Subgroups — C₇₁×#61993 #31882865

Order 18176.

1870 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3317	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3315	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3268	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#3250	C₂	1	2	yes	maximal, complemented
17	C₇₁×#3219	C₂	1	2	yes	maximal, complemented
18	C₇₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₇₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₁×#3035	C₂	1	2	yes	maximal, complemented
23	C₇₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	2	yes	—
25	C₂×#135×C₇₁	C₂²	1	2	yes	—
26	C₂×#135×C₇₁	C₂²	1	2	yes	—
27	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
28	#556×C₇₁	C₂²	1	1	yes	characteristic
29	#555×C₇₁	C₂²	1	1	yes	characteristic
30	#554×C₇₁	C₂²	1	1	yes	characteristic
31	#553×C₇₁	—	2	1	no	—
32	#553×C₇₁	—	2	2	no	—
33	#553×C₇₁	—	2	1	no	—
34	#552×C₇₁	—	2	1	no	—
35	#552×C₇₁	C₂²	1	2	yes	—
36	#551×C₇₁	—	2	2	no	—
37	#550×C₇₁	—	2	1	no	—
38	#550×C₇₁	C₂²	1	2	yes	—
39	#550×C₇₁	C₂²	1	1	yes	characteristic, complemented
40	#550×C₇₁	C₂²	1	1	yes	characteristic, complemented
41	#547×C₇₁	C₂²	1	2	yes	—
42	#547×C₇₁	C₂²	1	1	yes	characteristic
43	#547×C₇₁	C₂²	1	1	yes	characteristic, complemented
44	#546×C₇₁	C₂²	1	2	yes	—
45	#540×C₇₁	—	2	1	no	—
46	#540×C₇₁	—	2	2	no	—
47	#533×C₇₁	C₂²	1	1	yes	characteristic
48	#532×C₇₁	C₂²	1	1	yes	characteristic
49	#532×C₇₁	C₂²	1	2	yes	complemented
50	#529×C₇₁	—	2	2	no	—
51	#529×C₇₁	C₂²	1	1	yes	characteristic
52	#529×C₇₁	C₂²	1	2	yes	—
53	#529×C₇₁	C₂²	1	2	yes	complemented
54	#525×C₇₁	—	2	1	no	—
55	#520×C₇₁	—	2	1	no	—
56	C₄×#41×C₇₁	C₂²	1	2	yes	—
57	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
59	C₂×#117×C₇₁	—	2	1	no	—
60	#497×C₇₁	C₂²	1	2	yes	—
61	#496×C₇₁	C₂²	1	2	yes	—
62	#494×C₇₁	C₂²	1	1	yes	characteristic, complemented
63	#492×C₇₁	C₂²	1	1	yes	characteristic, complemented
64	#491×C₇₁	C₂²	1	2	yes	complemented
65	#490×C₇₁	C₂²	1	2	yes	complemented
66	#487×C₇₁	C₂²	1	1	yes	characteristic, complemented
67	#486×C₇₁	C₂²	1	1	yes	characteristic, complemented
68	#485×C₇₁	C₂²	1	2	yes	complemented
69	#484×C₇₁	C₂²	1	1	yes	characteristic
70	#482×C₇₁	C₂²	1	2	yes	complemented
71	#481×C₇₁	C₂²	1	1	yes	characteristic
72	#479×C₇₁	C₂²	1	2	yes	complemented
73	#479×C₇₁	C₂²	1	2	yes	complemented
74	#478×C₇₁	C₂²	1	1	yes	characteristic
75	#478×C₇₁	C₂²	1	1	yes	characteristic
76	#478×C₇₁	C₂²	1	2	yes	complemented
77	#477×C₇₁	C₂²	1	1	yes	characteristic, complemented
78	#476×C₇₁	C₂²	1	1	yes	characteristic, complemented
79	#470×C₇₁	C₂²	1	2	yes	—
80	#468×C₇₁	C₂²	1	2	yes	—
81	#467×C₇₁	C₂²	1	2	yes	complemented
82	#466×C₇₁	C₂²	1	2	yes	—
83	#465×C₇₁	C₂²	1	2	yes	—
84	#465×C₇₁	C₂²	1	2	yes	complemented
85	#464×C₇₁	C₂²	1	2	yes	—
86	#464×C₇₁	C₂²	1	2	yes	complemented
87	#464×C₇₁	C₂²	1	2	yes	complemented
88	#464×C₇₁	C₂²	1	2	yes	complemented
89	#463×C₇₁	C₂²	1	1	yes	characteristic
90	#463×C₇₁	C₂²	1	1	yes	characteristic
91	#463×C₇₁	C₂²	1	2	yes	—
92	#463×C₇₁	C₂²	1	2	yes	—
93	#463×C₇₁	C₂²	1	2	yes	—
94	#462×C₇₁	C₂²	1	2	yes	complemented
95	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
96	#461×C₇₁	C₂²	1	1	yes	characteristic
97	#461×C₇₁	C₂²	1	2	yes	—
98	#461×C₇₁	C₂²	1	1	yes	characteristic
99	#461×C₇₁	C₂²	1	1	yes	characteristic, complemented
100	#460×C₇₁	C₂²	1	2	yes	complemented
101	#459×C₇₁	C₂²	1	1	yes	characteristic
102	#459×C₇₁	C₂²	1	2	yes	—
103	#459×C₇₁	C₂²	1	1	yes	characteristic
104	#452×C₇₁	C₂²	1	2	yes	—
105	#452×C₇₁	C₂²	1	2	yes	—
106	#452×C₇₁	C₂²	1	2	yes	—
107	#452×C₇₁	C₂²	1	2	yes	complemented
108	#452×C₇₁	C₂²	1	2	yes	complemented
109	#450×C₇₁	C₂²	1	1	yes	characteristic
110	#449×C₇₁	C₂²	1	2	yes	—
111	#449×C₇₁	C₂²	1	2	yes	—
112	#449×C₇₁	C₂²	1	2	yes	—
113	#447×C₇₁	C₂²	1	1	yes	characteristic
114	#446×C₇₁	C₂²	1	1	yes	characteristic, complemented
115	#446×C₇₁	C₂²	1	1	yes	characteristic, complemented
116	#442×C₇₁	C₂²	1	2	yes	—
117	#441×C₇₁	C₂²	1	2	yes	complemented
118	#440×C₇₁	C₂²	1	2	yes	—
119	#440×C₇₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
124	#435×C₇₁	C₂²	1	2	yes	—
125	#435×C₇₁	C₂²	1	2	yes	—
126	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic, complemented
127	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic, complemented
128	#432×C₇₁	C₂²	1	2	yes	complemented
129	#431×C₇₁	C₂²	1	1	yes	characteristic
130	#423×C₇₁	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	complemented
132	#417×C₇₁	C₂²	1	2	yes	—
133	#416×C₇₁	C₂²	1	2	yes	complemented
134	#416×C₇₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₇₁	—	2	1	no	—
136	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₇₁	C₂³	1	2	yes	—
138	C₂×#41×C₇₁	C₂³	1	2	yes	—
139	C₂×#41×C₇₁	C₂³	1	2	yes	—
140	C₂×#41×C₇₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇₁	—	2	1	no	—
143	AGL(1,ℤ/8)×C₇₁	—	4	4	no	—
144	#135×C₇₁	—	4	4	no	—
145	#135×C₇₁	—	4	4	no	—
146	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₇₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
156	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₇₁	C₂³	1	2	yes	—
158	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₇₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
167	#127×C₇₁	—	2	2	no	—
168	#127×C₇₁	—	2	1	no	—
169	#127×C₇₁	C₂³	1	1	yes	characteristic
170	#127×C₇₁	C₂³	1	2	yes	—
171	#126×C₇₁	—	2	2	no	—
172	#126×C₇₁	—	2	2	no	—
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	—	2	1	no	—
175	#126×C₇₁	—	2	2	no	—
176	#125×C₇₁	—	2	2	no	—
177	#125×C₇₁	—	2	1	no	—
178	#125×C₇₁	—	2	2	no	—
179	#125×C₇₁	—	2	1	no	—
180	#125×C₇₁	C₂³	1	1	yes	characteristic
181	#125×C₇₁	C₂³	1	2	yes	—
182	#124×C₇₁	—	2	2	no	—
183	#124×C₇₁	C₂³	1	1	yes	characteristic
184	#124×C₇₁	C₂³	1	2	yes	—
185	#124×C₇₁	C₂³	1	2	yes	—
186	#123×C₇₁	—	2	2	no	—
187	#123×C₇₁	—	2	1	no	—
188	#123×C₇₁	—	2	2	no	—
189	#123×C₇₁	—	2	2	no	—
190	#123×C₇₁	—	2	2	no	—
191	#123×C₇₁	—	2	2	no	—
192	#123×C₇₁	—	2	2	no	—
193	#123×C₇₁	—	2	2	no	—
194	#123×C₇₁	—	2	2	no	—
195	C₂²⋊Q₈×C₇₁	—	2	1	no	—
196	C₂²⋊Q₈×C₇₁	—	2	1	no	—
197	C₂²⋊Q₈×C₇₁	—	2	1	no	—
198	C₂²⋊Q₈×C₇₁	—	2	2	no	—
199	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
200	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
203	#121×C₇₁	—	2	1	no	—
204	#121×C₇₁	—	2	1	no	—
205	#121×C₇₁	—	2	2	no	—
206	#121×C₇₁	—	2	1	no	—
207	#121×C₇₁	—	2	1	no	—
208	#121×C₇₁	—	2	1	no	—
209	#121×C₇₁	—	2	2	no	—
210	#121×C₇₁	—	2	2	no	—
211	#121×C₇₁	—	2	1	no	—
212	#121×C₇₁	—	2	2	no	—
213	#121×C₇₁	—	2	2	no	—
214	#121×C₇₁	—	2	2	no	—
215	#121×C₇₁	—	2	2	no	—
216	#121×C₇₁	—	2	2	no	—
217	#121×C₇₁	C₂³	1	1	yes	characteristic
218	#121×C₇₁	C₂³	1	2	yes	—
219	#121×C₇₁	C₂³	1	2	yes	—
220	#120×C₇₁	—	2	2	no	—
221	C₄×Q₈×C₇₁	—	2	1	no	—
222	C₄×Q₈×C₇₁	—	2	1	no	—
223	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
224	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₇₁	—	2	2	no	—
230	C₄×D₄×C₇₁	—	2	2	no	—
231	C₄×D₄×C₇₁	—	2	2	no	—
232	C₄×D₄×C₇₁	—	2	1	no	—
233	C₄×D₄×C₇₁	—	2	2	no	—
234	C₄×D₄×C₇₁	—	2	2	no	—
235	C₄×D₄×C₇₁	—	2	1	no	—
236	C₄×D₄×C₇₁	—	2	1	no	—
237	C₄×D₄×C₇₁	—	2	1	no	—
238	C₄×D₄×C₇₁	—	2	1	no	—
239	C₄×D₄×C₇₁	—	2	2	no	—
240	C₄×D₄×C₇₁	—	2	1	no	—
241	C₄×D₄×C₇₁	—	2	2	no	—
242	C₄×D₄×C₇₁	D₄	1	2	yes	—
243	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
244	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₇₁	C₂³	1	2	yes	—
248	C₄×D₄×C₇₁	C₂³	1	2	yes	—
249	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₇₁	C₂³	1	2	yes	—
253	#117×C₇₁	—	2	1	no	—
254	#117×C₇₁	—	2	1	no	—
255	#117×C₇₁	—	2	1	no	—
256	#117×C₇₁	—	2	2	no	—
257	#117×C₇₁	—	2	2	no	—
258	#117×C₇₁	—	2	2	no	—
259	#117×C₇₁	—	2	1	no	—
260	#117×C₇₁	—	2	2	no	—
261	#117×C₇₁	D₄	1	1	yes	characteristic
262	#117×C₇₁	D₄	1	2	yes	—
263	#117×C₇₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
265	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
267	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
271	C₂×C₄²×C₇₁	—	2	2	no	—
272	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
273	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
274	#107×C₇₁	C₂³	1	1	yes	characteristic
275	#107×C₇₁	C₂³	1	1	yes	characteristic
276	#107×C₇₁	C₂³	1	2	yes	—
277	#106×C₇₁	C₂³	1	1	yes	characteristic
278	#106×C₇₁	C₂³	1	1	yes	characteristic
279	#106×C₇₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
282	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
284	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
287	#103×C₇₁	C₂³	1	1	yes	characteristic
288	#103×C₇₁	C₂³	1	2	yes	—
289	#103×C₇₁	C₂³	1	2	yes	—
290	#103×C₇₁	C₂³	1	2	yes	—
291	#103×C₇₁	C₂³	1	2	yes	—
292	#103×C₇₁	C₂³	1	1	yes	characteristic
293	#103×C₇₁	C₂³	1	2	yes	—
294	#103×C₇₁	C₂³	1	2	yes	—
295	#103×C₇₁	C₂³	1	2	yes	—
296	#102×C₇₁	C₂³	1	1	yes	characteristic
297	#102×C₇₁	C₂³	1	2	yes	—
298	#102×C₇₁	C₂³	1	2	yes	—
299	#102×C₇₁	C₂³	1	2	yes	—
300	#102×C₇₁	C₂³	1	2	yes	—
301	#102×C₇₁	C₂³	1	1	yes	characteristic
302	#102×C₇₁	C₂³	1	1	yes	characteristic
303	#102×C₇₁	C₂³	1	1	yes	characteristic
304	#102×C₇₁	C₂³	1	1	yes	characteristic
305	#102×C₇₁	C₂³	1	1	yes	characteristic
306	#102×C₇₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
311	#97×C₇₁	C₂³	1	2	yes	—
312	#97×C₇₁	C₂³	1	2	yes	—
313	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₇₁	—	2	1	no	—
316	#41×C₇₁	—	2	4	no	—
317	#41×C₇₁	—	4	2	no	—
318	#41×C₇₁	—	4	2	no	—
319	#41×C₇₁	—	4	2	no	—
320	#41×C₇₁	—	4	2	no	—
321	#41×C₇₁	—	4	2	no	—
322	#41×C₇₁	—	4	2	no	—
323	#41×C₇₁	—	4	2	no	—
324	#41×C₇₁	—	4	2	no	—
325	#41×C₇₁	—	4	4	no	—
326	C₂×Q₈×C₇₁	—	2	1	no	—
327	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
331	C₂×D₄×C₇₁	—	2	2	no	—
332	C₂×D₄×C₇₁	—	2	2	no	—
333	C₂×D₄×C₇₁	—	2	2	no	—
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	1	no	—
340	C₂×D₄×C₇₁	—	2	2	no	—
341	C₂×D₄×C₇₁	—	2	1	no	—
342	C₂×D₄×C₇₁	—	2	2	no	—
343	C₂×D₄×C₇₁	—	2	1	no	—
344	C₂×D₄×C₇₁	—	4	1	no	—
345	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
348	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₇₁	—	2	1	no	—
352	C₂²×C₄×C₇₁	—	2	1	no	—
353	C₂²×C₄×C₇₁	—	2	2	no	—
354	C₂²×C₄×C₇₁	—	2	1	no	—
355	C₂²×C₄×C₇₁	—	2	2	no	—
356	C₂²×C₄×C₇₁	—	2	1	no	—
357	C₂²×C₄×C₇₁	—	2	1	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	—	2	2	no	—
363	C₂²×C₄×C₇₁	—	4	4	no	—
364	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₇₁	—	4	2	no	—
371	Q₁₆×C₇₁	—	4	2	no	—
372	Q₁₆×C₇₁	—	4	2	no	—
373	SD₁₆×C₇₁	—	2	2	no	—
374	SD₁₆×C₇₁	—	2	4	no	—
375	SD₁₆×C₇₁	—	4	2	no	—
376	SD₁₆×C₇₁	—	4	1	no	—
377	SD₁₆×C₇₁	—	4	2	no	—
378	SD₁₆×C₇₁	—	4	2	no	—
379	SD₁₆×C₇₁	—	4	2	no	—
380	D₈×C₇₁	—	2	2	no	—
381	D₈×C₇₁	—	2	4	no	—
382	D₈×C₇₁	—	4	1	no	—
383	D₈×C₇₁	—	4	2	no	—
384	M₁₆×C₇₁	—	4	2	no	—
385	C₂×C₈×C₇₁	—	4	2	no	—
386	C₂×C₈×C₇₁	—	4	2	no	—
387	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
392	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
393	C₄⋊C₄×C₇₁	—	2	2	no	—
394	C₄⋊C₄×C₇₁	—	2	1	no	—
395	C₄⋊C₄×C₇₁	—	2	1	no	—
396	C₄⋊C₄×C₇₁	—	2	1	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	1	no	—
401	C₄⋊C₄×C₇₁	—	2	1	no	—
402	C₄⋊C₄×C₇₁	—	2	1	no	—
403	C₄⋊C₄×C₇₁	—	2	2	no	—
404	C₄⋊C₄×C₇₁	—	2	2	no	—
405	C₄⋊C₄×C₇₁	—	2	1	no	—
406	C₄⋊C₄×C₇₁	—	2	2	no	—
407	C₄⋊C₄×C₇₁	—	2	1	no	—
408	C₄⋊C₄×C₇₁	—	2	2	no	—
409	C₄⋊C₄×C₇₁	—	2	2	no	—
410	C₄⋊C₄×C₇₁	—	2	1	no	—
411	C₄⋊C₄×C₇₁	—	2	2	no	—
412	C₄⋊C₄×C₇₁	—	2	1	no	—
413	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₇₁	—	2	2	no	—
423	C₂²⋊C₄×C₇₁	—	2	2	no	—
424	C₂²⋊C₄×C₇₁	—	2	1	no	—
425	C₂²⋊C₄×C₇₁	—	2	2	no	—
426	C₂²⋊C₄×C₇₁	—	2	2	no	—
427	C₂²⋊C₄×C₇₁	—	2	1	no	—
428	C₂²⋊C₄×C₇₁	—	2	2	no	—
429	C₂²⋊C₄×C₇₁	—	2	2	no	—
430	C₂²⋊C₄×C₇₁	—	2	1	no	—
431	C₂²⋊C₄×C₇₁	—	2	1	no	—
432	C₂²⋊C₄×C₇₁	—	2	1	no	—
433	C₂²⋊C₄×C₇₁	—	2	2	no	—
434	C₂²⋊C₄×C₇₁	—	2	1	no	—
435	C₂²⋊C₄×C₇₁	—	2	1	no	—
436	C₂²⋊C₄×C₇₁	—	2	2	no	—
437	C₂²⋊C₄×C₇₁	—	2	2	no	—
438	C₂²⋊C₄×C₇₁	—	2	1	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	—	2	1	no	—
443	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
446	C₄²×C₇₁	—	2	2	no	—
447	C₄²×C₇₁	—	2	2	no	—
448	C₄²×C₇₁	—	2	2	no	—
449	C₄²×C₇₁	—	2	2	no	—
450	C₄²×C₇₁	—	2	1	no	—
451	C₄²×C₇₁	C₂×D₄	1	2	yes	—
452	C₄²×C₇₁	C₂×D₄	1	2	yes	—
453	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₇₁	C₂⁴	1	2	yes	—
457	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₇₁	—	2	1	no	—
459	C₂³×C₇₁	—	2	1	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	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
467	Q₈×C₇₁	—	2	2	no	—
468	Q₈×C₇₁	—	2	2	no	—
469	Q₈×C₇₁	—	2	1	no	—
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	—	8	1	no	—
475	D₄×C₇₁	—	2	2	no	—
476	D₄×C₇₁	—	2	2	no	—
477	D₄×C₇₁	—	2	1	no	—
478	D₄×C₇₁	—	2	1	no	—
479	D₄×C₇₁	—	2	1	no	—
480	D₄×C₇₁	—	2	1	no	—
481	D₄×C₇₁	—	2	1	no	—
482	D₄×C₇₁	—	2	2	no	—
483	D₄×C₇₁	—	4	2	no	—
484	D₄×C₇₁	—	4	2	no	—
485	D₄×C₇₁	—	4	4	no	—
486	D₄×C₇₁	—	4	4	no	—
487	D₄×C₇₁	—	4	2	no	—
488	D₄×C₇₁	—	8	2	no	—
489	D₄×C₇₁	—	8	1	no	—
490	D₄×C₇₁	—	8	2	no	—
491	D₄×C₇₁	—	8	2	no	—
492	D₄×C₇₁	—	8	1	no	—
493	D₄×C₇₁	—	8	2	no	—
494	D₄×C₇₁	—	8	2	no	—
495	D₄×C₇₁	—	8	2	no	—
496	D₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
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	2	no	—
502	C₂×C₄×C₇₁	—	2	1	no	—
503	C₂×C₄×C₇₁	—	2	1	no	—
504	C₂×C₄×C₇₁	—	2	2	no	—
505	C₂×C₄×C₇₁	—	2	2	no	—
506	C₂×C₄×C₇₁	—	2	2	no	—
507	C₂×C₄×C₇₁	—	2	1	no	—
508	C₂×C₄×C₇₁	—	2	1	no	—
509	C₂×C₄×C₇₁	—	2	1	no	—
510	C₂×C₄×C₇₁	—	4	2	no	—
511	C₂×C₄×C₇₁	—	4	1	no	—
512	C₂×C₄×C₇₁	—	4	2	no	—
513	C₂×C₄×C₇₁	—	4	4	no	—
514	C₂×C₄×C₇₁	—	4	2	no	—
515	C₂×C₄×C₇₁	—	4	2	no	—
516	C₂×C₄×C₇₁	—	4	4	no	—
517	C₂×C₄×C₇₁	—	4	2	no	—
518	C₂×C₄×C₇₁	—	4	2	no	—
519	C₂×C₄×C₇₁	—	4	2	no	—
520	C₂×C₄×C₇₁	—	4	2	no	—
521	C₂×C₄×C₇₁	—	8	2	no	—
522	C₂×C₄×C₇₁	—	8	2	no	—
523	C₂×C₄×C₇₁	—	8	2	no	—
524	C₂×C₄×C₇₁	—	8	2	no	—
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	2	yes	—
528	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
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	C₈×C₇₁	—	2	1	no	—
539	C₈×C₇₁	—	2	1	no	—
540	C₂²×C₇₁	—	2	2	no	—
541	C₂²×C₇₁	—	2	1	no	—
542	C₂²×C₇₁	—	2	2	no	—
543	C₂²×C₇₁	—	2	1	no	—
544	C₂²×C₇₁	—	2	2	no	—
545	C₂²×C₇₁	—	2	1	no	—
546	C₂²×C₇₁	—	2	2	no	—
547	C₂²×C₇₁	—	4	1	no	—
548	C₂²×C₇₁	—	4	1	no	—
549	C₂²×C₇₁	—	4	1	no	—
550	C₂²×C₇₁	—	4	2	no	—
551	C₂²×C₇₁	—	4	1	no	—
552	C₂²×C₇₁	—	4	2	no	—
553	C₂²×C₇₁	—	4	1	no	—
554	C₂²×C₇₁	—	4	1	no	—
555	C₂²×C₇₁	—	4	1	no	—
556	C₂²×C₇₁	—	4	2	no	—
557	C₂²×C₇₁	—	4	1	no	—
558	C₂²×C₇₁	—	8	4	no	—
559	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
560	C₄×C₇₁	—	2	1	no	—
561	C₄×C₇₁	—	2	2	no	—
562	C₄×C₇₁	—	2	1	no	—
563	C₄×C₇₁	—	2	2	no	—
564	C₄×C₇₁	—	2	1	no	—
565	C₄×C₇₁	—	2	1	no	—
566	C₄×C₇₁	—	2	2	no	—
567	C₄×C₇₁	—	4	2	no	—
568	C₄×C₇₁	—	4	1	no	—
569	C₄×C₇₁	—	4	2	no	—
570	C₄×C₇₁	—	4	2	no	—
571	C₄×C₇₁	—	4	1	no	—
572	C₄×C₇₁	—	4	1	no	—
573	C₄×C₇₁	—	4	1	no	—
574	C₄×C₇₁	—	4	1	no	—
575	C₄×C₇₁	#575	1	2	yes	—
576	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₄×C₇₁	#585	1	1	yes	characteristic
578	#61993	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
579	C₂×C₇₁	—	4	2	no	—
580	C₂×C₇₁	—	4	1	no	—
581	C₂×C₇₁	—	4	2	no	—
582	C₂×C₇₁	—	8	2	no	—
583	C₂×C₇₁	—	8	1	no	—
584	C₂×C₇₁	—	8	1	no	—
585	C₂×C₇₁	#3488	1	1	yes	characteristic
586	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
587	C₂×C₇₁	#3584	1	1	yes	characteristic
588	#3517	C₂×C₇₁	1	1	yes	characteristic, complemented
589	#3475	C₂×C₇₁	1	1	yes	characteristic, complemented
590	#3398	C₂×C₇₁	1	1	yes	characteristic, complemented
591	#3397	C₂×C₇₁	1	1	yes	characteristic, complemented
592	#3372	C₂×C₇₁	1	1	yes	characteristic, complemented
593	#3366	C₂×C₇₁	1	1	yes	characteristic, complemented
594	#3317	C₂×C₇₁	1	2	yes	complemented
595	#3315	C₂×C₇₁	1	2	yes	complemented
596	#3305	C₂×C₇₁	1	1	yes	characteristic, complemented
597	#3303	C₂×C₇₁	1	1	yes	characteristic, complemented
598	#3284	C₂×C₇₁	1	1	yes	characteristic, complemented
599	#3283	C₂×C₇₁	1	1	yes	characteristic, complemented
600	#3268	C₂×C₇₁	1	2	yes	complemented
601	#3267	C₂×C₇₁	1	2	yes	complemented
602	#3252	C₂×C₇₁	1	1	yes	characteristic, complemented
603	#3250	C₂×C₇₁	1	2	yes	complemented
604	#3219	C₂×C₇₁	1	2	yes	complemented
605	#3210	C₂×C₇₁	1	1	yes	characteristic, complemented
606	#3111	C₂×C₇₁	1	2	yes	complemented
607	#3105	C₂×C₇₁	1	1	yes	characteristic, complemented
608	#3036	C₂×C₇₁	1	1	yes	characteristic, complemented
609	#3035	C₂×C₇₁	1	2	yes	complemented
610	#2990	C₂×C₇₁	1	1	yes	characteristic, complemented
611	C₇₁	#61993	1	1	yes	characteristic, direct product factor, Sylow
612	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	2	yes	—
613	C₂×#135	C₂²×C₇₁	1	2	yes	—
614	C₂×#135	C₂²×C₇₁	1	2	yes	—
615	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
616	#556	C₂²×C₇₁	1	1	yes	characteristic
617	#555	C₂²×C₇₁	1	1	yes	characteristic
618	#554	C₂²×C₇₁	1	1	yes	characteristic
619	#553	—	2	1	no	—
620	#553	—	2	2	no	—
621	#553	—	2	1	no	—
622	#552	—	2	1	no	—
623	#552	C₂²×C₇₁	1	2	yes	—
624	#551	—	2	2	no	—
625	#550	—	2	1	no	—
626	#550	C₂²×C₇₁	1	2	yes	—
627	#550	C₂²×C₇₁	1	1	yes	characteristic, complemented
628	#550	C₂²×C₇₁	1	1	yes	characteristic, complemented
629	#547	C₂²×C₇₁	1	1	yes	characteristic
630	#547	C₂²×C₇₁	1	2	yes	—
631	#547	C₂²×C₇₁	1	1	yes	characteristic, complemented
632	#546	C₂²×C₇₁	1	2	yes	—
633	#540	—	2	1	no	—
634	#540	—	2	2	no	—
635	#533	C₂²×C₇₁	1	1	yes	characteristic
636	#532	C₂²×C₇₁	1	1	yes	characteristic
637	#532	C₂²×C₇₁	1	2	yes	complemented
638	#529	—	2	2	no	—
639	#529	C₂²×C₇₁	1	1	yes	characteristic
640	#529	C₂²×C₇₁	1	2	yes	—
641	#529	C₂²×C₇₁	1	2	yes	complemented
642	#525	—	2	1	no	—
643	#520	—	2	1	no	—
644	C₄×#41	C₂²×C₇₁	1	2	yes	—
645	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
647	C₂×#117	—	2	1	no	—
648	#497	C₂²×C₇₁	1	2	yes	—
649	#496	C₂²×C₇₁	1	2	yes	—
650	#494	C₂²×C₇₁	1	1	yes	characteristic, complemented
651	#492	C₂²×C₇₁	1	1	yes	characteristic, complemented
652	#491	C₂²×C₇₁	1	2	yes	complemented
653	#490	C₂²×C₇₁	1	2	yes	complemented
654	#487	C₂²×C₇₁	1	1	yes	characteristic, complemented
655	#486	C₂²×C₇₁	1	1	yes	characteristic, complemented
656	#485	C₂²×C₇₁	1	2	yes	complemented
657	#484	C₂²×C₇₁	1	1	yes	characteristic
658	#482	C₂²×C₇₁	1	2	yes	complemented
659	#481	C₂²×C₇₁	1	1	yes	characteristic
660	#479	C₂²×C₇₁	1	2	yes	complemented
661	#479	C₂²×C₇₁	1	2	yes	complemented
662	#478	C₂²×C₇₁	1	1	yes	characteristic
663	#478	C₂²×C₇₁	1	1	yes	characteristic
664	#478	C₂²×C₇₁	1	2	yes	complemented
665	#477	C₂²×C₇₁	1	1	yes	characteristic, complemented
666	#476	C₂²×C₇₁	1	1	yes	characteristic, complemented
667	#470	C₂²×C₇₁	1	2	yes	—
668	#468	C₂²×C₇₁	1	2	yes	—
669	#467	C₂²×C₇₁	1	2	yes	complemented
670	#466	C₂²×C₇₁	1	2	yes	—
671	#465	C₂²×C₇₁	1	2	yes	—
672	#465	C₂²×C₇₁	1	2	yes	complemented
673	#464	C₂²×C₇₁	1	2	yes	—
674	#464	C₂²×C₇₁	1	2	yes	complemented
675	#464	C₂²×C₇₁	1	2	yes	complemented
676	#464	C₂²×C₇₁	1	2	yes	complemented
677	#463	C₂²×C₇₁	1	1	yes	characteristic
678	#463	C₂²×C₇₁	1	1	yes	characteristic
679	#463	C₂²×C₇₁	1	2	yes	—
680	#463	C₂²×C₇₁	1	2	yes	—
681	#463	C₂²×C₇₁	1	2	yes	—
682	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
683	#462	C₂²×C₇₁	1	2	yes	complemented
684	#461	C₂²×C₇₁	1	2	yes	—
685	#461	C₂²×C₇₁	1	1	yes	characteristic
686	#461	C₂²×C₇₁	1	1	yes	characteristic
687	#461	C₂²×C₇₁	1	1	yes	characteristic, complemented
688	#460	C₂²×C₇₁	1	2	yes	complemented
689	#459	C₂²×C₇₁	1	2	yes	—
690	#459	C₂²×C₇₁	1	1	yes	characteristic
691	#459	C₂²×C₇₁	1	1	yes	characteristic
692	#452	C₂²×C₇₁	1	2	yes	—
693	#452	C₂²×C₇₁	1	2	yes	—
694	#452	C₂²×C₇₁	1	2	yes	—
695	#452	C₂²×C₇₁	1	2	yes	complemented
696	#452	C₂²×C₇₁	1	2	yes	complemented
697	#450	C₂²×C₇₁	1	1	yes	characteristic
698	#449	C₂²×C₇₁	1	2	yes	—
699	#449	C₂²×C₇₁	1	2	yes	—
700	#449	C₂²×C₇₁	1	2	yes	—
701	#447	C₂²×C₇₁	1	1	yes	characteristic
702	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
703	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
704	#442	C₂²×C₇₁	1	2	yes	—
705	#441	C₂²×C₇₁	1	2	yes	complemented
706	#440	C₂²×C₇₁	1	2	yes	—
707	#440	C₂²×C₇₁	1	2	yes	complemented
708	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
709	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
710	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
711	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
712	#435	C₂²×C₇₁	1	2	yes	—
713	#435	C₂²×C₇₁	1	2	yes	—
714	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic, complemented
715	C₈×D₄	C₂²×C₇₁	1	1	yes	characteristic, complemented
716	#432	C₂²×C₇₁	1	2	yes	complemented
717	#431	C₂²×C₇₁	1	1	yes	characteristic
718	#423	C₂²×C₇₁	1	1	yes	characteristic
719	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	complemented
720	#417	C₂²×C₇₁	1	2	yes	—
721	#416	C₂²×C₇₁	1	2	yes	complemented
722	#416	C₂²×C₇₁	1	2	yes	complemented
723	C₂×#41	—	2	1	no	—
724	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
725	C₂×#41	C₂³×C₇₁	1	2	yes	—
726	C₂×#41	C₂³×C₇₁	1	2	yes	—
727	C₂×#41	C₂³×C₇₁	1	2	yes	—
728	C₂×#41	C₂³×C₇₁	1	2	yes	—
729	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
730	C₂³×C₄	—	2	1	no	—
731	AGL(1,ℤ/8)	—	4	4	no	—
732	#135	—	4	4	no	—
733	#135	—	4	4	no	—
734	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
744	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
745	C₂×D₈	C₂³×C₇₁	1	2	yes	—
746	C₂×D₈	C₂³×C₇₁	1	2	yes	—
747	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
749	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
750	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
753	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
754	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
755	#127	—	2	2	no	—
756	#127	—	2	1	no	—
757	#127	C₂³×C₇₁	1	1	yes	characteristic
758	#127	C₂³×C₇₁	1	2	yes	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	—	2	1	no	—
763	#126	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	—	2	1	no	—
766	#125	—	2	2	no	—
767	#125	—	2	1	no	—
768	#125	C₂³×C₇₁	1	1	yes	characteristic
769	#125	C₂³×C₇₁	1	2	yes	—
770	#124	—	2	2	no	—
771	#124	C₂³×C₇₁	1	1	yes	characteristic
772	#124	C₂³×C₇₁	1	2	yes	—
773	#124	C₂³×C₇₁	1	2	yes	—
774	#123	—	2	2	no	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
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	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
790	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	C₂³×C₇₁	1	2	yes	—
806	#121	C₂³×C₇₁	1	1	yes	characteristic
807	#121	C₂³×C₇₁	1	2	yes	—
808	#120	—	2	2	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
816	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	D₄×C₇₁	1	2	yes	—
831	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₇₁	1	2	yes	—
837	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₇₁	1	2	yes	—
839	C₄×D₄	C₂³×C₇₁	1	2	yes	—
840	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	—	2	1	no	—
848	#117	—	2	2	no	—
849	#117	D₄×C₇₁	1	1	yes	characteristic
850	#117	D₄×C₇₁	1	2	yes	—
851	#117	C₂³×C₇₁	1	2	yes	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	1	no	—
854	C₂×C₄⋊C₄	—	2	2	no	—
855	C₂×C₄⋊C₄	—	2	1	no	—
856	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
857	C₂×C₂²⋊C₄	—	2	1	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₄²	—	2	2	no	—
860	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
861	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
862	#107	C₂³×C₇₁	1	1	yes	characteristic
863	#107	C₂³×C₇₁	1	1	yes	characteristic
864	#107	C₂³×C₇₁	1	2	yes	—
865	#106	C₂³×C₇₁	1	1	yes	characteristic
866	#106	C₂³×C₇₁	1	1	yes	characteristic
867	#106	C₂³×C₇₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
870	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
871	C₄⋊C₈	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	#103	C₂³×C₇₁	1	1	yes	characteristic
876	#103	C₂³×C₇₁	1	2	yes	—
877	#103	C₂³×C₇₁	1	2	yes	—
878	#103	C₂³×C₇₁	1	2	yes	—
879	#103	C₂³×C₇₁	1	2	yes	—
880	#103	C₂³×C₇₁	1	1	yes	characteristic
881	#103	C₂³×C₇₁	1	2	yes	—
882	#103	C₂³×C₇₁	1	2	yes	—
883	#103	C₂³×C₇₁	1	2	yes	—
884	#102	C₂³×C₇₁	1	1	yes	characteristic
885	#102	C₂³×C₇₁	1	2	yes	—
886	#102	C₂³×C₇₁	1	2	yes	—
887	#102	C₂³×C₇₁	1	2	yes	—
888	#102	C₂³×C₇₁	1	2	yes	—
889	#102	C₂³×C₇₁	1	1	yes	characteristic
890	#102	C₂³×C₇₁	1	1	yes	characteristic
891	#102	C₂³×C₇₁	1	1	yes	characteristic
892	#102	C₂³×C₇₁	1	1	yes	characteristic
893	#102	C₂³×C₇₁	1	1	yes	characteristic
894	#102	C₂³×C₇₁	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
897	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
899	#97	C₂³×C₇₁	1	2	yes	—
900	#97	C₂³×C₇₁	1	2	yes	—
901	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
903	C₂⁴	—	2	1	no	—
904	#41	—	2	4	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	4	no	—
914	C₂×Q₈	—	2	1	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×Q₈	C₂⁴×C₇₁	1	2	yes	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	4	1	no	—
933	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
934	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
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	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	4	4	no	—
952	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
955	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
958	Q₁₆	—	4	2	no	—
959	Q₁₆	—	4	2	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	—	4	1	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	2	no	—
968	D₈	—	2	2	no	—
969	D₈	—	2	4	no	—
970	D₈	—	4	1	no	—
971	D₈	—	4	2	no	—
972	M₁₆	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
980	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
1008	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1040	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1041	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₇₁	1	2	yes	—
1045	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1054	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	8	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	1	no	—
1084	D₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	4	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1116	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1121	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	8	4	no	—
1147	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	#575×C₇₁	1	2	yes	—
1164	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
1165	C₄	#585×C₇₁	1	1	yes	characteristic
1166	C₂	—	4	1	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₇₁×#3488	1	1	yes	characteristic
1173	C₂	C₂×#575×C₇₁	1	1	yes	characteristic
1174	C₂	C₇₁×#3584	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×#3517	C₂	semidirect
2. C₇₁×#3475	C₂	semidirect
3. C₇₁×#3398	C₂	semidirect
4. C₇₁×#3397	C₂	semidirect
5. C₇₁×#3372	C₂	semidirect
6. C₇₁×#3366	C₂	semidirect
7. C₇₁×#3317	C₂	semidirect
8. C₇₁×#3315	C₂	semidirect
9. C₇₁×#3305	C₂	semidirect
10. C₇₁×#3303	C₂	semidirect
11. C₇₁×#3284	C₂	semidirect
12. C₇₁×#3283	C₂	semidirect
13. C₇₁×#3268	C₂	semidirect
14. C₇₁×#3267	C₂	semidirect
15. C₇₁×#3252	C₂	semidirect
16. C₇₁×#3250	C₂	semidirect
17. C₇₁×#3219	C₂	semidirect
18. C₇₁×#3210	C₂	semidirect
19. C₇₁×#3111	C₂	semidirect
20. C₇₁×#3105	C₂	semidirect
21. C₇₁×#3036	C₂	semidirect
22. C₇₁×#3035	C₂	semidirect
23. C₇₁×#2990	C₂	semidirect
27. #557×C₇₁	C₂²	semidirect
39. #550×C₇₁	C₂²	semidirect
40. #550×C₇₁	C₂²	semidirect
43. #547×C₇₁	C₂²	semidirect
49. #532×C₇₁	C₂²	semidirect
53. #529×C₇₁	C₂²	semidirect
62. #494×C₇₁	C₂²	semidirect
63. #492×C₇₁	C₂²	semidirect
64. #491×C₇₁	C₂²	semidirect
65. #490×C₇₁	C₂²	semidirect
66. #487×C₇₁	C₂²	semidirect
67. #486×C₇₁	C₂²	semidirect
68. #485×C₇₁	C₂²	semidirect
70. #482×C₇₁	C₂²	semidirect
72. #479×C₇₁	C₂²	semidirect
73. #479×C₇₁	C₂²	semidirect
76. #478×C₇₁	C₂²	semidirect
77. #477×C₇₁	C₂²	semidirect
78. #476×C₇₁	C₂²	semidirect
81. #467×C₇₁	C₂²	semidirect
84. #465×C₇₁	C₂²	semidirect
86. #464×C₇₁	C₂²	semidirect
87. #464×C₇₁	C₂²	semidirect
88. #464×C₇₁	C₂²	semidirect
94. #462×C₇₁	C₂²	semidirect
95. #462×C₇₁	C₂²	semidirect
99. #461×C₇₁	C₂²	semidirect
100. #460×C₇₁	C₂²	semidirect
107. #452×C₇₁	C₂²	semidirect
108. #452×C₇₁	C₂²	semidirect
114. #446×C₇₁	C₂²	semidirect
115. #446×C₇₁	C₂²	semidirect
117. #441×C₇₁	C₂²	semidirect
119. #440×C₇₁	C₂²	semidirect
126. C₈×D₄×C₇₁	C₂²	semidirect
127. C₈×D₄×C₇₁	C₂²	semidirect
128. #432×C₇₁	C₂²	semidirect
131. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
133. #416×C₇₁	C₂²	semidirect
134. #416×C₇₁	C₂²	semidirect
578. #61993	C₇₁	direct (N × H)
588. #3517	C₂×C₇₁	semidirect
589. #3475	C₂×C₇₁	semidirect
590. #3398	C₂×C₇₁	semidirect
591. #3397	C₂×C₇₁	semidirect
592. #3372	C₂×C₇₁	semidirect
593. #3366	C₂×C₇₁	semidirect
594. #3317	C₂×C₇₁	semidirect
595. #3315	C₂×C₇₁	semidirect
596. #3305	C₂×C₇₁	semidirect
597. #3303	C₂×C₇₁	semidirect
598. #3284	C₂×C₇₁	semidirect
599. #3283	C₂×C₇₁	semidirect
600. #3268	C₂×C₇₁	semidirect
601. #3267	C₂×C₇₁	semidirect
602. #3252	C₂×C₇₁	semidirect
603. #3250	C₂×C₇₁	semidirect
604. #3219	C₂×C₇₁	semidirect
605. #3210	C₂×C₇₁	semidirect
606. #3111	C₂×C₇₁	semidirect
607. #3105	C₂×C₇₁	semidirect
608. #3036	C₂×C₇₁	semidirect
609. #3035	C₂×C₇₁	semidirect
610. #2990	C₂×C₇₁	semidirect
611. C₇₁	#61993	direct (N × H)
615. #557	C₂²×C₇₁	semidirect
627. #550	C₂²×C₇₁	semidirect
628. #550	C₂²×C₇₁	semidirect
631. #547	C₂²×C₇₁	semidirect
637. #532	C₂²×C₇₁	semidirect
641. #529	C₂²×C₇₁	semidirect
650. #494	C₂²×C₇₁	semidirect
651. #492	C₂²×C₇₁	semidirect
652. #491	C₂²×C₇₁	semidirect
653. #490	C₂²×C₇₁	semidirect
654. #487	C₂²×C₇₁	semidirect
655. #486	C₂²×C₇₁	semidirect
656. #485	C₂²×C₇₁	semidirect
658. #482	C₂²×C₇₁	semidirect
660. #479	C₂²×C₇₁	semidirect
661. #479	C₂²×C₇₁	semidirect
664. #478	C₂²×C₇₁	semidirect
665. #477	C₂²×C₇₁	semidirect
666. #476	C₂²×C₇₁	semidirect
669. #467	C₂²×C₇₁	semidirect
672. #465	C₂²×C₇₁	semidirect
674. #464	C₂²×C₇₁	semidirect
675. #464	C₂²×C₇₁	semidirect
676. #464	C₂²×C₇₁	semidirect
682. #462	C₂²×C₇₁	semidirect
683. #462	C₂²×C₇₁	semidirect
687. #461	C₂²×C₇₁	semidirect
688. #460	C₂²×C₇₁	semidirect
695. #452	C₂²×C₇₁	semidirect
696. #452	C₂²×C₇₁	semidirect
702. #446	C₂²×C₇₁	semidirect
703. #446	C₂²×C₇₁	semidirect
705. #441	C₂²×C₇₁	semidirect
707. #440	C₂²×C₇₁	semidirect
714. C₈×D₄	C₂²×C₇₁	semidirect
715. C₈×D₄	C₂²×C₇₁	semidirect
716. #432	C₂²×C₇₁	semidirect
719. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
721. #416	C₂²×C₇₁	semidirect
722. #416	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×#3517	2
C₇₁×#3475	2
C₇₁×#3398	2
C₇₁×#3397	2
C₇₁×#3372	2
C₇₁×#3366	2
C₇₁×#3317	2
C₇₁×#3315	2
C₇₁×#3305	2
C₇₁×#3303	2
C₇₁×#3284	2
C₇₁×#3283	2
C₇₁×#3268	2
C₇₁×#3267	2
C₇₁×#3252	2
C₇₁×#3250	2
C₇₁×#3219	2
C₇₁×#3210	2
C₇₁×#3111	2
C₇₁×#3105	2
C₇₁×#3036	2
C₇₁×#3035	2
C₇₁×#2990	2
#61993	71

Subgroups — C71×#61993 #31882865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61993 #31882865