Subgroups — C₇₁×#60695 #31881567

Order 18176.

1978 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3460	C₂	1	2	yes	maximal, complemented
2	C₇₁×#3179	C₂	1	4	yes	maximal, complemented
3	C₇₁×#3176	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3175	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3171	C₂	1	4	yes	maximal, complemented
6	C₇₁×#3169	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3168	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3062	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×AGL(1,ℤ/8)×C₇₁	C₂	1	2	yes	maximal, complemented
15	C₄×#135×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#131×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	2	yes	—
19	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
23	#544×C₇₁	C₂²	1	2	yes	—
24	#542×C₇₁	—	2	2	no	—
25	#542×C₇₁	C₂²	1	4	yes	complemented
26	#540×C₇₁	—	2	2	no	—
27	#540×C₇₁	C₂²	1	4	yes	complemented
28	#538×C₇₁	—	2	4	no	—
29	#537×C₇₁	C₂²	1	2	yes	—
30	#535×C₇₁	C₂²	1	2	yes	—
31	#535×C₇₁	C₂²	1	2	yes	—
32	#532×C₇₁	—	2	2	no	—
33	#532×C₇₁	C₂²	1	4	yes	complemented
34	#529×C₇₁	—	2	2	no	—
35	#529×C₇₁	C₂²	1	4	yes	complemented
36	#525×C₇₁	—	2	4	no	—
37	C₄×#41×C₇₁	C₂²	1	2	yes	—
38	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
40	#501×C₇₁	C₂²	1	4	yes	complemented
41	#500×C₇₁	C₂²	1	2	yes	complemented
42	#499×C₇₁	C₂²	1	2	yes	complemented
43	#496×C₇₁	C₂²	1	4	yes	—
44	#495×C₇₁	C₂²	1	2	yes	—
45	#493×C₇₁	C₂²	1	2	yes	—
46	#490×C₇₁	C₂²	1	4	yes	complemented
47	#489×C₇₁	C₂²	1	4	yes	complemented
48	#488×C₇₁	C₂²	1	4	yes	complemented
49	#486×C₇₁	C₂²	1	4	yes	complemented
50	#469×C₇₁	C₂²	1	4	yes	—
51	#469×C₇₁	C₂²	1	4	yes	complemented
52	#468×C₇₁	C₂²	1	4	yes	complemented
53	#468×C₇₁	C₂²	1	4	yes	complemented
54	#467×C₇₁	C₂²	1	2	yes	complemented
55	#466×C₇₁	C₂²	1	2	yes	—
56	#466×C₇₁	C₂²	1	2	yes	—
57	#466×C₇₁	C₂²	1	2	yes	complemented
58	#466×C₇₁	C₂²	1	4	yes	complemented
59	#465×C₇₁	C₂²	1	4	yes	complemented
60	#442×C₇₁	C₂²	1	4	yes	complemented
61	#440×C₇₁	C₂²	1	4	yes	complemented
62	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
63	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
64	C₄×SD₁₆×C₇₁	C₂²	1	4	yes	complemented
65	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
66	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	complemented
67	C₄×D₈×C₇₁	C₂²	1	2	yes	—
68	C₄×D₈×C₇₁	C₂²	1	2	yes	—
69	C₄×D₈×C₇₁	C₂²	1	2	yes	—
70	C₄×D₈×C₇₁	C₂²	1	2	yes	—
71	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₈×C₇₁	C₂²	1	4	yes	complemented
73	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
74	#428×C₇₁	C₂²	1	2	yes	—
75	#427×C₇₁	C₂²	1	1	yes	characteristic
76	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
77	#418×C₇₁	C₂²	1	2	yes	—
78	#417×C₇₁	C₂²	1	2	yes	—
79	#416×C₇₁	C₂²	1	2	yes	—
80	C₂×#102×C₇₁	C₂²	1	2	yes	—
81	#405×C₇₁	C₂²	1	1	yes	characteristic
82	#405×C₇₁	C₂²	1	1	yes	characteristic
83	#405×C₇₁	C₂²	1	2	yes	complemented
84	#405×C₇₁	C₂²	1	2	yes	complemented
85	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₇₁	C₂²	1	2	yes	complemented
87	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	complemented
89	C₂×#41×C₇₁	—	2	4	no	—
90	C₂×#41×C₇₁	C₂³	1	2	yes	—
91	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₇₁	—	2	2	no	—
94	AGL(1,ℤ/8)×C₇₁	—	2	8	no	—
95	#135×C₇₁	—	2	4	no	—
96	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
99	C₂×D₈×C₇₁	—	2	4	no	—
100	C₂×D₈×C₇₁	C₂³	1	2	yes	—
101	C₂×D₈×C₇₁	C₂³	1	2	yes	—
102	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
103	C₂×D₈×C₇₁	C₂³	1	4	yes	—
104	#131×C₇₁	—	2	4	no	—
105	#131×C₇₁	—	2	4	no	—
106	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
108	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
109	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
112	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
113	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₇₁	—	2	2	no	—
115	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
116	#127×C₇₁	—	2	2	no	—
117	#127×C₇₁	C₂³	1	4	yes	—
118	#126×C₇₁	—	2	4	no	—
119	#126×C₇₁	—	2	4	no	—
120	#125×C₇₁	—	2	2	no	—
121	#125×C₇₁	C₂³	1	4	yes	—
122	#124×C₇₁	—	2	2	no	—
123	#124×C₇₁	—	2	4	no	—
124	#124×C₇₁	—	2	4	no	—
125	#124×C₇₁	C₂³	1	4	yes	—
126	#123×C₇₁	—	2	4	no	—
127	#123×C₇₁	—	2	4	no	—
128	#123×C₇₁	—	2	4	no	—
129	#123×C₇₁	—	2	4	no	—
130	C₂²⋊Q₈×C₇₁	—	2	2	no	—
131	C₂²⋊Q₈×C₇₁	—	2	4	no	—
132	C₂²⋊Q₈×C₇₁	—	2	4	no	—
133	C₂²⋊Q₈×C₇₁	C₂³	1	4	yes	—
134	#121×C₇₁	—	2	4	no	—
135	#121×C₇₁	—	2	2	no	—
136	#121×C₇₁	—	2	4	no	—
137	#121×C₇₁	—	2	2	no	—
138	#121×C₇₁	—	2	2	no	—
139	#121×C₇₁	—	2	4	no	—
140	#121×C₇₁	—	2	4	no	—
141	#121×C₇₁	C₂³	1	4	yes	—
142	#121×C₇₁	C₂³	1	4	yes	—
143	#121×C₇₁	C₂³	1	4	yes	—
144	#120×C₇₁	—	2	4	no	—
145	#120×C₇₁	—	2	4	no	—
146	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
147	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
150	C₄×D₄×C₇₁	—	2	2	no	—
151	C₄×D₄×C₇₁	—	2	2	no	—
152	C₄×D₄×C₇₁	—	2	4	no	—
153	C₄×D₄×C₇₁	—	2	2	no	—
154	C₄×D₄×C₇₁	—	2	2	no	—
155	C₄×D₄×C₇₁	—	2	4	no	—
156	C₄×D₄×C₇₁	D₄	1	2	yes	—
157	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
158	C₄×D₄×C₇₁	D₄	1	2	yes	—
159	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
160	C₄×D₄×C₇₁	C₂³	1	4	yes	—
161	C₄×D₄×C₇₁	C₂³	1	4	yes	—
162	C₄×D₄×C₇₁	C₂³	1	2	yes	—
163	C₄×D₄×C₇₁	C₂³	1	2	yes	—
164	#117×C₇₁	—	2	2	no	—
165	#117×C₇₁	—	2	4	no	—
166	#117×C₇₁	C₂³	1	2	yes	—
167	#117×C₇₁	C₂³	1	1	yes	characteristic
168	#117×C₇₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
171	C₂×C₄²×C₇₁	—	2	2	no	—
172	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
174	#107×C₇₁	C₂³	1	2	yes	—
175	#107×C₇₁	C₂³	1	2	yes	—
176	#107×C₇₁	C₂³	1	1	yes	characteristic
177	#107×C₇₁	C₂³	1	1	yes	characteristic
178	#107×C₇₁	C₂³	1	4	yes	—
179	#106×C₇₁	C₂³	1	2	yes	—
180	#106×C₇₁	C₂³	1	4	yes	—
181	#103×C₇₁	C₂³	1	2	yes	—
182	#103×C₇₁	C₂³	1	2	yes	—
183	#103×C₇₁	C₂³	1	4	yes	—
184	#102×C₇₁	C₂³	1	4	yes	—
185	#102×C₇₁	C₂³	1	4	yes	—
186	#102×C₇₁	C₂³	1	2	yes	—
187	#102×C₇₁	C₂³	1	2	yes	—
188	#102×C₇₁	C₂³	1	4	yes	—
189	#102×C₇₁	C₂³	1	4	yes	—
190	#102×C₇₁	C₂³	1	4	yes	—
191	#97×C₇₁	C₂³	1	2	yes	—
192	#97×C₇₁	C₂³	1	2	yes	—
193	#97×C₇₁	C₂³	1	2	yes	—
194	C₄×C₈×C₇₁	C₂³	1	2	yes	—
195	C₄×C₈×C₇₁	C₂³	1	2	yes	—
196	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₇₁	C₂³	1	2	yes	—
201	C₂⁴×C₇₁	—	2	2	no	—
202	#41×C₇₁	—	2	2	no	—
203	#41×C₇₁	—	2	2	no	—
204	#41×C₇₁	—	2	4	no	—
205	#41×C₇₁	—	2	4	no	—
206	#41×C₇₁	—	8	8	no	—
207	C₂×Q₈×C₇₁	—	2	4	no	—
208	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₇₁	—	2	2	no	—
211	C₂×D₄×C₇₁	—	2	4	no	—
212	C₂×D₄×C₇₁	—	2	4	no	—
213	C₂×D₄×C₇₁	—	2	4	no	—
214	C₂×D₄×C₇₁	—	2	2	no	—
215	C₂×D₄×C₇₁	—	2	4	no	—
216	C₂×D₄×C₇₁	—	2	4	no	—
217	C₂×D₄×C₇₁	—	2	4	no	—
218	C₂×D₄×C₇₁	—	2	4	no	—
219	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₇₁	C₂⁴	1	4	yes	—
222	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₇₁	—	2	2	no	—
224	C₂²×C₄×C₇₁	—	2	2	no	—
225	C₂²×C₄×C₇₁	—	2	2	no	—
226	C₂²×C₄×C₇₁	—	2	4	no	—
227	C₂²×C₄×C₇₁	—	2	2	no	—
228	C₂²×C₄×C₇₁	—	2	4	no	—
229	C₂²×C₄×C₇₁	—	8	4	no	—
230	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₇₁	—	2	2	no	—
237	SD₁₆×C₇₁	—	2	4	no	—
238	SD₁₆×C₇₁	—	2	8	no	—
239	D₈×C₇₁	—	2	4	no	—
240	D₈×C₇₁	—	2	4	no	—
241	D₈×C₇₁	—	2	2	no	—
242	D₈×C₇₁	—	2	8	no	—
243	M₁₆×C₇₁	—	2	2	no	—
244	M₁₆×C₇₁	—	2	4	no	—
245	M₁₆×C₇₁	—	2	4	no	—
246	M₁₆×C₇₁	#41	1	4	yes	complemented
247	C₂×C₈×C₇₁	—	2	2	no	—
248	C₂×C₈×C₇₁	—	2	4	no	—
249	C₂×C₈×C₇₁	—	2	4	no	—
250	C₂×C₈×C₇₁	#41	1	4	yes	complemented
251	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
253	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
256	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₇₁	—	2	2	no	—
258	C₄⋊C₄×C₇₁	—	2	2	no	—
259	C₄⋊C₄×C₇₁	—	2	2	no	—
260	C₄⋊C₄×C₇₁	—	2	4	no	—
261	C₄⋊C₄×C₇₁	—	2	4	no	—
262	C₄⋊C₄×C₇₁	—	2	4	no	—
263	C₄⋊C₄×C₇₁	—	2	4	no	—
264	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
267	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₇₁	C₂⁴	1	4	yes	—
270	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₇₁	—	2	2	no	—
272	C₂²⋊C₄×C₇₁	—	2	4	no	—
273	C₂²⋊C₄×C₇₁	—	2	4	no	—
274	C₂²⋊C₄×C₇₁	—	2	4	no	—
275	C₂²⋊C₄×C₇₁	—	2	2	no	—
276	C₂²⋊C₄×C₇₁	—	2	2	no	—
277	C₂²⋊C₄×C₇₁	—	2	4	no	—
278	C₂²⋊C₄×C₇₁	—	2	4	no	—
279	C₂²⋊C₄×C₇₁	—	2	4	no	—
280	C₂²⋊C₄×C₇₁	—	2	4	no	—
281	C₂²⋊C₄×C₇₁	—	2	4	no	—
282	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
285	C₄²×C₇₁	—	2	2	no	—
286	C₄²×C₇₁	—	2	2	no	—
287	C₄²×C₇₁	—	2	2	no	—
288	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₇₁	C₂×D₄	1	2	yes	—
290	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₇₁	C₂×D₄	1	2	yes	—
292	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
293	C₄²×C₇₁	C₂⁴	1	2	yes	—
294	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
295	C₂³×C₇₁	—	2	4	no	—
296	C₂³×C₇₁	—	2	2	no	—
297	C₂³×C₇₁	—	4	4	no	—
298	C₂³×C₇₁	—	8	2	no	—
299	C₂³×C₇₁	—	8	2	no	—
300	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
301	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₇₁	—	2	2	no	—
303	Q₈×C₇₁	—	2	2	no	—
304	Q₈×C₇₁	—	2	2	no	—
305	Q₈×C₇₁	—	8	4	no	—
306	D₄×C₇₁	—	2	4	no	—
307	D₄×C₇₁	—	2	2	no	—
308	D₄×C₇₁	—	2	4	no	—
309	D₄×C₇₁	—	2	2	no	—
310	D₄×C₇₁	—	2	4	no	—
311	D₄×C₇₁	—	2	2	no	—
312	D₄×C₇₁	—	4	4	no	—
313	D₄×C₇₁	—	4	4	no	—
314	D₄×C₇₁	—	8	4	no	—
315	D₄×C₇₁	—	8	4	no	—
316	D₄×C₇₁	—	8	4	no	—
317	D₄×C₇₁	—	8	4	no	—
318	D₄×C₇₁	—	8	4	no	—
319	C₂×C₄×C₇₁	—	2	2	no	—
320	C₂×C₄×C₇₁	—	2	4	no	—
321	C₂×C₄×C₇₁	—	2	2	no	—
322	C₂×C₄×C₇₁	—	2	2	no	—
323	C₂×C₄×C₇₁	—	2	2	no	—
324	C₂×C₄×C₇₁	—	2	2	no	—
325	C₂×C₄×C₇₁	—	2	2	no	—
326	C₂×C₄×C₇₁	—	2	4	no	—
327	C₂×C₄×C₇₁	—	4	1	no	—
328	C₂×C₄×C₇₁	—	4	2	no	—
329	C₂×C₄×C₇₁	—	4	4	no	—
330	C₂×C₄×C₇₁	—	4	8	no	—
331	C₂×C₄×C₇₁	—	4	4	no	—
332	C₂×C₄×C₇₁	—	8	2	no	—
333	C₂×C₄×C₇₁	—	8	4	no	—
334	C₂×C₄×C₇₁	—	8	2	no	—
335	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
344	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
345	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
346	C₈×C₇₁	—	2	1	no	—
347	C₈×C₇₁	—	2	1	no	—
348	C₈×C₇₁	—	2	2	no	—
349	C₈×C₇₁	C₂×#41	1	2	yes	—
350	C₈×C₇₁	C₂×#41	1	4	yes	—
351	C₈×C₇₁	C₂×#41	1	2	yes	—
352	C₂²×C₇₁	—	2	1	no	—
353	C₂²×C₇₁	—	2	1	no	—
354	C₂²×C₇₁	—	2	2	no	—
355	C₂²×C₇₁	—	2	2	no	—
356	C₂²×C₇₁	—	2	2	no	—
357	C₂²×C₇₁	—	4	2	no	—
358	C₂²×C₇₁	—	4	4	no	—
359	C₂²×C₇₁	—	4	2	no	—
360	C₂²×C₇₁	—	4	4	no	—
361	C₂²×C₇₁	—	4	4	no	—
362	C₂²×C₇₁	—	4	2	no	—
363	C₂²×C₇₁	—	8	8	no	—
364	C₂²×C₇₁	#532	1	2	yes	—
365	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₇₁	—	2	1	no	—
367	C₄×C₇₁	—	2	1	no	—
368	C₄×C₇₁	—	2	2	no	—
369	C₄×C₇₁	—	2	2	no	—
370	C₄×C₇₁	—	2	1	no	—
371	C₄×C₇₁	—	2	2	no	—
372	C₄×C₇₁	—	4	2	no	—
373	C₄×C₇₁	—	4	2	no	—
374	C₄×C₇₁	—	4	4	no	—
375	C₄×C₇₁	—	4	2	no	—
376	C₄×C₇₁	#532	1	2	yes	—
377	C₄×C₇₁	#576	1	2	yes	—
378	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
379	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
380	#60695	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₇₁	—	2	2	no	—
382	C₂×C₇₁	—	4	2	no	—
383	C₂×C₇₁	—	8	2	no	—
384	C₂×C₇₁	—	8	4	no	—
385	C₂×C₇₁	C₂×#532	1	1	yes	characteristic
386	C₂×C₇₁	C₂×#576	1	1	yes	characteristic
387	C₂×C₇₁	#3584	1	1	yes	characteristic
388	#3460	C₂×C₇₁	1	2	yes	complemented
389	#3179	C₂×C₇₁	1	4	yes	complemented
390	#3176	C₂×C₇₁	1	2	yes	complemented
391	#3175	C₂×C₇₁	1	2	yes	complemented
392	#3171	C₂×C₇₁	1	4	yes	complemented
393	#3169	C₂×C₇₁	1	2	yes	complemented
394	#3168	C₂×C₇₁	1	2	yes	complemented
395	#3164	C₂×C₇₁	1	1	yes	characteristic, complemented
396	#3155	C₂×C₇₁	1	1	yes	characteristic, complemented
397	#3136	C₂×C₇₁	1	2	yes	complemented
398	#3062	C₂×C₇₁	1	2	yes	complemented
399	#3061	C₂×C₇₁	1	1	yes	characteristic, complemented
400	#3058	C₂×C₇₁	1	1	yes	characteristic, complemented
401	C₄×AGL(1,ℤ/8)	C₂×C₇₁	1	2	yes	complemented
402	C₄×#135	C₂×C₇₁	1	1	yes	characteristic, complemented
403	C₂×C₄×D₈	C₂×C₇₁	1	1	yes	characteristic, complemented
404	C₄×#131	C₂×C₇₁	1	1	yes	characteristic, complemented
405	C₇₁	#60695	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	2	yes	—
407	C₂×#135	C₂²×C₇₁	1	1	yes	characteristic
408	C₂²×D₈	C₂²×C₇₁	1	1	yes	characteristic
409	C₂×#131	C₂²×C₇₁	1	1	yes	characteristic
410	C₂×#131	C₂²×C₇₁	1	1	yes	characteristic
411	#544	C₂²×C₇₁	1	2	yes	—
412	#542	—	2	2	no	—
413	#542	C₂²×C₇₁	1	4	yes	complemented
414	#540	—	2	2	no	—
415	#540	C₂²×C₇₁	1	4	yes	complemented
416	#538	—	2	4	no	—
417	#537	C₂²×C₇₁	1	2	yes	—
418	#535	C₂²×C₇₁	1	2	yes	—
419	#535	C₂²×C₇₁	1	2	yes	—
420	#532	—	2	2	no	—
421	#532	C₂²×C₇₁	1	4	yes	complemented
422	#529	—	2	2	no	—
423	#529	C₂²×C₇₁	1	4	yes	complemented
424	#525	—	2	4	no	—
425	C₄×#41	C₂²×C₇₁	1	2	yes	—
426	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
428	#501	C₂²×C₇₁	1	4	yes	complemented
429	#500	C₂²×C₇₁	1	2	yes	complemented
430	#499	C₂²×C₇₁	1	2	yes	complemented
431	#496	C₂²×C₇₁	1	4	yes	—
432	#495	C₂²×C₇₁	1	2	yes	—
433	#493	C₂²×C₇₁	1	2	yes	—
434	#490	C₂²×C₇₁	1	4	yes	complemented
435	#489	C₂²×C₇₁	1	4	yes	complemented
436	#488	C₂²×C₇₁	1	4	yes	complemented
437	#486	C₂²×C₇₁	1	4	yes	complemented
438	#469	C₂²×C₇₁	1	4	yes	—
439	#469	C₂²×C₇₁	1	4	yes	complemented
440	#468	C₂²×C₇₁	1	4	yes	complemented
441	#468	C₂²×C₇₁	1	4	yes	complemented
442	#467	C₂²×C₇₁	1	2	yes	complemented
443	#466	C₂²×C₇₁	1	2	yes	—
444	#466	C₂²×C₇₁	1	2	yes	—
445	#466	C₂²×C₇₁	1	2	yes	complemented
446	#466	C₂²×C₇₁	1	4	yes	complemented
447	#465	C₂²×C₇₁	1	4	yes	complemented
448	#442	C₂²×C₇₁	1	4	yes	complemented
449	#440	C₂²×C₇₁	1	4	yes	complemented
450	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
451	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
452	C₄×SD₁₆	C₂²×C₇₁	1	4	yes	complemented
453	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
454	C₄×SD₁₆	C₂²×C₇₁	1	2	yes	complemented
455	C₄×D₈	C₂²×C₇₁	1	2	yes	—
456	C₄×D₈	C₂²×C₇₁	1	2	yes	—
457	C₄×D₈	C₂²×C₇₁	1	2	yes	—
458	C₄×D₈	C₂²×C₇₁	1	2	yes	—
459	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
460	C₄×D₈	C₂²×C₇₁	1	4	yes	complemented
461	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
462	#428	C₂²×C₇₁	1	2	yes	—
463	#427	C₂²×C₇₁	1	1	yes	characteristic
464	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
465	#418	C₂²×C₇₁	1	2	yes	—
466	#417	C₂²×C₇₁	1	2	yes	—
467	#416	C₂²×C₇₁	1	2	yes	—
468	C₂×#102	C₂²×C₇₁	1	2	yes	—
469	#405	C₂²×C₇₁	1	1	yes	characteristic
470	#405	C₂²×C₇₁	1	1	yes	characteristic
471	#405	C₂²×C₇₁	1	2	yes	complemented
472	#405	C₂²×C₇₁	1	2	yes	complemented
473	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
474	C₄×M₁₆	C₂²×C₇₁	1	2	yes	complemented
475	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
476	C₂×C₄×C₈	C₂²×C₇₁	1	2	yes	complemented
477	C₂×#41	—	2	4	no	—
478	C₂×#41	C₂³×C₇₁	1	2	yes	—
479	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
480	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
481	C₂³×C₄	—	2	2	no	—
482	AGL(1,ℤ/8)	—	2	8	no	—
483	#135	—	2	4	no	—
484	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
485	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
486	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
487	C₂×D₈	—	2	4	no	—
488	C₂×D₈	C₂³×C₇₁	1	2	yes	—
489	C₂×D₈	C₂³×C₇₁	1	2	yes	—
490	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
491	C₂×D₈	C₂³×C₇₁	1	4	yes	—
492	#131	—	2	4	no	—
493	#131	—	2	4	no	—
494	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
495	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
496	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
497	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
500	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
501	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
502	C₄⋊Q₈	—	2	2	no	—
503	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
504	#127	—	2	2	no	—
505	#127	C₂³×C₇₁	1	4	yes	—
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#125	—	2	2	no	—
509	#125	C₂³×C₇₁	1	4	yes	—
510	#124	—	2	2	no	—
511	#124	—	2	4	no	—
512	#124	—	2	4	no	—
513	#124	C₂³×C₇₁	1	4	yes	—
514	#123	—	2	4	no	—
515	#123	—	2	4	no	—
516	#123	—	2	4	no	—
517	#123	—	2	4	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	C₂³×C₇₁	1	4	yes	—
522	#121	—	2	4	no	—
523	#121	—	2	2	no	—
524	#121	—	2	4	no	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#121	C₂³×C₇₁	1	4	yes	—
530	#121	C₂³×C₇₁	1	4	yes	—
531	#121	C₂³×C₇₁	1	4	yes	—
532	#120	—	2	4	no	—
533	#120	—	2	4	no	—
534	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
535	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
536	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
537	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	D₄×C₇₁	1	2	yes	—
545	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
546	C₄×D₄	D₄×C₇₁	1	2	yes	—
547	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
548	C₄×D₄	C₂³×C₇₁	1	4	yes	—
549	C₄×D₄	C₂³×C₇₁	1	4	yes	—
550	C₄×D₄	C₂³×C₇₁	1	2	yes	—
551	C₄×D₄	C₂³×C₇₁	1	2	yes	—
552	#117	—	2	2	no	—
553	#117	—	2	4	no	—
554	#117	C₂³×C₇₁	1	2	yes	—
555	#117	C₂³×C₇₁	1	1	yes	characteristic
556	#117	C₂³×C₇₁	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
558	C₂×C₂²⋊C₄	—	2	2	no	—
559	C₂×C₄²	—	2	2	no	—
560	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
562	#107	C₂³×C₇₁	1	2	yes	—
563	#107	C₂³×C₇₁	1	2	yes	—
564	#107	C₂³×C₇₁	1	1	yes	characteristic
565	#107	C₂³×C₇₁	1	1	yes	characteristic
566	#107	C₂³×C₇₁	1	4	yes	—
567	#106	C₂³×C₇₁	1	2	yes	—
568	#106	C₂³×C₇₁	1	4	yes	—
569	#103	C₂³×C₇₁	1	2	yes	—
570	#103	C₂³×C₇₁	1	2	yes	—
571	#103	C₂³×C₇₁	1	4	yes	—
572	#102	C₂³×C₇₁	1	4	yes	—
573	#102	C₂³×C₇₁	1	4	yes	—
574	#102	C₂³×C₇₁	1	2	yes	—
575	#102	C₂³×C₇₁	1	2	yes	—
576	#102	C₂³×C₇₁	1	4	yes	—
577	#102	C₂³×C₇₁	1	4	yes	—
578	#102	C₂³×C₇₁	1	4	yes	—
579	#97	C₂³×C₇₁	1	2	yes	—
580	#97	C₂³×C₇₁	1	2	yes	—
581	#97	C₂³×C₇₁	1	2	yes	—
582	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
583	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
584	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
586	C₄×C₈	C₂³×C₇₁	1	2	yes	—
587	C₄×C₈	C₂³×C₇₁	1	2	yes	—
588	C₄×C₈	C₂³×C₇₁	1	2	yes	—
589	C₂⁴	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	—	8	8	no	—
595	C₂×Q₈	—	2	4	no	—
596	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
597	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
608	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
609	C₂×D₄	C₂⁴×C₇₁	1	4	yes	—
610	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	8	4	no	—
618	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
620	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
624	Q₁₆	—	2	2	no	—
625	SD₁₆	—	2	4	no	—
626	SD₁₆	—	2	8	no	—
627	D₈	—	2	4	no	—
628	D₈	—	2	4	no	—
629	D₈	—	2	2	no	—
630	D₈	—	2	8	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	—	2	4	no	—
634	M₁₆	#41×C₇₁	1	4	yes	complemented
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	#41×C₇₁	1	4	yes	complemented
639	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
642	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
643	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
644	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
653	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
655	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₇₁	1	4	yes	—
658	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
678	C₄²	C₂×D₄×C₇₁	1	2	yes	—
679	C₄²	C₂×D₄×C₇₁	1	2	yes	—
680	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
681	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
682	C₄²	C₂⁴×C₇₁	1	2	yes	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	2	no	—
688	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
689	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	8	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	D₄	—	8	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
732	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
733	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂×#41×C₇₁	1	2	yes	—
738	C₈	C₂×#41×C₇₁	1	4	yes	—
739	C₈	C₂×#41×C₇₁	1	2	yes	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	8	8	no	—
752	C₂²	#532×C₇₁	1	2	yes	—
753	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	#532×C₇₁	1	2	yes	—
765	C₄	#576×C₇₁	1	2	yes	—
766	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
767	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	2	no	—
770	C₂	—	8	4	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×#532×C₇₁	1	1	yes	characteristic
773	C₂	C₂×#576×C₇₁	1	1	yes	characteristic
774	C₂	C₇₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3460	C₂	semidirect
2. C₇₁×#3179	C₂	semidirect
3. C₇₁×#3176	C₂	semidirect
4. C₇₁×#3175	C₂	semidirect
5. C₇₁×#3171	C₂	semidirect
6. C₇₁×#3169	C₂	semidirect
7. C₇₁×#3168	C₂	semidirect
8. C₇₁×#3164	C₂	semidirect
9. C₇₁×#3155	C₂	semidirect
10. C₇₁×#3136	C₂	semidirect
11. C₇₁×#3062	C₂	semidirect
12. C₇₁×#3061	C₂	semidirect
13. C₇₁×#3058	C₂	semidirect
14. C₄×AGL(1,ℤ/8)×C₇₁	C₂	semidirect
15. C₄×#135×C₇₁	C₂	semidirect
16. C₂×C₄×D₈×C₇₁	C₂	semidirect
17. C₄×#131×C₇₁	C₂	semidirect
25. #542×C₇₁	C₂²	semidirect
27. #540×C₇₁	C₂²	semidirect
33. #532×C₇₁	C₂²	semidirect
35. #529×C₇₁	C₂²	semidirect
40. #501×C₇₁	C₂²	semidirect
41. #500×C₇₁	C₂²	semidirect
42. #499×C₇₁	C₂²	semidirect
46. #490×C₇₁	C₂²	semidirect
47. #489×C₇₁	C₂²	semidirect
48. #488×C₇₁	C₂²	semidirect
49. #486×C₇₁	C₂²	semidirect
51. #469×C₇₁	C₂²	semidirect
52. #468×C₇₁	C₂²	semidirect
53. #468×C₇₁	C₂²	semidirect
54. #467×C₇₁	C₂²	semidirect
57. #466×C₇₁	C₂²	semidirect
58. #466×C₇₁	C₂²	semidirect
59. #465×C₇₁	C₂²	semidirect
60. #442×C₇₁	C₂²	semidirect
61. #440×C₇₁	C₂²	semidirect
62. C₄×Q₁₆×C₇₁	C₂²	semidirect
63. C₄×Q₁₆×C₇₁	C₂²	semidirect
64. C₄×SD₁₆×C₇₁	C₂²	semidirect
65. C₄×SD₁₆×C₇₁	C₂²	semidirect
66. C₄×SD₁₆×C₇₁	C₂²	semidirect
71. C₄×D₈×C₇₁	C₂²	semidirect
72. C₄×D₈×C₇₁	C₂²	semidirect
73. C₄×D₈×C₇₁	C₂²	semidirect
83. #405×C₇₁	C₂²	semidirect
84. #405×C₇₁	C₂²	semidirect
86. C₄×M₁₆×C₇₁	C₂²	semidirect
88. C₂×C₄×C₈×C₇₁	C₂²	semidirect
246. M₁₆×C₇₁	#41	semidirect
250. C₂×C₈×C₇₁	#41	semidirect
380. #60695	C₇₁	direct (N × H)
388. #3460	C₂×C₇₁	semidirect
389. #3179	C₂×C₇₁	semidirect
390. #3176	C₂×C₇₁	semidirect
391. #3175	C₂×C₇₁	semidirect
392. #3171	C₂×C₇₁	semidirect
393. #3169	C₂×C₇₁	semidirect
394. #3168	C₂×C₇₁	semidirect
395. #3164	C₂×C₇₁	semidirect
396. #3155	C₂×C₇₁	semidirect
397. #3136	C₂×C₇₁	semidirect
398. #3062	C₂×C₇₁	semidirect
399. #3061	C₂×C₇₁	semidirect
400. #3058	C₂×C₇₁	semidirect
401. C₄×AGL(1,ℤ/8)	C₂×C₇₁	semidirect
402. C₄×#135	C₂×C₇₁	semidirect
403. C₂×C₄×D₈	C₂×C₇₁	semidirect
404. C₄×#131	C₂×C₇₁	semidirect
405. C₇₁	#60695	direct (N × H)
413. #542	C₂²×C₇₁	semidirect
415. #540	C₂²×C₇₁	semidirect
421. #532	C₂²×C₇₁	semidirect
423. #529	C₂²×C₇₁	semidirect
428. #501	C₂²×C₇₁	semidirect
429. #500	C₂²×C₇₁	semidirect
430. #499	C₂²×C₇₁	semidirect
434. #490	C₂²×C₇₁	semidirect
435. #489	C₂²×C₇₁	semidirect
436. #488	C₂²×C₇₁	semidirect
437. #486	C₂²×C₇₁	semidirect
439. #469	C₂²×C₇₁	semidirect
440. #468	C₂²×C₇₁	semidirect
441. #468	C₂²×C₇₁	semidirect
442. #467	C₂²×C₇₁	semidirect
445. #466	C₂²×C₇₁	semidirect
446. #466	C₂²×C₇₁	semidirect
447. #465	C₂²×C₇₁	semidirect
448. #442	C₂²×C₇₁	semidirect
449. #440	C₂²×C₇₁	semidirect
450. C₄×Q₁₆	C₂²×C₇₁	semidirect
451. C₄×Q₁₆	C₂²×C₇₁	semidirect
452. C₄×SD₁₆	C₂²×C₇₁	semidirect
453. C₄×SD₁₆	C₂²×C₇₁	semidirect
454. C₄×SD₁₆	C₂²×C₇₁	semidirect
459. C₄×D₈	C₂²×C₇₁	semidirect
460. C₄×D₈	C₂²×C₇₁	semidirect
461. C₄×D₈	C₂²×C₇₁	semidirect
471. #405	C₂²×C₇₁	semidirect
472. #405	C₂²×C₇₁	semidirect
474. C₄×M₁₆	C₂²×C₇₁	semidirect
476. C₂×C₄×C₈	C₂²×C₇₁	semidirect
634. M₁₆	#41×C₇₁	semidirect
638. C₂×C₈	#41×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#3460	2
C₇₁×#3179	2
C₇₁×#3176	2
C₇₁×#3175	2
C₇₁×#3171	2
C₇₁×#3169	2
C₇₁×#3168	2
C₇₁×#3164	2
C₇₁×#3155	2
C₇₁×#3136	2
C₇₁×#3062	2
C₇₁×#3061	2
C₇₁×#3058	2
C₄×AGL(1,ℤ/8)×C₇₁	2
C₄×#135×C₇₁	2
C₂×C₄×D₈×C₇₁	2
C₄×#131×C₇₁	2
#60695	71

Subgroups — C71×#60695 #31881567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#60695 #31881567