Subgroups — #22602792

Order 9088.

932 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986750	C₂	1	1	yes	maximal, characteristic, complemented
3	#17986748	C₂	1	1	yes	maximal, characteristic, complemented
4	#17986745	C₂	1	1	yes	maximal, characteristic, complemented
5	#17986707	C₂	1	1	yes	maximal, characteristic, complemented
6	#17986703	C₂	1	1	yes	maximal, characteristic, complemented
7	#17986703	C₂	1	1	yes	maximal, characteristic, complemented
8	#17986698	C₂	1	1	yes	maximal, characteristic, complemented
9	#17986698	C₂	1	1	yes	maximal, characteristic, complemented
10	#17986697	C₂	1	1	yes	maximal, characteristic, complemented
11	#17986695	C₂	1	1	yes	maximal, characteristic, complemented
12	#17986690	C₂	1	1	yes	maximal, characteristic, complemented
13	#17986684	C₂	1	1	yes	maximal, characteristic, complemented
14	#17986683	C₂	1	1	yes	maximal, characteristic, complemented
15	#17986681	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986610	C₂	1	1	yes	maximal, characteristic, complemented
17	#17986609	C₂	1	1	yes	maximal, characteristic, complemented
18	#17986608	C₂	1	1	yes	maximal, characteristic, complemented
19	#17986607	C₂	1	1	yes	maximal, characteristic, complemented
20	#17986598	C₂	1	1	yes	maximal, characteristic, complemented
21	#17986598	C₂	1	1	yes	maximal, characteristic, complemented
22	#17986597	C₂	1	1	yes	maximal, characteristic, complemented
23	#17986596	C₂	1	1	yes	maximal, characteristic, complemented
24	#17986595	C₂	1	1	yes	maximal, characteristic, complemented
25	#17986595	C₂	1	1	yes	maximal, characteristic, complemented
26	#17986591	C₂	1	1	yes	maximal, characteristic, complemented
27	#17986591	C₂	1	1	yes	maximal, characteristic, complemented
28	#17986535	C₂	1	1	yes	maximal, characteristic, complemented
29	#17986529	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#14556118	C₂	1	1	yes	maximal, characteristic, complemented
31	#554×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
32	#14556127	C₂²	1	1	yes	characteristic
33	#14556126	C₂²	1	1	yes	characteristic
34	#14556126	C₂²	1	1	yes	characteristic
35	#14556123	C₂²	1	1	yes	characteristic
36	#14556123	C₂²	1	1	yes	characteristic
37	#14556123	C₂²	1	1	yes	characteristic
38	#14556123	C₂²	1	1	yes	characteristic
39	#14556123	C₂²	1	1	yes	characteristic
40	#14556123	C₂²	1	1	yes	characteristic
41	#14556123	C₂²	1	1	yes	characteristic
42	#14556123	C₂²	1	1	yes	characteristic
43	#14556123	C₂²	1	1	yes	characteristic
44	#14556123	C₂²	1	1	yes	characteristic
45	#14556123	C₂²	1	1	yes	characteristic
46	#14556122	C₂²	1	1	yes	characteristic
47	#14556122	C₂²	1	1	yes	characteristic
48	#14556122	C₂²	1	1	yes	characteristic
49	#14556122	C₂²	1	1	yes	characteristic
50	#14556121	C₂²	1	1	yes	characteristic
51	#14556121	C₂²	1	1	yes	characteristic
52	#14556121	C₂²	1	1	yes	characteristic
53	#14556121	C₂²	1	1	yes	characteristic
54	#14556121	C₂²	1	1	yes	characteristic
55	#14556120	C₂²	1	1	yes	characteristic
56	#14556120	C₂²	1	1	yes	characteristic
57	#14556120	C₂²	1	1	yes	characteristic
58	#14556119	C₂²	1	1	yes	characteristic
59	#14556119	C₂²	1	1	yes	characteristic
60	#14556119	C₂²	1	1	yes	characteristic
61	#14556119	C₂²	1	1	yes	characteristic
62	#14556119	C₂²	1	1	yes	characteristic
63	#14556119	C₂²	1	1	yes	characteristic
64	#14556118	C₂²	1	1	yes	characteristic
65	#14556118	C₂²	1	1	yes	characteristic
66	#14556118	C₂²	1	1	yes	characteristic
67	#14556118	C₂²	1	1	yes	characteristic
68	#14556118	C₂²	1	1	yes	characteristic
69	#14556118	C₂²	1	1	yes	characteristic
70	#14556118	C₂²	1	1	yes	characteristic
71	#14556118	C₂²	1	1	yes	characteristic
72	#14556118	C₂²	1	1	yes	characteristic
73	#14556118	C₂²	1	1	yes	characteristic
74	#14556118	C₂²	1	1	yes	characteristic
75	#14556118	C₂²	1	1	yes	characteristic
76	#14556118	C₂²	1	1	yes	characteristic
77	#14556118	C₂²	1	1	yes	characteristic
78	#14556118	C₂²	1	1	yes	characteristic
79	#14556118	C₂²	1	1	yes	characteristic
80	#14556118	C₂²	1	1	yes	characteristic
81	#14556118	C₂²	1	1	yes	characteristic
82	#14556118	C₂²	1	1	yes	characteristic
83	#14556117	C₂²	1	1	yes	characteristic
84	#14556114	C₂²	1	1	yes	characteristic
85	#14556113	C₂²	1	1	yes	characteristic
86	#14556113	C₂²	1	1	yes	characteristic
87	#14556113	C₂²	1	1	yes	characteristic
88	#14556113	C₂²	1	1	yes	characteristic
89	#14556113	C₂²	1	1	yes	characteristic
90	#14556113	C₂²	1	1	yes	characteristic
91	#14556113	C₂²	1	1	yes	characteristic
92	#14556113	C₂²	1	1	yes	characteristic
93	#14556112	C₂²	1	1	yes	characteristic
94	#14556112	C₂²	1	1	yes	characteristic
95	#14556112	C₂²	1	1	yes	characteristic
96	#14556111	C₂²	1	1	yes	characteristic
97	#14556111	C₂²	1	1	yes	characteristic
98	#14556111	C₂²	1	1	yes	characteristic
99	#14556111	C₂²	1	1	yes	characteristic
100	#14556110	C₂²	1	1	yes	characteristic
101	#14556110	C₂²	1	1	yes	characteristic
102	#14556110	C₂²	1	1	yes	characteristic
103	#14556110	C₂²	1	1	yes	characteristic
104	#14556109	C₂²	1	1	yes	characteristic
105	#14556108	C₂²	1	1	yes	characteristic
106	#14556108	C₂²	1	1	yes	characteristic
107	#14556107	C₂²	1	1	yes	characteristic
108	#14556107	C₂²	1	1	yes	characteristic
109	#14556106	C₂²	1	1	yes	characteristic
110	#14556106	C₂²	1	1	yes	characteristic
111	#14556106	C₂²	1	1	yes	characteristic
112	#14556106	C₂²	1	1	yes	characteristic
113	#14556106	C₂²	1	1	yes	characteristic
114	#14556106	C₂²	1	1	yes	characteristic
115	#14556105	C₂²	1	1	yes	characteristic
116	#14556105	C₂²	1	1	yes	characteristic
117	#14556105	C₂²	1	1	yes	characteristic
118	#14556104	C₂²	1	1	yes	characteristic
119	#14556104	C₂²	1	1	yes	characteristic
120	#14556104	C₂²	1	1	yes	characteristic
121	#14556104	C₂²	1	1	yes	characteristic
122	#14556104	C₂²	1	1	yes	characteristic
123	#14556104	C₂²	1	1	yes	characteristic
124	#14556104	C₂²	1	1	yes	characteristic
125	#14556103	C₂²	1	1	yes	characteristic
126	#14556102	C₂²	1	1	yes	characteristic
127	#14556102	C₂²	1	1	yes	characteristic
128	#14556102	C₂²	1	1	yes	characteristic
129	#14556102	C₂²	1	1	yes	characteristic
130	#14556101	C₂²	1	1	yes	characteristic
131	#14556101	C₂²	1	1	yes	characteristic
132	#14556100	C₂²	1	1	yes	characteristic
133	#14556100	C₂²	1	1	yes	characteristic
134	#14556100	C₂²	1	1	yes	characteristic
135	Q₈×Dic₇₁	C₂²	1	1	yes	characteristic
136	Q₈×Dic₇₁	C₂²	1	1	yes	characteristic
137	C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic
138	#14556093	C₂²	1	1	yes	characteristic
139	#14556093	C₂²	1	1	yes	characteristic
140	C₄×D₂₈₄	C₂²	1	1	yes	characteristic
141	#14556090	C₂²	1	1	yes	characteristic
142	#14556090	C₂²	1	1	yes	characteristic
143	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
144	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
145	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
147	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
150	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
151	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
152	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
153	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
154	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
155	#14556087	C₂²	1	1	yes	characteristic
156	#14556087	C₂²	1	1	yes	characteristic
157	#14556086	C₂²	1	1	yes	characteristic
158	#14556086	C₂²	1	1	yes	characteristic
159	#14556086	C₂²	1	1	yes	characteristic
160	#14556085	C₂²	1	1	yes	characteristic
161	#14556085	C₂²	1	1	yes	characteristic
162	#14556085	C₂²	1	1	yes	characteristic
163	C₂×C₄⋊Dic₇₁	C₂²	1	1	yes	characteristic
164	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic
165	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic
166	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic
167	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic
168	C₄⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
169	C₄⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
170	C₄⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
171	C₂×C₄×Dic₇₁	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
173	#125×C₇₁	C₂²	1	1	yes	characteristic
174	#125×C₇₁	C₂²	1	1	yes	characteristic
175	C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
176	C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
177	C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
178	C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
180	C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
181	C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
183	C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
187	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
188	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
189	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
190	C₂×D₂₈₄	C₂³	1	1	yes	characteristic
191	C₂×D₂₈₄	C₂³	1	1	yes	characteristic
192	C₂×D₂₈₄	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
199	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
200	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
201	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
202	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
204	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
210	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
228	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
229	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
270	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
271	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
272	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
294	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
295	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
296	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
297	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
298	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
299	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
300	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
301	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
302	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
303	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
304	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
305	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
306	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
307	C₂×Q₈×C₇₁	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₇₁	C₂³	1	1	yes	characteristic
309	C₂×Q₈×C₇₁	C₂³	1	1	yes	characteristic
310	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
311	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
312	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
313	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
314	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
315	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
316	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
339	C₄²×C₇₁	C₂³	1	1	yes	characteristic
340	C₄²×C₇₁	C₂³	1	1	yes	characteristic
341	C₄²×C₇₁	C₂³	1	1	yes	characteristic
342	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
343	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
344	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
345	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
346	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
347	Q₈×C₇₁	—	4	1	no	—
348	Q₈×C₇₁	—	4	1	no	—
349	Q₈×C₇₁	—	4	1	no	—
350	D₄×C₇₁	—	2	2	no	—
351	C₂×C₄×C₇₁	—	4	1	no	—
352	C₂×C₄×C₇₁	—	4	1	no	—
353	C₂×C₄×C₇₁	—	4	1	no	—
354	C₂×C₄×C₇₁	—	4	1	no	—
355	C₂×C₄×C₇₁	—	4	1	no	—
356	C₂×C₄×C₇₁	—	4	1	no	—
357	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
358	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
359	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
370	C₂²⋊D₇₁	—	2	2	no	—
371	C₂²⋊D₇₁	—	2	2	no	—
372	C₂²⋊D₇₁	—	2	2	no	—
373	C₂²⋊D₇₁	—	4	1	no	—
374	C₂²⋊D₇₁	—	4	1	no	—
375	C₂²⋊D₇₁	—	4	1	no	—
376	C₂×Dic₇₁	—	2	2	no	—
377	C₂×Dic₇₁	—	4	1	no	—
378	C₂×Dic₇₁	—	4	1	no	—
379	C₂×Dic₇₁	—	4	1	no	—
380	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
393	D₂₈₄	—	4	1	no	—
394	D₂₈₄	—	4	1	no	—
395	D₂₈₄	—	4	1	no	—
396	C₄×D₇₁	—	4	1	no	—
397	C₄×D₇₁	—	4	1	no	—
398	C₄×D₇₁	—	4	1	no	—
399	C₄×D₇₁	—	4	1	no	—
400	C₄×D₇₁	—	4	1	no	—
401	C₄×D₇₁	—	4	1	no	—
402	C₄×D₇₁	—	4	1	no	—
403	C₄×D₇₁	—	4	1	no	—
404	C₄×D₇₁	—	4	1	no	—
405	Dic₁₄₂	—	4	1	no	—
406	Dic₁₄₂	—	4	1	no	—
407	Dic₁₄₂	—	4	1	no	—
408	C₂²×C₇₁	—	2	1	no	—
409	C₂²×C₇₁	—	2	1	no	—
410	C₂²×C₇₁	—	2	1	no	—
411	C₂²×C₇₁	—	2	1	no	—
412	C₂²×C₇₁	—	2	1	no	—
413	C₂²×C₇₁	2₋¹⁺⁴	1	2	yes	—
414	C₂²×C₇₁	C₂⁵	1	1	yes	characteristic
415	C₂×D₇₁	—	2	1	no	—
416	C₂×D₇₁	—	2	1	no	—
417	C₂×D₇₁	—	2	1	no	—
418	C₂×D₇₁	—	2	1	no	—
419	C₂×D₇₁	—	2	1	no	—
420	C₂×D₇₁	—	2	1	no	—
421	C₂×D₇₁	—	2	1	no	—
422	C₂×D₇₁	—	2	1	no	—
423	C₂×D₇₁	—	2	1	no	—
424	C₄×C₇₁	—	2	1	no	—
425	C₄×C₇₁	—	2	1	no	—
426	C₄×C₇₁	—	2	1	no	—
427	C₄×C₇₁	—	2	1	no	—
428	C₄×C₇₁	—	2	1	no	—
429	C₄×C₇₁	—	2	1	no	—
430	C₄×C₇₁	—	2	1	no	—
431	C₄×C₇₁	—	2	1	no	—
432	C₄×C₇₁	—	2	1	no	—
433	C₄×C₇₁	—	2	1	no	—
434	C₄×C₇₁	—	2	1	no	—
435	C₄×C₇₁	—	2	1	no	—
436	C₄×C₇₁	—	2	1	no	—
437	Dic₇₁	—	2	1	no	—
438	Dic₇₁	—	2	1	no	—
439	Dic₇₁	—	2	1	no	—
440	Dic₇₁	—	2	1	no	—
441	Dic₇₁	—	2	1	no	—
442	Dic₇₁	—	2	1	no	—
443	Dic₇₁	—	2	1	no	—
444	Dic₇₁	—	2	1	no	—
445	Dic₇₁	—	2	1	no	—
446	Dic₇₁	—	2	1	no	—
447	Dic₇₁	—	2	1	no	—
448	Dic₇₁	—	2	1	no	—
449	Dic₇₁	—	2	1	no	—
450	C₂×C₇₁	—	2	2	no	—
451	C₂×C₇₁	—	4	1	no	—
452	C₂×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂×C₇₁	#585	1	1	yes	characteristic
454	C₂×C₇₁	#585	1	1	yes	characteristic
455	D₇₁	—	4	1	no	—
456	D₇₁	—	4	1	no	—
457	D₇₁	—	4	1	no	—
458	#3553	—	71	1	no	maximal, Sylow
459	C₇₁	#3553	1	1	yes	characteristic, complemented, Sylow
460	#564	—	71	1	no	—
461	#563	—	71	1	no	—
462	#563	—	71	1	no	—
463	#562	—	71	1	no	—
464	#554	—	71	1	no	—
465	#554	—	71	1	no	—
466	#554	—	71	1	no	—
467	#554	D₇₁	1	1	yes	characteristic, complemented
468	#553	—	71	1	no	—
469	#553	—	71	1	no	—
470	#553	—	71	1	no	—
471	#553	—	71	1	no	—
472	#552	—	71	1	no	—
473	#552	—	71	1	no	—
474	#552	—	71	1	no	—
475	#552	—	71	1	no	—
476	#541	—	71	1	no	—
477	#541	—	71	1	no	—
478	#541	—	71	1	no	—
479	#541	—	71	1	no	—
480	#539	—	71	1	no	—
481	#539	—	71	1	no	—
482	#539	—	71	1	no	—
483	#539	—	71	1	no	—
484	#539	—	71	1	no	—
485	#539	—	71	1	no	—
486	#539	—	71	1	no	—
487	#539	—	71	1	no	—
488	#529	—	71	1	no	—
489	#529	—	71	1	no	—
490	C₂×#125	—	71	1	no	—
491	C₄⋊Q₈	—	71	1	no	—
492	C₄⋊Q₈	—	71	1	no	—
493	C₄⋊Q₈	—	71	1	no	—
494	C₄⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
495	#126	—	71	1	no	—
496	#126	—	71	1	no	—
497	#126	—	71	1	no	—
498	#126	—	71	1	no	—
499	#126	—	71	1	no	—
500	#126	—	71	1	no	—
501	#126	—	71	1	no	—
502	#126	—	71	1	no	—
503	#126	—	71	1	no	—
504	#126	—	71	1	no	—
505	#126	—	71	1	no	—
506	#126	—	71	1	no	—
507	#126	—	71	1	no	—
508	#126	—	71	1	no	—
509	#126	—	71	1	no	—
510	#126	—	71	1	no	—
511	#126	—	71	1	no	—
512	#126	—	71	1	no	—
513	#126	—	71	1	no	—
514	#126	—	71	1	no	—
515	#125	—	71	1	no	—
516	#125	—	71	1	no	—
517	#125	—	71	1	no	—
518	#125	—	71	1	no	—
519	#125	—	71	1	no	—
520	#125	—	71	1	no	—
521	#125	—	71	1	no	—
522	#125	—	71	1	no	—
523	#125	—	71	1	no	—
524	#125	—	71	1	no	—
525	#125	—	71	1	no	—
526	#125	—	71	1	no	—
527	#125	—	71	1	no	—
528	#125	—	71	1	no	—
529	#125	—	71	1	no	—
530	#125	—	71	1	no	—
531	#125	—	71	1	no	—
532	#125	—	71	1	no	—
533	#125	—	71	1	no	—
534	#125	—	71	1	no	—
535	#125	—	71	1	no	—
536	#125	—	71	1	no	—
537	#125	—	71	1	no	—
538	#125	—	71	1	no	—
539	#125	—	71	1	no	—
540	#125	—	71	1	no	—
541	#125	—	71	1	no	—
542	#125	—	71	1	no	—
543	#125	C₂×D₇₁	1	1	yes	characteristic
544	#125	C₂×D₇₁	1	1	yes	characteristic
545	#124	—	71	1	no	—
546	#124	—	71	1	no	—
547	#123	—	71	1	no	—
548	#123	—	71	1	no	—
549	#123	—	71	1	no	—
550	#123	—	71	1	no	—
551	#123	—	71	1	no	—
552	#123	—	71	1	no	—
553	#123	—	71	1	no	—
554	#123	—	71	1	no	—
555	#123	—	71	1	no	—
556	#123	—	71	1	no	—
557	#123	—	71	1	no	—
558	#123	—	71	1	no	—
559	#123	—	71	1	no	—
560	#123	—	71	1	no	—
561	#123	—	71	1	no	—
562	#123	—	71	1	no	—
563	#123	—	71	1	no	—
564	#123	—	71	1	no	—
565	#123	—	71	1	no	—
566	#123	—	71	1	no	—
567	C₂²⋊Q₈	—	71	1	no	—
568	C₂²⋊Q₈	—	71	1	no	—
569	C₂²⋊Q₈	—	71	1	no	—
570	C₂²⋊Q₈	—	71	1	no	—
571	C₂²⋊Q₈	—	71	1	no	—
572	C₂²⋊Q₈	—	71	1	no	—
573	C₂²⋊Q₈	—	71	1	no	—
574	C₂²⋊Q₈	—	71	1	no	—
575	C₂²⋊Q₈	—	71	1	no	—
576	C₂²⋊Q₈	—	71	1	no	—
577	C₂²⋊Q₈	—	71	1	no	—
578	C₂²⋊Q₈	—	71	1	no	—
579	C₂²⋊Q₈	—	71	1	no	—
580	C₂²⋊Q₈	—	71	1	no	—
581	C₂²⋊Q₈	—	71	1	no	—
582	C₂²⋊Q₈	—	71	1	no	—
583	C₂²⋊Q₈	—	71	1	no	—
584	C₂²⋊Q₈	—	71	1	no	—
585	C₂²⋊Q₈	—	71	1	no	—
586	C₂²⋊Q₈	—	71	1	no	—
587	C₂²⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
588	C₂²⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
589	C₂²⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
590	C₂²⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
591	C₂²⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
592	C₂²⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
593	#121	—	71	1	no	—
594	#121	—	71	1	no	—
595	#121	—	71	1	no	—
596	#121	—	71	1	no	—
597	#121	—	71	1	no	—
598	#121	—	71	1	no	—
599	#121	—	71	1	no	—
600	#121	—	71	1	no	—
601	#121	—	71	1	no	—
602	#121	—	71	1	no	—
603	C₄×Q₈	—	71	1	no	—
604	C₄×Q₈	—	71	1	no	—
605	C₄×Q₈	—	71	1	no	—
606	C₄×Q₈	—	71	1	no	—
607	C₄×Q₈	—	71	1	no	—
608	C₄×Q₈	C₂×D₇₁	1	1	yes	characteristic
609	C₄×D₄	—	71	1	no	—
610	C₄×D₄	—	71	1	no	—
611	C₄×D₄	—	71	1	no	—
612	C₄×D₄	—	71	1	no	—
613	C₄×D₄	—	71	1	no	—
614	C₄×D₄	—	71	1	no	—
615	C₄×D₄	—	71	1	no	—
616	C₄×D₄	—	71	1	no	—
617	C₄×D₄	—	71	1	no	—
618	C₄×D₄	—	71	1	no	—
619	C₄×D₄	—	71	1	no	—
620	C₄×D₄	—	71	1	no	—
621	C₄×D₄	—	71	1	no	—
622	C₄×D₄	—	71	1	no	—
623	C₄×D₄	—	71	1	no	—
624	C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
625	C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
626	C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
627	#117	—	71	1	no	—
628	#117	—	71	1	no	—
629	#117	—	71	1	no	—
630	#117	—	71	1	no	—
631	#117	—	71	1	no	—
632	#117	—	71	1	no	—
633	#117	—	71	1	no	—
634	#117	—	71	1	no	—
635	C₂×C₄⋊C₄	—	71	1	no	—
636	C₂×C₄⋊C₄	—	71	1	no	—
637	C₂×C₄⋊C₄	—	71	1	no	—
638	C₂×C₄⋊C₄	—	71	1	no	—
639	C₂×C₄⋊C₄	—	71	1	no	—
640	C₂×C₄⋊C₄	—	71	1	no	—
641	C₂×C₄⋊C₄	—	71	1	no	—
642	C₂×C₄⋊C₄	—	71	1	no	—
643	C₂×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
645	C₂×C₄²	—	71	1	no	—
646	C₂×Q₈	—	71	1	no	—
647	C₂×Q₈	—	71	1	no	—
648	C₂×Q₈	—	71	1	no	—
649	C₂×Q₈	C₂²×D₇₁	1	1	yes	characteristic
650	C₂×Q₈	C₂²×D₇₁	1	1	yes	characteristic
651	C₂×Q₈	C₂²×D₇₁	1	1	yes	characteristic
652	C₂×D₄	—	71	1	no	—
653	C₂×D₄	—	71	1	no	—
654	C₂×D₄	—	71	1	no	—
655	C₂×D₄	—	71	1	no	—
656	C₂×D₄	—	71	1	no	—
657	C₂×D₄	—	71	1	no	—
658	C₂×D₄	—	71	1	no	—
659	C₂×D₄	—	71	1	no	—
660	C₂×D₄	—	71	1	no	—
661	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
662	C₂²×C₄	—	71	1	no	—
663	C₂²×C₄	—	71	1	no	—
664	C₂²×C₄	—	71	1	no	—
665	C₂²×C₄	—	71	1	no	—
666	C₂²×C₄	—	71	1	no	—
667	C₂²×C₄	—	71	1	no	—
668	C₂²×C₄	—	71	1	no	—
669	C₂²×C₄	—	71	1	no	—
670	C₂²×C₄	—	71	1	no	—
671	C₂²×C₄	—	71	1	no	—
672	C₂²×C₄	—	71	1	no	—
673	C₂²×C₄	—	71	1	no	—
674	C₂²×C₄	—	71	1	no	—
675	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
676	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
677	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
678	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
679	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
680	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
681	C₄⋊C₄	—	71	1	no	—
682	C₄⋊C₄	—	71	1	no	—
683	C₄⋊C₄	—	71	1	no	—
684	C₄⋊C₄	—	71	1	no	—
685	C₄⋊C₄	—	71	1	no	—
686	C₄⋊C₄	—	71	1	no	—
687	C₄⋊C₄	—	71	1	no	—
688	C₄⋊C₄	—	71	1	no	—
689	C₄⋊C₄	—	71	1	no	—
690	C₄⋊C₄	—	71	1	no	—
691	C₄⋊C₄	—	71	1	no	—
692	C₄⋊C₄	—	71	1	no	—
693	C₄⋊C₄	—	71	1	no	—
694	C₄⋊C₄	—	71	1	no	—
695	C₄⋊C₄	—	71	1	no	—
696	C₄⋊C₄	—	71	1	no	—
697	C₄⋊C₄	—	71	1	no	—
698	C₄⋊C₄	—	71	1	no	—
699	C₄⋊C₄	—	71	1	no	—
700	C₄⋊C₄	—	71	1	no	—
701	C₄⋊C₄	—	71	1	no	—
702	C₄⋊C₄	—	71	1	no	—
703	C₄⋊C₄	—	71	1	no	—
704	C₄⋊C₄	—	71	1	no	—
705	C₄⋊C₄	—	71	1	no	—
706	C₄⋊C₄	—	71	1	no	—
707	C₄⋊C₄	—	71	1	no	—
708	C₄⋊C₄	—	71	1	no	—
709	C₄⋊C₄	—	71	1	no	—
710	C₄⋊C₄	—	71	1	no	—
711	C₄⋊C₄	—	71	1	no	—
712	C₄⋊C₄	—	71	1	no	—
713	C₄⋊C₄	—	71	1	no	—
714	C₄⋊C₄	—	71	1	no	—
715	C₄⋊C₄	—	71	1	no	—
716	C₄⋊C₄	—	71	1	no	—
717	C₄⋊C₄	—	71	1	no	—
718	C₄⋊C₄	—	71	1	no	—
719	C₄⋊C₄	—	71	1	no	—
720	C₄⋊C₄	—	71	1	no	—
721	C₄⋊C₄	—	71	1	no	—
722	C₄⋊C₄	—	71	1	no	—
723	C₄⋊C₄	—	71	1	no	—
724	C₄⋊C₄	—	71	1	no	—
725	C₄⋊C₄	—	71	1	no	—
726	C₄⋊C₄	—	71	1	no	—
727	C₄⋊C₄	—	71	1	no	—
728	C₄⋊C₄	—	71	1	no	—
729	C₄⋊C₄	—	71	1	no	—
730	C₄⋊C₄	—	71	1	no	—
731	C₄⋊C₄	—	71	1	no	—
732	C₄⋊C₄	—	71	1	no	—
733	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
749	C₂²⋊C₄	—	71	1	no	—
750	C₂²⋊C₄	—	71	1	no	—
751	C₂²⋊C₄	—	71	1	no	—
752	C₂²⋊C₄	—	71	1	no	—
753	C₂²⋊C₄	—	71	1	no	—
754	C₂²⋊C₄	—	71	1	no	—
755	C₂²⋊C₄	—	71	1	no	—
756	C₂²⋊C₄	—	71	1	no	—
757	C₂²⋊C₄	—	71	1	no	—
758	C₂²⋊C₄	—	71	1	no	—
759	C₂²⋊C₄	—	71	1	no	—
760	C₂²⋊C₄	—	71	1	no	—
761	C₂²⋊C₄	—	71	1	no	—
762	C₂²⋊C₄	—	71	1	no	—
763	C₂²⋊C₄	—	71	1	no	—
764	C₂²⋊C₄	—	71	1	no	—
765	C₂²⋊C₄	—	71	1	no	—
766	C₂²⋊C₄	—	71	1	no	—
767	C₂²⋊C₄	—	71	1	no	—
768	C₂²⋊C₄	—	71	1	no	—
769	C₂²⋊C₄	—	71	1	no	—
770	C₂²⋊C₄	—	71	1	no	—
771	C₂²⋊C₄	—	71	1	no	—
772	C₂²⋊C₄	—	71	1	no	—
773	C₂²⋊C₄	—	71	1	no	—
774	C₂²⋊C₄	—	71	1	no	—
775	C₂²⋊C₄	—	71	1	no	—
776	C₂²⋊C₄	—	71	1	no	—
777	C₂²⋊C₄	—	71	1	no	—
778	C₂²⋊C₄	—	71	1	no	—
779	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
781	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
784	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
785	C₄²	—	71	1	no	—
786	C₄²	—	71	1	no	—
787	C₄²	—	71	1	no	—
788	C₄²	—	71	1	no	—
789	C₄²	—	71	1	no	—
790	C₄²	—	71	1	no	—
791	C₄²	—	71	1	no	—
792	C₄²	—	71	1	no	—
793	C₄²	—	71	1	no	—
794	C₄²	—	71	1	no	—
795	C₄²	—	71	1	no	—
796	C₄²	—	71	1	no	—
797	C₄²	—	71	1	no	—
798	C₄²	C₂²×D₇₁	1	1	yes	characteristic
799	C₄²	C₂²×D₇₁	1	1	yes	characteristic
800	C₄²	C₂²×D₇₁	1	1	yes	characteristic
801	C₂³	—	71	1	no	—
802	C₂³	—	71	1	no	—
803	C₂³	—	71	1	no	—
804	C₂³	C₂³×D₇₁	1	1	yes	characteristic
805	C₂³	C₂³×D₇₁	1	1	yes	characteristic
806	Q₈	—	4	1	no	—
807	Q₈	—	4	1	no	—
808	Q₈	—	4	1	no	—
809	Q₈	—	284	1	no	—
810	Q₈	—	284	1	no	—
811	Q₈	—	284	1	no	—
812	D₄	—	2	2	no	—
813	D₄	—	284	1	no	—
814	D₄	—	284	1	no	—
815	D₄	—	284	1	no	—
816	D₄	—	284	1	no	—
817	D₄	—	284	1	no	—
818	D₄	—	284	1	no	—
819	D₄	—	142	2	no	—
820	D₄	—	142	2	no	—
821	D₄	—	142	2	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	284	1	no	—
829	C₂×C₄	—	284	1	no	—
830	C₂×C₄	—	284	1	no	—
831	C₂×C₄	—	284	1	no	—
832	C₂×C₄	—	284	1	no	—
833	C₂×C₄	—	284	1	no	—
834	C₂×C₄	—	284	1	no	—
835	C₂×C₄	—	284	1	no	—
836	C₂×C₄	—	284	1	no	—
837	C₂×C₄	—	284	1	no	—
838	C₂×C₄	—	284	1	no	—
839	C₂×C₄	—	284	1	no	—
840	C₂×C₄	—	71	1	no	—
841	C₂×C₄	—	71	1	no	—
842	C₂×C₄	—	71	1	no	—
843	C₂×C₄	—	71	1	no	—
844	C₂×C₄	—	71	1	no	—
845	C₂×C₄	—	71	1	no	—
846	C₂×C₄	—	71	1	no	—
847	C₂×C₄	—	71	1	no	—
848	C₂×C₄	—	71	1	no	—
849	C₂×C₄	—	71	1	no	—
850	C₂×C₄	—	71	1	no	—
851	C₂×C₄	—	71	1	no	—
852	C₂×C₄	—	71	1	no	—
853	C₂×C₄	—	142	2	no	—
854	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
855	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	142	1	no	—
873	C₂²	—	142	1	no	—
874	C₂²	—	142	1	no	—
875	C₂²	—	142	1	no	—
876	C₂²	—	142	1	no	—
877	C₂²	—	142	1	no	—
878	C₂²	—	142	1	no	—
879	C₂²	—	142	1	no	—
880	C₂²	—	142	1	no	—
881	C₂²	#14556176	1	2	yes	—
882	C₂²	C₂⁴×D₇₁	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	142	1	no	—
897	C₄	—	142	1	no	—
898	C₄	—	142	1	no	—
899	C₄	—	142	1	no	—
900	C₄	—	142	1	no	—
901	C₄	—	142	1	no	—
902	C₄	—	142	1	no	—
903	C₄	—	142	1	no	—
904	C₄	—	142	1	no	—
905	C₄	—	142	1	no	—
906	C₄	—	142	1	no	—
907	C₄	—	142	1	no	—
908	C₄	—	142	1	no	—
909	C₂	—	2	2	no	—
910	C₂	—	4	1	no	—
911	C₂	—	284	1	no	—
912	C₂	—	284	1	no	—
913	C₂	—	284	1	no	—
914	C₂	C₂×#14556176	1	1	yes	characteristic
915	C₂	#17986834	1	1	yes	characteristic
916	C₂	#17986835	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₁
commutator, socle	C₂²×C₇₁	C₂⁵
Fitting	#554×C₇₁	C₂
hypercenter	#554	D₇₁
hypocenter	C₇₁	#3553
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₇₁⋊#564	C₂	semidirect
2. #17986750	C₂	semidirect
3. #17986748	C₂	semidirect
4. #17986745	C₂	semidirect
5. #17986707	C₂	semidirect
6. #17986703	C₂	semidirect
7. #17986703	C₂	semidirect
8. #17986698	C₂	semidirect
9. #17986698	C₂	semidirect
10. #17986697	C₂	semidirect
11. #17986695	C₂	semidirect
12. #17986690	C₂	semidirect
13. #17986684	C₂	semidirect
14. #17986683	C₂	semidirect
15. #17986681	C₂	semidirect
16. #17986610	C₂	semidirect
17. #17986609	C₂	semidirect
18. #17986608	C₂	semidirect
19. #17986607	C₂	semidirect
20. #17986598	C₂	semidirect
21. #17986598	C₂	semidirect
22. #17986597	C₂	semidirect
23. #17986596	C₂	semidirect
24. #17986595	C₂	semidirect
25. #17986595	C₂	semidirect
26. #17986591	C₂	semidirect
27. #17986591	C₂	semidirect
28. #17986535	C₂	semidirect
29. #17986529	C₂	semidirect
30. C₂×#14556118	C₂	semidirect
31. #554×C₇₁	C₂	semidirect
459. C₇₁	#3553	semidirect
467. #554	D₇₁	semidirect