Subgroups — C₇₁×#61996 #31882868

Order 18176.

1914 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3394	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3331	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3326	C₂	1	4	yes	maximal, complemented
7	C₇₁×#3275	C₂	1	4	yes	maximal, complemented
8	C₇₁×#3272	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3252	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3101	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#3036	C₂	1	2	yes	maximal, complemented
17	C₇₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₇₁	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	4	yes	—
20	#559×C₇₁	C₂²	1	1	yes	characteristic
21	#556×C₇₁	C₂²	1	2	yes	complemented
22	#555×C₇₁	—	2	1	no	—
23	#554×C₇₁	—	2	1	no	—
24	#554×C₇₁	C₂²	1	1	yes	characteristic
25	#554×C₇₁	C₂²	1	1	yes	characteristic
26	#553×C₇₁	—	2	2	no	—
27	#553×C₇₁	—	2	1	no	—
28	#553×C₇₁	C₂²	1	2	yes	—
29	#551×C₇₁	—	2	2	no	—
30	#548×C₇₁	C₂²	1	4	yes	complemented
31	#547×C₇₁	C₂²	1	2	yes	—
32	#546×C₇₁	—	2	1	no	—
33	#546×C₇₁	C₂²	1	2	yes	—
34	D₄²×C₇₁	C₂²	1	1	yes	characteristic
35	#542×C₇₁	—	2	2	no	—
36	#537×C₇₁	—	2	1	no	—
37	#533×C₇₁	C₂²	1	2	yes	complemented
38	#532×C₇₁	C₂²	1	1	yes	characteristic
39	#532×C₇₁	C₂²	1	2	yes	complemented
40	#532×C₇₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic, 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	#495×C₇₁	C₂²	1	4	yes	complemented
51	#492×C₇₁	C₂²	1	2	yes	—
52	#488×C₇₁	C₂²	1	4	yes	complemented
53	#487×C₇₁	C₂²	1	2	yes	complemented
54	#483×C₇₁	C₂²	1	4	yes	complemented
55	#482×C₇₁	C₂²	1	2	yes	complemented
56	#479×C₇₁	C₂²	1	4	yes	complemented
57	#477×C₇₁	C₂²	1	1	yes	characteristic, complemented
58	#476×C₇₁	C₂²	1	1	yes	characteristic
59	#476×C₇₁	C₂²	1	2	yes	complemented
60	#476×C₇₁	C₂²	1	2	yes	complemented
61	#470×C₇₁	C₂²	1	4	yes	complemented
62	#469×C₇₁	C₂²	1	4	yes	complemented
63	#468×C₇₁	C₂²	1	4	yes	—
64	#464×C₇₁	C₂²	1	4	yes	complemented
65	#463×C₇₁	C₂²	1	4	yes	—
66	#463×C₇₁	C₂²	1	4	yes	complemented
67	#462×C₇₁	C₂²	1	2	yes	complemented
68	#462×C₇₁	C₂²	1	2	yes	complemented
69	#461×C₇₁	C₂²	1	2	yes	—
70	#461×C₇₁	C₂²	1	2	yes	—
71	#461×C₇₁	C₂²	1	2	yes	complemented
72	#461×C₇₁	C₂²	1	2	yes	complemented
73	#460×C₇₁	C₂²	1	1	yes	characteristic, complemented
74	#459×C₇₁	C₂²	1	1	yes	characteristic
75	#459×C₇₁	C₂²	1	2	yes	—
76	#459×C₇₁	C₂²	1	2	yes	complemented
77	#452×C₇₁	C₂²	1	4	yes	complemented
78	#450×C₇₁	C₂²	1	4	yes	—
79	#449×C₇₁	C₂²	1	4	yes	—
80	#449×C₇₁	C₂²	1	2	yes	—
81	#448×C₇₁	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₇₁	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₇₁	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
86	C₄×D₈×C₇₁	C₂²	1	2	yes	—
87	#436×C₇₁	C₂²	1	2	yes	—
88	#436×C₇₁	C₂²	1	4	yes	complemented
89	#431×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	#423×C₇₁	C₂²	1	2	yes	complemented
93	#419×C₇₁	C₂²	1	2	yes	complemented
94	#417×C₇₁	C₂²	1	4	yes	complemented
95	C₂×#41×C₇₁	—	2	1	no	—
96	C₂×#41×C₇₁	—	2	1	no	—
97	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₇₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
101	C₂²×D₄×C₇₁	—	2	1	no	—
102	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₇₁	—	2	2	no	—
104	#137×C₇₁	—	4	4	no	—
105	AGL(1,ℤ/8)×C₇₁	—	4	8	no	—
106	C₂×Q₁₆×C₇₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
111	C₂×D₈×C₇₁	C₂³	1	2	yes	—
112	C₂×D₈×C₇₁	C₂³	1	4	yes	—
113	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
114	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₇₁	—	2	1	no	—
116	C₄⋊Q₈×C₇₁	—	2	1	no	—
117	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
121	#127×C₇₁	C₂³	1	1	yes	characteristic
122	#127×C₇₁	C₂³	1	1	yes	characteristic
123	#126×C₇₁	—	2	2	no	—
124	#126×C₇₁	—	2	4	no	—
125	#126×C₇₁	—	2	2	no	—
126	#125×C₇₁	—	2	1	no	—
127	#125×C₇₁	—	2	2	no	—
128	#125×C₇₁	C₂³	1	2	yes	—
129	#124×C₇₁	—	2	1	no	—
130	#124×C₇₁	—	2	4	no	—
131	#124×C₇₁	—	2	1	no	—
132	#124×C₇₁	—	2	1	no	—
133	#124×C₇₁	C₂³	1	4	yes	—
134	#124×C₇₁	C₂³	1	2	yes	—
135	#123×C₇₁	—	2	2	no	—
136	#123×C₇₁	—	2	2	no	—
137	#123×C₇₁	—	2	2	no	—
138	#123×C₇₁	—	2	2	no	—
139	#123×C₇₁	—	2	4	no	—
140	C₂²⋊Q₈×C₇₁	—	2	1	no	—
141	C₂²⋊Q₈×C₇₁	—	2	2	no	—
142	C₂²⋊Q₈×C₇₁	—	2	2	no	—
143	C₂²⋊Q₈×C₇₁	—	2	2	no	—
144	C₂²⋊Q₈×C₇₁	—	2	4	no	—
145	C₂²⋊Q₈×C₇₁	—	2	2	no	—
146	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
148	#121×C₇₁	—	2	2	no	—
149	#121×C₇₁	—	2	2	no	—
150	#121×C₇₁	—	2	4	no	—
151	#121×C₇₁	—	2	1	no	—
152	#121×C₇₁	—	2	2	no	—
153	#121×C₇₁	—	2	1	no	—
154	#121×C₇₁	—	2	2	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	#121×C₇₁	C₂³	1	2	yes	—
160	#120×C₇₁	—	2	2	no	—
161	#120×C₇₁	—	2	2	no	—
162	C₄×Q₈×C₇₁	—	2	2	no	—
163	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
165	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₇₁	—	2	1	no	—
169	C₄×D₄×C₇₁	—	2	2	no	—
170	C₄×D₄×C₇₁	—	2	1	no	—
171	C₄×D₄×C₇₁	—	2	1	no	—
172	C₄×D₄×C₇₁	—	2	1	no	—
173	C₄×D₄×C₇₁	—	2	2	no	—
174	C₄×D₄×C₇₁	—	2	4	no	—
175	C₄×D₄×C₇₁	—	2	1	no	—
176	C₄×D₄×C₇₁	—	2	2	no	—
177	C₄×D₄×C₇₁	—	2	2	no	—
178	C₄×D₄×C₇₁	—	2	2	no	—
179	C₄×D₄×C₇₁	—	2	2	no	—
180	C₄×D₄×C₇₁	—	2	1	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	2	yes	—
187	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₇₁	C₂³	1	2	yes	—
189	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₇₁	C₂³	1	2	yes	—
191	#117×C₇₁	—	2	2	no	—
192	#117×C₇₁	—	2	2	no	—
193	#117×C₇₁	—	2	1	no	—
194	#117×C₇₁	—	2	2	no	—
195	#117×C₇₁	D₄	1	1	yes	characteristic
196	#117×C₇₁	D₄	1	2	yes	—
197	#117×C₇₁	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₇₁	—	2	2	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	#106×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	2	yes	—
214	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
215	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
216	#103×C₇₁	C₂³	1	4	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	2	yes	—
221	#102×C₇₁	C₂³	1	2	yes	—
222	#102×C₇₁	C₂³	1	4	yes	—
223	#102×C₇₁	C₂³	1	2	yes	—
224	#102×C₇₁	C₂³	1	2	yes	—
225	#102×C₇₁	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
228	C₄×C₈×C₇₁	C₂³	1	2	yes	—
229	C₄×C₈×C₇₁	C₂³	1	4	yes	—
230	C₂⁴×C₇₁	—	2	2	no	—
231	#41×C₇₁	—	2	2	no	—
232	#41×C₇₁	—	4	2	no	—
233	#41×C₇₁	—	4	1	no	—
234	#41×C₇₁	—	4	4	no	—
235	#41×C₇₁	—	4	4	no	—
236	#41×C₇₁	—	4	4	no	—
237	#41×C₇₁	—	8	2	no	—
238	C₂×Q₈×C₇₁	—	2	1	no	—
239	C₂×Q₈×C₇₁	—	2	1	no	—
240	C₂×Q₈×C₇₁	—	2	2	no	—
241	C₂×Q₈×C₇₁	—	4	2	no	—
242	C₂×Q₈×C₇₁	—	4	2	no	—
243	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₇₁	C₂⁴	1	4	yes	—
245	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₇₁	—	2	4	no	—
247	C₂×D₄×C₇₁	—	2	1	no	—
248	C₂×D₄×C₇₁	—	2	2	no	—
249	C₂×D₄×C₇₁	—	2	2	no	—
250	C₂×D₄×C₇₁	—	2	2	no	—
251	C₂×D₄×C₇₁	—	2	4	no	—
252	C₂×D₄×C₇₁	—	2	1	no	—
253	C₂×D₄×C₇₁	—	2	2	no	—
254	C₂×D₄×C₇₁	—	2	1	no	—
255	C₂×D₄×C₇₁	—	2	1	no	—
256	C₂×D₄×C₇₁	—	2	1	no	—
257	C₂×D₄×C₇₁	—	4	2	no	—
258	C₂×D₄×C₇₁	—	4	4	no	—
259	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
262	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
263	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₇₁	—	2	2	no	—
265	C₂²×C₄×C₇₁	—	2	2	no	—
266	C₂²×C₄×C₇₁	—	2	1	no	—
267	C₂²×C₄×C₇₁	—	2	1	no	—
268	C₂²×C₄×C₇₁	—	2	1	no	—
269	C₂²×C₄×C₇₁	—	2	2	no	—
270	C₂²×C₄×C₇₁	—	2	2	no	—
271	C₂²×C₄×C₇₁	—	2	2	no	—
272	C₂²×C₄×C₇₁	—	2	4	no	—
273	C₂²×C₄×C₇₁	—	2	2	no	—
274	C₂²×C₄×C₇₁	—	8	4	no	—
275	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
281	Q₁₆×C₇₁	—	4	4	no	—
282	SD₁₆×C₇₁	—	2	8	no	—
283	SD₁₆×C₇₁	—	4	4	no	—
284	SD₁₆×C₇₁	—	4	2	no	—
285	SD₁₆×C₇₁	—	4	4	no	—
286	D₈×C₇₁	—	2	4	no	—
287	D₈×C₇₁	—	4	4	no	—
288	M₁₆×C₇₁	—	4	4	no	—
289	M₁₆×C₇₁	—	4	2	no	—
290	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
291	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
292	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₇₁	—	2	2	no	—
294	C₄⋊C₄×C₇₁	—	2	2	no	—
295	C₄⋊C₄×C₇₁	—	2	1	no	—
296	C₄⋊C₄×C₇₁	—	2	2	no	—
297	C₄⋊C₄×C₇₁	—	2	2	no	—
298	C₄⋊C₄×C₇₁	—	2	4	no	—
299	C₄⋊C₄×C₇₁	—	2	2	no	—
300	C₄⋊C₄×C₇₁	—	2	2	no	—
301	C₄⋊C₄×C₇₁	—	2	1	no	—
302	C₄⋊C₄×C₇₁	—	2	1	no	—
303	C₄⋊C₄×C₇₁	—	2	1	no	—
304	C₄⋊C₄×C₇₁	—	2	2	no	—
305	C₄⋊C₄×C₇₁	—	2	2	no	—
306	C₄⋊C₄×C₇₁	—	2	4	no	—
307	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
311	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
315	C₂²⋊C₄×C₇₁	—	2	2	no	—
316	C₂²⋊C₄×C₇₁	—	2	4	no	—
317	C₂²⋊C₄×C₇₁	—	2	1	no	—
318	C₂²⋊C₄×C₇₁	—	2	1	no	—
319	C₂²⋊C₄×C₇₁	—	2	2	no	—
320	C₂²⋊C₄×C₇₁	—	2	2	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	4	no	—
325	C₂²⋊C₄×C₇₁	—	2	1	no	—
326	C₂²⋊C₄×C₇₁	—	2	2	no	—
327	C₂²⋊C₄×C₇₁	—	2	2	no	—
328	C₂²⋊C₄×C₇₁	—	2	4	no	—
329	C₂²⋊C₄×C₇₁	—	2	2	no	—
330	C₂²⋊C₄×C₇₁	—	2	2	no	—
331	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
334	C₄²×C₇₁	—	2	1	no	—
335	C₄²×C₇₁	—	2	1	no	—
336	C₄²×C₇₁	—	2	1	no	—
337	C₄²×C₇₁	—	2	4	no	—
338	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₇₁	C₂×D₄	1	2	yes	—
341	C₄²×C₇₁	C₂×D₄	1	2	yes	—
342	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
343	C₄²×C₇₁	C₂⁴	1	2	yes	—
344	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
345	C₂³×C₇₁	—	2	1	no	—
346	C₂³×C₇₁	—	2	2	no	—
347	C₂³×C₇₁	—	2	2	no	—
348	C₂³×C₇₁	—	4	4	no	—
349	C₂³×C₇₁	—	4	4	no	—
350	C₂³×C₇₁	—	8	2	no	—
351	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
352	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
353	Q₈×C₇₁	—	2	2	no	—
354	Q₈×C₇₁	—	2	4	no	—
355	Q₈×C₇₁	—	2	1	no	—
356	Q₈×C₇₁	—	2	1	no	—
357	Q₈×C₇₁	—	2	4	no	—
358	Q₈×C₇₁	—	4	2	no	—
359	Q₈×C₇₁	—	8	2	no	—
360	Q₈×C₇₁	—	8	1	no	—
361	D₄×C₇₁	—	2	2	no	—
362	D₄×C₇₁	—	2	2	no	—
363	D₄×C₇₁	—	2	2	no	—
364	D₄×C₇₁	—	2	1	no	—
365	D₄×C₇₁	—	2	2	no	—
366	D₄×C₇₁	—	2	2	no	—
367	D₄×C₇₁	—	4	2	no	—
368	D₄×C₇₁	—	4	4	no	—
369	D₄×C₇₁	—	4	2	no	—
370	D₄×C₇₁	—	4	2	no	—
371	D₄×C₇₁	—	4	4	no	—
372	D₄×C₇₁	—	4	4	no	—
373	D₄×C₇₁	—	4	2	no	—
374	D₄×C₇₁	—	4	2	no	—
375	D₄×C₇₁	—	8	1	no	—
376	D₄×C₇₁	—	8	4	no	—
377	D₄×C₇₁	—	8	2	no	—
378	D₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄×C₇₁	—	2	2	no	—
380	C₂×C₄×C₇₁	—	2	4	no	—
381	C₂×C₄×C₇₁	—	2	2	no	—
382	C₂×C₄×C₇₁	—	2	2	no	—
383	C₂×C₄×C₇₁	—	2	1	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	1	no	—
390	C₂×C₄×C₇₁	—	2	4	no	—
391	C₂×C₄×C₇₁	—	2	2	no	—
392	C₂×C₄×C₇₁	—	4	2	no	—
393	C₂×C₄×C₇₁	—	4	2	no	—
394	C₂×C₄×C₇₁	—	4	2	no	—
395	C₂×C₄×C₇₁	—	4	4	no	—
396	C₂×C₄×C₇₁	—	4	2	no	—
397	C₂×C₄×C₇₁	—	4	4	no	—
398	C₂×C₄×C₇₁	—	8	2	no	—
399	C₂×C₄×C₇₁	—	8	2	no	—
400	C₂×C₄×C₇₁	—	8	4	no	—
401	C₂×C₄×C₇₁	—	8	2	no	—
402	C₂×C₄×C₇₁	—	8	2	no	—
403	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
412	C₈×C₇₁	—	2	2	no	—
413	C₈×C₇₁	—	2	4	no	—
414	C₈×C₇₁	—	2	2	no	—
415	C₂²×C₇₁	—	2	1	no	—
416	C₂²×C₇₁	—	2	2	no	—
417	C₂²×C₇₁	—	2	2	no	—
418	C₂²×C₇₁	—	2	1	no	—
419	C₂²×C₇₁	—	2	2	no	—
420	C₂²×C₇₁	—	2	2	no	—
421	C₂²×C₇₁	—	2	1	no	—
422	C₂²×C₇₁	—	4	1	no	—
423	C₂²×C₇₁	—	4	1	no	—
424	C₂²×C₇₁	—	4	2	no	—
425	C₂²×C₇₁	—	4	2	no	—
426	C₂²×C₇₁	—	4	2	no	—
427	C₂²×C₇₁	—	4	2	no	—
428	C₂²×C₇₁	—	4	2	no	—
429	C₂²×C₇₁	—	4	2	no	—
430	C₂²×C₇₁	—	8	8	no	—
431	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
432	C₄×C₇₁	—	2	1	no	—
433	C₄×C₇₁	—	2	2	no	—
434	C₄×C₇₁	—	2	1	no	—
435	C₄×C₇₁	—	2	2	no	—
436	C₄×C₇₁	—	2	2	no	—
437	C₄×C₇₁	—	2	1	no	—
438	C₄×C₇₁	—	4	1	no	—
439	C₄×C₇₁	—	4	4	no	—
440	C₄×C₇₁	—	4	1	no	—
441	C₄×C₇₁	—	4	2	no	—
442	C₄×C₇₁	—	4	1	no	—
443	C₄×C₇₁	—	4	2	no	—
444	C₄×C₇₁	#575	1	2	yes	—
445	C₄×C₇₁	#577	1	2	yes	—
446	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
447	C₄×C₇₁	#585	1	1	yes	characteristic
448	#61996	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂×C₇₁	—	4	1	no	—
450	C₂×C₇₁	—	4	2	no	—
451	C₂×C₇₁	—	4	2	no	—
452	C₂×C₇₁	—	8	2	no	—
453	C₂×C₇₁	—	8	2	no	—
454	C₂×C₇₁	#3488	1	1	yes	characteristic
455	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
456	C₂×C₇₁	C₂×#577	1	1	yes	characteristic
457	#3511	C₂×C₇₁	1	1	yes	characteristic, complemented
458	#3481	C₂×C₇₁	1	1	yes	characteristic, complemented
459	#3394	C₂×C₇₁	1	2	yes	complemented
460	#3360	C₂×C₇₁	1	2	yes	complemented
461	#3331	C₂×C₇₁	1	2	yes	complemented
462	#3326	C₂×C₇₁	1	4	yes	complemented
463	#3275	C₂×C₇₁	1	4	yes	complemented
464	#3272	C₂×C₇₁	1	2	yes	complemented
465	#3253	C₂×C₇₁	1	1	yes	characteristic, complemented
466	#3252	C₂×C₇₁	1	2	yes	complemented
467	#3212	C₂×C₇₁	1	2	yes	complemented
468	#3206	C₂×C₇₁	1	1	yes	characteristic, complemented
469	#3106	C₂×C₇₁	1	1	yes	characteristic, complemented
470	#3101	C₂×C₇₁	1	2	yes	complemented
471	#3039	C₂×C₇₁	1	1	yes	characteristic, complemented
472	#3036	C₂×C₇₁	1	2	yes	complemented
473	#2991	C₂×C₇₁	1	1	yes	characteristic, complemented
474	C₇₁	#61996	1	1	yes	characteristic, direct product factor, Sylow
475	C₂×#137	C₂²×C₇₁	1	2	yes	—
476	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	4	yes	—
477	#559	C₂²×C₇₁	1	1	yes	characteristic
478	#556	C₂²×C₇₁	1	2	yes	complemented
479	#555	—	2	1	no	—
480	#554	—	2	1	no	—
481	#554	C₂²×C₇₁	1	1	yes	characteristic
482	#554	C₂²×C₇₁	1	1	yes	characteristic
483	#553	—	2	2	no	—
484	#553	—	2	1	no	—
485	#553	C₂²×C₇₁	1	2	yes	—
486	#551	—	2	2	no	—
487	#548	C₂²×C₇₁	1	4	yes	complemented
488	#547	C₂²×C₇₁	1	2	yes	—
489	#546	—	2	1	no	—
490	#546	C₂²×C₇₁	1	2	yes	—
491	D₄²	C₂²×C₇₁	1	1	yes	characteristic
492	#542	—	2	2	no	—
493	#537	—	2	1	no	—
494	#533	C₂²×C₇₁	1	2	yes	complemented
495	#532	C₂²×C₇₁	1	1	yes	characteristic
496	#532	C₂²×C₇₁	1	2	yes	complemented
497	#532	C₂²×C₇₁	1	1	yes	characteristic, complemented
498	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
499	#529	—	2	1	no	—
500	#529	C₂²×C₇₁	1	2	yes	—
501	#525	—	2	2	no	—
502	#520	—	2	1	no	—
503	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
504	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
505	C₂×C₄×D₄	—	2	1	no	—
506	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
507	#495	C₂²×C₇₁	1	4	yes	complemented
508	#492	C₂²×C₇₁	1	2	yes	—
509	#488	C₂²×C₇₁	1	4	yes	complemented
510	#487	C₂²×C₇₁	1	2	yes	complemented
511	#483	C₂²×C₇₁	1	4	yes	complemented
512	#482	C₂²×C₇₁	1	2	yes	complemented
513	#479	C₂²×C₇₁	1	4	yes	complemented
514	#477	C₂²×C₇₁	1	1	yes	characteristic, complemented
515	#476	C₂²×C₇₁	1	1	yes	characteristic
516	#476	C₂²×C₇₁	1	2	yes	complemented
517	#476	C₂²×C₇₁	1	2	yes	complemented
518	#470	C₂²×C₇₁	1	4	yes	complemented
519	#469	C₂²×C₇₁	1	4	yes	complemented
520	#468	C₂²×C₇₁	1	4	yes	—
521	#464	C₂²×C₇₁	1	4	yes	complemented
522	#463	C₂²×C₇₁	1	4	yes	—
523	#463	C₂²×C₇₁	1	4	yes	complemented
524	#462	C₂²×C₇₁	1	2	yes	complemented
525	#462	C₂²×C₇₁	1	2	yes	complemented
526	#461	C₂²×C₇₁	1	2	yes	—
527	#461	C₂²×C₇₁	1	2	yes	—
528	#461	C₂²×C₇₁	1	2	yes	complemented
529	#461	C₂²×C₇₁	1	2	yes	complemented
530	#460	C₂²×C₇₁	1	1	yes	characteristic, complemented
531	#459	C₂²×C₇₁	1	1	yes	characteristic
532	#459	C₂²×C₇₁	1	2	yes	—
533	#459	C₂²×C₇₁	1	2	yes	complemented
534	#452	C₂²×C₇₁	1	4	yes	complemented
535	#450	C₂²×C₇₁	1	4	yes	—
536	#449	C₂²×C₇₁	1	2	yes	—
537	#449	C₂²×C₇₁	1	4	yes	—
538	#448	C₂²×C₇₁	1	4	yes	complemented
539	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
540	C₄×SD₁₆	C₂²×C₇₁	1	4	yes	—
541	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
542	C₄×SD₁₆	C₂²×C₇₁	1	4	yes	complemented
543	C₄×D₈	C₂²×C₇₁	1	2	yes	—
544	#436	C₂²×C₇₁	1	2	yes	—
545	#436	C₂²×C₇₁	1	4	yes	complemented
546	#431	C₂²×C₇₁	1	2	yes	complemented
547	#431	C₂²×C₇₁	1	1	yes	characteristic, complemented
548	#423	C₂²×C₇₁	1	2	yes	complemented
549	#423	C₂²×C₇₁	1	1	yes	characteristic, complemented
550	#419	C₂²×C₇₁	1	2	yes	complemented
551	#417	C₂²×C₇₁	1	4	yes	complemented
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	2	1	no	—
554	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
555	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
556	C₂×#41	C₂³×C₇₁	1	4	yes	—
557	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
560	C₂³×C₄	—	2	2	no	—
561	#137	—	4	4	no	—
562	AGL(1,ℤ/8)	—	4	8	no	—
563	C₂×Q₁₆	C₂³×C₇₁	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
565	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
568	C₂×D₈	C₂³×C₇₁	1	2	yes	—
569	C₂×D₈	C₂³×C₇₁	1	4	yes	—
570	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
571	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
572	C₄⋊Q₈	—	2	1	no	—
573	C₄⋊Q₈	—	2	1	no	—
574	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
577	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
578	#127	C₂³×C₇₁	1	1	yes	characteristic
579	#127	C₂³×C₇₁	1	1	yes	characteristic
580	#126	—	2	2	no	—
581	#126	—	2	4	no	—
582	#126	—	2	2	no	—
583	#125	—	2	1	no	—
584	#125	—	2	2	no	—
585	#125	C₂³×C₇₁	1	2	yes	—
586	#124	—	2	1	no	—
587	#124	—	2	4	no	—
588	#124	—	2	1	no	—
589	#124	—	2	1	no	—
590	#124	C₂³×C₇₁	1	2	yes	—
591	#124	C₂³×C₇₁	1	4	yes	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	#123	—	2	4	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	4	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	1	no	—
611	#121	—	2	2	no	—
612	#121	—	2	1	no	—
613	#121	—	2	2	no	—
614	#121	C₂³×C₇₁	1	2	yes	—
615	#121	C₂³×C₇₁	1	2	yes	—
616	#121	C₂³×C₇₁	1	2	yes	—
617	#120	—	2	2	no	—
618	#120	—	2	2	no	—
619	C₄×Q₈	—	2	2	no	—
620	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
621	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
623	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
624	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
639	C₄×D₄	D₄×C₇₁	1	2	yes	—
640	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
641	C₄×D₄	C₂³×C₇₁	1	2	yes	—
642	C₄×D₄	C₂³×C₇₁	1	2	yes	—
643	C₄×D₄	C₂³×C₇₁	1	2	yes	—
644	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
645	C₄×D₄	C₂³×C₇₁	1	2	yes	—
646	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
647	C₄×D₄	C₂³×C₇₁	1	2	yes	—
648	#117	—	2	2	no	—
649	#117	—	2	2	no	—
650	#117	—	2	1	no	—
651	#117	—	2	2	no	—
652	#117	D₄×C₇₁	1	1	yes	characteristic
653	#117	D₄×C₇₁	1	2	yes	—
654	#117	C₂³×C₇₁	1	1	yes	characteristic
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	—	2	2	no	—
659	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
660	C₂×C₂²⋊C₄	—	2	2	no	—
661	C₂×C₂²⋊C₄	—	2	2	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
664	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
665	#107	C₂³×C₇₁	1	2	yes	—
666	#106	C₂³×C₇₁	1	4	yes	—
667	#106	C₂³×C₇₁	1	2	yes	—
668	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
669	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
670	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
671	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
672	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
673	#103	C₂³×C₇₁	1	4	yes	—
674	#103	C₂³×C₇₁	1	4	yes	—
675	#103	C₂³×C₇₁	1	4	yes	—
676	#103	C₂³×C₇₁	1	4	yes	—
677	#103	C₂³×C₇₁	1	2	yes	—
678	#102	C₂³×C₇₁	1	2	yes	—
679	#102	C₂³×C₇₁	1	4	yes	—
680	#102	C₂³×C₇₁	1	2	yes	—
681	#102	C₂³×C₇₁	1	2	yes	—
682	#102	C₂³×C₇₁	1	4	yes	—
683	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
684	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
685	C₄×C₈	C₂³×C₇₁	1	2	yes	—
686	C₄×C₈	C₂³×C₇₁	1	4	yes	—
687	C₂⁴	—	2	2	no	—
688	#41	—	2	2	no	—
689	#41	—	4	2	no	—
690	#41	—	4	1	no	—
691	#41	—	4	4	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	#41	—	8	2	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
701	C₂×Q₈	C₂⁴×C₇₁	1	4	yes	—
702	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
717	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
718	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
719	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
720	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	8	4	no	—
732	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
735	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
738	Q₁₆	—	4	4	no	—
739	SD₁₆	—	2	8	no	—
740	SD₁₆	—	4	4	no	—
741	SD₁₆	—	4	2	no	—
742	SD₁₆	—	4	4	no	—
743	D₈	—	2	4	no	—
744	D₈	—	4	4	no	—
745	M₁₆	—	4	4	no	—
746	M₁₆	—	4	2	no	—
747	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
748	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
749	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
765	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
766	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
767	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
771	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
791	C₄²	—	2	1	no	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	1	no	—
794	C₄²	—	2	4	no	—
795	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
796	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
797	C₄²	C₂×D₄×C₇₁	1	2	yes	—
798	C₄²	C₂×D₄×C₇₁	1	2	yes	—
799	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
800	C₄²	C₂⁴×C₇₁	1	2	yes	—
801	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
802	C₂³	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	4	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	8	2	no	—
808	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
809	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
810	Q₈	—	2	2	no	—
811	Q₈	—	2	4	no	—
812	Q₈	—	2	1	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	4	no	—
815	Q₈	—	4	2	no	—
816	Q₈	—	8	2	no	—
817	Q₈	—	8	1	no	—
818	D₄	—	2	2	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	2	no	—
821	D₄	—	2	1	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	4	no	—
826	D₄	—	4	2	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	4	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	8	1	no	—
833	D₄	—	8	4	no	—
834	D₄	—	8	2	no	—
835	D₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	—	8	2	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
866	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
868	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
869	C₈	—	2	2	no	—
870	C₈	—	2	4	no	—
871	C₈	—	2	2	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	8	8	no	—
888	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
889	C₄	—	2	1	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	4	no	—
901	C₄	#575×C₇₁	1	2	yes	—
902	C₄	#577×C₇₁	1	2	yes	—
903	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
904	C₄	#585×C₇₁	1	1	yes	characteristic
905	C₂	—	4	2	no	—
906	C₂	—	4	1	no	—
907	C₂	—	4	2	no	—
908	C₂	—	8	2	no	—
909	C₂	—	8	2	no	—
910	C₂	C₇₁×#3488	1	1	yes	characteristic
911	C₂	C₂×#575×C₇₁	1	1	yes	characteristic
912	C₂	C₂×#577×C₇₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3511	C₂	semidirect
2. C₇₁×#3481	C₂	semidirect
3. C₇₁×#3394	C₂	semidirect
4. C₇₁×#3360	C₂	semidirect
5. C₇₁×#3331	C₂	semidirect
6. C₇₁×#3326	C₂	semidirect
7. C₇₁×#3275	C₂	semidirect
8. C₇₁×#3272	C₂	semidirect
9. C₇₁×#3253	C₂	semidirect
10. C₇₁×#3252	C₂	semidirect
11. C₇₁×#3212	C₂	semidirect
12. C₇₁×#3206	C₂	semidirect
13. C₇₁×#3106	C₂	semidirect
14. C₇₁×#3101	C₂	semidirect
15. C₇₁×#3039	C₂	semidirect
16. C₇₁×#3036	C₂	semidirect
17. C₇₁×#2991	C₂	semidirect
21. #556×C₇₁	C₂²	semidirect
30. #548×C₇₁	C₂²	semidirect
37. #533×C₇₁	C₂²	semidirect
39. #532×C₇₁	C₂²	semidirect
40. #532×C₇₁	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₇₁	C₂²	semidirect
50. #495×C₇₁	C₂²	semidirect
52. #488×C₇₁	C₂²	semidirect
53. #487×C₇₁	C₂²	semidirect
54. #483×C₇₁	C₂²	semidirect
55. #482×C₇₁	C₂²	semidirect
56. #479×C₇₁	C₂²	semidirect
57. #477×C₇₁	C₂²	semidirect
59. #476×C₇₁	C₂²	semidirect
60. #476×C₇₁	C₂²	semidirect
61. #470×C₇₁	C₂²	semidirect
62. #469×C₇₁	C₂²	semidirect
64. #464×C₇₁	C₂²	semidirect
66. #463×C₇₁	C₂²	semidirect
67. #462×C₇₁	C₂²	semidirect
68. #462×C₇₁	C₂²	semidirect
71. #461×C₇₁	C₂²	semidirect
72. #461×C₇₁	C₂²	semidirect
73. #460×C₇₁	C₂²	semidirect
76. #459×C₇₁	C₂²	semidirect
77. #452×C₇₁	C₂²	semidirect
81. #448×C₇₁	C₂²	semidirect
82. C₈×Q₈×C₇₁	C₂²	semidirect
84. C₄×SD₁₆×C₇₁	C₂²	semidirect
85. C₄×SD₁₆×C₇₁	C₂²	semidirect
88. #436×C₇₁	C₂²	semidirect
89. #431×C₇₁	C₂²	semidirect
90. #431×C₇₁	C₂²	semidirect
91. #423×C₇₁	C₂²	semidirect
92. #423×C₇₁	C₂²	semidirect
93. #419×C₇₁	C₂²	semidirect
94. #417×C₇₁	C₂²	semidirect
448. #61996	C₇₁	direct (N × H)
457. #3511	C₂×C₇₁	semidirect
458. #3481	C₂×C₇₁	semidirect
459. #3394	C₂×C₇₁	semidirect
460. #3360	C₂×C₇₁	semidirect
461. #3331	C₂×C₇₁	semidirect
462. #3326	C₂×C₇₁	semidirect
463. #3275	C₂×C₇₁	semidirect
464. #3272	C₂×C₇₁	semidirect
465. #3253	C₂×C₇₁	semidirect
466. #3252	C₂×C₇₁	semidirect
467. #3212	C₂×C₇₁	semidirect
468. #3206	C₂×C₇₁	semidirect
469. #3106	C₂×C₇₁	semidirect
470. #3101	C₂×C₇₁	semidirect
471. #3039	C₂×C₇₁	semidirect
472. #3036	C₂×C₇₁	semidirect
473. #2991	C₂×C₇₁	semidirect
474. C₇₁	#61996	direct (N × H)
478. #556	C₂²×C₇₁	semidirect
487. #548	C₂²×C₇₁	semidirect
494. #533	C₂²×C₇₁	semidirect
496. #532	C₂²×C₇₁	semidirect
497. #532	C₂²×C₇₁	semidirect
498. C₂×C₄⋊Q₈	C₂²×C₇₁	semidirect
507. #495	C₂²×C₇₁	semidirect
509. #488	C₂²×C₇₁	semidirect
510. #487	C₂²×C₇₁	semidirect
511. #483	C₂²×C₇₁	semidirect
512. #482	C₂²×C₇₁	semidirect
513. #479	C₂²×C₇₁	semidirect
514. #477	C₂²×C₇₁	semidirect
516. #476	C₂²×C₇₁	semidirect
517. #476	C₂²×C₇₁	semidirect
518. #470	C₂²×C₇₁	semidirect
519. #469	C₂²×C₇₁	semidirect
521. #464	C₂²×C₇₁	semidirect
523. #463	C₂²×C₇₁	semidirect
524. #462	C₂²×C₇₁	semidirect
525. #462	C₂²×C₇₁	semidirect
528. #461	C₂²×C₇₁	semidirect
529. #461	C₂²×C₇₁	semidirect
530. #460	C₂²×C₇₁	semidirect
533. #459	C₂²×C₇₁	semidirect
534. #452	C₂²×C₇₁	semidirect
538. #448	C₂²×C₇₁	semidirect
539. C₈×Q₈	C₂²×C₇₁	semidirect
541. C₄×SD₁₆	C₂²×C₇₁	semidirect
542. C₄×SD₁₆	C₂²×C₇₁	semidirect
545. #436	C₂²×C₇₁	semidirect
546. #431	C₂²×C₇₁	semidirect
547. #431	C₂²×C₇₁	semidirect
548. #423	C₂²×C₇₁	semidirect
549. #423	C₂²×C₇₁	semidirect
550. #419	C₂²×C₇₁	semidirect
551. #417	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×#3511	2
C₇₁×#3481	2
C₇₁×#3394	2
C₇₁×#3360	2
C₇₁×#3331	2
C₇₁×#3326	2
C₇₁×#3275	2
C₇₁×#3272	2
C₇₁×#3253	2
C₇₁×#3252	2
C₇₁×#3212	2
C₇₁×#3206	2
C₇₁×#3106	2
C₇₁×#3101	2
C₇₁×#3039	2
C₇₁×#3036	2
C₇₁×#2991	2
#61996	71

Subgroups — C71×#61996 #31882868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61996 #31882868