Subgroups — C₇₁×#61973 #31882845

Order 18176.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#3313	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3311	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₁×#3269	C₂	1	2	yes	maximal, complemented
14	C₇₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₇₁×#3252	C₂	1	2	yes	maximal, complemented
16	C₇₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₁×#3215	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×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₁×#3040	C₂	1	2	yes	maximal, complemented
22	C₇₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₇₁	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	2	yes	—
26	C₂×#135×C₇₁	C₂²	1	2	yes	complemented
27	#559×C₇₁	C₂²	1	1	yes	characteristic
28	#557×C₇₁	C₂²	1	1	yes	characteristic, complemented
29	#556×C₇₁	C₂²	1	1	yes	characteristic
30	#556×C₇₁	C₂²	1	1	yes	characteristic
31	#556×C₇₁	C₂²	1	2	yes	complemented
32	#555×C₇₁	—	2	1	no	—
33	#552×C₇₁	—	2	1	no	—
34	#552×C₇₁	—	2	2	no	—
35	#551×C₇₁	—	2	2	no	—
36	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
38	#548×C₇₁	—	2	1	no	—
39	#548×C₇₁	C₂²	1	2	yes	—
40	#547×C₇₁	C₂²	1	1	yes	characteristic
41	#547×C₇₁	C₂²	1	2	yes	complemented
42	#546×C₇₁	—	2	1	no	—
43	#546×C₇₁	C₂²	1	2	yes	—
44	D₄²×C₇₁	C₂²	1	1	yes	characteristic
45	#542×C₇₁	—	2	1	no	—
46	#538×C₇₁	—	2	2	no	—
47	#533×C₇₁	C₂²	1	1	yes	characteristic, complemented
48	#533×C₇₁	C₂²	1	2	yes	complemented
49	#532×C₇₁	C₂²	1	1	yes	characteristic
50	#529×C₇₁	—	2	1	no	—
51	#529×C₇₁	—	2	2	no	—
52	#529×C₇₁	C₂²	1	1	yes	characteristic
53	#529×C₇₁	C₂²	1	2	yes	—
54	C₂×#124×C₇₁	C₂²	1	2	yes	—
55	#518×C₇₁	—	2	1	no	—
56	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
57	C₄×#41×C₇₁	C₂²	1	2	yes	complemented
58	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Q₈×C₇₁	—	2	1	no	—
60	#497×C₇₁	C₂²	1	2	yes	—
61	#497×C₇₁	C₂²	1	2	yes	complemented
62	#494×C₇₁	C₂²	1	1	yes	characteristic, complemented
63	#492×C₇₁	C₂²	1	1	yes	characteristic
64	#489×C₇₁	C₂²	1	2	yes	—
65	#489×C₇₁	C₂²	1	2	yes	complemented
66	#487×C₇₁	C₂²	1	1	yes	characteristic, complemented
67	#486×C₇₁	C₂²	1	1	yes	characteristic
68	#485×C₇₁	C₂²	1	2	yes	complemented
69	#485×C₇₁	C₂²	1	1	yes	characteristic, complemented
70	#482×C₇₁	C₂²	1	1	yes	characteristic
71	#482×C₇₁	C₂²	1	2	yes	—
72	#479×C₇₁	C₂²	1	1	yes	characteristic, complemented
73	#479×C₇₁	C₂²	1	2	yes	complemented
74	#478×C₇₁	C₂²	1	1	yes	characteristic, complemented
75	#477×C₇₁	C₂²	1	2	yes	complemented
76	#476×C₇₁	C₂²	1	2	yes	complemented
77	#475×C₇₁	C₂²	1	1	yes	characteristic, complemented
78	#474×C₇₁	C₂²	1	1	yes	characteristic
79	#470×C₇₁	C₂²	1	2	yes	complemented
80	#470×C₇₁	C₂²	1	2	yes	complemented
81	#468×C₇₁	C₂²	1	2	yes	—
82	#468×C₇₁	C₂²	1	2	yes	—
83	#467×C₇₁	C₂²	1	2	yes	complemented
84	#465×C₇₁	C₂²	1	2	yes	—
85	#464×C₇₁	C₂²	1	2	yes	—
86	#464×C₇₁	C₂²	1	2	yes	—
87	#464×C₇₁	C₂²	1	1	yes	characteristic
88	#464×C₇₁	C₂²	1	2	yes	complemented
89	#464×C₇₁	C₂²	1	2	yes	complemented
90	#464×C₇₁	C₂²	1	2	yes	complemented
91	#464×C₇₁	C₂²	1	2	yes	complemented
92	#463×C₇₁	C₂²	1	1	yes	characteristic
93	#463×C₇₁	C₂²	1	2	yes	—
94	#463×C₇₁	C₂²	1	2	yes	complemented
95	#463×C₇₁	C₂²	1	2	yes	complemented
96	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
97	#462×C₇₁	C₂²	1	2	yes	complemented
98	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
99	#461×C₇₁	C₂²	1	1	yes	characteristic
100	#461×C₇₁	C₂²	1	1	yes	characteristic, complemented
101	#461×C₇₁	C₂²	1	2	yes	complemented
102	#460×C₇₁	C₂²	1	1	yes	characteristic
103	#459×C₇₁	C₂²	1	1	yes	characteristic
104	#452×C₇₁	C₂²	1	2	yes	complemented
105	#452×C₇₁	C₂²	1	2	yes	complemented
106	#452×C₇₁	C₂²	1	1	yes	characteristic, complemented
107	#452×C₇₁	C₂²	1	2	yes	complemented
108	#451×C₇₁	C₂²	1	2	yes	complemented
109	#451×C₇₁	C₂²	1	2	yes	complemented
110	#450×C₇₁	C₂²	1	2	yes	—
111	#450×C₇₁	C₂²	1	2	yes	—
112	#449×C₇₁	C₂²	1	1	yes	characteristic
113	#449×C₇₁	C₂²	1	2	yes	—
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	complemented
117	#441×C₇₁	C₂²	1	2	yes	complemented
118	#440×C₇₁	C₂²	1	2	yes	complemented
119	#440×C₇₁	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₇₁	C₂²	1	1	yes	characteristic
124	#436×C₇₁	C₂²	1	1	yes	characteristic
125	#436×C₇₁	C₂²	1	1	yes	characteristic
126	#435×C₇₁	C₂²	1	2	yes	complemented
127	#435×C₇₁	C₂²	1	2	yes	complemented
128	#432×C₇₁	C₂²	1	2	yes	complemented
129	#431×C₇₁	C₂²	1	1	yes	characteristic, complemented
130	#423×C₇₁	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
132	#419×C₇₁	C₂²	1	2	yes	complemented
133	#418×C₇₁	C₂²	1	2	yes	—
134	#416×C₇₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
136	C₂×#41×C₇₁	C₂³	1	2	yes	—
137	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₇₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₇₁	—	2	1	no	—
140	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₇₁	—	2	1	no	—
142	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
143	#137×C₇₁	—	4	4	no	—
144	AGL(1,ℤ/8)×C₇₁	—	4	4	no	—
145	#135×C₇₁	—	4	4	no	—
146	C₂×Q₁₆×C₇₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₇₁	C₂³	1	2	yes	—
150	C₂×Q₁₆×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	1	yes	characteristic
154	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₇₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×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	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₇₁	—	2	1	no	—
164	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
169	#127×C₇₁	C₂³	1	1	yes	characteristic
170	#126×C₇₁	—	2	2	no	—
171	#126×C₇₁	—	2	2	no	—
172	#126×C₇₁	—	2	2	no	—
173	#126×C₇₁	—	2	2	no	—
174	#126×C₇₁	—	2	2	no	—
175	#126×C₇₁	—	2	1	no	—
176	#125×C₇₁	—	2	1	no	—
177	#125×C₇₁	—	2	2	no	—
178	#125×C₇₁	—	2	2	no	—
179	#125×C₇₁	—	2	1	no	—
180	#125×C₇₁	C₂³	1	1	yes	characteristic
181	#124×C₇₁	—	2	1	no	—
182	#124×C₇₁	—	2	1	no	—
183	#124×C₇₁	—	2	2	no	—
184	#124×C₇₁	—	2	2	no	—
185	#124×C₇₁	—	2	2	no	—
186	#124×C₇₁	—	2	2	no	—
187	#124×C₇₁	C₂³	1	1	yes	characteristic
188	#124×C₇₁	C₂³	1	2	yes	—
189	#124×C₇₁	C₂³	1	2	yes	—
190	#124×C₇₁	C₂³	1	2	yes	—
191	#123×C₇₁	—	2	1	no	—
192	#123×C₇₁	—	2	2	no	—
193	#123×C₇₁	—	2	2	no	—
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	C₂²⋊Q₈×C₇₁	—	2	1	no	—
199	C₂²⋊Q₈×C₇₁	—	2	1	no	—
200	C₂²⋊Q₈×C₇₁	—	2	2	no	—
201	C₂²⋊Q₈×C₇₁	—	2	1	no	—
202	C₂²⋊Q₈×C₇₁	—	2	2	no	—
203	C₂²⋊Q₈×C₇₁	—	2	2	no	—
204	C₂²⋊Q₈×C₇₁	—	2	2	no	—
205	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
210	#121×C₇₁	—	2	1	no	—
211	#121×C₇₁	—	2	2	no	—
212	#121×C₇₁	—	2	2	no	—
213	#121×C₇₁	—	2	1	no	—
214	#121×C₇₁	—	2	1	no	—
215	#121×C₇₁	—	2	1	no	—
216	#121×C₇₁	—	2	2	no	—
217	#121×C₇₁	C₂³	1	1	yes	characteristic
218	#121×C₇₁	C₂³	1	2	yes	—
219	#120×C₇₁	—	2	2	no	—
220	#120×C₇₁	—	2	2	no	—
221	C₄×Q₈×C₇₁	—	2	1	no	—
222	C₄×Q₈×C₇₁	—	2	1	no	—
223	C₄×Q₈×C₇₁	—	2	2	no	—
224	C₄×Q₈×C₇₁	—	2	1	no	—
225	C₄×Q₈×C₇₁	—	2	2	no	—
226	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
227	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₇₁	—	2	1	no	—
235	C₄×D₄×C₇₁	—	2	2	no	—
236	C₄×D₄×C₇₁	—	2	1	no	—
237	C₄×D₄×C₇₁	—	2	1	no	—
238	C₄×D₄×C₇₁	—	2	2	no	—
239	C₄×D₄×C₇₁	—	2	2	no	—
240	C₄×D₄×C₇₁	—	2	1	no	—
241	C₄×D₄×C₇₁	—	2	1	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	D₄	1	1	yes	characteristic
246	C₄×D₄×C₇₁	D₄	1	2	yes	—
247	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₇₁	C₂³	1	2	yes	—
250	C₄×D₄×C₇₁	C₂³	1	2	yes	—
251	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₇₁	C₂³	1	2	yes	—
253	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
254	#117×C₇₁	—	2	2	no	—
255	#117×C₇₁	—	2	1	no	—
256	#117×C₇₁	—	2	1	no	—
257	#117×C₇₁	—	2	2	no	—
258	#117×C₇₁	—	2	1	no	—
259	#117×C₇₁	—	2	1	no	—
260	#117×C₇₁	—	2	2	no	—
261	#117×C₇₁	D₄	1	2	yes	—
262	#117×C₇₁	D₄	1	1	yes	characteristic
263	#117×C₇₁	C₂³	1	1	yes	characteristic
264	#117×C₇₁	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
270	C₂×C₄²×C₇₁	—	2	1	no	—
271	C₂×C₄²×C₇₁	—	2	2	no	—
272	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
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	2	yes	—
281	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
287	#103×C₇₁	C₂³	1	2	yes	—
288	#103×C₇₁	C₂³	1	2	yes	—
289	#103×C₇₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
294	#103×C₇₁	C₂³	1	1	yes	characteristic
295	#103×C₇₁	C₂³	1	2	yes	—
296	#103×C₇₁	C₂³	1	2	yes	—
297	#103×C₇₁	C₂³	1	2	yes	—
298	#102×C₇₁	C₂³	1	2	yes	—
299	#102×C₇₁	C₂³	1	2	yes	—
300	#102×C₇₁	C₂³	1	1	yes	characteristic
301	#102×C₇₁	C₂³	1	2	yes	—
302	#102×C₇₁	C₂³	1	2	yes	—
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	2	no	—
316	#41×C₇₁	—	2	2	no	—
317	#41×C₇₁	—	2	4	no	—
318	#41×C₇₁	—	4	2	no	—
319	#41×C₇₁	—	4	2	no	—
320	#41×C₇₁	—	4	1	no	—
321	#41×C₇₁	—	4	2	no	—
322	#41×C₇₁	—	4	2	no	—
323	C₂×Q₈×C₇₁	—	2	2	no	—
324	C₂×Q₈×C₇₁	—	2	1	no	—
325	C₂×Q₈×C₇₁	—	2	2	no	—
326	C₂×Q₈×C₇₁	—	4	2	no	—
327	C₂×Q₈×C₇₁	—	4	2	no	—
328	C₂×Q₈×C₇₁	—	4	4	no	—
329	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
334	C₂×D₄×C₇₁	—	2	2	no	—
335	C₂×D₄×C₇₁	—	2	2	no	—
336	C₂×D₄×C₇₁	—	2	1	no	—
337	C₂×D₄×C₇₁	—	2	1	no	—
338	C₂×D₄×C₇₁	—	2	2	no	—
339	C₂×D₄×C₇₁	—	2	1	no	—
340	C₂×D₄×C₇₁	—	2	1	no	—
341	C₂×D₄×C₇₁	—	2	2	no	—
342	C₂×D₄×C₇₁	—	4	2	no	—
343	C₂×D₄×C₇₁	—	4	2	no	—
344	C₂×D₄×C₇₁	—	4	4	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	1	yes	characteristic
348	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₇₁	—	2	2	no	—
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	2	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	2	no	—
359	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
361	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
365	Q₁₆×C₇₁	—	4	1	no	—
366	Q₁₆×C₇₁	—	4	2	no	—
367	Q₁₆×C₇₁	—	4	2	no	—
368	Q₁₆×C₇₁	—	4	2	no	—
369	Q₁₆×C₇₁	—	4	2	no	—
370	SD₁₆×C₇₁	—	2	4	no	—
371	SD₁₆×C₇₁	—	2	2	no	—
372	SD₁₆×C₇₁	—	4	2	no	—
373	SD₁₆×C₇₁	—	4	1	no	—
374	SD₁₆×C₇₁	—	4	2	no	—
375	SD₁₆×C₇₁	—	4	2	no	—
376	SD₁₆×C₇₁	—	4	2	no	—
377	D₈×C₇₁	—	2	4	no	—
378	D₈×C₇₁	—	2	2	no	—
379	M₁₆×C₇₁	—	4	2	no	—
380	M₁₆×C₇₁	—	4	2	no	—
381	C₂×C₈×C₇₁	—	4	2	no	—
382	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₇₁	—	2	2	no	—
389	C₄⋊C₄×C₇₁	—	2	1	no	—
390	C₄⋊C₄×C₇₁	—	2	2	no	—
391	C₄⋊C₄×C₇₁	—	2	2	no	—
392	C₄⋊C₄×C₇₁	—	2	2	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	1	no	—
397	C₄⋊C₄×C₇₁	—	2	2	no	—
398	C₄⋊C₄×C₇₁	—	2	1	no	—
399	C₄⋊C₄×C₇₁	—	2	2	no	—
400	C₄⋊C₄×C₇₁	—	2	1	no	—
401	C₄⋊C₄×C₇₁	—	2	2	no	—
402	C₄⋊C₄×C₇₁	—	2	2	no	—
403	C₄⋊C₄×C₇₁	—	2	1	no	—
404	C₄⋊C₄×C₇₁	—	2	2	no	—
405	C₄⋊C₄×C₇₁	—	2	1	no	—
406	C₄⋊C₄×C₇₁	—	2	1	no	—
407	C₄⋊C₄×C₇₁	—	2	2	no	—
408	C₄⋊C₄×C₇₁	—	2	1	no	—
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	1	yes	characteristic
412	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₁	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₇₁	—	2	2	no	—
419	C₂²⋊C₄×C₇₁	—	2	2	no	—
420	C₂²⋊C₄×C₇₁	—	2	2	no	—
421	C₂²⋊C₄×C₇₁	—	2	2	no	—
422	C₂²⋊C₄×C₇₁	—	2	2	no	—
423	C₂²⋊C₄×C₇₁	—	2	1	no	—
424	C₂²⋊C₄×C₇₁	—	2	1	no	—
425	C₂²⋊C₄×C₇₁	—	2	2	no	—
426	C₂²⋊C₄×C₇₁	—	2	1	no	—
427	C₂²⋊C₄×C₇₁	—	2	1	no	—
428	C₂²⋊C₄×C₇₁	—	2	1	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	2	no	—
434	C₂²⋊C₄×C₇₁	—	2	1	no	—
435	C₂²⋊C₄×C₇₁	—	2	2	no	—
436	C₂²⋊C₄×C₇₁	—	2	1	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	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
443	C₄²×C₇₁	—	2	1	no	—
444	C₄²×C₇₁	—	2	2	no	—
445	C₄²×C₇₁	—	2	1	no	—
446	C₄²×C₇₁	—	2	2	no	—
447	C₄²×C₇₁	—	2	2	no	—
448	C₄²×C₇₁	—	2	1	no	—
449	C₄²×C₇₁	—	2	2	no	—
450	C₄²×C₇₁	—	2	1	no	—
451	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₇₁	C₂×D₄	1	2	yes	—
453	C₄²×C₇₁	C₂×D₄	1	2	yes	—
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	—	4	4	no	—
462	C₂³×C₇₁	—	8	2	no	—
463	C₂³×C₇₁	—	8	2	no	—
464	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
465	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₇₁	—	2	2	no	—
467	Q₈×C₇₁	—	2	1	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	1	no	—
474	Q₈×C₇₁	—	2	2	no	—
475	Q₈×C₇₁	—	4	4	no	—
476	Q₈×C₇₁	—	4	2	no	—
477	Q₈×C₇₁	—	8	2	no	—
478	D₄×C₇₁	—	2	2	no	—
479	D₄×C₇₁	—	2	1	no	—
480	D₄×C₇₁	—	2	2	no	—
481	D₄×C₇₁	—	2	1	no	—
482	D₄×C₇₁	—	2	1	no	—
483	D₄×C₇₁	—	2	2	no	—
484	D₄×C₇₁	—	4	2	no	—
485	D₄×C₇₁	—	4	4	no	—
486	D₄×C₇₁	—	4	2	no	—
487	D₄×C₇₁	—	4	4	no	—
488	D₄×C₇₁	—	4	2	no	—
489	D₄×C₇₁	—	8	1	no	—
490	D₄×C₇₁	—	8	2	no	—
491	D₄×C₇₁	—	8	1	no	—
492	D₄×C₇₁	—	8	2	no	—
493	D₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄×C₇₁	—	2	2	no	—
495	C₂×C₄×C₇₁	—	2	1	no	—
496	C₂×C₄×C₇₁	—	2	2	no	—
497	C₂×C₄×C₇₁	—	2	2	no	—
498	C₂×C₄×C₇₁	—	2	1	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	2	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	2	no	—
509	C₂×C₄×C₇₁	—	4	1	no	—
510	C₂×C₄×C₇₁	—	4	2	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	4	no	—
515	C₂×C₄×C₇₁	—	4	2	no	—
516	C₂×C₄×C₇₁	—	4	2	no	—
517	C₂×C₄×C₇₁	—	8	2	no	—
518	C₂×C₄×C₇₁	—	8	2	no	—
519	C₂×C₄×C₇₁	—	8	2	no	—
520	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
527	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
529	C₈×C₇₁	—	2	2	no	—
530	C₈×C₇₁	—	2	2	no	—
531	C₈×C₇₁	—	2	1	no	—
532	C₈×C₇₁	—	2	1	no	—
533	C₈×C₇₁	—	2	1	no	—
534	C₈×C₇₁	—	2	1	no	—
535	C₂²×C₇₁	—	2	1	no	—
536	C₂²×C₇₁	—	2	2	no	—
537	C₂²×C₇₁	—	2	2	no	—
538	C₂²×C₇₁	—	2	1	no	—
539	C₂²×C₇₁	—	2	2	no	—
540	C₂²×C₇₁	—	2	1	no	—
541	C₂²×C₇₁	—	2	2	no	—
542	C₂²×C₇₁	—	4	1	no	—
543	C₂²×C₇₁	—	4	1	no	—
544	C₂²×C₇₁	—	4	2	no	—
545	C₂²×C₇₁	—	4	1	no	—
546	C₂²×C₇₁	—	4	2	no	—
547	C₂²×C₇₁	—	4	1	no	—
548	C₂²×C₇₁	—	4	1	no	—
549	C₂²×C₇₁	—	4	2	no	—
550	C₂²×C₇₁	—	16	4	no	—
551	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₇₁	—	2	1	no	—
553	C₄×C₇₁	—	2	2	no	—
554	C₄×C₇₁	—	2	1	no	—
555	C₄×C₇₁	—	2	1	no	—
556	C₄×C₇₁	—	2	2	no	—
557	C₄×C₇₁	—	2	1	no	—
558	C₄×C₇₁	—	2	2	no	—
559	C₄×C₇₁	—	4	1	no	—
560	C₄×C₇₁	—	4	1	no	—
561	C₄×C₇₁	—	4	1	no	—
562	C₄×C₇₁	—	4	2	no	—
563	C₄×C₇₁	—	4	2	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	#575	1	2	yes	—
569	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₄×C₇₁	#585	1	1	yes	characteristic
571	#61973	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂×C₇₁	—	4	1	no	—
573	C₂×C₇₁	—	4	2	no	—
574	C₂×C₇₁	—	4	2	no	—
575	C₂×C₇₁	—	8	2	no	—
576	C₂×C₇₁	—	8	1	no	—
577	C₂×C₇₁	#3488	1	1	yes	characteristic
578	C₂×C₇₁	C₂×#575	1	1	yes	characteristic
579	C₂×C₇₁	#3586	1	1	yes	characteristic
580	#3514	C₂×C₇₁	1	1	yes	characteristic, complemented
581	#3482	C₂×C₇₁	1	1	yes	characteristic, complemented
582	#3400	C₂×C₇₁	1	1	yes	characteristic, complemented
583	#3398	C₂×C₇₁	1	1	yes	characteristic, complemented
584	#3373	C₂×C₇₁	1	1	yes	characteristic, complemented
585	#3367	C₂×C₇₁	1	1	yes	characteristic, complemented
586	#3328	C₂×C₇₁	1	1	yes	characteristic, complemented
587	#3324	C₂×C₇₁	1	1	yes	characteristic, complemented
588	#3313	C₂×C₇₁	1	2	yes	complemented
589	#3311	C₂×C₇₁	1	2	yes	complemented
590	#3276	C₂×C₇₁	1	1	yes	characteristic, complemented
591	#3272	C₂×C₇₁	1	1	yes	characteristic, complemented
592	#3269	C₂×C₇₁	1	2	yes	complemented
593	#3267	C₂×C₇₁	1	2	yes	complemented
594	#3252	C₂×C₇₁	1	2	yes	complemented
595	#3248	C₂×C₇₁	1	1	yes	characteristic, complemented
596	#3215	C₂×C₇₁	1	2	yes	complemented
597	#3210	C₂×C₇₁	1	1	yes	characteristic, complemented
598	#3111	C₂×C₇₁	1	2	yes	complemented
599	#3102	C₂×C₇₁	1	1	yes	characteristic, complemented
600	#3040	C₂×C₇₁	1	2	yes	complemented
601	#3035	C₂×C₇₁	1	1	yes	characteristic, complemented
602	#2989	C₂×C₇₁	1	1	yes	characteristic, complemented
603	C₇₁	#61973	1	1	yes	characteristic, direct product factor, Sylow
604	C₂×#137	C₂²×C₇₁	1	2	yes	complemented
605	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	2	yes	—
606	C₂×#135	C₂²×C₇₁	1	2	yes	complemented
607	#559	C₂²×C₇₁	1	1	yes	characteristic
608	#557	C₂²×C₇₁	1	1	yes	characteristic, complemented
609	#556	C₂²×C₇₁	1	1	yes	characteristic
610	#556	C₂²×C₇₁	1	1	yes	characteristic
611	#556	C₂²×C₇₁	1	2	yes	complemented
612	#555	—	2	1	no	—
613	#552	—	2	1	no	—
614	#552	—	2	2	no	—
615	#551	—	2	2	no	—
616	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
618	#548	—	2	1	no	—
619	#548	C₂²×C₇₁	1	2	yes	—
620	#547	C₂²×C₇₁	1	1	yes	characteristic
621	#547	C₂²×C₇₁	1	2	yes	complemented
622	#546	—	2	1	no	—
623	#546	C₂²×C₇₁	1	2	yes	—
624	D₄²	C₂²×C₇₁	1	1	yes	characteristic
625	#542	—	2	1	no	—
626	#538	—	2	2	no	—
627	#533	C₂²×C₇₁	1	1	yes	characteristic, complemented
628	#533	C₂²×C₇₁	1	2	yes	complemented
629	#532	C₂²×C₇₁	1	1	yes	characteristic
630	#529	—	2	1	no	—
631	#529	—	2	2	no	—
632	#529	C₂²×C₇₁	1	1	yes	characteristic
633	#529	C₂²×C₇₁	1	2	yes	—
634	C₂×#124	C₂²×C₇₁	1	2	yes	—
635	#518	—	2	1	no	—
636	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
637	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic, complemented
638	C₄×#41	C₂²×C₇₁	1	2	yes	complemented
639	C₂×C₄×Q₈	—	2	1	no	—
640	#497	C₂²×C₇₁	1	2	yes	—
641	#497	C₂²×C₇₁	1	2	yes	complemented
642	#494	C₂²×C₇₁	1	1	yes	characteristic, complemented
643	#492	C₂²×C₇₁	1	1	yes	characteristic
644	#489	C₂²×C₇₁	1	2	yes	—
645	#489	C₂²×C₇₁	1	2	yes	complemented
646	#487	C₂²×C₇₁	1	1	yes	characteristic, complemented
647	#486	C₂²×C₇₁	1	1	yes	characteristic
648	#485	C₂²×C₇₁	1	2	yes	complemented
649	#485	C₂²×C₇₁	1	1	yes	characteristic, complemented
650	#482	C₂²×C₇₁	1	1	yes	characteristic
651	#482	C₂²×C₇₁	1	2	yes	—
652	#479	C₂²×C₇₁	1	1	yes	characteristic, complemented
653	#479	C₂²×C₇₁	1	2	yes	complemented
654	#478	C₂²×C₇₁	1	1	yes	characteristic, complemented
655	#477	C₂²×C₇₁	1	2	yes	complemented
656	#476	C₂²×C₇₁	1	2	yes	complemented
657	#475	C₂²×C₇₁	1	1	yes	characteristic, complemented
658	#474	C₂²×C₇₁	1	1	yes	characteristic
659	#470	C₂²×C₇₁	1	2	yes	complemented
660	#470	C₂²×C₇₁	1	2	yes	complemented
661	#468	C₂²×C₇₁	1	2	yes	—
662	#468	C₂²×C₇₁	1	2	yes	—
663	#467	C₂²×C₇₁	1	2	yes	complemented
664	#465	C₂²×C₇₁	1	2	yes	—
665	#464	C₂²×C₇₁	1	1	yes	characteristic
666	#464	C₂²×C₇₁	1	2	yes	—
667	#464	C₂²×C₇₁	1	2	yes	—
668	#464	C₂²×C₇₁	1	2	yes	complemented
669	#464	C₂²×C₇₁	1	2	yes	complemented
670	#464	C₂²×C₇₁	1	2	yes	complemented
671	#464	C₂²×C₇₁	1	2	yes	complemented
672	#463	C₂²×C₇₁	1	1	yes	characteristic
673	#463	C₂²×C₇₁	1	2	yes	—
674	#463	C₂²×C₇₁	1	2	yes	complemented
675	#463	C₂²×C₇₁	1	2	yes	complemented
676	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
677	#462	C₂²×C₇₁	1	2	yes	complemented
678	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
679	#461	C₂²×C₇₁	1	1	yes	characteristic
680	#461	C₂²×C₇₁	1	1	yes	characteristic, complemented
681	#461	C₂²×C₇₁	1	2	yes	complemented
682	#460	C₂²×C₇₁	1	1	yes	characteristic
683	#459	C₂²×C₇₁	1	1	yes	characteristic
684	#452	C₂²×C₇₁	1	1	yes	characteristic, complemented
685	#452	C₂²×C₇₁	1	2	yes	complemented
686	#452	C₂²×C₇₁	1	2	yes	complemented
687	#452	C₂²×C₇₁	1	2	yes	complemented
688	#451	C₂²×C₇₁	1	2	yes	complemented
689	#451	C₂²×C₇₁	1	2	yes	complemented
690	#450	C₂²×C₇₁	1	2	yes	—
691	#450	C₂²×C₇₁	1	2	yes	—
692	#449	C₂²×C₇₁	1	1	yes	characteristic
693	#449	C₂²×C₇₁	1	2	yes	—
694	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
695	#446	C₂²×C₇₁	1	1	yes	characteristic, complemented
696	#442	C₂²×C₇₁	1	2	yes	complemented
697	#441	C₂²×C₇₁	1	2	yes	complemented
698	#440	C₂²×C₇₁	1	2	yes	complemented
699	#440	C₂²×C₇₁	1	2	yes	complemented
700	C₄×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic, complemented
703	C₄×D₈	C₂²×C₇₁	1	1	yes	characteristic
704	#436	C₂²×C₇₁	1	1	yes	characteristic
705	#436	C₂²×C₇₁	1	1	yes	characteristic
706	#435	C₂²×C₇₁	1	2	yes	complemented
707	#435	C₂²×C₇₁	1	2	yes	complemented
708	#432	C₂²×C₇₁	1	2	yes	complemented
709	#431	C₂²×C₇₁	1	1	yes	characteristic, complemented
710	#423	C₂²×C₇₁	1	2	yes	complemented
711	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic, complemented
712	#419	C₂²×C₇₁	1	2	yes	complemented
713	#418	C₂²×C₇₁	1	2	yes	—
714	#416	C₂²×C₇₁	1	2	yes	complemented
715	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
716	C₂×#41	C₂³×C₇₁	1	2	yes	—
717	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
718	C₂×#41	C₂³×C₇₁	1	2	yes	—
719	C₂²×Q₈	—	2	1	no	—
720	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
723	#137	—	4	4	no	—
724	AGL(1,ℤ/8)	—	4	4	no	—
725	#135	—	4	4	no	—
726	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₇₁	1	1	yes	characteristic
730	C₂×Q₁₆	C₂³×C₇₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₇₁	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₇₁	1	2	yes	—
738	C₂×D₈	C₂³×C₇₁	1	2	yes	—
739	C₂×D₈	C₂³×C₇₁	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
741	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
742	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
747	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
749	#127	C₂³×C₇₁	1	1	yes	characteristic
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	1	no	—
756	#125	—	2	1	no	—
757	#125	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	—	2	1	no	—
760	#125	C₂³×C₇₁	1	1	yes	characteristic
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	C₂³×C₇₁	1	1	yes	characteristic
768	#124	C₂³×C₇₁	1	2	yes	—
769	#124	C₂³×C₇₁	1	2	yes	—
770	#124	C₂³×C₇₁	1	2	yes	—
771	#123	—	2	1	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
790	#121	—	2	1	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	C₂³×C₇₁	1	2	yes	—
798	#121	C₂³×C₇₁	1	1	yes	characteristic
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	2	no	—
806	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
811	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
826	C₄×D₄	D₄×C₇₁	1	2	yes	—
827	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₇₁	1	2	yes	—
830	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₇₁	1	2	yes	—
832	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₇₁	1	2	yes	—
834	#117	—	2	2	no	—
835	#117	—	2	1	no	—
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	D₄×C₇₁	1	2	yes	—
842	#117	D₄×C₇₁	1	1	yes	characteristic
843	#117	C₂³×C₇₁	1	2	yes	—
844	#117	C₂³×C₇₁	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	2	no	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	—	2	1	no	—
851	C₂×C₄²	—	2	2	no	—
852	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
853	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
854	#107	C₂³×C₇₁	1	1	yes	characteristic
855	#107	C₂³×C₇₁	1	1	yes	characteristic
856	#107	C₂³×C₇₁	1	2	yes	—
857	#106	C₂³×C₇₁	1	1	yes	characteristic
858	#106	C₂³×C₇₁	1	1	yes	characteristic
859	#106	C₂³×C₇₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
867	#103	C₂³×C₇₁	1	2	yes	—
868	#103	C₂³×C₇₁	1	2	yes	—
869	#103	C₂³×C₇₁	1	1	yes	characteristic
870	#103	C₂³×C₇₁	1	2	yes	—
871	#103	C₂³×C₇₁	1	2	yes	—
872	#103	C₂³×C₇₁	1	1	yes	characteristic
873	#103	C₂³×C₇₁	1	1	yes	characteristic
874	#103	C₂³×C₇₁	1	1	yes	characteristic
875	#103	C₂³×C₇₁	1	2	yes	—
876	#103	C₂³×C₇₁	1	2	yes	—
877	#103	C₂³×C₇₁	1	2	yes	—
878	#102	C₂³×C₇₁	1	2	yes	—
879	#102	C₂³×C₇₁	1	2	yes	—
880	#102	C₂³×C₇₁	1	1	yes	characteristic
881	#102	C₂³×C₇₁	1	2	yes	—
882	#102	C₂³×C₇₁	1	2	yes	—
883	#102	C₂³×C₇₁	1	1	yes	characteristic
884	#102	C₂³×C₇₁	1	1	yes	characteristic
885	#102	C₂³×C₇₁	1	1	yes	characteristic
886	#102	C₂³×C₇₁	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
891	#97	C₂³×C₇₁	1	2	yes	—
892	#97	C₂³×C₇₁	1	2	yes	—
893	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
895	C₂⁴	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	2	4	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	1	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	4	no	—
909	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	4	no	—
925	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
926	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
927	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
941	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
942	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
945	Q₁₆	—	4	1	no	—
946	Q₁₆	—	4	2	no	—
947	Q₁₆	—	4	2	no	—
948	Q₁₆	—	4	2	no	—
949	Q₁₆	—	4	2	no	—
950	SD₁₆	—	2	4	no	—
951	SD₁₆	—	2	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	1	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	2	4	no	—
958	D₈	—	2	2	no	—
959	M₁₆	—	4	2	no	—
960	M₁₆	—	4	2	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₇₁	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
967	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₇₁	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	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	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1032	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1033	C₄²	C₂×D₄×C₇₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₇₁	1	2	yes	—
1037	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
1045	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	4	4	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	8	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
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	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	#575×C₇₁	1	2	yes	—
1149	C₄	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
1150	C₄	#585×C₇₁	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	1	no	—
1155	C₂	—	8	2	no	—
1156	C₂	C₇₁×#3488	1	1	yes	characteristic
1157	C₂	C₂×#575×C₇₁	1	1	yes	characteristic
1158	C₂	C₇₁×#3586	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×#3514	C₂	semidirect
2. C₇₁×#3482	C₂	semidirect
3. C₇₁×#3400	C₂	semidirect
4. C₇₁×#3398	C₂	semidirect
5. C₇₁×#3373	C₂	semidirect
6. C₇₁×#3367	C₂	semidirect
7. C₇₁×#3328	C₂	semidirect
8. C₇₁×#3324	C₂	semidirect
9. C₇₁×#3313	C₂	semidirect
10. C₇₁×#3311	C₂	semidirect
11. C₇₁×#3276	C₂	semidirect
12. C₇₁×#3272	C₂	semidirect
13. C₇₁×#3269	C₂	semidirect
14. C₇₁×#3267	C₂	semidirect
15. C₇₁×#3252	C₂	semidirect
16. C₇₁×#3248	C₂	semidirect
17. C₇₁×#3215	C₂	semidirect
18. C₇₁×#3210	C₂	semidirect
19. C₇₁×#3111	C₂	semidirect
20. C₇₁×#3102	C₂	semidirect
21. C₇₁×#3040	C₂	semidirect
22. C₇₁×#3035	C₂	semidirect
23. C₇₁×#2989	C₂	semidirect
24. C₂×#137×C₇₁	C₂²	semidirect
26. C₂×#135×C₇₁	C₂²	semidirect
28. #557×C₇₁	C₂²	semidirect
31. #556×C₇₁	C₂²	semidirect
37. D₄×Q₈×C₇₁	C₂²	semidirect
41. #547×C₇₁	C₂²	semidirect
47. #533×C₇₁	C₂²	semidirect
48. #533×C₇₁	C₂²	semidirect
57. C₄×#41×C₇₁	C₂²	semidirect
58. C₄×#41×C₇₁	C₂²	semidirect
61. #497×C₇₁	C₂²	semidirect
62. #494×C₇₁	C₂²	semidirect
65. #489×C₇₁	C₂²	semidirect
66. #487×C₇₁	C₂²	semidirect
68. #485×C₇₁	C₂²	semidirect
69. #485×C₇₁	C₂²	semidirect
72. #479×C₇₁	C₂²	semidirect
73. #479×C₇₁	C₂²	semidirect
74. #478×C₇₁	C₂²	semidirect
75. #477×C₇₁	C₂²	semidirect
76. #476×C₇₁	C₂²	semidirect
77. #475×C₇₁	C₂²	semidirect
79. #470×C₇₁	C₂²	semidirect
80. #470×C₇₁	C₂²	semidirect
83. #467×C₇₁	C₂²	semidirect
88. #464×C₇₁	C₂²	semidirect
89. #464×C₇₁	C₂²	semidirect
90. #464×C₇₁	C₂²	semidirect
91. #464×C₇₁	C₂²	semidirect
94. #463×C₇₁	C₂²	semidirect
95. #463×C₇₁	C₂²	semidirect
96. #462×C₇₁	C₂²	semidirect
97. #462×C₇₁	C₂²	semidirect
98. #462×C₇₁	C₂²	semidirect
100. #461×C₇₁	C₂²	semidirect
101. #461×C₇₁	C₂²	semidirect
104. #452×C₇₁	C₂²	semidirect
105. #452×C₇₁	C₂²	semidirect
106. #452×C₇₁	C₂²	semidirect
107. #452×C₇₁	C₂²	semidirect
108. #451×C₇₁	C₂²	semidirect
109. #451×C₇₁	C₂²	semidirect
114. #446×C₇₁	C₂²	semidirect
115. #446×C₇₁	C₂²	semidirect
116. #442×C₇₁	C₂²	semidirect
117. #441×C₇₁	C₂²	semidirect
118. #440×C₇₁	C₂²	semidirect
119. #440×C₇₁	C₂²	semidirect
120. C₄×Q₁₆×C₇₁	C₂²	semidirect
122. C₄×SD₁₆×C₇₁	C₂²	semidirect
126. #435×C₇₁	C₂²	semidirect
127. #435×C₇₁	C₂²	semidirect
128. #432×C₇₁	C₂²	semidirect
129. #431×C₇₁	C₂²	semidirect
130. #423×C₇₁	C₂²	semidirect
131. C₂×C₄⋊C₈×C₇₁	C₂²	semidirect
132. #419×C₇₁	C₂²	semidirect
134. #416×C₇₁	C₂²	semidirect
571. #61973	C₇₁	direct (N × H)
580. #3514	C₂×C₇₁	semidirect
581. #3482	C₂×C₇₁	semidirect
582. #3400	C₂×C₇₁	semidirect
583. #3398	C₂×C₇₁	semidirect
584. #3373	C₂×C₇₁	semidirect
585. #3367	C₂×C₇₁	semidirect
586. #3328	C₂×C₇₁	semidirect
587. #3324	C₂×C₇₁	semidirect
588. #3313	C₂×C₇₁	semidirect
589. #3311	C₂×C₇₁	semidirect
590. #3276	C₂×C₇₁	semidirect
591. #3272	C₂×C₇₁	semidirect
592. #3269	C₂×C₇₁	semidirect
593. #3267	C₂×C₇₁	semidirect
594. #3252	C₂×C₇₁	semidirect
595. #3248	C₂×C₇₁	semidirect
596. #3215	C₂×C₇₁	semidirect
597. #3210	C₂×C₇₁	semidirect
598. #3111	C₂×C₇₁	semidirect
599. #3102	C₂×C₇₁	semidirect
600. #3040	C₂×C₇₁	semidirect
601. #3035	C₂×C₇₁	semidirect
602. #2989	C₂×C₇₁	semidirect
603. C₇₁	#61973	direct (N × H)
604. C₂×#137	C₂²×C₇₁	semidirect
606. C₂×#135	C₂²×C₇₁	semidirect
608. #557	C₂²×C₇₁	semidirect
611. #556	C₂²×C₇₁	semidirect
617. D₄×Q₈	C₂²×C₇₁	semidirect
621. #547	C₂²×C₇₁	semidirect
627. #533	C₂²×C₇₁	semidirect
628. #533	C₂²×C₇₁	semidirect
637. C₄×#41	C₂²×C₇₁	semidirect
638. C₄×#41	C₂²×C₇₁	semidirect
641. #497	C₂²×C₇₁	semidirect
642. #494	C₂²×C₇₁	semidirect
645. #489	C₂²×C₇₁	semidirect
646. #487	C₂²×C₇₁	semidirect
648. #485	C₂²×C₇₁	semidirect
649. #485	C₂²×C₇₁	semidirect
652. #479	C₂²×C₇₁	semidirect
653. #479	C₂²×C₇₁	semidirect
654. #478	C₂²×C₇₁	semidirect
655. #477	C₂²×C₇₁	semidirect
656. #476	C₂²×C₇₁	semidirect
657. #475	C₂²×C₇₁	semidirect
659. #470	C₂²×C₇₁	semidirect
660. #470	C₂²×C₇₁	semidirect
663. #467	C₂²×C₇₁	semidirect
668. #464	C₂²×C₇₁	semidirect
669. #464	C₂²×C₇₁	semidirect
670. #464	C₂²×C₇₁	semidirect
671. #464	C₂²×C₇₁	semidirect
674. #463	C₂²×C₇₁	semidirect
675. #463	C₂²×C₇₁	semidirect
676. #462	C₂²×C₇₁	semidirect
677. #462	C₂²×C₇₁	semidirect
678. #462	C₂²×C₇₁	semidirect
680. #461	C₂²×C₇₁	semidirect
681. #461	C₂²×C₇₁	semidirect
684. #452	C₂²×C₇₁	semidirect
685. #452	C₂²×C₇₁	semidirect
686. #452	C₂²×C₇₁	semidirect
687. #452	C₂²×C₇₁	semidirect
688. #451	C₂²×C₇₁	semidirect
689. #451	C₂²×C₇₁	semidirect
694. #446	C₂²×C₇₁	semidirect
695. #446	C₂²×C₇₁	semidirect
696. #442	C₂²×C₇₁	semidirect
697. #441	C₂²×C₇₁	semidirect
698. #440	C₂²×C₇₁	semidirect
699. #440	C₂²×C₇₁	semidirect
700. C₄×Q₁₆	C₂²×C₇₁	semidirect
702. C₄×SD₁₆	C₂²×C₇₁	semidirect
706. #435	C₂²×C₇₁	semidirect
707. #435	C₂²×C₇₁	semidirect
708. #432	C₂²×C₇₁	semidirect
709. #431	C₂²×C₇₁	semidirect
710. #423	C₂²×C₇₁	semidirect
711. C₂×C₄⋊C₈	C₂²×C₇₁	semidirect
712. #419	C₂²×C₇₁	semidirect
714. #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×#3514	2
C₇₁×#3482	2
C₇₁×#3400	2
C₇₁×#3398	2
C₇₁×#3373	2
C₇₁×#3367	2
C₇₁×#3328	2
C₇₁×#3324	2
C₇₁×#3313	2
C₇₁×#3311	2
C₇₁×#3276	2
C₇₁×#3272	2
C₇₁×#3269	2
C₇₁×#3267	2
C₇₁×#3252	2
C₇₁×#3248	2
C₇₁×#3215	2
C₇₁×#3210	2
C₇₁×#3111	2
C₇₁×#3102	2
C₇₁×#3040	2
C₇₁×#3035	2
C₇₁×#2989	2
#61973	71

Subgroups — C71×#61973 #31882845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61973 #31882845