Subgroups — #22601892

Order 9088.

1132 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986716	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986711	C₂	1	1	yes	maximal, characteristic, complemented
3	#17986703	C₂	1	1	yes	maximal, characteristic, complemented
4	#17986700	C₂	1	1	yes	maximal, characteristic, complemented
5	#17986692	C₂	1	1	yes	maximal, characteristic, complemented
6	#17986686	C₂	1	1	yes	maximal, characteristic, complemented
7	#17986685	C₂	1	1	yes	maximal, characteristic, complemented
8	#17986681	C₂	1	1	yes	maximal, characteristic, complemented
9	#17986681	C₂	1	1	yes	maximal, characteristic, complemented
10	#17986679	C₂	1	1	yes	maximal, characteristic, complemented
11	#17986676	C₂	1	1	yes	maximal, characteristic, complemented
12	#17986674	C₂	1	1	yes	maximal, characteristic, complemented
13	#17986672	C₂	1	1	yes	maximal, characteristic, complemented
14	#17986647	C₂	1	1	yes	maximal, characteristic, complemented
15	#17986641	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986638	C₂	1	1	yes	maximal, characteristic, complemented
17	#17986553	C₂	1	1	yes	maximal, characteristic, complemented
18	#17986536	C₂	1	1	yes	maximal, characteristic, complemented
19	#17986529	C₂	1	1	yes	maximal, characteristic, complemented
20	#17986529	C₂	1	1	yes	maximal, characteristic, complemented
21	#17986527	C₂	1	1	yes	maximal, characteristic, complemented
22	#17986527	C₂	1	1	yes	maximal, characteristic, complemented
23	#17986508	C₂	1	1	yes	maximal, characteristic, complemented
24	#17986508	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#11765865	C₂	1	1	yes	maximal, characteristic, complemented
26	#17986467	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#11765864	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×D₄×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#14556085	C₂	1	1	yes	maximal, characteristic, complemented
30	#117×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
31	#529×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11765865	C₂²	1	1	yes	characteristic
33	C₂×#11765865	C₂²	1	1	yes	characteristic
34	C₂×#11765864	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₇₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄×D₇₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₇₁	C₂²	1	1	yes	characteristic
38	#14556127	C₂²	1	1	yes	characteristic, complemented
39	#14556126	C₂²	1	1	yes	characteristic, complemented
40	#14556123	C₂²	1	1	yes	characteristic, complemented
41	#14556123	C₂²	1	1	yes	characteristic, complemented
42	#14556123	C₂²	1	1	yes	characteristic, complemented
43	#14556123	C₂²	1	1	yes	characteristic, complemented
44	#14556123	C₂²	1	1	yes	characteristic, complemented
45	#14556123	C₂²	1	1	yes	characteristic, complemented
46	#14556121	C₂²	1	1	yes	characteristic, complemented
47	#14556121	C₂²	1	1	yes	characteristic, complemented
48	#14556121	C₂²	1	1	yes	characteristic, complemented
49	#14556121	C₂²	1	1	yes	characteristic, complemented
50	#14556119	C₂²	1	1	yes	characteristic, complemented
51	#14556118	C₂²	1	1	yes	characteristic, complemented
52	#14556118	C₂²	1	1	yes	characteristic, complemented
53	#14556118	C₂²	1	1	yes	characteristic, complemented
54	#14556118	C₂²	1	1	yes	characteristic, complemented
55	#14556118	C₂²	1	1	yes	characteristic, complemented
56	#14556118	C₂²	1	1	yes	characteristic, complemented
57	#14556117	C₂²	1	1	yes	characteristic, complemented
58	#14556114	C₂²	1	1	yes	characteristic
59	#14556114	C₂²	1	1	yes	characteristic
60	#14556114	C₂²	1	1	yes	characteristic, complemented
61	#14556114	C₂²	1	1	yes	characteristic, complemented
62	#14556113	C₂²	1	1	yes	characteristic
63	#14556113	C₂²	1	1	yes	characteristic
64	#14556113	C₂²	1	1	yes	characteristic
65	#14556113	C₂²	1	1	yes	characteristic
66	#14556113	C₂²	1	1	yes	characteristic, complemented
67	#14556113	C₂²	1	1	yes	characteristic, complemented
68	#14556112	C₂²	1	1	yes	characteristic, complemented
69	#14556112	C₂²	1	1	yes	characteristic, complemented
70	#14556110	C₂²	1	1	yes	characteristic
71	#14556110	C₂²	1	1	yes	characteristic
72	#14556110	C₂²	1	1	yes	characteristic, complemented
73	#14556110	C₂²	1	1	yes	characteristic, complemented
74	#14556109	C₂²	1	1	yes	characteristic
75	#14556109	C₂²	1	1	yes	characteristic, complemented
76	#14556108	C₂²	1	1	yes	characteristic
77	#14556106	C₂²	1	1	yes	characteristic
78	#14556106	C₂²	1	1	yes	characteristic
79	#14556106	C₂²	1	1	yes	characteristic, complemented
80	#14556106	C₂²	1	1	yes	characteristic, complemented
81	#14556106	C₂²	1	1	yes	characteristic, complemented
82	#14556106	C₂²	1	1	yes	characteristic, complemented
83	#14556105	C₂²	1	1	yes	characteristic, complemented
84	#14556105	C₂²	1	1	yes	characteristic, complemented
85	#14556105	C₂²	1	1	yes	characteristic, complemented
86	#14556105	C₂²	1	1	yes	characteristic, complemented
87	#14556104	C₂²	1	1	yes	characteristic
88	#14556104	C₂²	1	1	yes	characteristic, complemented
89	#14556103	C₂²	1	1	yes	characteristic
90	#14556101	C₂²	1	1	yes	characteristic
91	#14556101	C₂²	1	1	yes	characteristic
92	#14556101	C₂²	1	1	yes	characteristic, complemented
93	#14556101	C₂²	1	1	yes	characteristic, complemented
94	#14556100	C₂²	1	1	yes	characteristic
95	#14556100	C₂²	1	1	yes	characteristic
96	#14556100	C₂²	1	1	yes	characteristic, complemented
97	#14556100	C₂²	1	1	yes	characteristic, complemented
98	#14556098	C₂²	1	1	yes	characteristic
99	#14556098	C₂²	1	1	yes	characteristic
100	#14556096	C₂²	1	1	yes	characteristic
101	#14556096	C₂²	1	1	yes	characteristic
102	C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic, complemented
103	C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic, complemented
104	C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic, complemented
105	C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic, complemented
106	#14556093	C₂²	1	1	yes	characteristic, complemented
107	#14556093	C₂²	1	1	yes	characteristic, complemented
108	#14556093	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₂₈₄	C₂²	1	1	yes	characteristic
110	C₄×D₂₈₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×D₂₈₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₂₈₄	C₂²	1	1	yes	characteristic, complemented
113	D₄×Dic₇₁	C₂²	1	1	yes	characteristic
114	D₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
115	#14556090	C₂²	1	1	yes	characteristic
116	#14556090	C₂²	1	1	yes	characteristic
117	#14556090	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
125	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
126	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
127	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
128	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
129	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
130	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
131	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
132	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
133	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
134	#14556087	C₂²	1	1	yes	characteristic, complemented
135	#14556087	C₂²	1	1	yes	characteristic, complemented
136	#14556086	C₂²	1	1	yes	characteristic
137	#14556086	C₂²	1	1	yes	characteristic
138	#14556086	C₂²	1	1	yes	characteristic, complemented
139	#14556085	C₂²	1	1	yes	characteristic
140	#14556085	C₂²	1	1	yes	characteristic
141	#14556085	C₂²	1	1	yes	characteristic
142	#14556085	C₂²	1	1	yes	characteristic
143	#14556085	C₂²	1	1	yes	characteristic
144	#14556085	C₂²	1	1	yes	characteristic, complemented
145	#14556085	C₂²	1	1	yes	characteristic, complemented
146	#14556085	C₂²	1	1	yes	characteristic, complemented
147	#14556085	C₂²	1	1	yes	characteristic, complemented
148	#14556085	C₂²	1	1	yes	characteristic, complemented
149	#14556085	C₂²	1	1	yes	characteristic, complemented
150	#14556085	C₂²	1	1	yes	characteristic, complemented
151	#14556084	C₂²	1	1	yes	characteristic, complemented
152	#14556084	C₂²	1	1	yes	characteristic, complemented
153	#14556084	C₂²	1	1	yes	characteristic, complemented
154	#14556084	C₂²	1	1	yes	characteristic, complemented
155	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	C₄⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
158	C₄⋊C₄×D₇₁	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₇₁	C₂²	1	1	yes	characteristic, complemented
160	C₂×(C₂×D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
161	C₂×(C₂×D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×D₇₁	C₂²	1	1	yes	characteristic
166	C₂×C₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
168	C₄²×D₇₁	C₂²	1	1	yes	characteristic
169	C₄²×D₇₁	C₂²	1	1	yes	characteristic, complemented
170	C₄²×D₇₁	C₂²	1	1	yes	characteristic, complemented
171	C₄²×D₇₁	C₂²	1	1	yes	characteristic, complemented
172	#126×C₇₁	C₂²	1	1	yes	characteristic, complemented
173	#126×C₇₁	C₂²	1	1	yes	characteristic, complemented
174	#125×C₇₁	C₂²	1	1	yes	characteristic, complemented
175	#124×C₇₁	C₂²	1	1	yes	characteristic, complemented
176	#123×C₇₁	C₂²	1	1	yes	characteristic
177	#123×C₇₁	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
179	#121×C₇₁	C₂²	1	1	yes	characteristic
180	C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic, complemented
184	#117×C₇₁	C₂²	1	1	yes	characteristic, complemented
185	#117×C₇₁	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄²×C₇₁	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₇₁	C₂³	1	1	yes	characteristic
188	C₂³×D₇₁	C₂³	1	1	yes	characteristic
189	#11765865	—	2	4	no	—
190	#11765865	—	2	4	no	—
191	#11765864	—	2	4	no	—
192	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
193	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
194	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
195	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
196	C₂×D₂₈₄	C₂³	1	1	yes	characteristic
197	C₂×D₂₈₄	C₂³	1	1	yes	characteristic
198	C₂×D₂₈₄	C₂³	1	1	yes	characteristic
199	C₂×D₂₈₄	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
208	D₄×D₇₁	—	2	4	no	—
209	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
210	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
211	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
212	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
213	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
214	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₇₁	—	2	4	no	—
216	C₂×C₄×D₇₁	—	2	4	no	—
217	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₇₁	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	Dic₇₁⋊C₄	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	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₇₁	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	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇₁)⋊C₄	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	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
308	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
309	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
310	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
311	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
312	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₇₁	C₂³	1	1	yes	characteristic
314	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
317	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
321	C₂²×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	C₂²⋊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	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
342	C₄²×C₇₁	C₂³	1	1	yes	characteristic
343	C₄²×C₇₁	C₂³	1	1	yes	characteristic
344	C₄²×C₇₁	C₂³	1	1	yes	characteristic
345	C₄²×C₇₁	C₂³	1	1	yes	characteristic
346	C₄²×C₇₁	C₂³	1	1	yes	characteristic
347	C₄²×C₇₁	C₂³	1	1	yes	characteristic
348	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
349	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
350	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
351	C₂²×D₇₁	—	2	2	no	—
352	C₂²×D₇₁	—	2	2	no	—
353	C₂²×D₇₁	—	2	2	no	—
354	C₂²×D₇₁	—	2	2	no	—
355	C₂²×D₇₁	—	4	1	no	—
356	C₂²×D₇₁	—	4	1	no	—
357	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
358	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
359	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
360	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
361	Q₈×C₇₁	—	4	1	no	—
362	D₄×C₇₁	—	2	2	no	—
363	D₄×C₇₁	—	2	2	no	—
364	D₄×C₇₁	—	4	1	no	—
365	C₂×C₄×C₇₁	—	2	2	no	—
366	C₂×C₄×C₇₁	—	2	2	no	—
367	C₂×C₄×C₇₁	—	2	2	no	—
368	C₂×C₄×C₇₁	—	2	2	no	—
369	C₂×C₄×C₇₁	—	4	1	no	—
370	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
382	C₂²⋊D₇₁	—	2	2	no	—
383	C₂²⋊D₇₁	—	2	2	no	—
384	C₂²⋊D₇₁	—	2	2	no	—
385	C₂²⋊D₇₁	—	2	2	no	—
386	C₂²⋊D₇₁	—	2	2	no	—
387	C₂²⋊D₇₁	—	4	1	no	—
388	C₂²⋊D₇₁	—	4	1	no	—
389	C₂²⋊D₇₁	#41	1	4	yes	complemented
390	C₂×Dic₇₁	—	2	2	no	—
391	C₂×Dic₇₁	—	2	2	no	—
392	C₂×Dic₇₁	—	2	2	no	—
393	C₂×Dic₇₁	—	2	2	no	—
394	C₂×Dic₇₁	—	4	1	no	—
395	C₂×Dic₇₁	—	4	1	no	—
396	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
408	D₂₈₄	—	2	2	no	—
409	D₂₈₄	—	2	2	no	—
410	D₂₈₄	—	2	2	no	—
411	D₂₈₄	—	4	1	no	—
412	C₄×D₇₁	—	2	2	no	—
413	C₄×D₇₁	—	2	2	no	—
414	C₄×D₇₁	—	2	2	no	—
415	C₄×D₇₁	—	2	2	no	—
416	C₄×D₇₁	—	2	2	no	—
417	C₄×D₇₁	—	2	2	no	—
418	C₄×D₇₁	—	2	2	no	—
419	C₄×D₇₁	—	2	2	no	—
420	C₄×D₇₁	—	2	2	no	—
421	C₄×D₇₁	—	2	2	no	—
422	C₄×D₇₁	—	2	2	no	—
423	C₄×D₇₁	—	4	1	no	—
424	C₄×D₇₁	—	4	1	no	—
425	C₄×D₇₁	—	4	1	no	—
426	C₄×D₇₁	—	4	1	no	—
427	C₄×D₇₁	#41	1	4	yes	complemented
428	Dic₁₄₂	—	2	2	no	—
429	Dic₁₄₂	—	2	2	no	—
430	Dic₁₄₂	—	2	2	no	—
431	Dic₁₄₂	—	4	1	no	—
432	C₂²×C₇₁	—	2	1	no	—
433	C₂²×C₇₁	—	2	1	no	—
434	C₂²×C₇₁	—	2	1	no	—
435	C₂²×C₇₁	—	2	1	no	—
436	C₂²×C₇₁	—	2	1	no	—
437	C₂²×C₇₁	—	2	1	no	—
438	C₂²×C₇₁	—	2	1	no	—
439	C₂²×C₇₁	—	2	1	no	—
440	C₂²×C₇₁	C₂×#41	1	2	yes	—
441	C₂²×C₇₁	C₂⁵	1	1	yes	characteristic
442	C₂×D₇₁	—	2	1	no	—
443	C₂×D₇₁	—	2	1	no	—
444	C₂×D₇₁	—	2	1	no	—
445	C₂×D₇₁	—	2	1	no	—
446	C₂×D₇₁	—	2	1	no	—
447	C₂×D₇₁	—	2	1	no	—
448	C₂×D₇₁	—	2	1	no	—
449	C₂×D₇₁	—	2	1	no	—
450	C₂×D₇₁	—	2	1	no	—
451	C₂×D₇₁	—	2	1	no	—
452	C₂×D₇₁	—	4	4	no	—
453	C₂×D₇₁	—	4	4	no	—
454	C₂×D₇₁	C₂×#41	1	2	yes	—
455	C₂×D₇₁	C₂×#41	1	2	yes	—
456	C₄×C₇₁	—	2	1	no	—
457	C₄×C₇₁	—	2	1	no	—
458	C₄×C₇₁	—	2	1	no	—
459	C₄×C₇₁	—	2	1	no	—
460	C₄×C₇₁	—	2	1	no	—
461	C₄×C₇₁	—	2	1	no	—
462	C₄×C₇₁	—	2	1	no	—
463	C₄×C₇₁	—	2	1	no	—
464	C₄×C₇₁	—	2	1	no	—
465	C₄×C₇₁	—	2	1	no	—
466	C₄×C₇₁	—	2	1	no	—
467	C₄×C₇₁	C₂×#41	1	2	yes	—
468	Dic₇₁	—	2	1	no	—
469	Dic₇₁	—	2	1	no	—
470	Dic₇₁	—	2	1	no	—
471	Dic₇₁	—	2	1	no	—
472	Dic₇₁	—	2	1	no	—
473	Dic₇₁	—	2	1	no	—
474	Dic₇₁	—	2	1	no	—
475	Dic₇₁	—	2	1	no	—
476	Dic₇₁	—	2	1	no	—
477	Dic₇₁	—	2	1	no	—
478	Dic₇₁	C₂×#41	1	2	yes	—
479	Dic₇₁	C₂×#41	1	2	yes	—
480	C₂×C₇₁	—	2	2	no	—
481	C₂×C₇₁	—	4	1	no	—
482	C₂×C₇₁	—	4	1	no	—
483	C₂×C₇₁	C₂²×#41	1	1	yes	characteristic
484	C₂×C₇₁	C₂²×#41	1	1	yes	characteristic
485	C₂×C₇₁	#585	1	1	yes	characteristic
486	D₇₁	—	2	2	no	—
487	D₇₁	—	2	2	no	—
488	D₇₁	—	4	1	no	—
489	D₇₁	—	4	1	no	—
490	#3475	—	71	1	no	maximal, Sylow
491	C₇₁	#3475	1	1	yes	characteristic, complemented, Sylow
492	#556	—	71	1	no	—
493	#555	—	71	1	no	—
494	#554	—	71	1	no	—
495	#553	—	71	1	no	—
496	#553	—	71	1	no	—
497	#552	—	71	1	no	—
498	#552	—	71	1	no	—
499	#552	—	71	1	no	—
500	#552	—	71	1	no	—
501	#551	—	71	1	no	—
502	#551	—	71	1	no	—
503	#551	—	71	1	no	—
504	#551	—	71	1	no	—
505	#547	—	71	1	no	—
506	#546	—	71	1	no	—
507	#546	—	71	1	no	—
508	#533	—	71	1	no	—
509	#529	—	71	1	no	—
510	#529	—	71	1	no	—
511	#529	—	71	1	no	—
512	#529	—	71	1	no	—
513	#529	—	71	1	no	—
514	#529	D₇₁	1	1	yes	characteristic, complemented
515	#525	—	71	1	no	—
516	#525	—	71	1	no	—
517	C₄×#41	—	71	1	no	—
518	C₄×#41	—	71	1	no	—
519	C₄×#41	—	71	1	no	—
520	C₂×C₄×D₄	—	71	1	no	—
521	C₂×#117	—	71	1	no	—
522	C₂×#117	—	71	1	no	—
523	C₂×#41	—	71	1	no	—
524	C₂×#41	—	71	1	no	—
525	C₂×#41	—	71	1	no	—
526	C₂²×D₄	—	71	1	no	—
527	C₂³×C₄	—	71	1	no	—
528	C₂³×C₄	—	71	1	no	—
529	C₄⋊Q₈	—	71	1	no	—
530	C₄⋊Q₈	—	71	1	no	—
531	#126	—	71	1	no	—
532	#126	—	71	1	no	—
533	#126	—	71	1	no	—
534	#126	—	71	1	no	—
535	#126	—	71	1	no	—
536	#126	—	71	1	no	—
537	#126	—	71	1	no	—
538	#126	—	71	1	no	—
539	#126	—	71	1	no	—
540	#126	—	71	1	no	—
541	#126	C₂×D₇₁	1	1	yes	characteristic, complemented
542	#126	C₂×D₇₁	1	1	yes	characteristic, complemented
543	#125	—	71	1	no	—
544	#125	—	71	1	no	—
545	#125	—	71	1	no	—
546	#125	—	71	1	no	—
547	#125	—	71	1	no	—
548	#125	—	71	1	no	—
549	#125	—	71	1	no	—
550	#125	C₂×D₇₁	1	1	yes	characteristic, complemented
551	#124	—	71	1	no	—
552	#124	—	71	1	no	—
553	#124	—	71	1	no	—
554	#124	—	71	1	no	—
555	#124	—	71	1	no	—
556	#124	C₂×D₇₁	1	1	yes	characteristic, complemented
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	#123	—	71	1	no	—
568	#123	—	71	1	no	—
569	#123	—	71	1	no	—
570	#123	—	71	1	no	—
571	#123	C₂×D₇₁	1	1	yes	characteristic
572	#123	C₂×D₇₁	1	1	yes	characteristic, complemented
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	C₂×D₇₁	1	1	yes	characteristic, complemented
587	#121	—	71	1	no	—
588	#121	—	71	1	no	—
589	#121	—	71	1	no	—
590	#121	—	71	1	no	—
591	#121	—	71	1	no	—
592	#121	—	71	1	no	—
593	#121	—	71	1	no	—
594	#121	—	71	1	no	—
595	#121	—	71	1	no	—
596	#121	C₂×D₇₁	1	1	yes	characteristic
597	#120	—	71	1	no	—
598	#120	—	71	1	no	—
599	#120	—	71	1	no	—
600	#120	—	71	1	no	—
601	C₄×Q₈	—	71	1	no	—
602	C₄×Q₈	—	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, complemented
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	—	71	1	no	—
625	C₄×D₄	—	71	1	no	—
626	C₄×D₄	—	71	1	no	—
627	C₄×D₄	—	71	1	no	—
628	C₄×D₄	—	71	1	no	—
629	C₄×D₄	—	71	1	no	—
630	C₄×D₄	—	71	1	no	—
631	C₄×D₄	—	71	1	no	—
632	C₄×D₄	—	71	1	no	—
633	C₄×D₄	—	71	1	no	—
634	C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
635	C₄×D₄	C₂×D₇₁	1	1	yes	characteristic, complemented
636	C₄×D₄	C₂×D₇₁	1	1	yes	characteristic, complemented
637	#117	—	71	1	no	—
638	#117	—	71	1	no	—
639	#117	—	71	1	no	—
640	#117	—	71	1	no	—
641	#117	—	71	1	no	—
642	#117	—	71	1	no	—
643	#117	—	71	1	no	—
644	#117	—	71	1	no	—
645	#117	—	71	1	no	—
646	#117	—	71	1	no	—
647	#117	—	71	1	no	—
648	#117	—	71	1	no	—
649	#117	—	71	1	no	—
650	#117	—	71	1	no	—
651	#117	—	71	1	no	—
652	#117	—	71	1	no	—
653	#117	—	71	1	no	—
654	#117	—	71	1	no	—
655	#117	—	71	1	no	—
656	#117	—	71	1	no	—
657	#117	—	71	1	no	—
658	#117	C₂×D₇₁	1	1	yes	characteristic, complemented
659	#117	C₂×D₇₁	1	1	yes	characteristic, complemented
660	C₂×C₄⋊C₄	—	71	1	no	—
661	C₂×C₄⋊C₄	—	71	1	no	—
662	C₂×C₄⋊C₄	—	71	1	no	—
663	C₂×C₄⋊C₄	—	71	1	no	—
664	C₂×C₄⋊C₄	—	71	1	no	—
665	C₂×C₂²⋊C₄	—	71	1	no	—
666	C₂×C₂²⋊C₄	—	71	1	no	—
667	C₂×C₂²⋊C₄	—	71	1	no	—
668	C₂×C₂²⋊C₄	—	71	1	no	—
669	C₂×C₂²⋊C₄	—	71	1	no	—
670	C₂×C₂²⋊C₄	—	71	1	no	—
671	C₂×C₄²	—	71	1	no	—
672	C₂×C₄²	—	71	1	no	—
673	C₂×C₄²	—	71	1	no	—
674	C₂×C₄²	—	71	1	no	—
675	C₂×C₄²	—	71	1	no	—
676	C₂×C₄²	—	71	1	no	—
677	C₂×C₄²	C₂×D₇₁	1	1	yes	characteristic, complemented
678	C₂⁴	—	71	1	no	—
679	C₂⁴	—	71	1	no	—
680	#41	—	142	4	no	—
681	#41	—	142	4	no	—
682	#41	—	142	4	no	—
683	C₂×Q₈	—	71	1	no	—
684	C₂×Q₈	—	71	1	no	—
685	C₂×Q₈	—	71	1	no	—
686	C₂×Q₈	—	71	1	no	—
687	C₂×Q₈	C₂²×D₇₁	1	1	yes	characteristic
688	C₂×D₄	—	71	1	no	—
689	C₂×D₄	—	71	1	no	—
690	C₂×D₄	—	71	1	no	—
691	C₂×D₄	—	71	1	no	—
692	C₂×D₄	—	71	1	no	—
693	C₂×D₄	—	71	1	no	—
694	C₂×D₄	—	71	1	no	—
695	C₂×D₄	—	71	1	no	—
696	C₂×D₄	—	71	1	no	—
697	C₂×D₄	—	71	1	no	—
698	C₂×D₄	—	71	1	no	—
699	C₂×D₄	—	71	1	no	—
700	C₂×D₄	—	142	4	no	—
701	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
702	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
703	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
704	C₂²×C₄	—	71	1	no	—
705	C₂²×C₄	—	71	1	no	—
706	C₂²×C₄	—	71	1	no	—
707	C₂²×C₄	—	71	1	no	—
708	C₂²×C₄	—	71	1	no	—
709	C₂²×C₄	—	71	1	no	—
710	C₂²×C₄	—	71	1	no	—
711	C₂²×C₄	—	71	1	no	—
712	C₂²×C₄	—	71	1	no	—
713	C₂²×C₄	—	71	1	no	—
714	C₂²×C₄	—	71	1	no	—
715	C₂²×C₄	—	71	1	no	—
716	C₂²×C₄	—	71	1	no	—
717	C₂²×C₄	—	71	1	no	—
718	C₂²×C₄	—	71	1	no	—
719	C₂²×C₄	—	71	1	no	—
720	C₂²×C₄	—	71	1	no	—
721	C₂²×C₄	—	71	1	no	—
722	C₂²×C₄	—	71	1	no	—
723	C₂²×C₄	—	71	1	no	—
724	C₂²×C₄	—	71	1	no	—
725	C₂²×C₄	—	71	1	no	—
726	C₂²×C₄	—	142	4	no	—
727	C₂²×C₄	—	142	4	no	—
728	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
733	C₄⋊C₄	—	71	1	no	—
734	C₄⋊C₄	—	71	1	no	—
735	C₄⋊C₄	—	71	1	no	—
736	C₄⋊C₄	—	71	1	no	—
737	C₄⋊C₄	—	71	1	no	—
738	C₄⋊C₄	—	71	1	no	—
739	C₄⋊C₄	—	71	1	no	—
740	C₄⋊C₄	—	71	1	no	—
741	C₄⋊C₄	—	71	1	no	—
742	C₄⋊C₄	—	71	1	no	—
743	C₄⋊C₄	—	71	1	no	—
744	C₄⋊C₄	—	71	1	no	—
745	C₄⋊C₄	—	71	1	no	—
746	C₄⋊C₄	—	71	1	no	—
747	C₄⋊C₄	—	71	1	no	—
748	C₄⋊C₄	—	71	1	no	—
749	C₄⋊C₄	—	71	1	no	—
750	C₄⋊C₄	—	71	1	no	—
751	C₄⋊C₄	—	71	1	no	—
752	C₄⋊C₄	—	71	1	no	—
753	C₄⋊C₄	—	71	1	no	—
754	C₄⋊C₄	—	71	1	no	—
755	C₄⋊C₄	—	71	1	no	—
756	C₄⋊C₄	—	71	1	no	—
757	C₄⋊C₄	—	71	1	no	—
758	C₄⋊C₄	—	71	1	no	—
759	C₄⋊C₄	—	71	1	no	—
760	C₄⋊C₄	—	71	1	no	—
761	C₄⋊C₄	—	71	1	no	—
762	C₄⋊C₄	—	71	1	no	—
763	C₄⋊C₄	—	71	1	no	—
764	C₄⋊C₄	—	71	1	no	—
765	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
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	—	71	1	no	—
780	C₂²⋊C₄	—	71	1	no	—
781	C₂²⋊C₄	—	71	1	no	—
782	C₂²⋊C₄	—	71	1	no	—
783	C₂²⋊C₄	—	71	1	no	—
784	C₂²⋊C₄	—	71	1	no	—
785	C₂²⋊C₄	—	71	1	no	—
786	C₂²⋊C₄	—	71	1	no	—
787	C₂²⋊C₄	—	71	1	no	—
788	C₂²⋊C₄	—	71	1	no	—
789	C₂²⋊C₄	—	71	1	no	—
790	C₂²⋊C₄	—	71	1	no	—
791	C₂²⋊C₄	—	71	1	no	—
792	C₂²⋊C₄	—	71	1	no	—
793	C₂²⋊C₄	—	71	1	no	—
794	C₂²⋊C₄	—	71	1	no	—
795	C₂²⋊C₄	—	71	1	no	—
796	C₂²⋊C₄	—	71	1	no	—
797	C₂²⋊C₄	—	71	1	no	—
798	C₂²⋊C₄	—	71	1	no	—
799	C₂²⋊C₄	—	71	1	no	—
800	C₂²⋊C₄	—	71	1	no	—
801	C₂²⋊C₄	—	71	1	no	—
802	C₂²⋊C₄	—	71	1	no	—
803	C₂²⋊C₄	—	71	1	no	—
804	C₂²⋊C₄	—	71	1	no	—
805	C₂²⋊C₄	—	71	1	no	—
806	C₂²⋊C₄	—	71	1	no	—
807	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
814	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
815	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
817	C₄²	—	71	1	no	—
818	C₄²	—	71	1	no	—
819	C₄²	—	71	1	no	—
820	C₄²	—	71	1	no	—
821	C₄²	—	71	1	no	—
822	C₄²	—	71	1	no	—
823	C₄²	—	71	1	no	—
824	C₄²	—	71	1	no	—
825	C₄²	—	71	1	no	—
826	C₄²	—	71	1	no	—
827	C₄²	—	71	1	no	—
828	C₄²	—	71	1	no	—
829	C₄²	—	71	1	no	—
830	C₄²	—	71	1	no	—
831	C₄²	—	71	1	no	—
832	C₄²	—	71	1	no	—
833	C₄²	C₂²×D₇₁	1	1	yes	characteristic
834	C₄²	C₂²×D₇₁	1	1	yes	characteristic
835	C₄²	C₂²×D₇₁	1	1	yes	characteristic
836	C₄²	C₂²×D₇₁	1	1	yes	characteristic
837	C₄²	C₂²×D₇₁	1	1	yes	characteristic
838	C₄²	C₂²×D₇₁	1	1	yes	characteristic
839	C₂³	—	284	1	no	—
840	C₂³	—	284	1	no	—
841	C₂³	—	71	1	no	—
842	C₂³	—	71	1	no	—
843	C₂³	—	71	1	no	—
844	C₂³	—	71	1	no	—
845	C₂³	—	142	2	no	—
846	C₂³	—	142	2	no	—
847	C₂³	—	142	2	no	—
848	C₂³	—	142	2	no	—
849	C₂³	C₂³×D₇₁	1	1	yes	characteristic
850	C₂³	C₂³×D₇₁	1	1	yes	characteristic
851	C₂³	C₂³×D₇₁	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	284	1	no	—
854	Q₈	—	142	2	no	—
855	Q₈	—	142	2	no	—
856	Q₈	—	142	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	4	1	no	—
860	D₄	—	284	1	no	—
861	D₄	—	284	1	no	—
862	D₄	—	284	1	no	—
863	D₄	—	71	4	no	—
864	D₄	—	142	2	no	—
865	D₄	—	142	2	no	—
866	D₄	—	142	2	no	—
867	D₄	—	142	2	no	—
868	D₄	—	142	2	no	—
869	D₄	—	142	2	no	—
870	D₄	—	142	2	no	—
871	D₄	—	142	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	284	1	no	—
878	C₂×C₄	—	284	1	no	—
879	C₂×C₄	—	284	1	no	—
880	C₂×C₄	—	284	1	no	—
881	C₂×C₄	—	284	1	no	—
882	C₂×C₄	—	284	1	no	—
883	C₂×C₄	—	71	1	no	—
884	C₂×C₄	—	71	1	no	—
885	C₂×C₄	—	71	4	no	—
886	C₂×C₄	—	71	1	no	—
887	C₂×C₄	—	71	1	no	—
888	C₂×C₄	—	71	1	no	—
889	C₂×C₄	—	71	1	no	—
890	C₂×C₄	—	71	1	no	—
891	C₂×C₄	—	71	1	no	—
892	C₂×C₄	—	71	1	no	—
893	C₂×C₄	—	71	1	no	—
894	C₂×C₄	—	71	1	no	—
895	C₂×C₄	—	71	1	no	—
896	C₂×C₄	—	142	2	no	—
897	C₂×C₄	—	142	2	no	—
898	C₂×C₄	—	142	2	no	—
899	C₂×C₄	—	142	2	no	—
900	C₂×C₄	—	142	2	no	—
901	C₂×C₄	—	142	2	no	—
902	C₂×C₄	—	142	2	no	—
903	C₂×C₄	—	142	2	no	—
904	C₂×C₄	—	142	2	no	—
905	C₂×C₄	—	142	2	no	—
906	C₂×C₄	—	142	2	no	—
907	C₂×C₄	—	142	2	no	—
908	C₂×C₄	—	142	2	no	—
909	C₂×C₄	—	142	2	no	—
910	C₂×C₄	—	142	2	no	—
911	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	284	4	no	—
932	C₂²	—	284	4	no	—
933	C₂²	—	71	2	no	—
934	C₂²	—	71	2	no	—
935	C₂²	—	142	1	no	—
936	C₂²	—	142	1	no	—
937	C₂²	—	142	1	no	—
938	C₂²	—	142	1	no	—
939	C₂²	—	142	1	no	—
940	C₂²	—	142	1	no	—
941	C₂²	—	142	1	no	—
942	C₂²	—	142	1	no	—
943	C₂²	—	142	1	no	—
944	C₂²	—	142	1	no	—
945	C₂²	#41×D₇₁	1	2	yes	—
946	C₂²	C₂⁴×D₇₁	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	71	2	no	—
959	C₄	—	71	2	no	—
960	C₄	—	142	1	no	—
961	C₄	—	142	1	no	—
962	C₄	—	142	1	no	—
963	C₄	—	142	1	no	—
964	C₄	—	142	1	no	—
965	C₄	—	142	1	no	—
966	C₄	—	142	1	no	—
967	C₄	—	142	1	no	—
968	C₄	—	142	1	no	—
969	C₄	—	142	1	no	—
970	C₄	#41×D₇₁	1	2	yes	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	284	1	no	—
975	C₂	—	284	1	no	—
976	C₂	—	142	2	no	—
977	C₂	—	142	2	no	—
978	C₂	C₂×#41×D₇₁	1	1	yes	characteristic
979	C₂	C₂×#41×D₇₁	1	1	yes	characteristic
980	C₂	#17986835	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂⁵
Frattini	C₂²	C₂⁴×D₇₁
Fitting	#529×C₇₁	C₂
hypercenter	#529	D₇₁
hypocenter	C₇₁	#3475
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #17986716	C₂	semidirect
2. #17986711	C₂	semidirect
3. #17986703	C₂	semidirect
4. #17986700	C₂	semidirect
5. #17986692	C₂	semidirect
6. #17986686	C₂	semidirect
7. #17986685	C₂	semidirect
8. #17986681	C₂	semidirect
9. #17986681	C₂	semidirect
10. #17986679	C₂	semidirect
11. #17986676	C₂	semidirect
12. #17986674	C₂	semidirect
13. #17986672	C₂	semidirect
14. #17986647	C₂	semidirect
15. #17986641	C₂	semidirect
16. #17986638	C₂	semidirect
17. #17986553	C₂	semidirect
18. #17986536	C₂	semidirect
19. #17986529	C₂	semidirect
20. #17986529	C₂	semidirect
21. #17986527	C₂	semidirect
22. #17986527	C₂	semidirect
23. #17986508	C₂	semidirect
24. #17986508	C₂	semidirect
25. C₄×#11765865	C₂	semidirect
26. #17986467	C₂	semidirect
27. C₄×#11765864	C₂	semidirect
28. C₄×D₄×D₇₁	C₂	semidirect
29. C₂×#14556085	C₂	semidirect
30. #117×D₇₁	C₂	semidirect
31. #529×C₇₁	C₂	semidirect
38. #14556127	C₂²	semidirect
39. #14556126	C₂²	semidirect
40. #14556123	C₂²	semidirect
41. #14556123	C₂²	semidirect
42. #14556123	C₂²	semidirect
43. #14556123	C₂²	semidirect
44. #14556123	C₂²	semidirect
45. #14556123	C₂²	semidirect
46. #14556121	C₂²	semidirect
47. #14556121	C₂²	semidirect
48. #14556121	C₂²	semidirect
49. #14556121	C₂²	semidirect
50. #14556119	C₂²	semidirect
51. #14556118	C₂²	semidirect
52. #14556118	C₂²	semidirect
53. #14556118	C₂²	semidirect
54. #14556118	C₂²	semidirect
55. #14556118	C₂²	semidirect
56. #14556118	C₂²	semidirect
57. #14556117	C₂²	semidirect
60. #14556114	C₂²	semidirect
61. #14556114	C₂²	semidirect
66. #14556113	C₂²	semidirect
67. #14556113	C₂²	semidirect
68. #14556112	C₂²	semidirect
69. #14556112	C₂²	semidirect
72. #14556110	C₂²	semidirect
73. #14556110	C₂²	semidirect
75. #14556109	C₂²	semidirect
79. #14556106	C₂²	semidirect
80. #14556106	C₂²	semidirect
81. #14556106	C₂²	semidirect
82. #14556106	C₂²	semidirect
83. #14556105	C₂²	semidirect
84. #14556105	C₂²	semidirect
85. #14556105	C₂²	semidirect
86. #14556105	C₂²	semidirect
88. #14556104	C₂²	semidirect
92. #14556101	C₂²	semidirect
93. #14556101	C₂²	semidirect
96. #14556100	C₂²	semidirect
97. #14556100	C₂²	semidirect
102. C₄×Dic₁₄₂	C₂²	semidirect
103. C₄×Dic₁₄₂	C₂²	semidirect
104. C₄×Dic₁₄₂	C₂²	semidirect
105. C₄×Dic₁₄₂	C₂²	semidirect
106. #14556093	C₂²	semidirect
107. #14556093	C₂²	semidirect
108. #14556093	C₂²	semidirect
110. C₄×D₂₈₄	C₂²	semidirect
111. C₄×D₂₈₄	C₂²	semidirect
112. C₄×D₂₈₄	C₂²	semidirect
114. D₄×Dic₇₁	C₂²	semidirect
121. C₄×C₂²⋊D₇₁	C₂²	semidirect
122. C₄×C₂²⋊D₇₁	C₂²	semidirect
123. C₄×C₂²⋊D₇₁	C₂²	semidirect
124. C₄×C₂²⋊D₇₁	C₂²	semidirect
125. C₄×C₂²⋊D₇₁	C₂²	semidirect
131. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
132. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
133. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
134. #14556087	C₂²	semidirect
135. #14556087	C₂²	semidirect
138. #14556086	C₂²	semidirect
144. #14556085	C₂²	semidirect
145. #14556085	C₂²	semidirect
146. #14556085	C₂²	semidirect
147. #14556085	C₂²	semidirect
148. #14556085	C₂²	semidirect
149. #14556085	C₂²	semidirect
150. #14556085	C₂²	semidirect
151. #14556084	C₂²	semidirect
152. #14556084	C₂²	semidirect
153. #14556084	C₂²	semidirect
154. #14556084	C₂²	semidirect
155. C₂×Dic₇₁⋊C₄	C₂²	semidirect
156. C₂×Dic₇₁⋊C₄	C₂²	semidirect
158. C₄⋊C₄×D₇₁	C₂²	semidirect
159. C₄⋊C₄×D₇₁	C₂²	semidirect
166. C₂×C₄×Dic₇₁	C₂²	semidirect
167. C₂×C₄×Dic₇₁	C₂²	semidirect
169. C₄²×D₇₁	C₂²	semidirect
170. C₄²×D₇₁	C₂²	semidirect
171. C₄²×D₇₁	C₂²	semidirect
172. #126×C₇₁	C₂²	semidirect
173. #126×C₇₁	C₂²	semidirect
174. #125×C₇₁	C₂²	semidirect
175. #124×C₇₁	C₂²	semidirect
177. #123×C₇₁	C₂²	semidirect
178. C₂²⋊Q₈×C₇₁	C₂²	semidirect
180. C₄×Q₈×C₇₁	C₂²	semidirect
182. C₄×D₄×C₇₁	C₂²	semidirect
183. C₄×D₄×C₇₁	C₂²	semidirect
184. #117×C₇₁	C₂²	semidirect
185. #117×C₇₁	C₂²	semidirect
186. C₂×C₄²×C₇₁	C₂²	semidirect
389. C₂²⋊D₇₁	#41	semidirect
427. C₄×D₇₁	#41	semidirect
491. C₇₁	#3475	semidirect
514. #529	D₇₁	semidirect
541. #126	C₂×D₇₁	semidirect
542. #126	C₂×D₇₁	semidirect
550. #125	C₂×D₇₁	semidirect
556. #124	C₂×D₇₁	semidirect
572. #123	C₂×D₇₁	semidirect
586. C₂²⋊Q₈	C₂×D₇₁	semidirect
608. C₄×Q₈	C₂×D₇₁	semidirect
635. C₄×D₄	C₂×D₇₁	semidirect
636. C₄×D₄	C₂×D₇₁	semidirect
658. #117	C₂×D₇₁	semidirect
659. #117	C₂×D₇₁	semidirect
677. C₂×C₄²	C₂×D₇₁	semidirect