₁	1	2	yes	complemented
459	#3218	C₂×C₇₁	1	2	yes	complemented
460	#3206	C₂×C₇₁	1	1	yes	characteristic, complemented
461	#3110	C₂×C₇₁	1	2	yes	complemented
462	#3107	C₂×C₇₁	1	1	yes	characteristic, complemented
463	#3039	C₂×C₇₁	1	1	yes	characteristic, complemented
464	C₂×#461	C₂×C₇₁	1	2	yes	complemented
465	#2990	C₂×C₇₁	1	1	yes	characteristic, complemented
466	C₇₁	#61980	1	1	yes	characteristic, direct product factor, Sylow
467	C₂×#137	C₂²×C₇₁	1	2	yes	—
468	C₂²×SD₁₆	C₂²×C₇₁	1	4	yes	—
469	#559	C₂²×C₇₁	1	1	yes	characteristic
470	Q₈²	—	2	1	no	—
471	#557	C₂²×C₇₁	1	2	yes	complemented
472	#554	—	2	1	no	—
473	#554	—	2	2	no	—
474	#554	C₂²×C₇₁	1	1	yes	characteristic
475	#554	C₂²×C₇₁	1	1	yes	characteristic
476	#553	—	2	1	no	—
477	#553	C₂²×C₇₁	1	2	yes	—
478	#551	—	2	2	no	—
479	D₄×Q₈	C₂²×C₇₁	1	2	yes	—
480	D₄×Q₈	C₂²×C₇₁	1	4	yes	complemented
481	#546	—	2	1	no	—
482	#546	C₂²×C₇₁	1	2	yes	—
483	D₄²	C₂²×C₇₁	1	1	yes	characteristic
484	#544	—	2	2	no	—
485	#544	—	2	1	no	—
486	#533	C₂²×C₇₁	1	1	yes	characteristic, complemented
487	#533	C₂²×C₇₁	1	2	yes	complemented
488	#532	C₂²×C₇₁	1	1	yes	characteristic
489	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
490	C₂×C₄⋊Q₈	C₂²×C₇₁	1	2	yes	complemented
491	#529	—	2	1	no	—
492	#529	C₂²×C₇₁	1	2	yes	—
493	#525	—	2	2	no	—
494	#520	—	2	1	no	—
495	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
496	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
497	C₂×C₄×D₄	—	2	1	no	—
498	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
499	#497	C₂²×C₇₁	1	4	yes	complemented
500	#492	C₂²×C₇₁	1	2	yes	—
501	#491	C₂²×C₇₁	1	4	yes	complemented
502	#487	C₂²×C₇₁	1	2	yes	complemented
503	#485	C₂²×C₇₁	1	2	yes	complemented
504	#484	C₂²×C₇₁	1	4	yes	complemented
505	#479	C₂²×C₇₁	1	4	yes	complemented
506	#477	C₂²×C₇₁	1	2	yes	complemented
507	#475	C₂²×C₇₁	1	1	yes	characteristic, complemented
508	#474	C₂²×C₇₁	1	1	yes	characteristic
509	#474	C₂²×C₇₁	1	2	yes	complemented
510	#468	C₂²×C₇₁	1	4	yes	complemented
511	#467	C₂²×C₇₁	1	4	yes	complemented
512	#465	C₂²×C₇₁	1	4	yes	—
513	#464	C₂²×C₇₁	1	4	yes	complemented
514	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
515	#462	C₂²×C₇₁	1	2	yes	complemented
516	#462	C₂²×C₇₁	1	2	yes	complemented
517	#461	C₂²×C₇₁	1	1	yes	characteristic
518	#461	C₂²×C₇₁	1	2	yes	—
519	#461	C₂²×C₇₁	1	4	yes	—
520	#461	C₂²×C₇₁	1	2	yes	—
521	#461	C₂²×C₇₁	1	2	yes	complemented
522	#461	C₂²×C₇₁	1	4	yes	complemented
523	#461	C₂²×C₇₁	1	2	yes	complemented
524	#461	C₂²×C₇₁	1	2	yes	complemented
525	#460	C₂²×C₇₁	1	2	yes	—
526	#452	C₂²×C₇₁	1	2	yes	—
527	#451	C₂²×C₇₁	1	4	yes	complemented
528	#450	C₂²×C₇₁	1	4	yes	—
529	#448	C₂²×C₇₁	1	4	yes	—
530	#448	C₂²×C₇₁	1	4	yes	complemented
531	#446	C₂²×C₇₁	1	2	yes	complemented
532	#440	C₂²×C₇₁	1	4	yes	—
533	#440	C₂²×C₇₁	1	4	yes	complemented
534	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
535	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	—
536	#435	C₂²×C₇₁	1	4	yes	complemented
537	C₈×D₄	C₂²×C₇₁	1	2	yes	—
538	#432	C₂²×C₇₁	1	2	yes	complemented
539	#431	C₂²×C₇₁	1	1	yes	characteristic, complemented
540	#423	C₂²×C₇₁	1	1	yes	characteristic, complemented
541	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	complemented
542	#419	C₂²×C₇₁	1	2	yes	complemented
543	C₂×#103	C₂²×C₇₁	1	4	yes	complemented
544	C₂×#41	—	2	1	no	—
545	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
546	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₇₁	1	4	yes	—
548	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
551	C₂³×C₄	—	2	2	no	—
552	#137	—	4	4	no	—
553	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
554	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
555	C₂×SD₁₆	—	4	8	no	—
556	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
559	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
560	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
561	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
562	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
563	C₄⋊Q₈	—	2	2	no	—
564	C₄⋊Q₈	—	2	4	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	—	2	2	no	—
567	C₄⋊Q₈	—	2	1	no	—
568	C₄⋊Q₈	—	2	2	no	—
569	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
570	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
571	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
572	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
573	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
574	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
575	#127	C₂³×C₇₁	1	1	yes	characteristic
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#125	—	2	1	no	—
579	#125	—	2	2	no	—
580	#125	—	2	4	no	—
581	#125	—	2	1	no	—
582	#125	—	2	2	no	—
583	#125	C₂³×C₇₁	1	2	yes	—
584	#124	—	2	1	no	—
585	#124	—	2	1	no	—
586	#124	C₂³×C₇₁	1	2	yes	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	4	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
601	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
602	#121	—	2	2	no	—
603	#121	—	2	1	no	—
604	#121	—	2	1	no	—
605	#121	—	2	2	no	—
606	#121	C₂³×C₇₁	1	2	yes	—
607	#121	C₂³×C₇₁	1	2	yes	—
608	#120	—	2	2	no	—
609	#120	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
617	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
618	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
631	C₄×D₄	D₄×C₇₁	1	2	yes	—
632	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₇₁	1	2	yes	—
634	C₄×D₄	C₂³×C₇₁	1	2	yes	—
635	C₄×D₄	C₂³×C₇₁	1	2	yes	—
636	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
638	C₄×D₄	C₂³×C₇₁	1	2	yes	—
639	#117	—	2	2	no	—
640	#117	—	2	1	no	—
641	#117	—	2	1	no	—
642	#117	—	2	2	no	—
643	#117	D₄×C₇₁	1	2	yes	—
644	#117	D₄×C₇₁	1	1	yes	characteristic
645	#117	C₂³×C₇₁	1	1	yes	characteristic
646	C₂×C₄⋊C₄	—	2	2	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
656	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
657	#107	C₂³×C₇₁	1	2	yes	—
658	#107	C₂³×C₇₁	1	4	yes	—
659	#106	C₂³×C₇₁	1	2	yes	—
660	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
661	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
662	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
663	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
664	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
665	#103	C₂³×C₇₁	1	2	yes	—
666	#103	C₂³×C₇₁	1	4	yes	—
667	#103	C₂³×C₇₁	1	4	yes	—
668	#103	C₂³×C₇₁	1	4	yes	—
669	#103	C₂³×C₇₁	1	4	yes	—
670	#103	C₂³×C₇₁	1	2	yes	—
671	#103	C₂³×C₇₁	1	2	yes	—
672	#103	C₂³×C₇₁	1	4	yes	—
673	#102	C₂³×C₇₁	1	2	yes	—
674	#102	C₂³×C₇₁	1	4	yes	—
675	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
677	#97	C₂³×C₇₁	1	4	yes	—
678	C₄×C₈	C₂³×C₇₁	1	2	yes	—
679	C₂⁴	—	2	2	no	—
680	#41	—	2	4	no	—
681	#41	—	2	2	no	—
682	#41	—	4	1	no	—
683	#41	—	8	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	4	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	4	no	—
691	C₂×Q₈	—	4	2	no	—
692	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
693	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
694	C₂×Q₈	C₂⁴×C₇₁	1	4	yes	—
695	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
708	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	8	4	no	—
719	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
720	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
725	Q₁₆	—	4	2	no	—
726	Q₁₆	—	4	4	no	—
727	SD₁₆	—	2	4	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	4	4	no	—
730	SD₁₆	—	4	4	no	—
731	SD₁₆	—	4	4	no	—
732	M₁₆	—	4	2	no	—
733	C₂×C₈	—	4	4	no	—
734	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
735	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
736	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
758	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
759	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	1	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	2	no	—
786	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
787	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₇₁	1	2	yes	—
789	C₄²	C₂×D₄×C₇₁	1	2	yes	—
790	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
791	C₄²	C₂⁴×C₇₁	1	2	yes	—
792	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	4	no	—
796	C₂³	—	4	4	no	—
797	C₂³	—	8	2	no	—
798	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
799	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	4	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	2	4	no	—
805	Q₈	—	2	1	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	—	8	4	no	—
810	Q₈	—	8	1	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	1	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	2	no	—
819	D₄	—	8	1	no	—
820	D₄	—	8	2	no	—
821	D₄	#137×C₇₁	1	4	yes	complemented
822	D₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	2	no	—
844	C₂×C₄	—	8	2	no	—
845	C₂×C₄	—	8	4	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
851	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
855	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
856	C₈	—	2	2	no	—
857	C₈	—	2	4	no	—
858	C₈	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	8	8	no	—
871	C₂²	C₂×#137×C₇₁	1	4	yes	—
872	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	4	no	—
886	C₄	C₂×#137×C₇₁	1	2	yes	—
887	C₄	#577×C₇₁	1	2	yes	—
888	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
889	C₄	#585×C₇₁	1	1	yes	characteristic
890	C₂	—	2	4	no	—
891	C₂	—	4	1	no	—
892	C₂	—	4	2	no	—
893	C₂	—	8	2	no	—
894	C₂	C₇₁×#3488	1	1	yes	characteristic
895	C₂	C₂²×#137×C₇₁	1	1	yes	characteristic
896	C₂	C₂×#577×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₇₁×#3481	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₄×#41×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3503	C₂	semidirect
3. C₇₁×#3400	C₂	semidirect
4. C₇₁×#3372	C₂	semidirect
5. C₇₁×#3320	C₂	semidirect
6. C₇₁×#3299	C₂	semidirect
7. D₄×SD₁₆×C₇₁	C₂	semidirect
8. C₇₁×#3266	C₂	semidirect
9. C₇₁×#3254	C₂	semidirect
10. C₇₁×#3248	C₂	semidirect
11. C₇₁×#3218	C₂	semidirect
12. C₇₁×#3206	C₂	semidirect
13. C₇₁×#3110	C₂	semidirect
14. C₇₁×#3107	C₂	semidirect
15. C₇₁×#3039	C₂	semidirect
16. C₂×#461×C₇₁	C₂	semidirect
17. C₇₁×#2990	C₂	semidirect
22. #557×C₇₁	C₂²	semidirect
31. D₄×Q₈×C₇₁	C₂²	semidirect
37. #533×C₇₁	C₂²	semidirect
38. #533×C₇₁	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₇₁	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₇₁	C₂²	semidirect
50. #497×C₇₁	C₂²	semidirect
52. #491×C₇₁	C₂²	semidirect
53. #487×C₇₁	C₂²	semidirect
54. #485×C₇₁	C₂²	semidirect
55. #484×C₇₁	C₂²	semidirect
56. #479×C₇₁	C₂²	semidirect
57. #477×C₇₁	C₂²	semidirect
58. #475×C₇₁	C₂²	semidirect
60. #474×C₇₁	C₂²	semidirect
61. #468×C₇₁	C₂²	semidirect
62. #467×C₇₁	C₂²	semidirect
64. #464×C₇₁	C₂²	semidirect
65. #462×C₇₁	C₂²	semidirect
66. #462×C₇₁	C₂²	semidirect
67. #462×C₇₁	C₂²	semidirect
72. #461×C₇₁	C₂²	semidirect
73. #461×C₇₁	C₂²	semidirect
74. #461×C₇₁	C₂²	semidirect
75. #461×C₇₁	C₂²	semidirect
78. #451×C₇₁	C₂²	semidirect
81. #448×C₇₁	C₂²	semidirect
82. #446×C₇₁	C₂²	semidirect
84. #440×C₇₁	C₂²	semidirect
85. C₄×Q₁₆×C₇₁	C₂²	semidirect
87. #435×C₇₁	C₂²	semidirect
89. #432×C₇₁	C₂²	semidirect
90. #431×C₇₁	C₂²	semidirect
91. #423×C₇₁	C₂²	semidirect
92. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
93. #419×C₇₁	C₂²	semidirect
94. C₂×#103×C₇₁	C₂²	semidirect
372. D₄×C₇₁	#137	semidirect
441. #61980	C₇₁	direct (N × H)
449. #3503	C₂×C₇₁	semidirect
451. #3400	C₂×C₇₁	semidirect
452. #3372	C₂×C₇₁	semidirect
453. #3320	C₂×C₇₁	semidirect
454. #3299	C₂×C₇₁	semidirect
455. D₄×SD₁₆	C₂×C₇₁	semidirect
456. #3266	C₂×C₇₁	semidirect
457. #3254	C₂×C₇₁	semidirect
458. #3248	C₂×C₇₁	semidirect
459. #3218	C₂×C₇₁	semidirect
460. #3206	C₂×C₇₁	semidirect
461. #3110	C₂×C₇₁	semidirect
462. #3107	C₂×C₇₁	semidirect
463. #3039	C₂×C₇₁	semidirect
464. C₂×#461	C₂×C₇₁	semidirect
465. #2990	C₂×C₇₁	semidirect
466. C₇₁	#61980	direct (N × H)
471. #557	C₂²×C₇₁	semidirect
480. D₄×Q₈	C₂²×C₇₁	semidirect
486. #533	C₂²×C₇₁	semidirect
487. #533	C₂²×C₇₁	semidirect
489. C₂×C₄⋊Q₈	C₂²×C₇₁	semidirect
490. C₂×C₄⋊Q₈	C₂²×C₇₁	semidirect
499. #497	C₂²×C₇₁	semidirect
501. #491	C₂²×C₇₁	semidirect
502. #487	C₂²×C₇₁	semidirect
503. #485	C₂²×C₇₁	semidirect
504. #484	C₂²×C₇₁	semidirect
505. #479	C₂²×C₇₁	semidirect
506. #477	C₂²×C₇₁	semidirect
507. #475	C₂²×C₇₁	semidirect
509. #474	C₂²×C₇₁	semidirect
510. #468	C₂²×C₇₁	semidirect
511. #467	C₂²×C₇₁	semidirect
513. #464	C₂²×C₇₁	semidirect
514. #462	C₂²×C₇₁	semidirect
515. #462	C₂²×C₇₁	semidirect
516. #462	C₂²×C₇₁	semidirect
521. #461	C₂²×C₇₁	semidirect
522. #461	C₂²×C₇₁	semidirect
523. #461	C₂²×C₇₁	semidirect
524. #461	C₂²×C₇₁	semidirect
527. #451	C₂²×C₇₁	semidirect
530. #448	C₂²×C₇₁	semidirect
531. #446	C₂²×C₇₁	semidirect
533. #440	C₂²×C₇₁	semidirect
534. C₄×Q₁₆	C₂²×C₇₁	semidirect
536. #435	C₂²×C₇₁	semidirect
538. #432	C₂²×C₇₁	semidirect
539. #431	C₂²×C₇₁	semidirect
540. #423	C₂²×C₇₁	semidirect
541. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
542. #419	C₂²×C₇₁	semidirect
543. C₂×#103	C₂²×C₇₁	semidirect
821. D₄	#137×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#3503	2
C₇₁×#3481	2
C₇₁×#3400	2
C₇₁×#3372	2
C₇₁×#3320	2
C₇₁×#3299	2
D₄×SD₁₆×C₇₁	2
C₇₁×#3266	2
C₇₁×#3254	2
C₇₁×#3248	2
C₇₁×#3218	2
C₇₁×#3206	2
C₇₁×#3110	2
C₇₁×#3107	2
C₇₁×#3039	2
C₂×#461×C₇₁	2
C₇₁×#2990	2
#61980	71

Subgroups — C71×#61980 #31882852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61980 #31882852