Subgroups — C₇₁×#60926 #31881798

Order 18176.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3263	C₂	1	2	yes	maximal, complemented
4	C₇₁×#3262	C₂	1	2	yes	maximal, complemented
5	C₇₁×#3257	C₂	1	2	yes	maximal, complemented
6	C₇₁×#3257	C₂	1	2	yes	maximal, complemented
7	C₇₁×#3256	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3251	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3250	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3247	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₁×#3041	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#463×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₇₁	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₇₁	C₂²	1	1	yes	characteristic
28	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
29	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
30	#559×C₇₁	—	2	1	no	—
31	#559×C₇₁	—	2	1	no	—
32	#556×C₇₁	—	2	1	no	—
33	#556×C₇₁	—	2	1	no	—
34	#551×C₇₁	—	2	2	no	—
35	#551×C₇₁	—	2	2	no	—
36	#544×C₇₁	C₂²	1	1	yes	characteristic
37	#542×C₇₁	—	2	1	no	—
38	#542×C₇₁	C₂²	1	2	yes	complemented
39	#542×C₇₁	C₂²	1	2	yes	complemented
40	#542×C₇₁	C₂²	1	2	yes	complemented
41	#540×C₇₁	—	2	1	no	—
42	#540×C₇₁	C₂²	1	2	yes	complemented
43	#538×C₇₁	—	2	2	no	—
44	#537×C₇₁	C₂²	1	1	yes	characteristic
45	#536×C₇₁	C₂²	1	1	yes	characteristic
46	#535×C₇₁	C₂²	1	1	yes	characteristic
47	#535×C₇₁	C₂²	1	1	yes	characteristic
48	#535×C₇₁	C₂²	1	1	yes	characteristic
49	#533×C₇₁	C₂²	1	1	yes	characteristic
50	#532×C₇₁	—	2	1	no	—
51	#532×C₇₁	C₂²	1	2	yes	complemented
52	#529×C₇₁	—	2	1	no	—
53	#529×C₇₁	C₂²	1	2	yes	complemented
54	#529×C₇₁	C₂²	1	2	yes	complemented
55	#529×C₇₁	C₂²	1	2	yes	complemented
56	C₂×#124×C₇₁	C₂²	1	1	yes	characteristic
57	#525×C₇₁	—	2	2	no	—
58	#519×C₇₁	C₂²	1	1	yes	characteristic
59	#518×C₇₁	C₂²	1	1	yes	characteristic
60	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
63	#479×C₇₁	C₂²	1	1	yes	characteristic, complemented
64	#479×C₇₁	C₂²	1	1	yes	characteristic, complemented
65	#479×C₇₁	C₂²	1	2	yes	complemented
66	#479×C₇₁	C₂²	1	2	yes	complemented
67	#478×C₇₁	C₂²	1	1	yes	characteristic, complemented
68	#478×C₇₁	C₂²	1	1	yes	characteristic, complemented
69	#478×C₇₁	C₂²	1	2	yes	complemented
70	#478×C₇₁	C₂²	1	2	yes	complemented
71	#478×C₇₁	C₂²	1	2	yes	complemented
72	#478×C₇₁	C₂²	1	2	yes	complemented
73	#477×C₇₁	C₂²	1	1	yes	characteristic, complemented
74	#477×C₇₁	C₂²	1	2	yes	complemented
75	#476×C₇₁	C₂²	1	1	yes	characteristic, complemented
76	#476×C₇₁	C₂²	1	2	yes	complemented
77	#476×C₇₁	C₂²	1	2	yes	complemented
78	#475×C₇₁	C₂²	1	1	yes	characteristic, complemented
79	#475×C₇₁	C₂²	1	2	yes	complemented
80	#474×C₇₁	C₂²	1	1	yes	characteristic, complemented
81	#474×C₇₁	C₂²	1	2	yes	complemented
82	#474×C₇₁	C₂²	1	2	yes	complemented
83	#470×C₇₁	C₂²	1	2	yes	complemented
84	#469×C₇₁	C₂²	1	2	yes	—
85	#469×C₇₁	C₂²	1	2	yes	—
86	#469×C₇₁	C₂²	1	2	yes	complemented
87	#468×C₇₁	C₂²	1	2	yes	complemented
88	#468×C₇₁	C₂²	1	2	yes	complemented
89	#468×C₇₁	C₂²	1	2	yes	complemented
90	#468×C₇₁	C₂²	1	2	yes	complemented
91	#467×C₇₁	C₂²	1	2	yes	complemented
92	#466×C₇₁	C₂²	1	2	yes	—
93	#466×C₇₁	C₂²	1	2	yes	—
94	#466×C₇₁	C₂²	1	2	yes	complemented
95	#465×C₇₁	C₂²	1	2	yes	complemented
96	#465×C₇₁	C₂²	1	2	yes	complemented
97	#465×C₇₁	C₂²	1	2	yes	complemented
98	#465×C₇₁	C₂²	1	2	yes	complemented
99	#464×C₇₁	C₂²	1	2	yes	complemented
100	#464×C₇₁	C₂²	1	2	yes	complemented
101	#464×C₇₁	C₂²	1	2	yes	complemented
102	#464×C₇₁	C₂²	1	2	yes	complemented
103	#463×C₇₁	C₂²	1	2	yes	—
104	#463×C₇₁	C₂²	1	2	yes	—
105	#463×C₇₁	C₂²	1	2	yes	—
106	#463×C₇₁	C₂²	1	2	yes	—
107	#463×C₇₁	C₂²	1	2	yes	—
108	#463×C₇₁	C₂²	1	2	yes	—
109	#463×C₇₁	C₂²	1	2	yes	complemented
110	#463×C₇₁	C₂²	1	2	yes	complemented
111	#460×C₇₁	C₂²	1	2	yes	complemented
112	#460×C₇₁	C₂²	1	2	yes	complemented
113	#459×C₇₁	C₂²	1	2	yes	—
114	#459×C₇₁	C₂²	1	2	yes	—
115	#428×C₇₁	C₂²	1	1	yes	characteristic
116	#428×C₇₁	C₂²	1	1	yes	characteristic
117	#427×C₇₁	C₂²	1	1	yes	characteristic
118	#427×C₇₁	C₂²	1	1	yes	characteristic
119	#424×C₇₁	C₂²	1	1	yes	characteristic
120	#424×C₇₁	C₂²	1	1	yes	characteristic
121	#424×C₇₁	C₂²	1	2	yes	complemented
122	#424×C₇₁	C₂²	1	2	yes	complemented
123	#423×C₇₁	C₂²	1	1	yes	characteristic
124	#423×C₇₁	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	complemented
127	#419×C₇₁	C₂²	1	1	yes	characteristic
128	#418×C₇₁	C₂²	1	1	yes	characteristic
129	#418×C₇₁	C₂²	1	1	yes	characteristic
130	#418×C₇₁	C₂²	1	1	yes	characteristic
131	#416×C₇₁	C₂²	1	1	yes	characteristic
132	#416×C₇₁	C₂²	1	1	yes	characteristic
133	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
134	C₂×#102×C₇₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₇₁	—	2	2	no	—
136	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇₁	—	2	1	no	—
142	#137×C₇₁	—	4	2	no	—
143	AGL(1,ℤ/8)×C₇₁	—	4	2	no	—
144	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₇₁	—	4	2	no	—
146	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
150	C₂×D₈×C₇₁	—	4	2	no	—
151	C₂×D₈×C₇₁	C₂³	1	2	yes	—
152	C₂×D₈×C₇₁	C₂³	1	2	yes	—
153	C₂×D₈×C₇₁	C₂³	1	2	yes	—
154	#131×C₇₁	—	4	2	no	—
155	#131×C₇₁	—	4	2	no	—
156	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
159	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
163	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₇₁	—	2	1	no	—
165	C₄⋊Q₈×C₇₁	—	2	1	no	—
166	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
169	#127×C₇₁	—	2	1	no	—
170	#127×C₇₁	—	2	1	no	—
171	#127×C₇₁	C₂³	1	2	yes	—
172	#126×C₇₁	—	2	2	no	—
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	—	2	2	no	—
175	#126×C₇₁	—	2	2	no	—
176	#126×C₇₁	—	2	2	no	—
177	#126×C₇₁	—	2	2	no	—
178	#125×C₇₁	—	2	1	no	—
179	#125×C₇₁	C₂³	1	1	yes	characteristic
180	#125×C₇₁	C₂³	1	1	yes	characteristic
181	#125×C₇₁	C₂³	1	2	yes	—
182	#124×C₇₁	—	2	1	no	—
183	#124×C₇₁	—	2	1	no	—
184	#124×C₇₁	—	2	1	no	—
185	#124×C₇₁	—	2	2	no	—
186	#124×C₇₁	—	2	2	no	—
187	#124×C₇₁	—	2	2	no	—
188	#124×C₇₁	—	2	1	no	—
189	#124×C₇₁	—	2	1	no	—
190	#124×C₇₁	—	2	2	no	—
191	#124×C₇₁	C₂³	1	2	yes	—
192	#124×C₇₁	C₂³	1	2	yes	—
193	#124×C₇₁	C₂³	1	2	yes	—
194	#123×C₇₁	—	2	2	no	—
195	#123×C₇₁	—	2	2	no	—
196	#123×C₇₁	—	2	2	no	—
197	#123×C₇₁	—	2	2	no	—
198	#123×C₇₁	—	2	2	no	—
199	#123×C₇₁	—	2	2	no	—
200	#123×C₇₁	—	2	2	no	—
201	#123×C₇₁	—	2	2	no	—
202	#123×C₇₁	—	2	2	no	—
203	C₂²⋊Q₈×C₇₁	—	2	1	no	—
204	C₂²⋊Q₈×C₇₁	—	2	1	no	—
205	C₂²⋊Q₈×C₇₁	—	2	1	no	—
206	C₂²⋊Q₈×C₇₁	—	2	2	no	—
207	C₂²⋊Q₈×C₇₁	—	2	2	no	—
208	C₂²⋊Q₈×C₇₁	—	2	2	no	—
209	C₂²⋊Q₈×C₇₁	—	2	2	no	—
210	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
213	#121×C₇₁	—	2	2	no	—
214	#121×C₇₁	—	2	1	no	—
215	#121×C₇₁	—	2	2	no	—
216	#121×C₇₁	—	2	1	no	—
217	#121×C₇₁	—	2	1	no	—
218	#121×C₇₁	—	2	2	no	—
219	#121×C₇₁	—	2	2	no	—
220	#121×C₇₁	C₂³	1	2	yes	—
221	#121×C₇₁	C₂³	1	2	yes	—
222	#121×C₇₁	C₂³	1	2	yes	—
223	#121×C₇₁	C₂³	1	2	yes	—
224	#121×C₇₁	C₂³	1	2	yes	—
225	#120×C₇₁	—	2	2	no	—
226	#120×C₇₁	—	2	2	no	—
227	#120×C₇₁	—	2	2	no	—
228	C₄×Q₈×C₇₁	—	2	1	no	—
229	C₄×Q₈×C₇₁	—	2	1	no	—
230	C₄×Q₈×C₇₁	—	2	1	no	—
231	C₄×Q₈×C₇₁	—	2	1	no	—
232	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
233	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₇₁	—	2	1	no	—
239	C₄×D₄×C₇₁	—	2	1	no	—
240	C₄×D₄×C₇₁	—	2	2	no	—
241	C₄×D₄×C₇₁	—	2	2	no	—
242	C₄×D₄×C₇₁	—	2	2	no	—
243	C₄×D₄×C₇₁	—	2	1	no	—
244	C₄×D₄×C₇₁	—	2	1	no	—
245	C₄×D₄×C₇₁	—	2	1	no	—
246	C₄×D₄×C₇₁	—	2	1	no	—
247	C₄×D₄×C₇₁	—	2	2	no	—
248	C₄×D₄×C₇₁	D₄	1	2	yes	—
249	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
250	C₄×D₄×C₇₁	D₄	1	2	yes	—
251	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
252	C₄×D₄×C₇₁	C₂³	1	2	yes	—
253	C₄×D₄×C₇₁	C₂³	1	2	yes	—
254	C₄×D₄×C₇₁	C₂³	1	2	yes	—
255	C₄×D₄×C₇₁	C₂³	1	2	yes	—
256	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
258	#117×C₇₁	—	2	2	no	—
259	#117×C₇₁	—	2	1	no	—
260	#117×C₇₁	—	2	2	no	—
261	#117×C₇₁	—	2	2	no	—
262	#117×C₇₁	—	2	2	no	—
263	#117×C₇₁	C₂³	1	1	yes	characteristic
264	#117×C₇₁	C₂³	1	1	yes	characteristic
265	#117×C₇₁	C₂³	1	1	yes	characteristic
266	#117×C₇₁	C₂³	1	1	yes	characteristic
267	#117×C₇₁	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
273	C₂×C₄²×C₇₁	—	2	1	no	—
274	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
276	#107×C₇₁	C₂³	1	1	yes	characteristic
277	#107×C₇₁	C₂³	1	1	yes	characteristic
278	#107×C₇₁	C₂³	1	1	yes	characteristic
279	#107×C₇₁	C₂³	1	1	yes	characteristic
280	#107×C₇₁	C₂³	1	2	yes	—
281	#107×C₇₁	C₂³	1	2	yes	—
282	#106×C₇₁	C₂³	1	1	yes	characteristic
283	#106×C₇₁	C₂³	1	1	yes	characteristic
284	#106×C₇₁	C₂³	1	1	yes	characteristic
285	#106×C₇₁	C₂³	1	1	yes	characteristic
286	#106×C₇₁	C₂³	1	2	yes	—
287	#106×C₇₁	C₂³	1	2	yes	—
288	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
293	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
294	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
295	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
296	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
297	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
298	#103×C₇₁	C₂³	1	2	yes	—
299	#103×C₇₁	C₂³	1	2	yes	—
300	#103×C₇₁	C₂³	1	1	yes	characteristic
301	#103×C₇₁	C₂³	1	1	yes	characteristic
302	#103×C₇₁	C₂³	1	1	yes	characteristic
303	#103×C₇₁	C₂³	1	1	yes	characteristic
304	#103×C₇₁	C₂³	1	2	yes	—
305	#103×C₇₁	C₂³	1	2	yes	—
306	#102×C₇₁	C₂³	1	2	yes	—
307	#102×C₇₁	C₂³	1	2	yes	—
308	#102×C₇₁	C₂³	1	1	yes	characteristic
309	#102×C₇₁	C₂³	1	1	yes	characteristic
310	#102×C₇₁	C₂³	1	1	yes	characteristic
311	#102×C₇₁	C₂³	1	1	yes	characteristic
312	#102×C₇₁	C₂³	1	2	yes	—
313	#102×C₇₁	C₂³	1	2	yes	—
314	#102×C₇₁	C₂³	1	2	yes	—
315	#102×C₇₁	C₂³	1	2	yes	—
316	#102×C₇₁	C₂³	1	2	yes	—
317	#102×C₇₁	C₂³	1	2	yes	—
318	C₂⁴×C₇₁	—	2	1	no	—
319	C₂⁴×C₇₁	—	2	1	no	—
320	#41×C₇₁	—	2	2	no	—
321	#41×C₇₁	—	2	2	no	—
322	#41×C₇₁	—	2	2	no	—
323	#41×C₇₁	—	2	2	no	—
324	#41×C₇₁	—	8	4	no	—
325	C₂×Q₈×C₇₁	—	2	1	no	—
326	C₂×Q₈×C₇₁	—	2	1	no	—
327	C₂×Q₈×C₇₁	—	2	1	no	—
328	C₂×Q₈×C₇₁	—	2	2	no	—
329	C₂×Q₈×C₇₁	—	2	2	no	—
330	C₂×Q₈×C₇₁	—	2	2	no	—
331	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₇₁	—	2	1	no	—
335	C₂×D₄×C₇₁	—	2	2	no	—
336	C₂×D₄×C₇₁	—	2	2	no	—
337	C₂×D₄×C₇₁	—	2	2	no	—
338	C₂×D₄×C₇₁	—	2	2	no	—
339	C₂×D₄×C₇₁	—	2	2	no	—
340	C₂×D₄×C₇₁	—	2	1	no	—
341	C₂×D₄×C₇₁	—	2	1	no	—
342	C₂×D₄×C₇₁	—	2	2	no	—
343	C₂×D₄×C₇₁	—	2	2	no	—
344	C₂×D₄×C₇₁	—	2	2	no	—
345	C₂×D₄×C₇₁	—	2	2	no	—
346	C₂×D₄×C₇₁	—	2	2	no	—
347	C₂×D₄×C₇₁	—	2	2	no	—
348	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
351	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₇₁	—	2	1	no	—
354	C₂²×C₄×C₇₁	—	2	1	no	—
355	C₂²×C₄×C₇₁	—	2	1	no	—
356	C₂²×C₄×C₇₁	—	2	1	no	—
357	C₂²×C₄×C₇₁	—	2	2	no	—
358	C₂²×C₄×C₇₁	—	2	1	no	—
359	C₂²×C₄×C₇₁	—	2	2	no	—
360	C₂²×C₄×C₇₁	—	2	2	no	—
361	C₂²×C₄×C₇₁	—	2	2	no	—
362	C₂²×C₄×C₇₁	—	8	2	no	—
363	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
366	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
369	Q₁₆×C₇₁	—	4	2	no	—
370	SD₁₆×C₇₁	—	4	2	no	—
371	SD₁₆×C₇₁	—	4	2	no	—
372	SD₁₆×C₇₁	—	4	2	no	—
373	SD₁₆×C₇₁	—	4	2	no	—
374	D₈×C₇₁	—	4	2	no	—
375	D₈×C₇₁	—	4	2	no	—
376	D₈×C₇₁	—	4	2	no	—
377	M₁₆×C₇₁	—	2	2	no	—
378	M₁₆×C₇₁	—	2	2	no	—
379	M₁₆×C₇₁	—	4	2	no	—
380	M₁₆×C₇₁	—	4	2	no	—
381	C₂×C₈×C₇₁	—	2	2	no	—
382	C₂×C₈×C₇₁	—	2	2	no	—
383	C₂×C₈×C₇₁	—	4	2	no	—
384	C₂×C₈×C₇₁	—	4	2	no	—
385	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₇₁	—	2	1	no	—
392	C₄⋊C₄×C₇₁	—	2	1	no	—
393	C₄⋊C₄×C₇₁	—	2	1	no	—
394	C₄⋊C₄×C₇₁	—	2	1	no	—
395	C₄⋊C₄×C₇₁	—	2	1	no	—
396	C₄⋊C₄×C₇₁	—	2	2	no	—
397	C₄⋊C₄×C₇₁	—	2	2	no	—
398	C₄⋊C₄×C₇₁	—	2	2	no	—
399	C₄⋊C₄×C₇₁	—	2	2	no	—
400	C₄⋊C₄×C₇₁	—	2	2	no	—
401	C₄⋊C₄×C₇₁	—	2	2	no	—
402	C₄⋊C₄×C₇₁	—	2	1	no	—
403	C₄⋊C₄×C₇₁	—	2	1	no	—
404	C₄⋊C₄×C₇₁	—	2	2	no	—
405	C₄⋊C₄×C₇₁	—	2	2	no	—
406	C₄⋊C₄×C₇₁	—	2	1	no	—
407	C₄⋊C₄×C₇₁	—	2	1	no	—
408	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄×C₇₁	—	2	1	no	—
420	C₂²⋊C₄×C₇₁	—	2	1	no	—
421	C₂²⋊C₄×C₇₁	—	2	1	no	—
422	C₂²⋊C₄×C₇₁	—	2	2	no	—
423	C₂²⋊C₄×C₇₁	—	2	2	no	—
424	C₂²⋊C₄×C₇₁	—	2	2	no	—
425	C₂²⋊C₄×C₇₁	—	2	2	no	—
426	C₂²⋊C₄×C₇₁	—	2	2	no	—
427	C₂²⋊C₄×C₇₁	—	2	2	no	—
428	C₂²⋊C₄×C₇₁	—	2	2	no	—
429	C₂²⋊C₄×C₇₁	—	2	2	no	—
430	C₂²⋊C₄×C₇₁	—	2	2	no	—
431	C₂²⋊C₄×C₇₁	—	2	2	no	—
432	C₂²⋊C₄×C₇₁	—	2	2	no	—
433	C₂²⋊C₄×C₇₁	—	2	1	no	—
434	C₂²⋊C₄×C₇₁	—	2	1	no	—
435	C₂²⋊C₄×C₇₁	—	2	2	no	—
436	C₂²⋊C₄×C₇₁	—	2	2	no	—
437	C₂²⋊C₄×C₇₁	—	2	2	no	—
438	C₂²⋊C₄×C₇₁	—	2	2	no	—
439	C₂²⋊C₄×C₇₁	—	2	2	no	—
440	C₂²⋊C₄×C₇₁	—	2	2	no	—
441	C₂²⋊C₄×C₇₁	—	2	2	no	—
442	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
445	C₄²×C₇₁	—	2	1	no	—
446	C₄²×C₇₁	—	2	1	no	—
447	C₄²×C₇₁	—	2	1	no	—
448	C₄²×C₇₁	—	2	2	no	—
449	C₄²×C₇₁	—	2	2	no	—
450	C₄²×C₇₁	—	2	1	no	—
451	C₄²×C₇₁	—	2	1	no	—
452	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₇₁	C₂×D₄	1	2	yes	—
454	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇₁	C₂×D₄	1	2	yes	—
456	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
457	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
458	C₄²×C₇₁	C₂⁴	1	2	yes	—
459	C₂³×C₇₁	—	2	2	no	—
460	C₂³×C₇₁	—	2	2	no	—
461	C₂³×C₇₁	—	2	1	no	—
462	C₂³×C₇₁	—	4	2	no	—
463	C₂³×C₇₁	—	4	2	no	—
464	C₂³×C₇₁	—	8	1	no	—
465	C₂³×C₇₁	—	8	1	no	—
466	C₂³×C₇₁	—	8	1	no	—
467	C₂³×C₇₁	—	8	1	no	—
468	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
469	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₇₁	—	2	2	no	—
471	Q₈×C₇₁	—	2	2	no	—
472	Q₈×C₇₁	—	2	1	no	—
473	Q₈×C₇₁	—	2	2	no	—
474	Q₈×C₇₁	—	2	1	no	—
475	Q₈×C₇₁	—	4	2	no	—
476	Q₈×C₇₁	—	8	1	no	—
477	Q₈×C₇₁	—	8	1	no	—
478	Q₈×C₇₁	—	8	2	no	—
479	D₄×C₇₁	—	2	4	no	—
480	D₄×C₇₁	—	2	2	no	—
481	D₄×C₇₁	—	2	2	no	—
482	D₄×C₇₁	—	2	2	no	—
483	D₄×C₇₁	—	2	1	no	—
484	D₄×C₇₁	—	2	2	no	—
485	D₄×C₇₁	—	2	2	no	—
486	D₄×C₇₁	—	2	1	no	—
487	D₄×C₇₁	—	4	2	no	—
488	D₄×C₇₁	—	4	2	no	—
489	D₄×C₇₁	—	4	2	no	—
490	D₄×C₇₁	—	8	2	no	—
491	D₄×C₇₁	—	8	2	no	—
492	D₄×C₇₁	—	8	2	no	—
493	D₄×C₇₁	—	8	2	no	—
494	D₄×C₇₁	—	8	2	no	—
495	D₄×C₇₁	—	8	2	no	—
496	D₄×C₇₁	—	8	2	no	—
497	C₂×C₄×C₇₁	—	2	2	no	—
498	C₂×C₄×C₇₁	—	2	2	no	—
499	C₂×C₄×C₇₁	—	2	1	no	—
500	C₂×C₄×C₇₁	—	2	1	no	—
501	C₂×C₄×C₇₁	—	2	1	no	—
502	C₂×C₄×C₇₁	—	2	2	no	—
503	C₂×C₄×C₇₁	—	2	1	no	—
504	C₂×C₄×C₇₁	—	2	1	no	—
505	C₂×C₄×C₇₁	—	2	1	no	—
506	C₂×C₄×C₇₁	—	2	1	no	—
507	C₂×C₄×C₇₁	—	2	2	no	—
508	C₂×C₄×C₇₁	—	4	1	no	—
509	C₂×C₄×C₇₁	—	4	2	no	—
510	C₂×C₄×C₇₁	—	4	1	no	—
511	C₂×C₄×C₇₁	—	4	2	no	—
512	C₂×C₄×C₇₁	—	4	4	no	—
513	C₂×C₄×C₇₁	—	4	2	no	—
514	C₂×C₄×C₇₁	—	4	2	no	—
515	C₂×C₄×C₇₁	—	4	2	no	—
516	C₂×C₄×C₇₁	—	8	2	no	—
517	C₂×C₄×C₇₁	—	8	1	no	—
518	C₂×C₄×C₇₁	—	8	2	no	—
519	C₂×C₄×C₇₁	—	8	2	no	—
520	C₂×C₄×C₇₁	—	8	1	no	—
521	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
530	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
531	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
532	C₈×C₇₁	—	2	1	no	—
533	C₈×C₇₁	—	2	1	no	—
534	C₈×C₇₁	—	2	1	no	—
535	C₈×C₇₁	—	2	1	no	—
536	C₈×C₇₁	—	2	2	no	—
537	C₈×C₇₁	—	2	2	no	—
538	C₂²×C₇₁	—	2	1	no	—
539	C₂²×C₇₁	—	2	1	no	—
540	C₂²×C₇₁	—	2	2	no	—
541	C₂²×C₇₁	—	2	2	no	—
542	C₂²×C₇₁	—	2	2	no	—
543	C₂²×C₇₁	—	4	1	no	—
544	C₂²×C₇₁	—	4	2	no	—
545	C₂²×C₇₁	—	4	2	no	—
546	C₂²×C₇₁	—	4	2	no	—
547	C₂²×C₇₁	—	4	1	no	—
548	C₂²×C₇₁	—	4	2	no	—
549	C₂²×C₇₁	—	4	1	no	—
550	C₂²×C₇₁	—	4	2	no	—
551	C₂²×C₇₁	—	4	2	no	—
552	C₂²×C₇₁	—	8	4	no	—
553	C₂²×C₇₁	—	16	2	no	—
554	C₂²×C₇₁	#537	1	2	yes	—
555	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
556	C₄×C₇₁	—	2	1	no	—
557	C₄×C₇₁	—	2	2	no	—
558	C₄×C₇₁	—	2	1	no	—
559	C₄×C₇₁	—	2	1	no	—
560	C₄×C₇₁	—	2	1	no	—
561	C₄×C₇₁	—	2	2	no	—
562	C₄×C₇₁	—	2	2	no	—
563	C₄×C₇₁	—	4	1	no	—
564	C₄×C₇₁	—	4	1	no	—
565	C₄×C₇₁	—	4	1	no	—
566	C₄×C₇₁	—	4	2	no	—
567	C₄×C₇₁	—	4	1	no	—
568	C₄×C₇₁	—	4	1	no	—
569	C₄×C₇₁	—	4	1	no	—
570	C₄×C₇₁	—	4	1	no	—
571	C₄×C₇₁	—	4	2	no	—
572	C₄×C₇₁	#537	1	2	yes	—
573	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₄×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
575	#60926	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
576	C₂×C₇₁	—	2	2	no	—
577	C₂×C₇₁	—	4	2	no	—
578	C₂×C₇₁	—	8	1	no	—
579	C₂×C₇₁	—	8	2	no	—
580	C₂×C₇₁	—	8	2	no	—
581	C₂×C₇₁	C₂×#537	1	1	yes	characteristic
582	C₂×C₇₁	#3584	1	1	yes	characteristic
583	C₂×C₇₁	#3585	1	1	yes	characteristic
584	#3510	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3460	C₂×C₇₁	1	1	yes	characteristic, complemented
586	#3263	C₂×C₇₁	1	2	yes	complemented
587	#3262	C₂×C₇₁	1	2	yes	complemented
588	#3257	C₂×C₇₁	1	2	yes	complemented
589	#3257	C₂×C₇₁	1	2	yes	complemented
590	#3256	C₂×C₇₁	1	2	yes	complemented
591	#3251	C₂×C₇₁	1	2	yes	complemented
592	#3250	C₂×C₇₁	1	2	yes	complemented
593	#3247	C₂×C₇₁	1	2	yes	complemented
594	#3082	C₂×C₇₁	1	1	yes	characteristic, complemented
595	#3081	C₂×C₇₁	1	1	yes	characteristic, complemented
596	#3077	C₂×C₇₁	1	1	yes	characteristic, complemented
597	#3076	C₂×C₇₁	1	1	yes	characteristic, complemented
598	#3063	C₂×C₇₁	1	1	yes	characteristic, complemented
599	#3062	C₂×C₇₁	1	1	yes	characteristic, complemented
600	#3058	C₂×C₇₁	1	1	yes	characteristic, complemented
601	#3057	C₂×C₇₁	1	1	yes	characteristic, complemented
602	#3043	C₂×C₇₁	1	1	yes	characteristic, complemented
603	#3041	C₂×C₇₁	1	1	yes	characteristic, complemented
604	#3040	C₂×C₇₁	1	1	yes	characteristic, complemented
605	C₂×#463	C₂×C₇₁	1	1	yes	characteristic, complemented
606	#2906	C₂×C₇₁	1	1	yes	characteristic, complemented
607	C₇₁	#60926	1	1	yes	characteristic, direct product factor, Sylow
608	C₂×#137	C₂²×C₇₁	1	1	yes	characteristic
609	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	1	yes	characteristic
610	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
611	C₂²×D₈	C₂²×C₇₁	1	1	yes	characteristic
612	C₂×#131	C₂²×C₇₁	1	1	yes	characteristic
613	C₂×#131	C₂²×C₇₁	1	1	yes	characteristic
614	#559	—	2	1	no	—
615	#559	—	2	1	no	—
616	#556	—	2	1	no	—
617	#556	—	2	1	no	—
618	#551	—	2	2	no	—
619	#551	—	2	2	no	—
620	#544	C₂²×C₇₁	1	1	yes	characteristic
621	#542	—	2	1	no	—
622	#542	C₂²×C₇₁	1	2	yes	complemented
623	#542	C₂²×C₇₁	1	2	yes	complemented
624	#542	C₂²×C₇₁	1	2	yes	complemented
625	#540	—	2	1	no	—
626	#540	C₂²×C₇₁	1	2	yes	complemented
627	#538	—	2	2	no	—
628	#537	C₂²×C₇₁	1	1	yes	characteristic
629	#536	C₂²×C₇₁	1	1	yes	characteristic
630	#535	C₂²×C₇₁	1	1	yes	characteristic
631	#535	C₂²×C₇₁	1	1	yes	characteristic
632	#535	C₂²×C₇₁	1	1	yes	characteristic
633	#533	C₂²×C₇₁	1	1	yes	characteristic
634	#532	—	2	1	no	—
635	#532	C₂²×C₇₁	1	2	yes	complemented
636	#529	—	2	1	no	—
637	#529	C₂²×C₇₁	1	2	yes	complemented
638	#529	C₂²×C₇₁	1	2	yes	complemented
639	#529	C₂²×C₇₁	1	2	yes	complemented
640	C₂×#124	C₂²×C₇₁	1	1	yes	characteristic
641	#525	—	2	2	no	—
642	#519	C₂²×C₇₁	1	1	yes	characteristic
643	#518	C₂²×C₇₁	1	1	yes	characteristic
644	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
645	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
647	#479	C₂²×C₇₁	1	1	yes	characteristic, complemented
648	#479	C₂²×C₇₁	1	1	yes	characteristic, complemented
649	#479	C₂²×C₇₁	1	2	yes	complemented
650	#479	C₂²×C₇₁	1	2	yes	complemented
651	#478	C₂²×C₇₁	1	1	yes	characteristic, complemented
652	#478	C₂²×C₇₁	1	1	yes	characteristic, complemented
653	#478	C₂²×C₇₁	1	2	yes	complemented
654	#478	C₂²×C₇₁	1	2	yes	complemented
655	#478	C₂²×C₇₁	1	2	yes	complemented
656	#478	C₂²×C₇₁	1	2	yes	complemented
657	#477	C₂²×C₇₁	1	1	yes	characteristic, complemented
658	#477	C₂²×C₇₁	1	2	yes	complemented
659	#476	C₂²×C₇₁	1	1	yes	characteristic, complemented
660	#476	C₂²×C₇₁	1	2	yes	complemented
661	#476	C₂²×C₇₁	1	2	yes	complemented
662	#475	C₂²×C₇₁	1	1	yes	characteristic, complemented
663	#475	C₂²×C₇₁	1	2	yes	complemented
664	#474	C₂²×C₇₁	1	1	yes	characteristic, complemented
665	#474	C₂²×C₇₁	1	2	yes	complemented
666	#474	C₂²×C₇₁	1	2	yes	complemented
667	#470	C₂²×C₇₁	1	2	yes	complemented
668	#469	C₂²×C₇₁	1	2	yes	—
669	#469	C₂²×C₇₁	1	2	yes	—
670	#469	C₂²×C₇₁	1	2	yes	complemented
671	#468	C₂²×C₇₁	1	2	yes	complemented
672	#468	C₂²×C₇₁	1	2	yes	complemented
673	#468	C₂²×C₇₁	1	2	yes	complemented
674	#468	C₂²×C₇₁	1	2	yes	complemented
675	#467	C₂²×C₇₁	1	2	yes	complemented
676	#466	C₂²×C₇₁	1	2	yes	—
677	#466	C₂²×C₇₁	1	2	yes	—
678	#466	C₂²×C₇₁	1	2	yes	complemented
679	#465	C₂²×C₇₁	1	2	yes	complemented
680	#465	C₂²×C₇₁	1	2	yes	complemented
681	#465	C₂²×C₇₁	1	2	yes	complemented
682	#465	C₂²×C₇₁	1	2	yes	complemented
683	#464	C₂²×C₇₁	1	2	yes	complemented
684	#464	C₂²×C₇₁	1	2	yes	complemented
685	#464	C₂²×C₇₁	1	2	yes	complemented
686	#464	C₂²×C₇₁	1	2	yes	complemented
687	#463	C₂²×C₇₁	1	2	yes	—
688	#463	C₂²×C₇₁	1	2	yes	—
689	#463	C₂²×C₇₁	1	2	yes	—
690	#463	C₂²×C₇₁	1	2	yes	—
691	#463	C₂²×C₇₁	1	2	yes	—
692	#463	C₂²×C₇₁	1	2	yes	—
693	#463	C₂²×C₇₁	1	2	yes	complemented
694	#463	C₂²×C₇₁	1	2	yes	complemented
695	#460	C₂²×C₇₁	1	2	yes	complemented
696	#460	C₂²×C₇₁	1	2	yes	complemented
697	#459	C₂²×C₇₁	1	2	yes	—
698	#459	C₂²×C₇₁	1	2	yes	—
699	#428	C₂²×C₇₁	1	1	yes	characteristic
700	#428	C₂²×C₇₁	1	1	yes	characteristic
701	#427	C₂²×C₇₁	1	1	yes	characteristic
702	#427	C₂²×C₇₁	1	1	yes	characteristic
703	#424	C₂²×C₇₁	1	1	yes	characteristic
704	#424	C₂²×C₇₁	1	1	yes	characteristic
705	#424	C₂²×C₇₁	1	2	yes	complemented
706	#424	C₂²×C₇₁	1	2	yes	complemented
707	#423	C₂²×C₇₁	1	1	yes	characteristic
708	#423	C₂²×C₇₁	1	2	yes	complemented
709	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
710	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	complemented
711	#419	C₂²×C₇₁	1	1	yes	characteristic
712	#418	C₂²×C₇₁	1	1	yes	characteristic
713	#418	C₂²×C₇₁	1	1	yes	characteristic
714	#418	C₂²×C₇₁	1	1	yes	characteristic
715	#416	C₂²×C₇₁	1	1	yes	characteristic
716	#416	C₂²×C₇₁	1	1	yes	characteristic
717	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
718	C₂×#102	C₂²×C₇₁	1	1	yes	characteristic
719	C₂×#41	—	2	2	no	—
720	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
721	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
723	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
724	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
725	C₂³×C₄	—	2	1	no	—
726	#137	—	4	2	no	—
727	AGL(1,ℤ/8)	—	4	2	no	—
728	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
729	C₂×SD₁₆	—	4	2	no	—
730	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
734	C₂×D₈	—	4	2	no	—
735	C₂×D₈	C₂³×C₇₁	1	2	yes	—
736	C₂×D₈	C₂³×C₇₁	1	2	yes	—
737	C₂×D₈	C₂³×C₇₁	1	2	yes	—
738	#131	—	4	2	no	—
739	#131	—	4	2	no	—
740	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
743	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
744	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
747	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
748	C₄⋊Q₈	—	2	1	no	—
749	C₄⋊Q₈	—	2	1	no	—
750	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
753	#127	—	2	1	no	—
754	#127	—	2	1	no	—
755	#127	C₂³×C₇₁	1	2	yes	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#125	—	2	1	no	—
763	#125	C₂³×C₇₁	1	1	yes	characteristic
764	#125	C₂³×C₇₁	1	1	yes	characteristic
765	#125	C₂³×C₇₁	1	2	yes	—
766	#124	—	2	1	no	—
767	#124	—	2	1	no	—
768	#124	—	2	1	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	1	no	—
773	#124	—	2	1	no	—
774	#124	—	2	2	no	—
775	#124	C₂³×C₇₁	1	2	yes	—
776	#124	C₂³×C₇₁	1	2	yes	—
777	#124	C₂³×C₇₁	1	2	yes	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	C₂³×C₇₁	1	2	yes	—
805	#121	C₂³×C₇₁	1	2	yes	—
806	#121	C₂³×C₇₁	1	2	yes	—
807	#121	C₂³×C₇₁	1	2	yes	—
808	#121	C₂³×C₇₁	1	2	yes	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
817	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
821	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	D₄×C₇₁	1	2	yes	—
833	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
834	C₄×D₄	D₄×C₇₁	1	2	yes	—
835	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₇₁	1	2	yes	—
837	C₄×D₄	C₂³×C₇₁	1	2	yes	—
838	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₇₁	1	2	yes	—
841	C₄×D₄	C₂³×C₇₁	1	2	yes	—
842	#117	—	2	2	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	C₂³×C₇₁	1	1	yes	characteristic
848	#117	C₂³×C₇₁	1	1	yes	characteristic
849	#117	C₂³×C₇₁	1	1	yes	characteristic
850	#117	C₂³×C₇₁	1	1	yes	characteristic
851	#117	C₂³×C₇₁	1	2	yes	—
852	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₄²	—	2	1	no	—
858	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
859	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
860	#107	C₂³×C₇₁	1	1	yes	characteristic
861	#107	C₂³×C₇₁	1	1	yes	characteristic
862	#107	C₂³×C₇₁	1	1	yes	characteristic
863	#107	C₂³×C₇₁	1	1	yes	characteristic
864	#107	C₂³×C₇₁	1	2	yes	—
865	#107	C₂³×C₇₁	1	2	yes	—
866	#106	C₂³×C₇₁	1	1	yes	characteristic
867	#106	C₂³×C₇₁	1	1	yes	characteristic
868	#106	C₂³×C₇₁	1	1	yes	characteristic
869	#106	C₂³×C₇₁	1	1	yes	characteristic
870	#106	C₂³×C₇₁	1	2	yes	—
871	#106	C₂³×C₇₁	1	2	yes	—
872	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
877	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
878	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
879	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
880	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
881	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
882	#103	C₂³×C₇₁	1	2	yes	—
883	#103	C₂³×C₇₁	1	2	yes	—
884	#103	C₂³×C₇₁	1	1	yes	characteristic
885	#103	C₂³×C₇₁	1	1	yes	characteristic
886	#103	C₂³×C₇₁	1	1	yes	characteristic
887	#103	C₂³×C₇₁	1	1	yes	characteristic
888	#103	C₂³×C₇₁	1	2	yes	—
889	#103	C₂³×C₇₁	1	2	yes	—
890	#102	C₂³×C₇₁	1	2	yes	—
891	#102	C₂³×C₇₁	1	2	yes	—
892	#102	C₂³×C₇₁	1	1	yes	characteristic
893	#102	C₂³×C₇₁	1	1	yes	characteristic
894	#102	C₂³×C₇₁	1	1	yes	characteristic
895	#102	C₂³×C₇₁	1	1	yes	characteristic
896	#102	C₂³×C₇₁	1	2	yes	—
897	#102	C₂³×C₇₁	1	2	yes	—
898	#102	C₂³×C₇₁	1	2	yes	—
899	#102	C₂³×C₇₁	1	2	yes	—
900	#102	C₂³×C₇₁	1	2	yes	—
901	#102	C₂³×C₇₁	1	2	yes	—
902	C₂⁴	—	2	1	no	—
903	C₂⁴	—	2	1	no	—
904	#41	—	2	2	no	—
905	#41	—	2	2	no	—
906	#41	—	2	2	no	—
907	#41	—	2	2	no	—
908	#41	—	8	4	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
917	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
933	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	8	2	no	—
947	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
948	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
949	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
950	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
953	Q₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	D₈	—	4	2	no	—
959	D₈	—	4	2	no	—
960	D₈	—	4	2	no	—
961	M₁₆	—	2	2	no	—
962	M₁₆	—	2	2	no	—
963	M₁₆	—	4	2	no	—
964	M₁₆	—	4	2	no	—
965	C₂×C₈	—	2	2	no	—
966	C₂×C₈	—	2	2	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
970	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
973	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1037	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1038	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1039	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1040	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₇₁	1	2	yes	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	4	2	no	—
1048	C₂³	—	8	1	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	1	no	—
1051	C₂³	—	8	1	no	—
1052	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1053	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	8	2	no	—
1061	Q₈	—	8	1	no	—
1062	Q₈	—	8	1	no	—
1063	D₄	—	2	4	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1113	C₂×C₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
1114	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
1115	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	2	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	8	4	no	—
1137	C₂²	—	16	2	no	—
1138	C₂²	#537×C₇₁	1	2	yes	—
1139	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	#537×C₇₁	1	2	yes	—
1157	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
1158	C₄	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
1159	C₂	—	2	2	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	—	8	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₂×#537×C₇₁	1	1	yes	characteristic
1165	C₂	C₇₁×#3584	1	1	yes	characteristic
1166	C₂	C₇₁×#3585	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×#3510	C₂	semidirect
2. C₇₁×#3460	C₂	semidirect
3. C₇₁×#3263	C₂	semidirect
4. C₇₁×#3262	C₂	semidirect
5. C₇₁×#3257	C₂	semidirect
6. C₇₁×#3257	C₂	semidirect
7. C₇₁×#3256	C₂	semidirect
8. C₇₁×#3251	C₂	semidirect
9. C₇₁×#3250	C₂	semidirect
10. C₇₁×#3247	C₂	semidirect
11. C₇₁×#3082	C₂	semidirect
12. C₇₁×#3081	C₂	semidirect
13. C₇₁×#3077	C₂	semidirect
14. C₇₁×#3076	C₂	semidirect
15. C₇₁×#3063	C₂	semidirect
16. C₇₁×#3062	C₂	semidirect
17. C₇₁×#3058	C₂	semidirect
18. C₇₁×#3057	C₂	semidirect
19. C₇₁×#3043	C₂	semidirect
20. C₇₁×#3041	C₂	semidirect
21. C₇₁×#3040	C₂	semidirect
22. C₂×#463×C₇₁	C₂	semidirect
23. C₇₁×#2906	C₂	semidirect
38. #542×C₇₁	C₂²	semidirect
39. #542×C₇₁	C₂²	semidirect
40. #542×C₇₁	C₂²	semidirect
42. #540×C₇₁	C₂²	semidirect
51. #532×C₇₁	C₂²	semidirect
53. #529×C₇₁	C₂²	semidirect
54. #529×C₇₁	C₂²	semidirect
55. #529×C₇₁	C₂²	semidirect
63. #479×C₇₁	C₂²	semidirect
64. #479×C₇₁	C₂²	semidirect
65. #479×C₇₁	C₂²	semidirect
66. #479×C₇₁	C₂²	semidirect
67. #478×C₇₁	C₂²	semidirect
68. #478×C₇₁	C₂²	semidirect
69. #478×C₇₁	C₂²	semidirect
70. #478×C₇₁	C₂²	semidirect
71. #478×C₇₁	C₂²	semidirect
72. #478×C₇₁	C₂²	semidirect
73. #477×C₇₁	C₂²	semidirect
74. #477×C₇₁	C₂²	semidirect
75. #476×C₇₁	C₂²	semidirect
76. #476×C₇₁	C₂²	semidirect
77. #476×C₇₁	C₂²	semidirect
78. #475×C₇₁	C₂²	semidirect
79. #475×C₇₁	C₂²	semidirect
80. #474×C₇₁	C₂²	semidirect
81. #474×C₇₁	C₂²	semidirect
82. #474×C₇₁	C₂²	semidirect
83. #470×C₇₁	C₂²	semidirect
86. #469×C₇₁	C₂²	semidirect
87. #468×C₇₁	C₂²	semidirect
88. #468×C₇₁	C₂²	semidirect
89. #468×C₇₁	C₂²	semidirect
90. #468×C₇₁	C₂²	semidirect
91. #467×C₇₁	C₂²	semidirect
94. #466×C₇₁	C₂²	semidirect
95. #465×C₇₁	C₂²	semidirect
96. #465×C₇₁	C₂²	semidirect
97. #465×C₇₁	C₂²	semidirect
98. #465×C₇₁	C₂²	semidirect
99. #464×C₇₁	C₂²	semidirect
100. #464×C₇₁	C₂²	semidirect
101. #464×C₇₁	C₂²	semidirect
102. #464×C₇₁	C₂²	semidirect
109. #463×C₇₁	C₂²	semidirect
110. #463×C₇₁	C₂²	semidirect
111. #460×C₇₁	C₂²	semidirect
112. #460×C₇₁	C₂²	semidirect
121. #424×C₇₁	C₂²	semidirect
122. #424×C₇₁	C₂²	semidirect
124. #423×C₇₁	C₂²	semidirect
126. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
575. #60926	C₇₁	direct (N × H)
584. #3510	C₂×C₇₁	semidirect
585. #3460	C₂×C₇₁	semidirect
586. #3263	C₂×C₇₁	semidirect
587. #3262	C₂×C₇₁	semidirect
588. #3257	C₂×C₇₁	semidirect
589. #3257	C₂×C₇₁	semidirect
590. #3256	C₂×C₇₁	semidirect
591. #3251	C₂×C₇₁	semidirect
592. #3250	C₂×C₇₁	semidirect
593. #3247	C₂×C₇₁	semidirect
594. #3082	C₂×C₇₁	semidirect
595. #3081	C₂×C₇₁	semidirect
596. #3077	C₂×C₇₁	semidirect
597. #3076	C₂×C₇₁	semidirect
598. #3063	C₂×C₇₁	semidirect
599. #3062	C₂×C₇₁	semidirect
600. #3058	C₂×C₇₁	semidirect
601. #3057	C₂×C₇₁	semidirect
602. #3043	C₂×C₇₁	semidirect
603. #3041	C₂×C₇₁	semidirect
604. #3040	C₂×C₇₁	semidirect
605. C₂×#463	C₂×C₇₁	semidirect
606. #2906	C₂×C₇₁	semidirect
607. C₇₁	#60926	direct (N × H)
622. #542	C₂²×C₇₁	semidirect
623. #542	C₂²×C₇₁	semidirect
624. #542	C₂²×C₇₁	semidirect
626. #540	C₂²×C₇₁	semidirect
635. #532	C₂²×C₇₁	semidirect
637. #529	C₂²×C₇₁	semidirect
638. #529	C₂²×C₇₁	semidirect
639. #529	C₂²×C₇₁	semidirect
647. #479	C₂²×C₇₁	semidirect
648. #479	C₂²×C₇₁	semidirect
649. #479	C₂²×C₇₁	semidirect
650. #479	C₂²×C₇₁	semidirect
651. #478	C₂²×C₇₁	semidirect
652. #478	C₂²×C₇₁	semidirect
653. #478	C₂²×C₇₁	semidirect
654. #478	C₂²×C₇₁	semidirect
655. #478	C₂²×C₇₁	semidirect
656. #478	C₂²×C₇₁	semidirect
657. #477	C₂²×C₇₁	semidirect
658. #477	C₂²×C₇₁	semidirect
659. #476	C₂²×C₇₁	semidirect
660. #476	C₂²×C₇₁	semidirect
661. #476	C₂²×C₇₁	semidirect
662. #475	C₂²×C₇₁	semidirect
663. #475	C₂²×C₇₁	semidirect
664. #474	C₂²×C₇₁	semidirect
665. #474	C₂²×C₇₁	semidirect
666. #474	C₂²×C₇₁	semidirect
667. #470	C₂²×C₇₁	semidirect
670. #469	C₂²×C₇₁	semidirect
671. #468	C₂²×C₇₁	semidirect
672. #468	C₂²×C₇₁	semidirect
673. #468	C₂²×C₇₁	semidirect
674. #468	C₂²×C₇₁	semidirect
675. #467	C₂²×C₇₁	semidirect
678. #466	C₂²×C₇₁	semidirect
679. #465	C₂²×C₇₁	semidirect
680. #465	C₂²×C₇₁	semidirect
681. #465	C₂²×C₇₁	semidirect
682. #465	C₂²×C₇₁	semidirect
683. #464	C₂²×C₇₁	semidirect
684. #464	C₂²×C₇₁	semidirect
685. #464	C₂²×C₇₁	semidirect
686. #464	C₂²×C₇₁	semidirect
693. #463	C₂²×C₇₁	semidirect
694. #463	C₂²×C₇₁	semidirect
695. #460	C₂²×C₇₁	semidirect
696. #460	C₂²×C₇₁	semidirect
705. #424	C₂²×C₇₁	semidirect
706. #424	C₂²×C₇₁	semidirect
708. #423	C₂²×C₇₁	semidirect
710. C₂×C₄⋊C₈	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×#3510	2
C₇₁×#3460	2
C₇₁×#3263	2
C₇₁×#3262	2
C₇₁×#3257	2
C₇₁×#3256	2
C₇₁×#3251	2
C₇₁×#3250	2
C₇₁×#3247	2
C₇₁×#3082	2
C₇₁×#3081	2
C₇₁×#3077	2
C₇₁×#3076	2
C₇₁×#3063	2
C₇₁×#3062	2
C₇₁×#3058	2
C₇₁×#3057	2
C₇₁×#3043	2
C₇₁×#3041	2
C₇₁×#3040	2
C₂×#463×C₇₁	2
C₇₁×#2906	2
#60926	71

Subgroups — C71×#60926 #31881798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#60926 #31881798