Subgroups — C₇₁×#61995 #31882867

Order 18176.

1978 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3396	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3333	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3322	C₂	1	4	yes	maximal, complemented
7	C₇₁×#3274	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3273	C₂	1	4	yes	maximal, complemented
9	C₇₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3251	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3100	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3038	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×AGL(1,ℤ/8)×C₇₁	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	4	yes	complemented
20	#559×C₇₁	—	2	1	no	—
21	#559×C₇₁	C₂²	1	2	yes	complemented
22	#559×C₇₁	C₂²	1	1	yes	characteristic, complemented
23	#554×C₇₁	C₂²	1	1	yes	characteristic, complemented
24	#554×C₇₁	C₂²	1	1	yes	characteristic, complemented
25	#553×C₇₁	—	2	1	no	—
26	#553×C₇₁	C₂²	1	2	yes	—
27	#551×C₇₁	—	2	2	no	—
28	#550×C₇₁	—	2	1	no	—
29	#550×C₇₁	C₂²	1	2	yes	—
30	#546×C₇₁	—	2	1	no	—
31	#546×C₇₁	—	2	2	no	—
32	#546×C₇₁	C₂²	1	2	yes	—
33	#546×C₇₁	C₂²	1	4	yes	complemented
34	D₄²×C₇₁	C₂²	1	1	yes	characteristic, complemented
35	#540×C₇₁	—	2	2	no	—
36	#535×C₇₁	—	2	1	no	—
37	#533×C₇₁	C₂²	1	1	yes	characteristic, complemented
38	#532×C₇₁	C₂²	1	1	yes	characteristic
39	#532×C₇₁	C₂²	1	2	yes	complemented
40	#532×C₇₁	C₂²	1	2	yes	complemented
41	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic, complemented
42	#529×C₇₁	—	2	1	no	—
43	#529×C₇₁	C₂²	1	2	yes	complemented
44	#525×C₇₁	—	2	2	no	—
45	#518×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	complemented
50	#495×C₇₁	C₂²	1	4	yes	complemented
51	#493×C₇₁	C₂²	1	2	yes	—
52	#488×C₇₁	C₂²	1	4	yes	complemented
53	#486×C₇₁	C₂²	1	2	yes	complemented
54	#485×C₇₁	C₂²	1	2	yes	complemented
55	#480×C₇₁	C₂²	1	4	yes	complemented
56	#478×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, complemented
60	#474×C₇₁	C₂²	1	2	yes	complemented
61	#469×C₇₁	C₂²	1	4	yes	complemented
62	#468×C₇₁	C₂²	1	4	yes	complemented
63	#468×C₇₁	C₂²	1	4	yes	complemented
64	#463×C₇₁	C₂²	1	4	yes	complemented
65	#463×C₇₁	C₂²	1	4	yes	complemented
66	#463×C₇₁	C₂²	1	4	yes	complemented
67	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
68	#461×C₇₁	C₂²	1	1	yes	characteristic, complemented
69	#461×C₇₁	C₂²	1	2	yes	complemented
70	#460×C₇₁	C₂²	1	2	yes	complemented
71	#460×C₇₁	C₂²	1	2	yes	complemented
72	#460×C₇₁	C₂²	1	2	yes	complemented
73	#459×C₇₁	C₂²	1	2	yes	—
74	#459×C₇₁	C₂²	1	2	yes	—
75	#459×C₇₁	C₂²	1	2	yes	complemented
76	#459×C₇₁	C₂²	1	2	yes	complemented
77	#452×C₇₁	C₂²	1	2	yes	—
78	#452×C₇₁	C₂²	1	4	yes	complemented
79	#449×C₇₁	C₂²	1	4	yes	complemented
80	#447×C₇₁	C₂²	1	4	yes	complemented
81	#447×C₇₁	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
85	C₄×D₈×C₇₁	C₂²	1	4	yes	complemented
86	C₄×D₈×C₇₁	C₂²	1	4	yes	complemented
87	#436×C₇₁	C₂²	1	4	yes	complemented
88	#436×C₇₁	C₂²	1	2	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	#418×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	2	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×D₄×C₇₁	—	2	1	no	—
101	C₂²×D₄×C₇₁	—	2	1	no	—
102	C₂²×D₄×C₇₁	—	2	1	no	—
103	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
104	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
105	C₂³×C₄×C₇₁	—	2	2	no	—
106	AGL(1,ℤ/8)×C₇₁	—	4	4	no	—
107	AGL(1,ℤ/8)×C₇₁	—	4	8	no	—
108	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
112	C₂×D₈×C₇₁	C₂³	1	4	yes	—
113	C₂×D₈×C₇₁	C₂³	1	4	yes	—
114	C₂×D₈×C₇₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
116	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
120	#127×C₇₁	—	2	2	no	—
121	#127×C₇₁	—	2	1	no	—
122	#127×C₇₁	—	2	1	no	—
123	#127×C₇₁	C₂³	1	2	yes	—
124	#127×C₇₁	C₂³	1	2	yes	—
125	#127×C₇₁	C₂³	1	1	yes	characteristic
126	#126×C₇₁	—	2	2	no	—
127	#126×C₇₁	—	2	2	no	—
128	#125×C₇₁	—	2	1	no	—
129	#125×C₇₁	—	2	1	no	—
130	#125×C₇₁	C₂³	1	2	yes	—
131	#124×C₇₁	—	2	1	no	—
132	#124×C₇₁	—	2	2	no	—
133	#124×C₇₁	—	2	1	no	—
134	#124×C₇₁	—	2	2	no	—
135	#124×C₇₁	C₂³	1	4	yes	—
136	#124×C₇₁	C₂³	1	2	yes	—
137	#123×C₇₁	—	2	2	no	—
138	#123×C₇₁	—	2	2	no	—
139	#123×C₇₁	—	2	2	no	—
140	#123×C₇₁	—	2	4	no	—
141	#123×C₇₁	—	2	4	no	—
142	#123×C₇₁	—	2	2	no	—
143	C₂²⋊Q₈×C₇₁	—	2	1	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	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
149	#121×C₇₁	—	2	2	no	—
150	#121×C₇₁	—	2	1	no	—
151	#121×C₇₁	—	2	2	no	—
152	#121×C₇₁	—	2	2	no	—
153	#121×C₇₁	—	2	2	no	—
154	#121×C₇₁	—	2	1	no	—
155	#121×C₇₁	—	2	2	no	—
156	#121×C₇₁	—	2	4	no	—
157	#121×C₇₁	—	2	4	no	—
158	#121×C₇₁	C₂³	1	2	yes	—
159	#121×C₇₁	C₂³	1	4	yes	—
160	#121×C₇₁	C₂³	1	2	yes	—
161	#120×C₇₁	—	2	2	no	—
162	#120×C₇₁	—	2	4	no	—
163	#120×C₇₁	—	2	2	no	—
164	C₄×Q₈×C₇₁	—	2	1	no	—
165	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
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	1	no	—
173	C₄×D₄×C₇₁	—	2	1	no	—
174	C₄×D₄×C₇₁	—	2	1	no	—
175	C₄×D₄×C₇₁	—	2	2	no	—
176	C₄×D₄×C₇₁	—	2	2	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	—	2	2	no	—
182	C₄×D₄×C₇₁	—	2	2	no	—
183	C₄×D₄×C₇₁	—	2	2	no	—
184	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
185	C₄×D₄×C₇₁	D₄	1	2	yes	—
186	C₄×D₄×C₇₁	C₂³	1	2	yes	—
187	C₄×D₄×C₇₁	C₂³	1	2	yes	—
188	C₄×D₄×C₇₁	C₂³	1	4	yes	—
189	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₇₁	C₂³	1	2	yes	—
192	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₇₁	C₂³	1	2	yes	—
194	#117×C₇₁	—	2	1	no	—
195	#117×C₇₁	—	2	1	no	—
196	#117×C₇₁	—	2	2	no	—
197	#117×C₇₁	D₄	1	1	yes	characteristic
198	#117×C₇₁	D₄	1	2	yes	—
199	#117×C₇₁	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₇₁	—	2	4	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	2	yes	—
212	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
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	2	yes	—
217	#103×C₇₁	C₂³	1	4	yes	—
218	#103×C₇₁	C₂³	1	2	yes	—
219	#103×C₇₁	C₂³	1	2	yes	—
220	#102×C₇₁	C₂³	1	4	yes	—
221	#102×C₇₁	C₂³	1	4	yes	—
222	#102×C₇₁	C₂³	1	4	yes	—
223	#102×C₇₁	C₂³	1	2	yes	—
224	#102×C₇₁	C₂³	1	4	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	C₄×C₈×C₇₁	C₂³	1	4	yes	—
229	C₄×C₈×C₇₁	C₂³	1	2	yes	—
230	C₂⁴×C₇₁	—	2	2	no	—
231	C₂⁴×C₇₁	—	2	2	no	—
232	#41×C₇₁	—	2	2	no	—
233	#41×C₇₁	—	4	2	no	—
234	#41×C₇₁	—	4	1	no	—
235	#41×C₇₁	—	4	4	no	—
236	#41×C₇₁	—	4	4	no	—
237	#41×C₇₁	—	8	2	no	—
238	#41×C₇₁	—	8	4	no	—
239	C₂×Q₈×C₇₁	—	2	1	no	—
240	C₂×Q₈×C₇₁	—	2	1	no	—
241	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₇₁	—	2	4	no	—
245	C₂×D₄×C₇₁	—	2	1	no	—
246	C₂×D₄×C₇₁	—	2	2	no	—
247	C₂×D₄×C₇₁	—	2	4	no	—
248	C₂×D₄×C₇₁	—	2	2	no	—
249	C₂×D₄×C₇₁	—	2	4	no	—
250	C₂×D₄×C₇₁	—	2	2	no	—
251	C₂×D₄×C₇₁	—	2	1	no	—
252	C₂×D₄×C₇₁	—	2	2	no	—
253	C₂×D₄×C₇₁	—	2	2	no	—
254	C₂×D₄×C₇₁	—	2	2	no	—
255	C₂×D₄×C₇₁	—	2	1	no	—
256	C₂×D₄×C₇₁	—	2	2	no	—
257	C₂×D₄×C₇₁	—	2	2	no	—
258	C₂×D₄×C₇₁	—	4	2	no	—
259	C₂×D₄×C₇₁	—	4	2	no	—
260	C₂×D₄×C₇₁	—	4	2	no	—
261	C₂×D₄×C₇₁	—	4	4	no	—
262	C₂×D₄×C₇₁	—	4	4	no	—
263	C₂×D₄×C₇₁	—	8	2	no	—
264	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₇₁	C₂⁴	1	4	yes	—
267	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
268	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇₁	—	2	2	no	—
270	C₂²×C₄×C₇₁	—	2	1	no	—
271	C₂²×C₄×C₇₁	—	2	1	no	—
272	C₂²×C₄×C₇₁	—	2	1	no	—
273	C₂²×C₄×C₇₁	—	2	2	no	—
274	C₂²×C₄×C₇₁	—	2	2	no	—
275	C₂²×C₄×C₇₁	—	2	4	no	—
276	C₂²×C₄×C₇₁	—	2	4	no	—
277	C₂²×C₄×C₇₁	—	2	2	no	—
278	C₂²×C₄×C₇₁	—	8	4	no	—
279	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
285	Q₁₆×C₇₁	—	4	2	no	—
286	SD₁₆×C₇₁	—	2	4	no	—
287	SD₁₆×C₇₁	—	4	4	no	—
288	SD₁₆×C₇₁	—	4	4	no	—
289	D₈×C₇₁	—	2	8	no	—
290	D₈×C₇₁	—	4	4	no	—
291	D₈×C₇₁	—	4	4	no	—
292	M₁₆×C₇₁	—	4	2	no	—
293	M₁₆×C₇₁	—	4	4	no	—
294	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
295	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
296	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₇₁	—	2	1	no	—
298	C₄⋊C₄×C₇₁	—	2	2	no	—
299	C₄⋊C₄×C₇₁	—	2	2	no	—
300	C₄⋊C₄×C₇₁	—	2	1	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	1	no	—
307	C₄⋊C₄×C₇₁	—	2	2	no	—
308	C₄⋊C₄×C₇₁	—	2	2	no	—
309	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₇₁	C₂×D₄	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	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
317	C₂²⋊C₄×C₇₁	—	2	2	no	—
318	C₂²⋊C₄×C₇₁	—	2	2	no	—
319	C₂²⋊C₄×C₇₁	—	2	1	no	—
320	C₂²⋊C₄×C₇₁	—	2	1	no	—
321	C₂²⋊C₄×C₇₁	—	2	4	no	—
322	C₂²⋊C₄×C₇₁	—	2	4	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	2	no	—
327	C₂²⋊C₄×C₇₁	—	2	2	no	—
328	C₂²⋊C₄×C₇₁	—	2	1	no	—
329	C₂²⋊C₄×C₇₁	—	2	2	no	—
330	C₂²⋊C₄×C₇₁	—	2	2	no	—
331	C₂²⋊C₄×C₇₁	—	2	4	no	—
332	C₂²⋊C₄×C₇₁	—	2	4	no	—
333	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
336	C₄²×C₇₁	—	2	1	no	—
337	C₄²×C₇₁	—	2	1	no	—
338	C₄²×C₇₁	—	2	1	no	—
339	C₄²×C₇₁	—	2	2	no	—
340	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₇₁	C₂×D₄	1	2	yes	—
343	C₄²×C₇₁	C₂×D₄	1	2	yes	—
344	C₄²×C₇₁	C₂⁴	1	2	yes	—
345	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
346	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
347	C₂³×C₇₁	—	2	1	no	—
348	C₂³×C₇₁	—	2	2	no	—
349	C₂³×C₇₁	—	2	4	no	—
350	C₂³×C₇₁	—	4	4	no	—
351	C₂³×C₇₁	—	4	4	no	—
352	C₂³×C₇₁	—	4	4	no	—
353	C₂³×C₇₁	—	8	2	no	—
354	C₂³×C₇₁	—	8	2	no	—
355	C₂³×C₇₁	—	8	2	no	—
356	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
357	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
358	Q₈×C₇₁	—	2	2	no	—
359	Q₈×C₇₁	—	2	2	no	—
360	Q₈×C₇₁	—	2	1	no	—
361	Q₈×C₇₁	—	2	1	no	—
362	Q₈×C₇₁	—	2	2	no	—
363	Q₈×C₇₁	—	4	2	no	—
364	Q₈×C₇₁	—	8	1	no	—
365	D₄×C₇₁	—	2	2	no	—
366	D₄×C₇₁	—	2	4	no	—
367	D₄×C₇₁	—	2	2	no	—
368	D₄×C₇₁	—	2	1	no	—
369	D₄×C₇₁	—	2	2	no	—
370	D₄×C₇₁	—	2	4	no	—
371	D₄×C₇₁	—	4	2	no	—
372	D₄×C₇₁	—	4	4	no	—
373	D₄×C₇₁	—	4	4	no	—
374	D₄×C₇₁	—	4	2	no	—
375	D₄×C₇₁	—	4	4	no	—
376	D₄×C₇₁	—	4	2	no	—
377	D₄×C₇₁	—	4	4	no	—
378	D₄×C₇₁	—	4	4	no	—
379	D₄×C₇₁	—	8	2	no	—
380	D₄×C₇₁	—	8	2	no	—
381	D₄×C₇₁	—	8	1	no	—
382	D₄×C₇₁	—	8	4	no	—
383	D₄×C₇₁	—	8	2	no	—
384	D₄×C₇₁	—	8	4	no	—
385	D₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
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	—	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	2	no	—
399	C₂×C₄×C₇₁	—	4	2	no	—
400	C₂×C₄×C₇₁	—	4	2	no	—
401	C₂×C₄×C₇₁	—	4	2	no	—
402	C₂×C₄×C₇₁	—	4	2	no	—
403	C₂×C₄×C₇₁	—	4	4	no	—
404	C₂×C₄×C₇₁	—	8	2	no	—
405	C₂×C₄×C₇₁	—	8	2	no	—
406	C₂×C₄×C₇₁	—	8	4	no	—
407	C₂×C₄×C₇₁	—	8	4	no	—
408	C₂×C₄×C₇₁	—	8	2	no	—
409	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
418	C₈×C₇₁	—	2	4	no	—
419	C₈×C₇₁	—	2	2	no	—
420	C₈×C₇₁	—	2	2	no	—
421	C₂²×C₇₁	—	2	1	no	—
422	C₂²×C₇₁	—	2	2	no	—
423	C₂²×C₇₁	—	2	2	no	—
424	C₂²×C₇₁	—	2	1	no	—
425	C₂²×C₇₁	—	2	2	no	—
426	C₂²×C₇₁	—	2	2	no	—
427	C₂²×C₇₁	—	2	1	no	—
428	C₂²×C₇₁	—	4	1	no	—
429	C₂²×C₇₁	—	4	1	no	—
430	C₂²×C₇₁	—	4	4	no	—
431	C₂²×C₇₁	—	4	2	no	—
432	C₂²×C₇₁	—	4	2	no	—
433	C₂²×C₇₁	—	4	4	no	—
434	C₂²×C₇₁	—	4	2	no	—
435	C₂²×C₇₁	—	4	4	no	—
436	C₂²×C₇₁	—	8	8	no	—
437	C₂²×C₇₁	—	16	4	no	—
438	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₇₁	—	2	1	no	—
440	C₄×C₇₁	—	2	2	no	—
441	C₄×C₇₁	—	2	1	no	—
442	C₄×C₇₁	—	2	2	no	—
443	C₄×C₇₁	—	2	2	no	—
444	C₄×C₇₁	—	2	1	no	—
445	C₄×C₇₁	—	4	1	no	—
446	C₄×C₇₁	—	4	2	no	—
447	C₄×C₇₁	—	4	1	no	—
448	C₄×C₇₁	—	4	1	no	—
449	C₄×C₇₁	—	4	2	no	—
450	C₄×C₇₁	—	4	2	no	—
451	C₄×C₇₁	#575	1	2	yes	—
452	C₄×C₇₁	#576	1	2	yes	—
453	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
454	C₄×C₇₁	#585	1	1	yes	characteristic
455	#61995	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂×C₇₁	—	4	2	no	—
457	C₂×C₇₁	—	4	1	no	—
458	C₂×C₇₁	—	4	2	no	—
459	C₂×C₇₁	—	8	2	no	—
460	C₂×C₇₁	—	8	4	no	—
461	C₂×C₇₁	#3488	1	1	yes	characteristic
462	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
463	C₂×C₇₁	C₂×#576	1	1	yes	characteristic
464	#3508	C₂×C₇₁	1	1	yes	characteristic, complemented
465	#3481	C₂×C₇₁	1	1	yes	characteristic, complemented
466	#3396	C₂×C₇₁	1	2	yes	complemented
467	#3361	C₂×C₇₁	1	2	yes	complemented
468	#3333	C₂×C₇₁	1	2	yes	complemented
469	#3322	C₂×C₇₁	1	4	yes	complemented
470	#3274	C₂×C₇₁	1	2	yes	complemented
471	#3273	C₂×C₇₁	1	4	yes	complemented
472	#3254	C₂×C₇₁	1	1	yes	characteristic, complemented
473	#3251	C₂×C₇₁	1	2	yes	complemented
474	#3212	C₂×C₇₁	1	2	yes	complemented
475	#3205	C₂×C₇₁	1	1	yes	characteristic, complemented
476	#3107	C₂×C₇₁	1	1	yes	characteristic, complemented
477	#3100	C₂×C₇₁	1	2	yes	complemented
478	#3038	C₂×C₇₁	1	1	yes	characteristic, complemented
479	#3036	C₂×C₇₁	1	2	yes	complemented
480	#2991	C₂×C₇₁	1	1	yes	characteristic, complemented
481	C₇₁	#61995	1	1	yes	characteristic, direct product factor, Sylow
482	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	2	yes	—
483	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	4	yes	complemented
484	#559	—	2	1	no	—
485	#559	C₂²×C₇₁	1	2	yes	complemented
486	#559	C₂²×C₇₁	1	1	yes	characteristic, complemented
487	#554	C₂²×C₇₁	1	1	yes	characteristic, complemented
488	#554	C₂²×C₇₁	1	1	yes	characteristic, complemented
489	#553	—	2	1	no	—
490	#553	C₂²×C₇₁	1	2	yes	—
491	#551	—	2	2	no	—
492	#550	—	2	1	no	—
493	#550	C₂²×C₇₁	1	2	yes	—
494	#546	—	2	1	no	—
495	#546	—	2	2	no	—
496	#546	C₂²×C₇₁	1	2	yes	—
497	#546	C₂²×C₇₁	1	4	yes	complemented
498	D₄²	C₂²×C₇₁	1	1	yes	characteristic, complemented
499	#540	—	2	2	no	—
500	#535	—	2	1	no	—
501	#533	C₂²×C₇₁	1	1	yes	characteristic, complemented
502	#532	C₂²×C₇₁	1	1	yes	characteristic
503	#532	C₂²×C₇₁	1	2	yes	complemented
504	#532	C₂²×C₇₁	1	2	yes	complemented
505	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic, complemented
506	#529	—	2	1	no	—
507	#529	C₂²×C₇₁	1	2	yes	complemented
508	#525	—	2	2	no	—
509	#518	—	2	1	no	—
510	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
511	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
512	C₂×C₄×D₄	—	2	1	no	—
513	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	complemented
514	#495	C₂²×C₇₁	1	4	yes	complemented
515	#493	C₂²×C₇₁	1	2	yes	—
516	#488	C₂²×C₇₁	1	4	yes	complemented
517	#486	C₂²×C₇₁	1	2	yes	complemented
518	#485	C₂²×C₇₁	1	2	yes	complemented
519	#480	C₂²×C₇₁	1	4	yes	complemented
520	#478	C₂²×C₇₁	1	4	yes	complemented
521	#477	C₂²×C₇₁	1	2	yes	complemented
522	#475	C₂²×C₇₁	1	1	yes	characteristic, complemented
523	#474	C₂²×C₇₁	1	1	yes	characteristic, complemented
524	#474	C₂²×C₇₁	1	2	yes	complemented
525	#469	C₂²×C₇₁	1	4	yes	complemented
526	#468	C₂²×C₇₁	1	4	yes	complemented
527	#468	C₂²×C₇₁	1	4	yes	complemented
528	#463	C₂²×C₇₁	1	4	yes	complemented
529	#463	C₂²×C₇₁	1	4	yes	complemented
530	#463	C₂²×C₇₁	1	4	yes	complemented
531	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
532	#461	C₂²×C₇₁	1	1	yes	characteristic, complemented
533	#461	C₂²×C₇₁	1	2	yes	complemented
534	#460	C₂²×C₇₁	1	2	yes	complemented
535	#460	C₂²×C₇₁	1	2	yes	complemented
536	#460	C₂²×C₇₁	1	2	yes	complemented
537	#459	C₂²×C₇₁	1	2	yes	—
538	#459	C₂²×C₇₁	1	2	yes	—
539	#459	C₂²×C₇₁	1	2	yes	complemented
540	#459	C₂²×C₇₁	1	2	yes	complemented
541	#452	C₂²×C₇₁	1	2	yes	—
542	#452	C₂²×C₇₁	1	4	yes	complemented
543	#449	C₂²×C₇₁	1	4	yes	complemented
544	#447	C₂²×C₇₁	1	4	yes	complemented
545	#447	C₂²×C₇₁	1	4	yes	complemented
546	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
547	C₄×Q₁₆	C₂²×C₇₁	1	2	yes	complemented
548	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
549	C₄×D₈	C₂²×C₇₁	1	4	yes	complemented
550	C₄×D₈	C₂²×C₇₁	1	4	yes	complemented
551	#436	C₂²×C₇₁	1	2	yes	complemented
552	#436	C₂²×C₇₁	1	4	yes	complemented
553	#431	C₂²×C₇₁	1	2	yes	complemented
554	#431	C₂²×C₇₁	1	1	yes	characteristic, complemented
555	#423	C₂²×C₇₁	1	2	yes	complemented
556	#423	C₂²×C₇₁	1	1	yes	characteristic, complemented
557	#418	C₂²×C₇₁	1	2	yes	complemented
558	#417	C₂²×C₇₁	1	4	yes	complemented
559	C₂×#41	—	2	1	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
562	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
563	C₂×#41	C₂³×C₇₁	1	4	yes	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
568	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
569	C₂³×C₄	—	2	2	no	—
570	AGL(1,ℤ/8)	—	4	4	no	—
571	AGL(1,ℤ/8)	—	4	8	no	—
572	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
574	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
575	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
576	C₂×D₈	C₂³×C₇₁	1	4	yes	—
577	C₂×D₈	C₂³×C₇₁	1	4	yes	—
578	C₂×D₈	C₂³×C₇₁	1	4	yes	—
579	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
580	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
581	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
584	#127	—	2	2	no	—
585	#127	—	2	1	no	—
586	#127	—	2	1	no	—
587	#127	C₂³×C₇₁	1	2	yes	—
588	#127	C₂³×C₇₁	1	2	yes	—
589	#127	C₂³×C₇₁	1	1	yes	characteristic
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#125	—	2	1	no	—
593	#125	—	2	1	no	—
594	#125	C₂³×C₇₁	1	2	yes	—
595	#124	—	2	1	no	—
596	#124	—	2	2	no	—
597	#124	—	2	1	no	—
598	#124	—	2	2	no	—
599	#124	C₂³×C₇₁	1	2	yes	—
600	#124	C₂³×C₇₁	1	4	yes	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	4	no	—
605	#123	—	2	4	no	—
606	#123	—	2	2	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
612	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
613	#121	—	2	2	no	—
614	#121	—	2	1	no	—
615	#121	—	2	2	no	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	1	no	—
619	#121	—	2	2	no	—
620	#121	—	2	4	no	—
621	#121	—	2	4	no	—
622	#121	C₂³×C₇₁	1	2	yes	—
623	#121	C₂³×C₇₁	1	2	yes	—
624	#121	C₂³×C₇₁	1	4	yes	—
625	#120	—	2	2	no	—
626	#120	—	2	4	no	—
627	#120	—	2	2	no	—
628	C₄×Q₈	—	2	1	no	—
629	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
630	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
631	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
632	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
633	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
649	C₄×D₄	D₄×C₇₁	1	2	yes	—
650	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₇₁	1	2	yes	—
652	C₄×D₄	C₂³×C₇₁	1	2	yes	—
653	C₄×D₄	C₂³×C₇₁	1	2	yes	—
654	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₇₁	1	4	yes	—
656	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
657	C₄×D₄	C₂³×C₇₁	1	2	yes	—
658	#117	—	2	1	no	—
659	#117	—	2	1	no	—
660	#117	—	2	2	no	—
661	#117	D₄×C₇₁	1	1	yes	characteristic
662	#117	D₄×C₇₁	1	2	yes	—
663	#117	C₂³×C₇₁	1	1	yes	characteristic
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	—	2	2	no	—
668	C₂×C₂²⋊C₄	—	2	4	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
671	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
672	#107	C₂³×C₇₁	1	2	yes	—
673	#107	C₂³×C₇₁	1	4	yes	—
674	#106	C₂³×C₇₁	1	2	yes	—
675	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
676	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
677	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
678	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
679	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
680	#103	C₂³×C₇₁	1	2	yes	—
681	#103	C₂³×C₇₁	1	4	yes	—
682	#103	C₂³×C₇₁	1	2	yes	—
683	#103	C₂³×C₇₁	1	2	yes	—
684	#102	C₂³×C₇₁	1	4	yes	—
685	#102	C₂³×C₇₁	1	4	yes	—
686	#102	C₂³×C₇₁	1	4	yes	—
687	#102	C₂³×C₇₁	1	2	yes	—
688	#102	C₂³×C₇₁	1	4	yes	—
689	#102	C₂³×C₇₁	1	4	yes	—
690	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
692	C₄×C₈	C₂³×C₇₁	1	4	yes	—
693	C₄×C₈	C₂³×C₇₁	1	2	yes	—
694	C₂⁴	—	2	2	no	—
695	C₂⁴	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	4	2	no	—
698	#41	—	4	1	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	8	2	no	—
702	#41	—	8	4	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
706	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
707	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	4	no	—
727	C₂×D₄	—	8	2	no	—
728	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
729	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
730	C₂×D₄	C₂⁴×C₇₁	1	4	yes	—
731	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
732	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	8	4	no	—
743	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
745	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
749	Q₁₆	—	4	2	no	—
750	SD₁₆	—	2	4	no	—
751	SD₁₆	—	4	4	no	—
752	SD₁₆	—	4	4	no	—
753	D₈	—	2	8	no	—
754	D₈	—	4	4	no	—
755	D₈	—	4	4	no	—
756	M₁₆	—	4	2	no	—
757	M₁₆	—	4	4	no	—
758	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
759	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
760	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
774	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
775	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
776	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
778	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
780	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
798	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
799	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
800	C₄²	—	2	1	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	1	no	—
803	C₄²	—	2	2	no	—
804	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
806	C₄²	C₂×D₄×C₇₁	1	2	yes	—
807	C₄²	C₂×D₄×C₇₁	1	2	yes	—
808	C₄²	C₂⁴×C₇₁	1	2	yes	—
809	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
810	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
811	C₂³	—	2	1	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	8	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
821	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	4	no	—
831	D₄	—	2	2	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	4	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	1	no	—
846	D₄	—	8	4	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	4	no	—
849	D₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	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	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
881	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	8	8	no	—
901	C₂²	—	16	4	no	—
902	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
903	C₄	—	2	1	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	2	no	—
915	C₄	#575×C₇₁	1	2	yes	—
916	C₄	#576×C₇₁	1	2	yes	—
917	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
918	C₄	#585×C₇₁	1	1	yes	characteristic
919	C₂	—	4	2	no	—
920	C₂	—	4	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	8	2	no	—
923	C₂	—	8	4	no	—
924	C₂	C₇₁×#3488	1	1	yes	characteristic
925	C₂	C₂×#575×C₇₁	1	1	yes	characteristic
926	C₂	C₂×#576×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×#3508	C₂	semidirect
2. C₇₁×#3481	C₂	semidirect
3. C₇₁×#3396	C₂	semidirect
4. C₇₁×#3361	C₂	semidirect
5. C₇₁×#3333	C₂	semidirect
6. C₇₁×#3322	C₂	semidirect
7. C₇₁×#3274	C₂	semidirect
8. C₇₁×#3273	C₂	semidirect
9. C₇₁×#3254	C₂	semidirect
10. C₇₁×#3251	C₂	semidirect
11. C₇₁×#3212	C₂	semidirect
12. C₇₁×#3205	C₂	semidirect
13. C₇₁×#3107	C₂	semidirect
14. C₇₁×#3100	C₂	semidirect
15. C₇₁×#3038	C₂	semidirect
16. C₇₁×#3036	C₂	semidirect
17. C₇₁×#2991	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₇₁	C₂²	semidirect
21. #559×C₇₁	C₂²	semidirect
22. #559×C₇₁	C₂²	semidirect
23. #554×C₇₁	C₂²	semidirect
24. #554×C₇₁	C₂²	semidirect
33. #546×C₇₁	C₂²	semidirect
34. D₄²×C₇₁	C₂²	semidirect
37. #533×C₇₁	C₂²	semidirect
39. #532×C₇₁	C₂²	semidirect
40. #532×C₇₁	C₂²	semidirect
41. C₂×#127×C₇₁	C₂²	semidirect
43. #529×C₇₁	C₂²	semidirect
49. C₂×C₄×D₄×C₇₁	C₂²	semidirect
50. #495×C₇₁	C₂²	semidirect
52. #488×C₇₁	C₂²	semidirect
53. #486×C₇₁	C₂²	semidirect
54. #485×C₇₁	C₂²	semidirect
55. #480×C₇₁	C₂²	semidirect
56. #478×C₇₁	C₂²	semidirect
57. #477×C₇₁	C₂²	semidirect
58. #475×C₇₁	C₂²	semidirect
59. #474×C₇₁	C₂²	semidirect
60. #474×C₇₁	C₂²	semidirect
61. #469×C₇₁	C₂²	semidirect
62. #468×C₇₁	C₂²	semidirect
63. #468×C₇₁	C₂²	semidirect
64. #463×C₇₁	C₂²	semidirect
65. #463×C₇₁	C₂²	semidirect
66. #463×C₇₁	C₂²	semidirect
67. #462×C₇₁	C₂²	semidirect
68. #461×C₇₁	C₂²	semidirect
69. #461×C₇₁	C₂²	semidirect
70. #460×C₇₁	C₂²	semidirect
71. #460×C₇₁	C₂²	semidirect
72. #460×C₇₁	C₂²	semidirect
75. #459×C₇₁	C₂²	semidirect
76. #459×C₇₁	C₂²	semidirect
78. #452×C₇₁	C₂²	semidirect
79. #449×C₇₁	C₂²	semidirect
80. #447×C₇₁	C₂²	semidirect
81. #447×C₇₁	C₂²	semidirect
82. C₈×Q₈×C₇₁	C₂²	semidirect
83. C₄×Q₁₆×C₇₁	C₂²	semidirect
84. C₄×SD₁₆×C₇₁	C₂²	semidirect
85. C₄×D₈×C₇₁	C₂²	semidirect
86. C₄×D₈×C₇₁	C₂²	semidirect
87. #436×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. #418×C₇₁	C₂²	semidirect
94. #417×C₇₁	C₂²	semidirect
455. #61995	C₇₁	direct (N × H)
464. #3508	C₂×C₇₁	semidirect
465. #3481	C₂×C₇₁	semidirect
466. #3396	C₂×C₇₁	semidirect
467. #3361	C₂×C₇₁	semidirect
468. #3333	C₂×C₇₁	semidirect
469. #3322	C₂×C₇₁	semidirect
470. #3274	C₂×C₇₁	semidirect
471. #3273	C₂×C₇₁	semidirect
472. #3254	C₂×C₇₁	semidirect
473. #3251	C₂×C₇₁	semidirect
474. #3212	C₂×C₇₁	semidirect
475. #3205	C₂×C₇₁	semidirect
476. #3107	C₂×C₇₁	semidirect
477. #3100	C₂×C₇₁	semidirect
478. #3038	C₂×C₇₁	semidirect
479. #3036	C₂×C₇₁	semidirect
480. #2991	C₂×C₇₁	semidirect
481. C₇₁	#61995	direct (N × H)
483. C₂×AGL(1,ℤ/8)	C₂²×C₇₁	semidirect
485. #559	C₂²×C₇₁	semidirect
486. #559	C₂²×C₇₁	semidirect
487. #554	C₂²×C₇₁	semidirect
488. #554	C₂²×C₇₁	semidirect
497. #546	C₂²×C₇₁	semidirect
498. D₄²	C₂²×C₇₁	semidirect
501. #533	C₂²×C₇₁	semidirect
503. #532	C₂²×C₇₁	semidirect
504. #532	C₂²×C₇₁	semidirect
505. C₂×#127	C₂²×C₇₁	semidirect
507. #529	C₂²×C₇₁	semidirect
513. C₂×C₄×D₄	C₂²×C₇₁	semidirect
514. #495	C₂²×C₇₁	semidirect
516. #488	C₂²×C₇₁	semidirect
517. #486	C₂²×C₇₁	semidirect
518. #485	C₂²×C₇₁	semidirect
519. #480	C₂²×C₇₁	semidirect
520. #478	C₂²×C₇₁	semidirect
521. #477	C₂²×C₇₁	semidirect
522. #475	C₂²×C₇₁	semidirect
523. #474	C₂²×C₇₁	semidirect
524. #474	C₂²×C₇₁	semidirect
525. #469	C₂²×C₇₁	semidirect
526. #468	C₂²×C₇₁	semidirect
527. #468	C₂²×C₇₁	semidirect
528. #463	C₂²×C₇₁	semidirect
529. #463	C₂²×C₇₁	semidirect
530. #463	C₂²×C₇₁	semidirect
531. #462	C₂²×C₇₁	semidirect
532. #461	C₂²×C₇₁	semidirect
533. #461	C₂²×C₇₁	semidirect
534. #460	C₂²×C₇₁	semidirect
535. #460	C₂²×C₇₁	semidirect
536. #460	C₂²×C₇₁	semidirect
539. #459	C₂²×C₇₁	semidirect
540. #459	C₂²×C₇₁	semidirect
542. #452	C₂²×C₇₁	semidirect
543. #449	C₂²×C₇₁	semidirect
544. #447	C₂²×C₇₁	semidirect
545. #447	C₂²×C₇₁	semidirect
546. C₈×Q₈	C₂²×C₇₁	semidirect
547. C₄×Q₁₆	C₂²×C₇₁	semidirect
548. C₄×SD₁₆	C₂²×C₇₁	semidirect
549. C₄×D₈	C₂²×C₇₁	semidirect
550. C₄×D₈	C₂²×C₇₁	semidirect
551. #436	C₂²×C₇₁	semidirect
552. #436	C₂²×C₇₁	semidirect
553. #431	C₂²×C₇₁	semidirect
554. #431	C₂²×C₇₁	semidirect
555. #423	C₂²×C₇₁	semidirect
556. #423	C₂²×C₇₁	semidirect
557. #418	C₂²×C₇₁	semidirect
558. #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×#3508	2
C₇₁×#3481	2
C₇₁×#3396	2
C₇₁×#3361	2
C₇₁×#3333	2
C₇₁×#3322	2
C₇₁×#3274	2
C₇₁×#3273	2
C₇₁×#3254	2
C₇₁×#3251	2
C₇₁×#3212	2
C₇₁×#3205	2
C₇₁×#3107	2
C₇₁×#3100	2
C₇₁×#3038	2
C₇₁×#3036	2
C₇₁×#2991	2
#61995	71

Subgroups — C71×#61995 #31882867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61995 #31882867