Subgroups — #32880173

Order 18176.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22602412	C₂	1	2	yes	maximal, complemented
2	#22601329	C₂	1	1	yes	maximal, characteristic, complemented
3	#22601208	C₂	1	1	yes	maximal, characteristic, complemented
4	#22601169	C₂	1	2	yes	maximal, complemented
5	#22600771	C₂	1	1	yes	maximal, characteristic, complemented
6	#22600743	C₂	1	1	yes	maximal, characteristic, complemented
7	#22600709	C₂	1	1	yes	maximal, characteristic, complemented
8	#22600558	C₂	1	2	yes	maximal, complemented
9	#22600378	C₂	1	2	yes	maximal, complemented
10	#22600318	C₂	1	2	yes	maximal, complemented
11	#22600062	C₂	1	1	yes	maximal, characteristic, complemented
12	#22600027	C₂	1	1	yes	maximal, characteristic, complemented
13	#22600027	C₂	1	1	yes	maximal, characteristic, complemented
14	#22598999	C₂	1	1	yes	maximal, characteristic, complemented
15	#22598979	C₂	1	1	yes	maximal, characteristic, complemented
16	#22598910	C₂	1	1	yes	maximal, characteristic, complemented
17	#22598619	C₂	1	2	yes	maximal, complemented
18	#22598593	C₂	1	2	yes	maximal, complemented
19	#22598451	C₂	1	2	yes	maximal, complemented
20	#22597217	C₂	1	1	yes	maximal, characteristic, complemented
21	#22597193	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14556150	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556150	C₂²	1	1	yes	characteristic
25	C₂×#14556150	C₂²	1	1	yes	characteristic
26	C₂²×D₅₆₈	C₂²	1	1	yes	characteristic
27	#17986722	C₂²	1	2	yes	complemented
28	#17986719	C₂²	1	2	yes	—
29	#17986709	C₂²	1	2	yes	complemented
30	#17986695	C₂²	1	2	yes	complemented
31	#17986694	—	2	2	no	—
32	#17986689	C₂²	1	2	yes	—
33	#17986681	—	2	2	no	—
34	#17986679	—	2	2	no	—
35	#17986677	—	2	2	no	—
36	#17986654	C₂²	1	2	yes	complemented
37	#17986645	C₂²	1	2	yes	—
38	#17986645	C₂²	1	2	yes	—
39	#17986620	C₂²	1	2	yes	complemented
40	#17986611	C₂²	1	2	yes	—
41	#17986595	—	2	2	no	—
42	#17986581	—	2	2	no	—
43	#17986533	C₂²	1	2	yes	complemented
44	#17986532	—	2	2	no	—
45	#126×D₇₁	—	2	2	no	—
46	#17986479	C₂²	1	2	yes	complemented
47	#17986473	C₂²	1	2	yes	—
48	C₄×#11765865	C₂²	1	2	yes	complemented
49	#17986404	C₂²	1	1	yes	characteristic, complemented
50	#17986401	C₂²	1	1	yes	characteristic, complemented
51	#17986401	C₂²	1	1	yes	characteristic, complemented
52	#17986383	C₂²	1	1	yes	characteristic
53	#17986383	C₂²	1	1	yes	characteristic
54	#17986379	C₂²	1	1	yes	characteristic, complemented
55	#17986368	C₂²	1	2	yes	complemented
56	#17986359	C₂²	1	2	yes	complemented
57	#17986354	C₂²	1	2	yes	complemented
58	#17986341	C₂²	1	2	yes	—
59	#17986341	C₂²	1	2	yes	—
60	#17986341	C₂²	1	2	yes	complemented
61	#17986330	C₂²	1	2	yes	complemented
62	#17986324	C₂²	1	2	yes	complemented
63	#17986318	C₂²	1	2	yes	complemented
64	#17986307	C₂²	1	2	yes	complemented
65	#17986300	C₂²	1	2	yes	complemented
66	#17986300	C₂²	1	2	yes	complemented
67	#17986300	C₂²	1	2	yes	complemented
68	#17986290	C₂²	1	2	yes	complemented
69	#17986285	C₂²	1	2	yes	complemented
70	#17986257	C₂²	1	2	yes	—
71	#17986245	C₂²	1	2	yes	complemented
72	#17986240	C₂²	1	1	yes	characteristic
73	#17986240	C₂²	1	1	yes	characteristic
74	#17986240	C₂²	1	1	yes	characteristic, complemented
75	#17986240	C₂²	1	1	yes	characteristic, complemented
76	#17986235	C₂²	1	1	yes	characteristic
77	#17986235	C₂²	1	1	yes	characteristic
78	#17986228	C₂²	1	2	yes	complemented
79	#17986222	C₂²	1	2	yes	complemented
80	#17986222	C₂²	1	2	yes	complemented
81	#17986215	C₂²	1	2	yes	—
82	#17986215	C₂²	1	2	yes	—
83	#17986205	C₂²	1	2	yes	complemented
84	#17986205	C₂²	1	2	yes	complemented
85	#17986163	C₂²	1	2	yes	complemented
86	#17986163	C₂²	1	2	yes	complemented
87	#17986152	C₂²	1	2	yes	—
88	#17986152	C₂²	1	2	yes	—
89	#17986146	C₂²	1	2	yes	—
90	#17986146	C₂²	1	2	yes	—
91	#17986112	C₂²	1	2	yes	—
92	#17986112	C₂²	1	2	yes	—
93	#17986107	C₂²	1	2	yes	complemented
94	#17986101	C₂²	1	2	yes	complemented
95	#17986101	C₂²	1	2	yes	complemented
96	#17986101	C₂²	1	2	yes	complemented
97	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic, complemented
99	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic, complemented
100	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic, complemented
101	C₄×#11765854	C₂²	1	2	yes	complemented
102	C₄×#11765854	C₂²	1	2	yes	complemented
103	C₄×#11765854	C₂²	1	2	yes	complemented
104	C₄×D₅₆₈	C₂²	1	1	yes	characteristic
105	C₄×D₅₆₈	C₂²	1	1	yes	characteristic
106	C₄×D₅₆₈	C₂²	1	1	yes	characteristic
107	C₄×D₅₆₈	C₂²	1	1	yes	characteristic
108	C₄×D₅₆₈	C₂²	1	1	yes	characteristic
109	C₄×D₅₆₈	C₂²	1	1	yes	characteristic
110	#17986037	C₂²	1	1	yes	characteristic
111	#17986037	C₂²	1	1	yes	characteristic, complemented
112	C₂×#14556062	C₂²	1	1	yes	characteristic, complemented
113	#17986005	C₂²	1	2	yes	—
114	#17986001	C₂²	1	2	yes	complemented
115	#17985996	C₂²	1	2	yes	complemented
116	#529×C₇₁	C₂²	1	1	yes	characteristic
117	#446×C₇₁	C₂²	1	1	yes	characteristic, complemented
118	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
119	#436×C₇₁	C₂²	1	1	yes	characteristic
120	#435×C₇₁	C₂²	1	1	yes	characteristic
121	#435×C₇₁	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic, complemented
125	#433×C₇₁	C₂²	1	1	yes	characteristic
126	#433×C₇₁	C₂²	1	1	yes	characteristic, complemented
127	#432×C₇₁	C₂²	1	1	yes	characteristic, complemented
128	#405×C₇₁	C₂²	1	1	yes	characteristic
129	#405×C₇₁	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
131	C₂×#11765865	C₂³	1	2	yes	—
132	C₂×#11765865	C₂³	1	2	yes	—
133	C₂²×D₂₈₄	C₂³	1	2	yes	—
134	#14556150	—	2	4	no	—
135	#14556150	—	2	4	no	—
136	C₂×Dic₂₈₄	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₈₄	C₂³	1	1	yes	characteristic
138	C₂×Dic₂₈₄	C₂³	1	2	yes	—
139	C₂×#11765854	C₂³	1	2	yes	—
140	C₂×#11765854	C₂³	1	2	yes	—
141	C₂×#11765854	C₂³	1	2	yes	—
142	C₂×#11765854	C₂³	1	2	yes	—
143	C₂×D₅₆₈	—	2	4	no	—
144	C₂×D₅₆₈	C₂³	1	1	yes	characteristic
145	C₂×D₅₆₈	C₂³	1	2	yes	—
146	C₂×D₅₆₈	C₂³	1	1	yes	characteristic
147	#14556128	C₂³	1	2	yes	—
148	#14556128	C₂³	1	2	yes	—
149	#14556123	—	2	2	no	—
150	#14556123	—	2	2	no	—
151	#14556123	—	2	2	no	—
152	#14556123	—	2	2	no	—
153	#14556122	—	2	2	no	—
154	#14556121	—	2	2	no	—
155	#14556121	—	2	2	no	—
156	#14556121	—	2	2	no	—
157	#14556121	—	2	2	no	—
158	#14556121	—	2	2	no	—
159	#14556120	C₂³	1	2	yes	—
160	#14556120	C₂³	1	2	yes	—
161	#14556118	—	2	2	no	—
162	#14556118	—	2	2	no	—
163	#14556118	—	2	2	no	—
164	#14556116	C₂³	1	2	yes	—
165	#14556116	C₂³	1	2	yes	—
166	#14556115	—	2	2	no	—
167	#14556114	—	2	2	no	—
168	#14556113	—	2	2	no	—
169	#14556113	—	2	2	no	—
170	#14556111	—	2	2	no	—
171	#14556110	—	2	2	no	—
172	#14556110	—	2	2	no	—
173	#14556110	—	2	2	no	—
174	#14556110	—	2	2	no	—
175	#14556109	—	2	2	no	—
176	#14556107	C₂³	1	2	yes	—
177	#14556107	C₂³	1	2	yes	—
178	#14556107	C₂³	1	2	yes	—
179	#14556107	C₂³	1	2	yes	—
180	#14556106	—	2	2	no	—
181	#14556106	—	2	2	no	—
182	#14556106	—	2	2	no	—
183	#14556104	—	2	2	no	—
184	#14556104	—	2	2	no	—
185	#14556102	C₂³	1	2	yes	—
186	#14556102	C₂³	1	2	yes	—
187	#14556101	—	2	2	no	—
188	#14556101	—	2	2	no	—
189	#14556100	—	2	2	no	—
190	#14556099	—	2	2	no	—
191	#14556096	—	2	2	no	—
192	#14556096	—	2	2	no	—
193	C₄×Dic₁₄₂	C₂³	1	2	yes	—
194	C₄×Dic₁₄₂	C₂³	1	2	yes	—
195	C₄×Dic₁₄₂	C₂³	1	2	yes	—
196	C₄×Dic₁₄₂	C₂³	1	2	yes	—
197	#14556093	—	2	2	no	—
198	C₄×D₂₈₄	C₂³	1	2	yes	—
199	C₄×D₂₈₄	C₂³	1	2	yes	—
200	C₄×D₂₈₄	C₂³	1	2	yes	—
201	C₄×D₂₈₄	C₂³	1	2	yes	—
202	C₄×D₂₈₄	C₂³	1	2	yes	—
203	C₄×D₂₈₄	C₂³	1	2	yes	—
204	#14556090	—	2	2	no	—
205	#14556090	—	2	2	no	—
206	C₄×C₂²⋊D₇₁	—	2	2	no	—
207	C₄×C₂²⋊D₇₁	—	2	2	no	—
208	C₄×C₂²⋊D₇₁	—	2	2	no	—
209	(C₂²⋊D₇₁)⋊C₄	—	2	2	no	—
210	(C₂²⋊D₇₁)⋊C₄	—	2	2	no	—
211	(C₂²⋊D₇₁)⋊C₄	—	2	2	no	—
212	#14556087	C₂³	1	2	yes	—
213	#14556087	C₂³	1	2	yes	—
214	#14556086	—	2	2	no	—
215	#14556086	—	2	2	no	—
216	#14556085	—	2	2	no	—
217	#14556085	—	2	2	no	—
218	#14556084	—	2	2	no	—
219	C₂×C₄⋊Dic₇₁	C₂³	1	2	yes	—
220	C₄⋊C₄×D₇₁	—	2	2	no	—
221	C₄⋊C₄×D₇₁	—	2	2	no	—
222	C₄⋊C₄×D₇₁	—	2	2	no	—
223	C₂²⋊C₄×D₇₁	—	2	2	no	—
224	C₂²⋊C₄×D₇₁	—	2	2	no	—
225	C₂²⋊C₄×D₇₁	—	2	2	no	—
226	C₂²⋊C₄×D₇₁	—	2	2	no	—
227	C₄²×D₇₁	—	2	2	no	—
228	#14556062	C₂³	1	2	yes	—
229	#14556062	C₂³	1	1	yes	characteristic
230	#14556062	C₂³	1	1	yes	characteristic
231	#14556062	C₂³	1	1	yes	characteristic
232	#14556062	C₂³	1	1	yes	characteristic
233	#14556062	C₂³	1	2	yes	—
234	#14556060	C₂³	1	2	yes	—
235	#14556060	C₂³	1	2	yes	—
236	#14556060	C₂³	1	2	yes	—
237	#14556060	C₂³	1	2	yes	—
238	#14556053	C₂³	1	2	yes	—
239	#14556053	C₂³	1	2	yes	—
240	#14556053	C₂³	1	2	yes	—
241	#14556053	C₂³	1	2	yes	—
242	#14556053	C₂³	1	2	yes	—
243	#14556053	C₂³	1	2	yes	—
244	#14556053	C₂³	1	2	yes	—
245	#14556053	C₂³	1	2	yes	—
246	#14556050	C₂³	1	2	yes	—
247	#14556050	C₂³	1	2	yes	—
248	#14556050	C₂³	1	2	yes	—
249	#14556050	C₂³	1	2	yes	—
250	#14556050	C₂³	1	2	yes	—
251	#14556050	C₂³	1	2	yes	—
252	#14556050	C₂³	1	2	yes	—
253	#14556050	C₂³	1	2	yes	—
254	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
255	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
256	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
257	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
258	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
259	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
260	#126×C₇₁	D₄	1	1	yes	characteristic
261	#126×C₇₁	D₄	1	1	yes	characteristic
262	#125×C₇₁	D₄	1	1	yes	characteristic
263	#124×C₇₁	D₄	1	1	yes	characteristic
264	#123×C₇₁	D₄	1	1	yes	characteristic
265	#123×C₇₁	D₄	1	1	yes	characteristic
266	C₂²⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
267	#121×C₇₁	D₄	1	1	yes	characteristic
268	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
272	#117×C₇₁	C₂³	1	1	yes	characteristic
273	#117×C₇₁	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
287	#97×C₇₁	C₂³	1	1	yes	characteristic
288	#97×C₇₁	C₂³	1	1	yes	characteristic
289	#97×C₇₁	C₂³	1	1	yes	characteristic
290	#97×C₇₁	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
297	C₂³×D₇₁	—	2	2	no	—
298	#11765865	—	2	4	no	—
299	#11765865	—	2	4	no	—
300	#11765865	—	4	2	no	—
301	#11765865	—	4	2	no	—
302	C₂×Dic₁₄₂	—	2	2	no	—
303	C₂×Dic₁₄₂	C₂⁴	1	2	yes	—
304	C₂×Dic₁₄₂	C₂⁴	1	2	yes	—
305	C₂×D₂₈₄	—	2	4	no	—
306	C₂×D₂₈₄	—	2	2	no	—
307	C₂×D₂₈₄	—	4	2	no	—
308	C₂×D₂₈₄	C₂⁴	1	2	yes	—
309	C₂×D₂₈₄	C₂⁴	1	2	yes	—
310	C₂×C₂²⋊D₇₁	—	2	2	no	—
311	C₂×C₂²⋊D₇₁	—	2	2	no	—
312	C₂×C₂²⋊D₇₁	—	2	2	no	—
313	C₂×C₂²⋊D₇₁	—	2	2	no	—
314	C₂²×Dic₇₁	—	2	2	no	—
315	C₂×C₄×D₇₁	—	2	2	no	—
316	C₂×C₄×D₇₁	—	2	2	no	—
317	C₂×C₄×D₇₁	—	2	2	no	—
318	C₂×C₄×D₇₁	—	2	2	no	—
319	C₂×C₄×D₇₁	—	2	2	no	—
320	C₂×C₄×D₇₁	—	2	2	no	—
321	C₂×C₄×D₇₁	—	2	2	no	—
322	C₂×C₄×D₇₁	—	2	2	no	—
323	Dic₂₈₄	—	2	2	no	—
324	Dic₂₈₄	—	2	2	no	—
325	Dic₂₈₄	—	4	2	no	—
326	#11765854	—	2	4	no	—
327	#11765854	—	2	4	no	—
328	#11765854	—	4	2	no	—
329	#11765854	—	4	2	no	—
330	D₅₆₈	—	2	4	no	—
331	D₅₆₈	—	2	2	no	—
332	D₅₆₈	#41	1	4	yes	—
333	C₄⋊Dic₇₁	—	2	2	no	—
334	C₄⋊Dic₇₁	—	2	2	no	—
335	C₄⋊Dic₇₁	—	2	2	no	—
336	C₄⋊Dic₇₁	—	2	2	no	—
337	C₄⋊Dic₇₁	C₂⁴	1	2	yes	—
338	C₄⋊Dic₇₁	C₂⁴	1	2	yes	—
339	C₄⋊Dic₇₁	C₂⁴	1	2	yes	—
340	C₄⋊Dic₇₁	C₂⁴	1	2	yes	—
341	Dic₇₁⋊C₄	—	2	2	no	—
342	Dic₇₁⋊C₄	—	2	2	no	—
343	Dic₇₁⋊C₄	—	2	2	no	—
344	Dic₇₁⋊C₄	—	2	2	no	—
345	Dic₇₁⋊C₄	—	2	2	no	—
346	Dic₇₁⋊C₄	—	2	2	no	—
347	Dic₇₁⋊C₄	—	2	2	no	—
348	Dic₇₁⋊C₄	—	2	2	no	—
349	Dic₇₁⋊C₄	—	2	2	no	—
350	Dic₇₁⋊C₄	—	2	2	no	—
351	Dic₇₁⋊C₄	—	2	2	no	—
352	Dic₇₁⋊C₄	—	2	2	no	—
353	C₂²⋊Dic₇₁	—	2	2	no	—
354	C₂²⋊Dic₇₁	—	2	2	no	—
355	C₂²⋊Dic₇₁	—	2	2	no	—
356	C₂²⋊Dic₇₁	—	2	2	no	—
357	C₂²⋊Dic₇₁	—	2	2	no	—
358	C₂²⋊Dic₇₁	—	2	2	no	—
359	(C₂×D₇₁)⋊C₄	—	2	2	no	—
360	(C₂×D₇₁)⋊C₄	—	2	2	no	—
361	(C₂×D₇₁)⋊C₄	—	2	2	no	—
362	(C₂×D₇₁)⋊C₄	—	2	2	no	—
363	(C₂×D₇₁)⋊C₄	—	2	2	no	—
364	(C₂×D₇₁)⋊C₄	—	2	2	no	—
365	(C₂×D₇₁)⋊C₄	—	2	2	no	—
366	(C₂×D₇₁)⋊C₄	—	2	2	no	—
367	(C₂×D₇₁)⋊C₄	—	2	2	no	—
368	(C₂×D₇₁)⋊C₄	—	2	2	no	—
369	(C₂×D₇₁)⋊C₄	—	2	2	no	—
370	(C₂×D₇₁)⋊C₄	—	2	2	no	—
371	C₄×Dic₇₁	—	2	2	no	—
372	C₄×Dic₇₁	—	2	2	no	—
373	C₄×Dic₇₁	—	2	2	no	—
374	C₄×Dic₇₁	—	2	2	no	—
375	C₄×Dic₇₁	—	2	2	no	—
376	C₄×Dic₇₁	—	2	2	no	—
377	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
380	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
386	M₁₆×C₇₁	—	4	1	no	—
387	M₁₆×C₇₁	—	4	1	no	—
388	C₂×C₈×C₇₁	—	2	2	no	—
389	C₂×C₈×C₇₁	—	2	2	no	—
390	C₂×C₈×C₇₁	—	2	2	no	—
391	C₂×C₈×C₇₁	—	4	1	no	—
392	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
410	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
412	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
414	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
415	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
416	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
417	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
418	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
419	C₂²⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
420	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
423	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
424	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
425	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
426	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
427	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
429	C₂²×D₇₁	—	2	2	no	—
430	C₂²×D₇₁	—	2	2	no	—
431	C₂²×D₇₁	—	4	4	no	—
432	C₂²×D₇₁	—	8	2	no	—
433	C₂²×D₇₁	—	8	2	no	—
434	Q₈×C₇₁	—	4	1	no	—
435	D₄×C₇₁	—	4	1	no	—
436	D₄×C₇₁	—	4	1	no	—
437	D₄×C₇₁	—	4	1	no	—
438	C₂×C₄×C₇₁	—	2	1	no	—
439	C₂×C₄×C₇₁	—	2	1	no	—
440	C₂×C₄×C₇₁	—	2	1	no	—
441	C₂×C₄×C₇₁	—	2	1	no	—
442	C₂×C₄×C₇₁	—	2	1	no	—
443	C₂×C₄×C₇₁	—	2	1	no	—
444	C₂×C₄×C₇₁	—	4	1	no	—
445	C₂×C₄×C₇₁	—	4	1	no	—
446	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
458	C₂²⋊D₇₁	—	4	4	no	—
459	C₂²⋊D₇₁	—	4	4	no	—
460	C₂²⋊D₇₁	—	8	2	no	—
461	C₂²⋊D₇₁	—	8	2	no	—
462	C₂×Dic₇₁	—	2	2	no	—
463	C₂×Dic₇₁	—	2	2	no	—
464	C₂×Dic₇₁	—	2	2	no	—
465	C₂×Dic₇₁	—	2	2	no	—
466	C₂×Dic₇₁	—	2	2	no	—
467	C₂×Dic₇₁	—	2	2	no	—
468	C₂×Dic₇₁	—	8	2	no	—
469	D₂₈₄	—	2	2	no	—
470	D₂₈₄	—	2	2	no	—
471	D₂₈₄	—	2	2	no	—
472	D₂₈₄	—	4	4	no	—
473	D₂₈₄	C₂×#41	1	4	yes	—
474	C₄×D₇₁	—	4	4	no	—
475	C₄×D₇₁	—	4	4	no	—
476	C₄×D₇₁	—	8	2	no	—
477	C₄×D₇₁	—	8	2	no	—
478	C₄×D₇₁	—	8	2	no	—
479	C₄×D₇₁	—	8	2	no	—
480	C₄×D₇₁	—	8	2	no	—
481	C₄×D₇₁	—	8	2	no	—
482	Dic₁₄₂	—	2	2	no	—
483	Dic₁₄₂	—	2	2	no	—
484	Dic₁₄₂	—	2	2	no	—
485	Dic₁₄₂	—	2	2	no	—
486	Dic₁₄₂	—	8	2	no	—
487	C₈×C₇₁	—	2	1	no	—
488	C₈×C₇₁	—	2	1	no	—
489	C₈×C₇₁	—	2	1	no	—
490	C₈×C₇₁	—	2	1	no	—
491	C₈×C₇₁	—	2	1	no	—
492	C₈×C₇₁	—	2	1	no	—
493	C₈×C₇₁	—	2	1	no	—
494	C₈×C₇₁	C₂×#41	1	2	yes	—
495	C₂²×C₇₁	—	2	1	no	—
496	C₂²×C₇₁	—	2	1	no	—
497	C₂²×C₇₁	—	2	1	no	—
498	C₂²×C₇₁	—	2	1	no	—
499	C₂²×C₇₁	—	2	1	no	—
500	C₂²×C₇₁	—	2	1	no	—
501	C₂²×C₇₁	—	2	1	no	—
502	C₂²×C₇₁	—	2	1	no	—
503	C₂²×C₇₁	—	2	1	no	—
504	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
505	C₂×D₇₁	—	2	4	no	—
506	C₂×D₇₁	—	4	2	no	—
507	C₂×D₇₁	—	4	2	no	—
508	C₂×D₇₁	—	4	2	no	—
509	C₂×D₇₁	—	4	2	no	—
510	C₂×D₇₁	—	4	2	no	—
511	C₂×D₇₁	—	16	4	no	—
512	C₄×C₇₁	—	2	1	no	—
513	C₄×C₇₁	—	2	1	no	—
514	C₄×C₇₁	—	2	1	no	—
515	C₄×C₇₁	—	2	1	no	—
516	C₄×C₇₁	—	2	1	no	—
517	C₄×C₇₁	—	2	1	no	—
518	C₄×C₇₁	—	2	1	no	—
519	C₄×C₇₁	—	2	1	no	—
520	C₄×C₇₁	—	2	1	no	—
521	C₄×C₇₁	—	2	1	no	—
522	C₄×C₇₁	—	2	1	no	—
523	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
524	C₄×C₇₁	#585	1	1	yes	characteristic
525	Dic₇₁	—	4	2	no	—
526	Dic₇₁	—	4	2	no	—
527	Dic₇₁	—	4	2	no	—
528	Dic₇₁	—	4	2	no	—
529	Dic₇₁	—	4	2	no	—
530	Dic₇₁	—	4	2	no	—
531	#61487	—	71	1	no	maximal, Sylow
532	C₂×C₇₁	—	4	1	no	—
533	C₂×C₇₁	—	4	1	no	—
534	C₂×C₇₁	—	4	1	no	—
535	C₂×C₇₁	D₄×#41	1	1	yes	characteristic
536	C₂×C₇₁	#3584	1	1	yes	characteristic
537	C₂×C₇₁	#3584	1	1	yes	characteristic
538	D₇₁	—	4	4	no	—
539	D₇₁	—	8	2	no	—
540	#3521	—	71	2	no	—
541	#3393	—	71	1	no	—
542	#3380	—	71	1	no	—
543	#3376	—	71	2	no	—
544	#3342	—	71	1	no	—
545	#3339	—	71	1	no	—
546	#3336	—	71	1	no	—
547	#3323	—	71	2	no	—
548	#3311	—	71	2	no	—
549	#3307	—	71	2	no	—
550	#3283	—	71	1	no	—
551	#3280	—	71	1	no	—
552	#3280	—	71	1	no	—
553	#3177	—	71	1	no	—
554	#3175	—	71	1	no	—
555	#3168	—	71	1	no	—
556	#3125	—	71	2	no	—
557	#3123	—	71	2	no	—
558	#3111	—	71	2	no	—
559	#2966	D₇₁	1	1	yes	characteristic, complemented
560	#2951	—	71	1	no	—
561	#2948	—	71	1	no	—
562	C₄×#135	—	71	1	no	—
563	C₇₁	#61487	1	1	yes	characteristic, complemented, Sylow
564	C₂×#135	—	71	1	no	—
565	C₂×#135	—	71	1	no	—
566	C₂²×D₈	—	71	1	no	—
567	#556	—	71	2	no	—
568	#556	—	71	2	no	—
569	#554	—	71	2	no	—
570	#553	—	71	2	no	—
571	#553	—	142	2	no	—
572	#552	—	71	2	no	—
573	#552	—	142	2	no	—
574	#551	—	142	2	no	—
575	#551	—	142	2	no	—
576	#547	—	71	2	no	—
577	#546	—	71	2	no	—
578	#546	—	71	2	no	—
579	#542	—	71	2	no	—
580	#541	—	71	2	no	—
581	#539	—	142	2	no	—
582	#538	—	142	2	no	—
583	#529	—	71	2	no	—
584	#529	—	142	2	no	—
585	#529	C₂×D₇₁	1	1	yes	characteristic
586	C₂×#126	—	142	2	no	—
587	#520	—	71	2	no	—
588	#518	—	71	2	no	—
589	C₄×#41	—	71	2	no	—
590	#500	—	71	1	no	—
591	#499	—	71	1	no	—
592	#499	—	71	1	no	—
593	#495	—	71	1	no	—
594	#495	—	71	1	no	—
595	#494	—	71	1	no	—
596	#491	—	71	2	no	—
597	#489	—	71	2	no	—
598	#488	—	71	2	no	—
599	#485	—	71	2	no	—
600	#485	—	71	2	no	—
601	#485	—	71	2	no	—
602	#483	—	71	2	no	—
603	#482	—	71	2	no	—
604	#481	—	71	2	no	—
605	#479	—	71	2	no	—
606	#478	—	71	2	no	—
607	#478	—	71	2	no	—
608	#478	—	71	2	no	—
609	#476	—	71	2	no	—
610	#475	—	71	2	no	—
611	#470	—	71	2	no	—
612	#468	—	71	2	no	—
613	#467	—	71	1	no	—
614	#467	—	71	1	no	—
615	#467	—	71	1	no	—
616	#467	—	71	1	no	—
617	#466	—	71	1	no	—
618	#466	—	71	1	no	—
619	#465	—	71	2	no	—
620	#464	—	71	2	no	—
621	#464	—	71	2	no	—
622	#463	—	71	2	no	—
623	#463	—	71	2	no	—
624	#461	—	71	2	no	—
625	#461	—	71	2	no	—
626	#452	—	71	2	no	—
627	#452	—	71	2	no	—
628	#450	—	71	2	no	—
629	#450	—	71	2	no	—
630	#449	—	71	2	no	—
631	#449	—	71	2	no	—
632	#446	C₂×D₇₁	1	1	yes	characteristic, complemented
633	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic, complemented
634	#442	—	71	2	no	—
635	#442	—	71	2	no	—
636	#441	—	71	2	no	—
637	#440	—	71	2	no	—
638	#440	—	71	2	no	—
639	#440	—	71	2	no	—
640	C₄×Q₁₆	—	71	1	no	—
641	C₄×Q₁₆	—	71	1	no	—
642	C₄×Q₁₆	—	71	1	no	—
643	C₄×Q₁₆	—	71	1	no	—
644	C₄×SD₁₆	—	71	2	no	—
645	C₄×SD₁₆	—	71	2	no	—
646	C₄×SD₁₆	—	71	2	no	—
647	C₄×D₈	—	71	1	no	—
648	C₄×D₈	—	71	1	no	—
649	C₄×D₈	—	71	1	no	—
650	C₄×D₈	—	71	1	no	—
651	C₄×D₈	—	71	1	no	—
652	C₄×D₈	—	71	1	no	—
653	#436	C₂×D₇₁	1	1	yes	characteristic
654	#435	C₂×D₇₁	1	1	yes	characteristic
655	#435	C₂×D₇₁	1	1	yes	characteristic, complemented
656	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
657	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
658	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic, complemented
659	#433	C₂×D₇₁	1	1	yes	characteristic
660	#433	C₂×D₇₁	1	1	yes	characteristic, complemented
661	#432	C₂×D₇₁	1	1	yes	characteristic, complemented
662	#427	—	71	1	no	—
663	#427	—	71	1	no	—
664	C₂×#107	—	71	1	no	—
665	#418	—	71	2	no	—
666	#417	—	71	2	no	—
667	#416	—	71	2	no	—
668	#405	C₂×D₇₁	1	1	yes	characteristic
669	#405	C₂×D₇₁	1	1	yes	characteristic, complemented
670	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic, complemented
671	C₂×#41	—	71	2	no	—
672	C₂×#41	—	71	2	no	—
673	C₂²×D₄	—	71	2	no	—
674	#135	—	142	4	no	—
675	#135	—	142	4	no	—
676	C₂×Q₁₆	—	71	2	no	—
677	C₂×Q₁₆	—	71	1	no	—
678	C₂×Q₁₆	—	71	1	no	—
679	C₂×SD₁₆	—	71	2	no	—
680	C₂×SD₁₆	—	71	2	no	—
681	C₂×SD₁₆	—	71	2	no	—
682	C₂×SD₁₆	—	71	2	no	—
683	C₂×D₈	—	71	1	no	—
684	C₂×D₈	—	71	1	no	—
685	C₂×D₈	—	71	2	no	—
686	C₂×D₈	—	142	4	no	—
687	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
688	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
689	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
690	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
691	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
692	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
693	C₄⋊Q₈	—	71	2	no	—
694	C₄⋊Q₈	—	71	2	no	—
695	#126	—	142	2	no	—
696	#126	—	142	2	no	—
697	#126	—	142	2	no	—
698	#126	—	142	2	no	—
699	#126	—	142	2	no	—
700	#126	—	142	2	no	—
701	#126	—	142	2	no	—
702	#126	—	142	2	no	—
703	#126	—	142	2	no	—
704	#126	—	142	2	no	—
705	#126	D₂₈₄	1	1	yes	characteristic
706	#126	D₂₈₄	1	1	yes	characteristic
707	#125	—	71	2	no	—
708	#125	—	71	2	no	—
709	#125	—	142	2	no	—
710	#125	—	142	2	no	—
711	#125	—	142	2	no	—
712	#125	D₂₈₄	1	1	yes	characteristic
713	#124	—	71	2	no	—
714	#124	—	71	2	no	—
715	#124	—	142	2	no	—
716	#124	—	142	2	no	—
717	#124	D₂₈₄	1	1	yes	characteristic
718	#123	—	142	2	no	—
719	#123	—	142	2	no	—
720	#123	—	142	2	no	—
721	#123	—	142	2	no	—
722	#123	—	142	2	no	—
723	#123	—	142	2	no	—
724	#123	—	142	2	no	—
725	#123	—	142	2	no	—
726	#123	D₂₈₄	1	1	yes	characteristic
727	#123	D₂₈₄	1	1	yes	characteristic
728	C₂²⋊Q₈	—	71	2	no	—
729	C₂²⋊Q₈	—	71	2	no	—
730	C₂²⋊Q₈	—	71	2	no	—
731	C₂²⋊Q₈	—	71	2	no	—
732	C₂²⋊Q₈	—	142	2	no	—
733	C₂²⋊Q₈	—	142	2	no	—
734	C₂²⋊Q₈	—	142	2	no	—
735	C₂²⋊Q₈	—	142	2	no	—
736	C₂²⋊Q₈	—	142	2	no	—
737	C₂²⋊Q₈	D₂₈₄	1	1	yes	characteristic
738	#121	—	71	2	no	—
739	#121	—	71	2	no	—
740	#121	—	142	2	no	—
741	#121	—	142	2	no	—
742	#121	—	142	2	no	—
743	#121	—	142	2	no	—
744	#121	D₂₈₄	1	1	yes	characteristic
745	#120	—	142	2	no	—
746	#120	—	142	2	no	—
747	C₄×Q₈	—	71	2	no	—
748	C₄×Q₈	—	71	2	no	—
749	C₄×Q₈	—	71	2	no	—
750	C₄×Q₈	—	71	2	no	—
751	C₄×Q₈	—	142	2	no	—
752	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
753	C₄×D₄	—	71	2	no	—
754	C₄×D₄	—	71	2	no	—
755	C₄×D₄	—	71	2	no	—
756	C₄×D₄	—	71	2	no	—
757	C₄×D₄	—	71	2	no	—
758	C₄×D₄	—	71	2	no	—
759	C₄×D₄	—	142	2	no	—
760	C₄×D₄	—	142	2	no	—
761	C₄×D₄	—	142	2	no	—
762	C₄×D₄	—	142	2	no	—
763	C₄×D₄	—	142	2	no	—
764	C₄×D₄	—	142	2	no	—
765	C₄×D₄	—	142	2	no	—
766	C₄×D₄	—	142	2	no	—
767	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
768	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
769	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
770	#117	—	71	2	no	—
771	#117	—	71	2	no	—
772	#117	—	142	2	no	—
773	#117	—	142	2	no	—
774	#117	—	142	2	no	—
775	#117	—	142	2	no	—
776	#117	—	142	2	no	—
777	#117	C₂²×D₇₁	1	1	yes	characteristic
778	#117	C₂²×D₇₁	1	1	yes	characteristic
779	C₂×C₄⋊C₄	—	71	2	no	—
780	C₂×C₄⋊C₄	—	142	2	no	—
781	C₂×C₄⋊C₄	—	142	2	no	—
782	C₂×C₄⋊C₄	—	142	2	no	—
783	C₂×C₂²⋊C₄	—	142	2	no	—
784	C₂×C₂²⋊C₄	—	142	2	no	—
785	C₂×C₂²⋊C₄	—	142	2	no	—
786	C₂×C₂²⋊C₄	—	142	2	no	—
787	C₂×C₄²	—	142	2	no	—
788	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
789	#107	—	71	1	no	—
790	#107	—	71	1	no	—
791	#107	—	71	2	no	—
792	#107	—	71	1	no	—
793	#107	—	71	1	no	—
794	#107	—	71	2	no	—
795	#106	—	71	2	no	—
796	#106	—	71	2	no	—
797	#106	—	71	2	no	—
798	#106	—	71	2	no	—
799	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
800	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
801	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
802	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
803	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
804	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
805	#103	—	71	2	no	—
806	#103	—	71	2	no	—
807	#103	—	71	2	no	—
808	#103	—	71	2	no	—
809	#103	—	71	2	no	—
810	#103	—	71	2	no	—
811	#103	—	71	2	no	—
812	#103	—	71	2	no	—
813	#102	—	71	2	no	—
814	#102	—	71	2	no	—
815	#102	—	71	2	no	—
816	#102	—	71	2	no	—
817	#102	—	71	2	no	—
818	#102	—	71	2	no	—
819	#102	—	71	2	no	—
820	#102	—	71	2	no	—
821	C₂²⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
822	C₂²⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
823	C₂²⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
824	C₂²⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
825	C₂²⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
826	C₂²⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
827	#97	C₂²×D₇₁	1	1	yes	characteristic
828	#97	C₂²×D₇₁	1	1	yes	characteristic
829	#97	C₂²×D₇₁	1	1	yes	characteristic
830	#97	C₂²×D₇₁	1	1	yes	characteristic
831	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
832	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
833	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
834	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
835	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
836	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
837	C₂⁴	—	142	2	no	—
838	#41	—	284	2	no	—
839	#41	—	284	2	no	—
840	#41	—	142	4	no	—
841	#41	—	142	4	no	—
842	C₂×Q₈	—	71	2	no	—
843	C₂×Q₈	—	71	2	no	—
844	C₂×Q₈	—	142	2	no	—
845	C₂×Q₈	C₂×D₂₈₄	1	1	yes	characteristic
846	C₂×D₄	—	284	2	no	—
847	C₂×D₄	—	71	2	no	—
848	C₂×D₄	—	71	2	no	—
849	C₂×D₄	—	142	4	no	—
850	C₂×D₄	—	142	2	no	—
851	C₂×D₄	—	142	2	no	—
852	C₂×D₄	—	142	2	no	—
853	C₂×D₄	—	142	2	no	—
854	C₂×D₄	—	142	2	no	—
855	C₂×D₄	C₂×D₂₈₄	1	1	yes	characteristic
856	C₂×D₄	C₂×D₂₈₄	1	1	yes	characteristic
857	C₂×D₄	C₂×D₂₈₄	1	1	yes	characteristic
858	C₂²×C₄	—	142	2	no	—
859	C₂²×C₄	—	142	2	no	—
860	C₂²×C₄	—	142	2	no	—
861	C₂²×C₄	—	142	2	no	—
862	C₂²×C₄	—	142	2	no	—
863	C₂²×C₄	—	142	2	no	—
864	C₂²×C₄	—	142	2	no	—
865	C₂²×C₄	—	142	2	no	—
866	C₂²×C₄	—	142	2	no	—
867	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
869	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
870	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
871	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
872	Q₁₆	—	284	2	no	—
873	Q₁₆	—	142	2	no	—
874	Q₁₆	—	142	2	no	—
875	SD₁₆	—	284	2	no	—
876	SD₁₆	—	284	2	no	—
877	SD₁₆	—	142	4	no	—
878	SD₁₆	—	142	4	no	—
879	D₈	—	71	4	no	—
880	D₈	—	142	4	no	—
881	D₈	—	142	2	no	—
882	M₁₆	—	4	1	no	—
883	M₁₆	—	4	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	4	1	no	—
888	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
892	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
896	C₄⋊C₄	—	71	2	no	—
897	C₄⋊C₄	—	71	2	no	—
898	C₄⋊C₄	—	71	2	no	—
899	C₄⋊C₄	—	71	2	no	—
900	C₄⋊C₄	—	142	2	no	—
901	C₄⋊C₄	—	142	2	no	—
902	C₄⋊C₄	—	142	2	no	—
903	C₄⋊C₄	—	142	2	no	—
904	C₄⋊C₄	—	142	2	no	—
905	C₄⋊C₄	—	142	2	no	—
906	C₄⋊C₄	—	142	2	no	—
907	C₄⋊C₄	—	142	2	no	—
908	C₄⋊C₄	—	142	2	no	—
909	C₄⋊C₄	—	142	2	no	—
910	C₄⋊C₄	—	142	2	no	—
911	C₄⋊C₄	—	142	2	no	—
912	C₄⋊C₄	—	142	2	no	—
913	C₄⋊C₄	—	142	2	no	—
914	C₄⋊C₄	—	142	2	no	—
915	C₄⋊C₄	—	142	2	no	—
916	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
921	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
922	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
925	C₄⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
926	C₂²⋊C₄	—	142	2	no	—
927	C₂²⋊C₄	—	142	2	no	—
928	C₂²⋊C₄	—	142	2	no	—
929	C₂²⋊C₄	—	142	2	no	—
930	C₂²⋊C₄	—	142	2	no	—
931	C₂²⋊C₄	—	142	2	no	—
932	C₂²⋊C₄	—	142	2	no	—
933	C₂²⋊C₄	—	142	2	no	—
934	C₂²⋊C₄	—	142	2	no	—
935	C₂²⋊C₄	—	142	2	no	—
936	C₂²⋊C₄	—	142	2	no	—
937	C₂²⋊C₄	—	142	2	no	—
938	C₂²⋊C₄	—	142	2	no	—
939	C₂²⋊C₄	—	142	2	no	—
940	C₂²⋊C₄	—	142	2	no	—
941	C₂²⋊C₄	—	142	2	no	—
942	C₂²⋊C₄	—	142	2	no	—
943	C₂²⋊C₄	—	142	2	no	—
944	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
945	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
946	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
947	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
948	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
949	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
950	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
951	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
952	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
953	C₂²⋊C₄	C₂×D₂₈₄	1	1	yes	characteristic
954	C₄²	—	142	2	no	—
955	C₄²	—	142	2	no	—
956	C₄²	—	142	2	no	—
957	C₄²	—	142	2	no	—
958	C₄²	—	142	2	no	—
959	C₄²	—	142	2	no	—
960	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
961	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
962	C₄²	C₂³×D₇₁	1	1	yes	characteristic
963	C₄²	C₂³×D₇₁	1	1	yes	characteristic
964	C₄²	C₂³×D₇₁	1	1	yes	characteristic
965	C₄²	C₂³×D₇₁	1	1	yes	characteristic
966	C₂³	—	284	4	no	—
967	C₂³	—	568	2	no	—
968	C₂³	—	568	2	no	—
969	C₂³	—	142	2	no	—
970	C₂³	—	142	2	no	—
971	C₂³	C₂²×D₂₈₄	1	1	yes	characteristic
972	C₂³	C₂²×D₂₈₄	1	1	yes	characteristic
973	C₂³	C₂²×D₂₈₄	1	1	yes	characteristic
974	Q₈	—	4	1	no	—
975	Q₈	—	568	2	no	—
976	Q₈	—	142	2	no	—
977	Q₈	—	142	2	no	—
978	Q₈	—	142	2	no	—
979	Q₈	—	142	2	no	—
980	D₄	—	4	1	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	1	no	—
983	D₄	—	284	4	no	—
984	D₄	—	284	4	no	—
985	D₄	—	284	4	no	—
986	D₄	—	568	2	no	—
987	D₄	—	568	2	no	—
988	D₄	—	71	4	no	—
989	D₄	—	142	2	no	—
990	D₄	—	142	2	no	—
991	D₄	—	142	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	1	no	—
1000	C₂×C₄	—	284	4	no	—
1001	C₂×C₄	—	284	4	no	—
1002	C₂×C₄	—	568	2	no	—
1003	C₂×C₄	—	568	2	no	—
1004	C₂×C₄	—	568	2	no	—
1005	C₂×C₄	—	568	2	no	—
1006	C₂×C₄	—	568	2	no	—
1007	C₂×C₄	—	568	2	no	—
1008	C₂×C₄	—	568	2	no	—
1009	C₂×C₄	—	142	2	no	—
1010	C₂×C₄	—	142	2	no	—
1011	C₂×C₄	—	142	2	no	—
1012	C₂×C₄	—	142	2	no	—
1013	C₂×C₄	—	142	2	no	—
1014	C₂×C₄	—	142	2	no	—
1015	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
1026	C₂×C₄	C₂⁴×D₇₁	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	#41×D₇₁	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	284	2	no	—
1045	C₂²	—	284	2	no	—
1046	C₂²	—	284	2	no	—
1047	C₂²	—	284	2	no	—
1048	C₂²	—	284	2	no	—
1049	C₂²	—	1136	4	no	—
1050	C₂²	—	142	4	no	—
1051	C₂²	C₂³×D₂₈₄	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	284	2	no	—
1064	C₄	—	284	2	no	—
1065	C₄	—	284	2	no	—
1066	C₄	—	284	2	no	—
1067	C₄	—	284	2	no	—
1068	C₄	—	284	2	no	—
1069	C₄	C₂×#41×D₇₁	1	1	yes	characteristic
1070	C₄	#17986835	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	284	4	no	—
1075	C₂	—	568	2	no	—
1076	C₂	#41×D₂₈₄	1	1	yes	characteristic
1077	C₂	#22603114	1	1	yes	characteristic
1078	C₂	#22603114	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₂₈₄
commutator, cosocle	C₂×C₄×C₇₁	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₁
Fitting	C₇₁×#2966	C₂
socle	C₂²×C₇₁	C₂³×D₄
hypercenter	#2966	D₇₁
hypocenter	C₇₁	#61487
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #22602412	C₂	semidirect
2. #22601329	C₂	semidirect
3. #22601208	C₂	semidirect
4. #22601169	C₂	semidirect
5. #22600771	C₂	semidirect
6. #22600743	C₂	semidirect
7. #22600709	C₂	semidirect
8. #22600558	C₂	semidirect
9. #22600378	C₂	semidirect
10. #22600318	C₂	semidirect
11. #22600062	C₂	semidirect
12. #22600027	C₂	semidirect
13. #22600027	C₂	semidirect
14. #22598999	C₂	semidirect
15. #22598979	C₂	semidirect
16. #22598910	C₂	semidirect
17. #22598619	C₂	semidirect
18. #22598593	C₂	semidirect
19. #22598451	C₂	semidirect
20. #22597217	C₂	semidirect
21. #22597193	C₂	semidirect
22. C₄×#14556150	C₂	semidirect
23. C₇₁×#2966	C₂	semidirect
27. #17986722	C₂²	semidirect
29. #17986709	C₂²	semidirect
30. #17986695	C₂²	semidirect
36. #17986654	C₂²	semidirect
39. #17986620	C₂²	semidirect
43. #17986533	C₂²	semidirect
46. #17986479	C₂²	semidirect
48. C₄×#11765865	C₂²	semidirect
49. #17986404	C₂²	semidirect
50. #17986401	C₂²	semidirect
51. #17986401	C₂²	semidirect
54. #17986379	C₂²	semidirect
55. #17986368	C₂²	semidirect
56. #17986359	C₂²	semidirect
57. #17986354	C₂²	semidirect
60. #17986341	C₂²	semidirect
61. #17986330	C₂²	semidirect
62. #17986324	C₂²	semidirect
63. #17986318	C₂²	semidirect
64. #17986307	C₂²	semidirect
65. #17986300	C₂²	semidirect
66. #17986300	C₂²	semidirect
67. #17986300	C₂²	semidirect
68. #17986290	C₂²	semidirect
69. #17986285	C₂²	semidirect
71. #17986245	C₂²	semidirect
74. #17986240	C₂²	semidirect
75. #17986240	C₂²	semidirect
78. #17986228	C₂²	semidirect
79. #17986222	C₂²	semidirect
80. #17986222	C₂²	semidirect
83. #17986205	C₂²	semidirect
84. #17986205	C₂²	semidirect
85. #17986163	C₂²	semidirect
86. #17986163	C₂²	semidirect
93. #17986107	C₂²	semidirect
94. #17986101	C₂²	semidirect
95. #17986101	C₂²	semidirect
96. #17986101	C₂²	semidirect
97. C₄×Dic₂₈₄	C₂²	semidirect
98. C₄×Dic₂₈₄	C₂²	semidirect
99. C₄×Dic₂₈₄	C₂²	semidirect
100. C₄×Dic₂₈₄	C₂²	semidirect
101. C₄×#11765854	C₂²	semidirect
102. C₄×#11765854	C₂²	semidirect
103. C₄×#11765854	C₂²	semidirect
111. #17986037	C₂²	semidirect
112. C₂×#14556062	C₂²	semidirect
114. #17986001	C₂²	semidirect
115. #17985996	C₂²	semidirect
117. #446×C₇₁	C₂²	semidirect
118. C₈×Q₈×C₇₁	C₂²	semidirect
121. #435×C₇₁	C₂²	semidirect
124. C₈×D₄×C₇₁	C₂²	semidirect
126. #433×C₇₁	C₂²	semidirect
127. #432×C₇₁	C₂²	semidirect
129. #405×C₇₁	C₂²	semidirect
130. C₂×C₄×C₈×C₇₁	C₂²	semidirect
559. #2966	D₇₁	semidirect
563. C₇₁	#61487	semidirect
632. #446	C₂×D₇₁	semidirect
633. C₈×Q₈	C₂×D₇₁	semidirect
655. #435	C₂×D₇₁	semidirect
658. C₈×D₄	C₂×D₇₁	semidirect
660. #433	C₂×D₇₁	semidirect
661. #432	C₂×D₇₁	semidirect
669. #405	C₂×D₇₁	semidirect
670. C₂×C₄×C₈	C₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22602412	2
#22601329	2
#22601208	2
#22601169	2
#22600771	2
#22600743	2
#22600709	2
#22600558	2
#22600378	2
#22600318	2
#22600062	2
#22600027	2
#22598999	2
#22598979	2
#22598910	2
#22598619	2
#22598593	2
#22598451	2
#22597217	2
#22597193	2
C₄×#14556150	2
C₇₁×#2966	2
#61487	71