Subgroups — #22602643

Order 9088.

1160 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	#17986744	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986743	C₂	1	1	yes	maximal, characteristic, complemented
3	#17986737	C₂	1	1	yes	maximal, characteristic, complemented
4	#17986736	C₂	1	1	yes	maximal, characteristic, complemented
5	#17986711	C₂	1	1	yes	maximal, characteristic, complemented
6	#17986692	C₂	1	1	yes	maximal, characteristic, complemented
7	#17986682	C₂	1	1	yes	maximal, characteristic, complemented
8	#17986680	C₂	1	1	yes	maximal, characteristic, complemented
9	#17986673	C₂	1	1	yes	maximal, characteristic, complemented
10	#17986669	C₂	1	1	yes	maximal, characteristic, complemented
11	#17986648	C₂	1	1	yes	maximal, characteristic, complemented
12	#17986638	C₂	1	1	yes	maximal, characteristic, complemented
13	#17986637	C₂	1	1	yes	maximal, characteristic, complemented
14	#17986636	C₂	1	1	yes	maximal, characteristic, complemented
15	#17986636	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986631	C₂	1	1	yes	maximal, characteristic, complemented
17	#17986613	C₂	1	1	yes	maximal, characteristic, complemented
18	#17986603	C₂	1	1	yes	maximal, characteristic, complemented
19	#17986599	C₂	1	1	yes	maximal, characteristic, complemented
20	#17986599	C₂	1	1	yes	maximal, characteristic, complemented
21	#17986586	C₂	1	1	yes	maximal, characteristic, complemented
22	#17986583	C₂	1	1	yes	maximal, characteristic, complemented
23	#17986576	C₂	1	1	yes	maximal, characteristic, complemented
24	#17986564	C₂	1	1	yes	maximal, characteristic, complemented
25	#17986562	C₂	1	1	yes	maximal, characteristic, complemented
26	#17986559	C₂	1	1	yes	maximal, characteristic, complemented
27	#17986558	C₂	1	1	yes	maximal, characteristic, complemented
28	#17986505	C₂	1	1	yes	maximal, characteristic, complemented
29	#17986505	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#14556100	C₂	1	1	yes	maximal, characteristic, complemented
31	#535×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11765864	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11765864	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11765864	C₂²	1	1	yes	characteristic, complemented
35	C₂×#11765864	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₇₁	C₂²	1	1	yes	characteristic
40	C₂×D₄×D₇₁	C₂²	1	1	yes	characteristic, complemented
41	C₂³×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
42	#14556126	C₂²	1	1	yes	characteristic, complemented
43	#14556124	C₂²	1	1	yes	characteristic, complemented
44	#14556124	C₂²	1	1	yes	characteristic, complemented
45	#14556124	C₂²	1	1	yes	characteristic, complemented
46	#14556123	C₂²	1	1	yes	characteristic, complemented
47	#14556123	C₂²	1	1	yes	characteristic, complemented
48	#14556122	C₂²	1	1	yes	characteristic, complemented
49	#14556122	C₂²	1	1	yes	characteristic, complemented
50	#14556121	C₂²	1	1	yes	characteristic, complemented
51	#14556121	C₂²	1	1	yes	characteristic, complemented
52	#14556120	C₂²	1	1	yes	characteristic, complemented
53	#14556118	C₂²	1	1	yes	characteristic, complemented
54	#14556118	C₂²	1	1	yes	characteristic, complemented
55	#14556117	C₂²	1	1	yes	characteristic, complemented
56	#14556116	C₂²	1	1	yes	characteristic, complemented
57	#14556115	C₂²	1	1	yes	characteristic, complemented
58	#14556114	C₂²	1	1	yes	characteristic, complemented
59	#14556114	C₂²	1	1	yes	characteristic, complemented
60	#14556114	C₂²	1	1	yes	characteristic, complemented
61	#14556114	C₂²	1	1	yes	characteristic, complemented
62	#14556113	C₂²	1	1	yes	characteristic, complemented
63	#14556113	C₂²	1	1	yes	characteristic, complemented
64	#14556112	C₂²	1	1	yes	characteristic
65	#14556112	C₂²	1	1	yes	characteristic, complemented
66	#14556112	C₂²	1	1	yes	characteristic, complemented
67	#14556112	C₂²	1	1	yes	characteristic, complemented
68	#14556111	C₂²	1	1	yes	characteristic
69	#14556111	C₂²	1	1	yes	characteristic, complemented
70	#14556111	C₂²	1	1	yes	characteristic, complemented
71	#14556111	C₂²	1	1	yes	characteristic, complemented
72	#14556110	C₂²	1	1	yes	characteristic, complemented
73	#14556110	C₂²	1	1	yes	characteristic, complemented
74	#14556110	C₂²	1	1	yes	characteristic, complemented
75	#14556110	C₂²	1	1	yes	characteristic, complemented
76	#14556109	C₂²	1	1	yes	characteristic, complemented
77	#14556109	C₂²	1	1	yes	characteristic, complemented
78	#14556109	C₂²	1	1	yes	characteristic, complemented
79	#14556109	C₂²	1	1	yes	characteristic, complemented
80	#14556109	C₂²	1	1	yes	characteristic, complemented
81	#14556109	C₂²	1	1	yes	characteristic, complemented
82	#14556109	C₂²	1	1	yes	characteristic, complemented
83	#14556109	C₂²	1	1	yes	characteristic, complemented
84	#14556107	C₂²	1	1	yes	characteristic, complemented
85	#14556106	C₂²	1	1	yes	characteristic, complemented
86	#14556106	C₂²	1	1	yes	characteristic, complemented
87	#14556105	C₂²	1	1	yes	characteristic, complemented
88	#14556105	C₂²	1	1	yes	characteristic, complemented
89	#14556105	C₂²	1	1	yes	characteristic, complemented
90	#14556105	C₂²	1	1	yes	characteristic, complemented
91	#14556105	C₂²	1	1	yes	characteristic, complemented
92	#14556105	C₂²	1	1	yes	characteristic, complemented
93	#14556104	C₂²	1	1	yes	characteristic, complemented
94	#14556104	C₂²	1	1	yes	characteristic, complemented
95	#14556102	C₂²	1	1	yes	characteristic, complemented
96	#14556101	C₂²	1	1	yes	characteristic, complemented
97	#14556101	C₂²	1	1	yes	characteristic, complemented
98	#14556101	C₂²	1	1	yes	characteristic, complemented
99	#14556101	C₂²	1	1	yes	characteristic, complemented
100	#14556101	C₂²	1	1	yes	characteristic, complemented
101	#14556101	C₂²	1	1	yes	characteristic, complemented
102	#14556100	C₂²	1	1	yes	characteristic
103	#14556100	C₂²	1	1	yes	characteristic
104	#14556100	C₂²	1	1	yes	characteristic
105	#14556100	C₂²	1	1	yes	characteristic
106	#14556100	C₂²	1	1	yes	characteristic, complemented
107	#14556100	C₂²	1	1	yes	characteristic, complemented
108	#14556100	C₂²	1	1	yes	characteristic, complemented
109	#14556100	C₂²	1	1	yes	characteristic, complemented
110	#14556100	C₂²	1	1	yes	characteristic, complemented
111	#14556100	C₂²	1	1	yes	characteristic, complemented
112	#14556100	C₂²	1	1	yes	characteristic, complemented
113	#14556100	C₂²	1	1	yes	characteristic, complemented
114	#14556100	C₂²	1	1	yes	characteristic, complemented
115	#14556100	C₂²	1	1	yes	characteristic, complemented
116	#14556100	C₂²	1	1	yes	characteristic, complemented
117	#14556100	C₂²	1	1	yes	characteristic, complemented
118	#14556100	C₂²	1	1	yes	characteristic, complemented
119	#14556100	C₂²	1	1	yes	characteristic, complemented
120	#14556100	C₂²	1	1	yes	characteristic, complemented
121	#14556100	C₂²	1	1	yes	characteristic, complemented
122	#14556100	C₂²	1	1	yes	characteristic, complemented
123	#14556100	C₂²	1	1	yes	characteristic, complemented
124	#14556100	C₂²	1	1	yes	characteristic, complemented
125	#14556100	C₂²	1	1	yes	characteristic, complemented
126	#14556099	C₂²	1	1	yes	characteristic, complemented
127	#14556099	C₂²	1	1	yes	characteristic, complemented
128	#14556099	C₂²	1	1	yes	characteristic, complemented
129	#14556099	C₂²	1	1	yes	characteristic, complemented
130	#14556098	C₂²	1	1	yes	characteristic
131	#14556098	C₂²	1	1	yes	characteristic, complemented
132	#14556097	C₂²	1	1	yes	characteristic
133	#14556097	C₂²	1	1	yes	characteristic, complemented
134	#14556096	C₂²	1	1	yes	characteristic, complemented
135	#14556096	C₂²	1	1	yes	characteristic, complemented
136	#14556096	C₂²	1	1	yes	characteristic, complemented
137	#14556096	C₂²	1	1	yes	characteristic, complemented
138	#14556096	C₂²	1	1	yes	characteristic, complemented
139	#14556096	C₂²	1	1	yes	characteristic, complemented
140	#14556096	C₂²	1	1	yes	characteristic, complemented
141	#14556096	C₂²	1	1	yes	characteristic, complemented
142	C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic, complemented
143	C₄×D₂₈₄	C₂²	1	1	yes	characteristic, complemented
144	D₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
145	D₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
146	D₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
147	D₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
148	D₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
149	D₄×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic
153	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	#14556085	C₂²	1	1	yes	characteristic, complemented
159	#14556085	C₂²	1	1	yes	characteristic, complemented
160	#14556084	C₂²	1	1	yes	characteristic, complemented
161	#14556084	C₂²	1	1	yes	characteristic, complemented
162	#14556084	C₂²	1	1	yes	characteristic, complemented
163	#14556084	C₂²	1	1	yes	characteristic, complemented
164	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₂×Dic₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	C₂×C₂²⋊Dic₇₁	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊Dic₇₁	C₂²	1	1	yes	characteristic, complemented
168	C₂×(C₂×D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	C₂×(C₂×D₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₇₁	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₇₁	C₂²	1	1	yes	characteristic, complemented
172	C₂×#41×C₇₁	C₂²	1	1	yes	characteristic, complemented
173	C₂²×D₄×C₇₁	C₂²	1	1	yes	characteristic, complemented
174	#127×C₇₁	C₂²	1	1	yes	characteristic, complemented
175	#127×C₇₁	C₂²	1	1	yes	characteristic, complemented
176	#124×C₇₁	C₂²	1	1	yes	characteristic, complemented
177	#124×C₇₁	C₂²	1	1	yes	characteristic, complemented
178	#121×C₇₁	C₂²	1	1	yes	characteristic, complemented
179	#121×C₇₁	C₂²	1	1	yes	characteristic, complemented
180	#121×C₇₁	C₂²	1	1	yes	characteristic, complemented
181	#121×C₇₁	C₂²	1	1	yes	characteristic, complemented
182	#120×C₇₁	C₂²	1	1	yes	characteristic
183	#120×C₇₁	C₂²	1	1	yes	characteristic, complemented
184	#120×C₇₁	C₂²	1	1	yes	characteristic, complemented
185	#120×C₇₁	C₂²	1	1	yes	characteristic, complemented
186	#117×C₇₁	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₇₁	C₂³	1	1	yes	characteristic
188	C₂³×D₇₁	C₂³	1	1	yes	characteristic
189	C₂³×D₇₁	C₂³	1	1	yes	characteristic
190	#11765864	—	4	2	no	—
191	#11765864	—	4	2	no	—
192	#11765864	—	4	2	no	—
193	#11765864	—	4	2	no	—
194	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
195	C₂×Dic₁₄₂	C₂³	1	1	yes	characteristic
196	C₂×Dic₁₄₂	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	—	4	2	no	—
201	C₂×C₂²⋊D₇₁	—	4	2	no	—
202	C₂×C₂²⋊D₇₁	—	4	2	no	—
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	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₇₁	C₂³	1	1	yes	characteristic
225	D₄×D₇₁	—	4	2	no	—
226	D₄×D₇₁	—	4	2	no	—
227	C₂²×Dic₇₁	—	4	2	no	—
228	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
229	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
230	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
231	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
232	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
233	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
234	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
235	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
236	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
237	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
238	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
239	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
240	C₂²×Dic₇₁	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₇₁	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
249	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
250	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
251	C₄⋊Dic₇₁	C₂³	1	1	yes	characteristic
252	C₄⋊Dic₇₁	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	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
268	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
269	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
270	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
271	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
272	Dic₇₁⋊C₄	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₇₁	C₂³	1	1	yes	characteristic
290	C₂²⋊Dic₇₁	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	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₇₁)⋊C₄	C₂³	1	1	yes	characteristic
311	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
312	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
313	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
314	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
315	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
316	C₄×Dic₇₁	C₂³	1	1	yes	characteristic
317	C₂⁴×C₇₁	C₂³	1	1	yes	characteristic
318	C₂⁴×C₇₁	C₂³	1	1	yes	characteristic
319	#41×C₇₁	—	4	2	no	—
320	C₂×Q₈×C₇₁	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₇₁	—	4	2	no	—
322	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
323	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
324	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
325	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
326	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
327	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
328	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
329	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
330	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
331	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
332	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
333	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
334	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
335	C₂×D₄×C₇₁	C₂³	1	1	yes	characteristic
336	C₂×D₄×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	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
341	C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
349	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
350	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
351	C₂²⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
352	C₄²×C₇₁	C₂³	1	1	yes	characteristic
353	C₄²×C₇₁	C₂³	1	1	yes	characteristic
354	C₂³×C₇₁	—	2	2	no	—
355	C₂³×C₇₁	—	2	2	no	—
356	C₂³×C₇₁	—	4	1	no	—
357	C₂³×C₇₁	—	4	1	no	—
358	C₂³×C₇₁	—	4	1	no	—
359	C₂³×C₇₁	—	4	1	no	—
360	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
361	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
362	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
363	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
364	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
365	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
366	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
367	C₂²×D₇₁	—	2	2	no	—
368	C₂²×D₇₁	—	4	1	no	—
369	C₂²×D₇₁	—	4	1	no	—
370	C₂²×D₇₁	—	4	1	no	—
371	C₂²×D₇₁	—	4	1	no	—
372	C₂²×D₇₁	—	4	1	no	—
373	C₂²×D₇₁	—	4	1	no	—
374	C₂²×D₇₁	—	4	1	no	—
375	C₂²×D₇₁	—	4	1	no	—
376	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
377	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
378	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
379	C₂²×D₇₁	C₂⁴	1	1	yes	characteristic
380	Q₈×C₇₁	—	4	1	no	—
381	D₄×C₇₁	—	2	2	no	—
382	D₄×C₇₁	—	2	2	no	—
383	D₄×C₇₁	—	4	1	no	—
384	D₄×C₇₁	—	4	1	no	—
385	D₄×C₇₁	—	4	1	no	—
386	D₄×C₇₁	—	4	1	no	—
387	D₄×C₇₁	—	4	1	no	—
388	D₄×C₇₁	—	4	1	no	—
389	D₄×C₇₁	—	4	1	no	—
390	D₄×C₇₁	—	4	1	no	—
391	D₄×C₇₁	—	4	1	no	—
392	D₄×C₇₁	—	4	1	no	—
393	D₄×C₇₁	—	4	1	no	—
394	D₄×C₇₁	—	4	1	no	—
395	D₄×C₇₁	—	4	1	no	—
396	C₂×C₄×C₇₁	—	2	2	no	—
397	C₂×C₄×C₇₁	—	4	1	no	—
398	C₂×C₄×C₇₁	—	4	1	no	—
399	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
407	C₂²⋊D₇₁	—	2	2	no	—
408	C₂²⋊D₇₁	—	2	2	no	—
409	C₂²⋊D₇₁	—	2	2	no	—
410	C₂²⋊D₇₁	—	2	2	no	—
411	C₂²⋊D₇₁	—	2	2	no	—
412	C₂²⋊D₇₁	—	4	1	no	—
413	C₂²⋊D₇₁	—	4	1	no	—
414	C₂²⋊D₇₁	—	4	1	no	—
415	C₂²⋊D₇₁	—	4	1	no	—
416	C₂²⋊D₇₁	—	4	1	no	—
417	C₂²⋊D₇₁	—	4	1	no	—
418	C₂²⋊D₇₁	—	4	1	no	—
419	C₂²⋊D₇₁	—	4	1	no	—
420	C₂²⋊D₇₁	—	4	1	no	—
421	C₂²⋊D₇₁	—	4	1	no	—
422	C₂²⋊D₇₁	—	4	1	no	—
423	C₂²⋊D₇₁	—	4	1	no	—
424	C₂²⋊D₇₁	—	4	1	no	—
425	C₂²⋊D₇₁	—	4	1	no	—
426	C₂²⋊D₇₁	—	4	1	no	—
427	C₂²⋊D₇₁	—	4	1	no	—
428	C₂²⋊D₇₁	—	4	1	no	—
429	C₂×Dic₇₁	—	2	2	no	—
430	C₂×Dic₇₁	—	2	2	no	—
431	C₂×Dic₇₁	—	2	2	no	—
432	C₂×Dic₇₁	—	2	2	no	—
433	C₂×Dic₇₁	—	2	2	no	—
434	C₂×Dic₇₁	—	4	1	no	—
435	C₂×Dic₇₁	—	4	1	no	—
436	C₂×Dic₇₁	—	4	1	no	—
437	C₂×Dic₇₁	—	4	1	no	—
438	C₂×Dic₇₁	—	4	1	no	—
439	C₂×Dic₇₁	—	4	1	no	—
440	C₂×Dic₇₁	—	4	1	no	—
441	C₂×Dic₇₁	—	4	1	no	—
442	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
445	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
446	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
448	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
449	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
450	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
451	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
452	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
453	C₂×Dic₇₁	C₂⁴	1	1	yes	characteristic
454	D₂₈₄	—	4	1	no	—
455	D₂₈₄	—	4	1	no	—
456	D₂₈₄	—	4	1	no	—
457	C₄×D₇₁	—	2	2	no	—
458	C₄×D₇₁	—	4	1	no	—
459	C₄×D₇₁	—	4	1	no	—
460	C₄×D₇₁	—	4	1	no	—
461	C₄×D₇₁	—	4	1	no	—
462	C₄×D₇₁	—	4	1	no	—
463	Dic₁₄₂	—	2	2	no	—
464	Dic₁₄₂	—	4	1	no	—
465	Dic₁₄₂	—	4	1	no	—
466	C₂²×C₇₁	—	2	1	no	—
467	C₂²×C₇₁	—	2	1	no	—
468	C₂²×C₇₁	—	2	1	no	—
469	C₂²×C₇₁	—	2	1	no	—
470	C₂²×C₇₁	—	2	1	no	—
471	C₂²×C₇₁	—	2	1	no	—
472	C₂²×C₇₁	—	2	1	no	—
473	C₂²×C₇₁	—	2	1	no	—
474	C₂²×C₇₁	—	2	1	no	—
475	C₂²×C₇₁	—	2	1	no	—
476	C₂²×C₇₁	—	2	1	no	—
477	C₂²×C₇₁	—	2	1	no	—
478	C₂²×C₇₁	—	2	1	no	—
479	C₂²×C₇₁	—	2	1	no	—
480	C₂²×C₇₁	—	2	1	no	—
481	C₂²×C₇₁	—	2	1	no	—
482	C₂²×C₇₁	—	2	1	no	—
483	C₂²×C₇₁	—	2	1	no	—
484	C₂²×C₇₁	—	2	1	no	—
485	C₂²×C₇₁	—	2	1	no	—
486	C₂²×C₇₁	—	4	4	no	—
487	C₂²×C₇₁	—	8	2	no	—
488	C₂²×C₇₁	H(5,𝔽₂)	1	2	yes	—
489	C₂²×C₇₁	C₂⁵	1	1	yes	characteristic
490	C₂×D₇₁	—	2	1	no	—
491	C₂×D₇₁	—	2	1	no	—
492	C₂×D₇₁	—	2	1	no	—
493	C₂×D₇₁	—	2	1	no	—
494	C₂×D₇₁	—	2	1	no	—
495	C₂×D₇₁	—	2	1	no	—
496	C₂×D₇₁	—	2	1	no	—
497	C₂×D₇₁	—	2	1	no	—
498	C₂×D₇₁	—	2	1	no	—
499	C₂×D₇₁	—	2	1	no	—
500	C₂×D₇₁	—	2	1	no	—
501	C₂×D₇₁	—	2	1	no	—
502	C₂×D₇₁	—	8	2	no	—
503	C₂×D₇₁	—	8	2	no	—
504	C₂×D₇₁	—	8	2	no	—
505	C₄×C₇₁	—	2	1	no	—
506	C₄×C₇₁	—	2	1	no	—
507	C₄×C₇₁	—	2	1	no	—
508	C₄×C₇₁	—	2	1	no	—
509	C₄×C₇₁	—	2	1	no	—
510	C₄×C₇₁	—	2	1	no	—
511	C₄×C₇₁	—	2	1	no	—
512	C₄×C₇₁	—	2	1	no	—
513	Dic₇₁	—	2	1	no	—
514	Dic₇₁	—	2	1	no	—
515	Dic₇₁	—	2	1	no	—
516	Dic₇₁	—	2	1	no	—
517	Dic₇₁	—	2	1	no	—
518	Dic₇₁	—	2	1	no	—
519	Dic₇₁	—	2	1	no	—
520	Dic₇₁	—	2	1	no	—
521	Dic₇₁	—	2	1	no	—
522	Dic₇₁	—	2	1	no	—
523	Dic₇₁	—	2	1	no	—
524	Dic₇₁	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₇₁	—	2	2	no	—
526	C₂×C₇₁	—	4	1	no	—
527	C₂×C₇₁	—	4	1	no	—
528	C₂×C₇₁	—	4	1	no	—
529	C₂×C₇₁	—	4	1	no	—
530	C₂×C₇₁	—	4	1	no	—
531	C₂×C₇₁	—	4	1	no	—
532	C₂×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂×C₇₁	#585	1	1	yes	characteristic
535	D₇₁	—	4	1	no	—
536	D₇₁	—	4	1	no	—
537	D₇₁	—	4	1	no	—
538	D₇₁	—	4	1	no	—
539	#3542	—	71	1	no	maximal, Sylow
540	C₇₁	#3542	1	1	yes	characteristic, complemented, Sylow
541	#562	—	71	1	no	—
542	#562	—	71	1	no	—
543	#560	—	71	1	no	—
544	#560	—	71	1	no	—
545	#555	—	71	1	no	—
546	#553	—	71	1	no	—
547	#552	—	71	1	no	—
548	#551	—	71	1	no	—
549	#551	—	71	1	no	—
550	#550	—	71	1	no	—
551	#547	—	71	1	no	—
552	#546	—	71	1	no	—
553	#546	—	71	1	no	—
554	#546	—	71	1	no	—
555	#546	—	71	1	no	—
556	D₄²	—	71	1	no	—
557	#542	—	71	1	no	—
558	#540	—	71	1	no	—
559	#540	—	71	1	no	—
560	#540	—	71	1	no	—
561	#538	—	71	1	no	—
562	#538	—	71	1	no	—
563	#537	—	71	1	no	—
564	#535	—	71	1	no	—
565	#535	—	71	1	no	—
566	#535	D₇₁	1	1	yes	characteristic, complemented
567	#534	—	71	1	no	—
568	#534	—	71	1	no	—
569	#525	—	71	1	no	—
570	#525	—	71	1	no	—
571	C₂×#121	—	71	1	no	—
572	C₂×#41	—	71	1	no	—
573	C₂×#41	—	71	1	no	—
574	C₂×#41	—	71	1	no	—
575	C₂×#41	—	71	1	no	—
576	C₂×#41	C₂×D₇₁	1	1	yes	characteristic, complemented
577	C₂²×D₄	—	71	1	no	—
578	C₂²×D₄	—	71	1	no	—
579	C₂²×D₄	—	71	1	no	—
580	C₂²×D₄	—	71	1	no	—
581	C₂²×D₄	—	71	1	no	—
582	C₂²×D₄	C₂×D₇₁	1	1	yes	characteristic, complemented
583	C₂³×C₄	—	71	1	no	—
584	C₄⋊Q₈	—	71	1	no	—
585	#127	—	71	1	no	—
586	#127	—	71	1	no	—
587	#127	—	71	1	no	—
588	#127	C₂×D₇₁	1	1	yes	characteristic, complemented
589	#127	C₂×D₇₁	1	1	yes	characteristic, complemented
590	#126	—	71	1	no	—
591	#126	—	71	1	no	—
592	#126	—	71	1	no	—
593	#126	—	71	1	no	—
594	#126	—	71	1	no	—
595	#126	—	71	1	no	—
596	#125	—	71	1	no	—
597	#125	—	71	1	no	—
598	#125	—	71	1	no	—
599	#124	—	71	1	no	—
600	#124	—	71	1	no	—
601	#124	—	71	1	no	—
602	#124	—	71	1	no	—
603	#124	—	71	1	no	—
604	#124	—	71	1	no	—
605	#124	—	71	1	no	—
606	#124	C₂×D₇₁	1	1	yes	characteristic, complemented
607	#124	C₂×D₇₁	1	1	yes	characteristic, complemented
608	#123	—	71	1	no	—
609	#123	—	71	1	no	—
610	#123	—	71	1	no	—
611	#123	—	71	1	no	—
612	#123	—	71	1	no	—
613	#123	—	71	1	no	—
614	#123	—	71	1	no	—
615	#123	—	71	1	no	—
616	#123	—	71	1	no	—
617	#123	—	71	1	no	—
618	#123	—	71	1	no	—
619	#123	—	71	1	no	—
620	#123	—	71	1	no	—
621	#123	—	71	1	no	—
622	#123	—	71	1	no	—
623	#123	—	71	1	no	—
624	#123	—	71	1	no	—
625	#123	—	71	1	no	—
626	#123	—	71	1	no	—
627	#123	—	71	1	no	—
628	#123	—	71	1	no	—
629	#123	—	71	1	no	—
630	C₂²⋊Q₈	—	71	1	no	—
631	C₂²⋊Q₈	—	71	1	no	—
632	C₂²⋊Q₈	—	71	1	no	—
633	C₂²⋊Q₈	—	71	1	no	—
634	C₂²⋊Q₈	—	71	1	no	—
635	C₂²⋊Q₈	—	71	1	no	—
636	C₂²⋊Q₈	—	71	1	no	—
637	C₂²⋊Q₈	—	71	1	no	—
638	C₂²⋊Q₈	—	71	1	no	—
639	C₂²⋊Q₈	—	71	1	no	—
640	C₂²⋊Q₈	—	71	1	no	—
641	#121	—	71	1	no	—
642	#121	—	71	1	no	—
643	#121	—	71	1	no	—
644	#121	—	71	1	no	—
645	#121	—	71	1	no	—
646	#121	—	71	1	no	—
647	#121	—	71	1	no	—
648	#121	—	71	1	no	—
649	#121	—	71	1	no	—
650	#121	—	71	1	no	—
651	#121	—	71	1	no	—
652	#121	—	71	1	no	—
653	#121	—	71	1	no	—
654	#121	—	71	1	no	—
655	#121	—	71	1	no	—
656	#121	—	71	1	no	—
657	#121	—	71	1	no	—
658	#121	—	71	1	no	—
659	#121	—	71	1	no	—
660	#121	—	71	1	no	—
661	#121	—	71	1	no	—
662	#121	—	71	1	no	—
663	#121	—	71	1	no	—
664	#121	—	71	1	no	—
665	#121	—	71	1	no	—
666	#121	—	71	1	no	—
667	#121	—	71	1	no	—
668	#121	—	71	1	no	—
669	#121	—	71	1	no	—
670	#121	—	71	1	no	—
671	#121	—	71	1	no	—
672	#121	—	71	1	no	—
673	#121	—	71	1	no	—
674	#121	—	71	1	no	—
675	#121	—	71	1	no	—
676	#121	C₂×D₇₁	1	1	yes	characteristic, complemented
677	#121	C₂×D₇₁	1	1	yes	characteristic, complemented
678	#121	C₂×D₇₁	1	1	yes	characteristic, complemented
679	#121	C₂×D₇₁	1	1	yes	characteristic, complemented
680	#120	—	71	1	no	—
681	#120	—	71	1	no	—
682	#120	—	71	1	no	—
683	#120	—	71	1	no	—
684	#120	—	71	1	no	—
685	#120	—	71	1	no	—
686	#120	—	71	1	no	—
687	#120	—	71	1	no	—
688	#120	—	71	1	no	—
689	#120	—	71	1	no	—
690	#120	—	71	1	no	—
691	#120	—	71	1	no	—
692	#120	C₂×D₇₁	1	1	yes	characteristic
693	#120	C₂×D₇₁	1	1	yes	characteristic, complemented
694	#120	C₂×D₇₁	1	1	yes	characteristic, complemented
695	#120	C₂×D₇₁	1	1	yes	characteristic, complemented
696	C₄×Q₈	—	71	1	no	—
697	C₄×D₄	—	71	1	no	—
698	C₄×D₄	—	71	1	no	—
699	C₄×D₄	—	71	1	no	—
700	C₄×D₄	—	71	1	no	—
701	C₄×D₄	—	71	1	no	—
702	C₄×D₄	—	71	1	no	—
703	C₄×D₄	—	71	1	no	—
704	C₄×D₄	—	71	1	no	—
705	C₄×D₄	—	71	1	no	—
706	C₄×D₄	—	71	1	no	—
707	C₄×D₄	—	71	1	no	—
708	C₄×D₄	—	71	1	no	—
709	C₄×D₄	—	71	1	no	—
710	C₄×D₄	—	71	1	no	—
711	C₄×D₄	—	71	1	no	—
712	#117	—	71	1	no	—
713	#117	—	71	1	no	—
714	#117	—	71	1	no	—
715	#117	—	71	1	no	—
716	#117	—	71	1	no	—
717	#117	—	71	1	no	—
718	#117	C₂×D₇₁	1	1	yes	characteristic, complemented
719	C₂×C₄⋊C₄	—	71	1	no	—
720	C₂×C₄⋊C₄	—	71	1	no	—
721	C₂×C₂²⋊C₄	—	71	1	no	—
722	C₂×C₂²⋊C₄	—	71	1	no	—
723	C₂×C₂²⋊C₄	—	71	1	no	—
724	C₂×C₂²⋊C₄	—	71	1	no	—
725	C₂×C₂²⋊C₄	—	71	1	no	—
726	C₂×C₂²⋊C₄	—	71	1	no	—
727	C₂⁴	—	71	1	no	—
728	C₂⁴	—	71	1	no	—
729	C₂⁴	—	71	1	no	—
730	C₂⁴	C₂²×D₇₁	1	1	yes	characteristic
731	C₂⁴	C₂²×D₇₁	1	1	yes	characteristic
732	#41	—	4	2	no	—
733	#41	—	284	2	no	—
734	#41	—	284	2	no	—
735	#41	—	284	2	no	—
736	#41	—	284	2	no	—
737	C₂×Q₈	—	71	1	no	—
738	C₂×Q₈	—	71	1	no	—
739	C₂×Q₈	—	71	1	no	—
740	C₂×Q₈	C₂²×D₇₁	1	1	yes	characteristic
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	284	2	no	—
743	C₂×D₄	—	284	2	no	—
744	C₂×D₄	—	284	2	no	—
745	C₂×D₄	—	284	2	no	—
746	C₂×D₄	—	284	2	no	—
747	C₂×D₄	—	71	1	no	—
748	C₂×D₄	—	71	1	no	—
749	C₂×D₄	—	71	1	no	—
750	C₂×D₄	—	71	1	no	—
751	C₂×D₄	—	71	1	no	—
752	C₂×D₄	—	71	1	no	—
753	C₂×D₄	—	71	1	no	—
754	C₂×D₄	—	71	1	no	—
755	C₂×D₄	—	71	1	no	—
756	C₂×D₄	—	71	1	no	—
757	C₂×D₄	—	71	1	no	—
758	C₂×D₄	—	71	1	no	—
759	C₂×D₄	—	71	1	no	—
760	C₂×D₄	—	71	1	no	—
761	C₂×D₄	—	71	1	no	—
762	C₂×D₄	—	71	1	no	—
763	C₂×D₄	—	71	1	no	—
764	C₂×D₄	—	71	1	no	—
765	C₂×D₄	—	71	1	no	—
766	C₂×D₄	—	71	1	no	—
767	C₂×D₄	—	71	1	no	—
768	C₂×D₄	—	71	1	no	—
769	C₂×D₄	—	71	1	no	—
770	C₂×D₄	—	71	1	no	—
771	C₂×D₄	—	71	1	no	—
772	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
773	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
774	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
775	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
776	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
777	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
778	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
779	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
780	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
781	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
782	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
783	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
784	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
785	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
786	C₂×D₄	C₂²×D₇₁	1	1	yes	characteristic
787	C₂²×C₄	—	284	2	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	C₄⋊C₄	—	71	1	no	—
811	C₄⋊C₄	—	71	1	no	—
812	C₄⋊C₄	—	71	1	no	—
813	C₄⋊C₄	—	71	1	no	—
814	C₄⋊C₄	—	71	1	no	—
815	C₄⋊C₄	—	71	1	no	—
816	C₄⋊C₄	—	71	1	no	—
817	C₄⋊C₄	—	71	1	no	—
818	C₄⋊C₄	—	71	1	no	—
819	C₄⋊C₄	—	71	1	no	—
820	C₄⋊C₄	—	71	1	no	—
821	C₄⋊C₄	—	71	1	no	—
822	C₄⋊C₄	—	71	1	no	—
823	C₄⋊C₄	—	71	1	no	—
824	C₄⋊C₄	—	71	1	no	—
825	C₄⋊C₄	—	71	1	no	—
826	C₄⋊C₄	—	71	1	no	—
827	C₄⋊C₄	—	71	1	no	—
828	C₄⋊C₄	—	71	1	no	—
829	C₄⋊C₄	—	71	1	no	—
830	C₄⋊C₄	—	71	1	no	—
831	C₄⋊C₄	—	71	1	no	—
832	C₄⋊C₄	—	71	1	no	—
833	C₄⋊C₄	—	71	1	no	—
834	C₄⋊C₄	—	71	1	no	—
835	C₄⋊C₄	—	71	1	no	—
836	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
838	C₂²⋊C₄	—	71	1	no	—
839	C₂²⋊C₄	—	71	1	no	—
840	C₂²⋊C₄	—	71	1	no	—
841	C₂²⋊C₄	—	71	1	no	—
842	C₂²⋊C₄	—	71	1	no	—
843	C₂²⋊C₄	—	71	1	no	—
844	C₂²⋊C₄	—	71	1	no	—
845	C₂²⋊C₄	—	71	1	no	—
846	C₂²⋊C₄	—	71	1	no	—
847	C₂²⋊C₄	—	71	1	no	—
848	C₂²⋊C₄	—	71	1	no	—
849	C₂²⋊C₄	—	71	1	no	—
850	C₂²⋊C₄	—	71	1	no	—
851	C₂²⋊C₄	—	71	1	no	—
852	C₂²⋊C₄	—	71	1	no	—
853	C₂²⋊C₄	—	71	1	no	—
854	C₂²⋊C₄	—	71	1	no	—
855	C₂²⋊C₄	—	71	1	no	—
856	C₂²⋊C₄	—	71	1	no	—
857	C₂²⋊C₄	—	71	1	no	—
858	C₂²⋊C₄	—	71	1	no	—
859	C₂²⋊C₄	—	71	1	no	—
860	C₂²⋊C₄	—	71	1	no	—
861	C₂²⋊C₄	—	71	1	no	—
862	C₂²⋊C₄	—	71	1	no	—
863	C₂²⋊C₄	—	71	1	no	—
864	C₂²⋊C₄	—	71	1	no	—
865	C₂²⋊C₄	—	71	1	no	—
866	C₂²⋊C₄	—	71	1	no	—
867	C₂²⋊C₄	—	71	1	no	—
868	C₂²⋊C₄	—	71	1	no	—
869	C₂²⋊C₄	—	71	1	no	—
870	C₂²⋊C₄	—	71	1	no	—
871	C₂²⋊C₄	—	71	1	no	—
872	C₂²⋊C₄	—	71	1	no	—
873	C₂²⋊C₄	—	71	1	no	—
874	C₂²⋊C₄	—	71	1	no	—
875	C₂²⋊C₄	—	71	1	no	—
876	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
877	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
878	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
880	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
881	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
882	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
883	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₇₁	1	1	yes	characteristic
886	C₄²	—	71	1	no	—
887	C₄²	—	71	1	no	—
888	C₄²	—	71	1	no	—
889	C₄²	—	71	1	no	—
890	C₄²	—	71	1	no	—
891	C₄²	—	71	1	no	—
892	C₄²	C₂²×D₇₁	1	1	yes	characteristic
893	C₄²	C₂²×D₇₁	1	1	yes	characteristic
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	4	1	no	—
897	C₂³	—	4	1	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	284	1	no	—
901	C₂³	—	284	1	no	—
902	C₂³	—	284	1	no	—
903	C₂³	—	284	1	no	—
904	C₂³	—	284	1	no	—
905	C₂³	—	284	1	no	—
906	C₂³	—	284	1	no	—
907	C₂³	—	284	1	no	—
908	C₂³	—	71	1	no	—
909	C₂³	—	71	1	no	—
910	C₂³	—	71	1	no	—
911	C₂³	—	71	1	no	—
912	C₂³	—	142	2	no	—
913	C₂³	C₂³×D₇₁	1	1	yes	characteristic
914	C₂³	C₂³×D₇₁	1	1	yes	characteristic
915	C₂³	C₂³×D₇₁	1	1	yes	characteristic
916	C₂³	C₂³×D₇₁	1	1	yes	characteristic
917	C₂³	C₂³×D₇₁	1	1	yes	characteristic
918	C₂³	C₂³×D₇₁	1	1	yes	characteristic
919	C₂³	C₂³×D₇₁	1	1	yes	characteristic
920	Q₈	—	4	1	no	—
921	Q₈	—	284	1	no	—
922	Q₈	—	284	1	no	—
923	Q₈	—	142	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	2	2	no	—
926	D₄	—	4	1	no	—
927	D₄	—	4	1	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	1	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	1	no	—
939	D₄	—	284	1	no	—
940	D₄	—	284	1	no	—
941	D₄	—	284	1	no	—
942	D₄	—	284	1	no	—
943	D₄	—	284	1	no	—
944	D₄	—	284	1	no	—
945	D₄	—	284	1	no	—
946	D₄	—	284	1	no	—
947	D₄	—	284	1	no	—
948	D₄	—	284	1	no	—
949	D₄	—	284	1	no	—
950	D₄	—	284	1	no	—
951	D₄	—	284	1	no	—
952	D₄	—	284	1	no	—
953	D₄	—	284	1	no	—
954	D₄	—	284	1	no	—
955	D₄	—	284	1	no	—
956	D₄	—	284	1	no	—
957	D₄	—	284	1	no	—
958	D₄	—	284	1	no	—
959	D₄	—	142	2	no	—
960	D₄	—	142	2	no	—
961	D₄	—	142	2	no	—
962	D₄	—	142	2	no	—
963	D₄	—	142	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	284	1	no	—
968	C₂×C₄	—	284	1	no	—
969	C₂×C₄	—	284	1	no	—
970	C₂×C₄	—	284	1	no	—
971	C₂×C₄	—	284	1	no	—
972	C₂×C₄	—	284	1	no	—
973	C₂×C₄	—	284	1	no	—
974	C₂×C₄	—	284	1	no	—
975	C₂×C₄	—	284	1	no	—
976	C₂×C₄	—	284	1	no	—
977	C₂×C₄	—	284	1	no	—
978	C₂×C₄	—	284	1	no	—
979	C₂×C₄	—	284	1	no	—
980	C₂×C₄	—	71	1	no	—
981	C₂×C₄	—	71	1	no	—
982	C₂×C₄	—	71	1	no	—
983	C₂×C₄	—	71	1	no	—
984	C₂×C₄	—	71	1	no	—
985	C₂×C₄	—	71	1	no	—
986	C₂×C₄	—	71	1	no	—
987	C₂×C₄	—	71	1	no	—
988	C₂×C₄	—	71	1	no	—
989	C₂×C₄	—	71	1	no	—
990	C₂×C₄	—	71	1	no	—
991	C₂×C₄	—	71	1	no	—
992	C₂×C₄	—	142	2	no	—
993	C₂×C₄	—	142	2	no	—
994	C₂×C₄	—	142	2	no	—
995	C₂×C₄	—	142	2	no	—
996	C₂×C₄	—	142	2	no	—
997	C₂×C₄	—	142	2	no	—
998	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₇₁	1	1	yes	characteristic
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	2	1	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	4	4	no	—
1027	C₂²	—	8	2	no	—
1028	C₂²	—	568	2	no	—
1029	C₂²	—	568	2	no	—
1030	C₂²	—	568	2	no	—
1031	C₂²	—	142	1	no	—
1032	C₂²	—	142	1	no	—
1033	C₂²	—	142	1	no	—
1034	C₂²	—	142	1	no	—
1035	C₂²	—	142	1	no	—
1036	C₂²	—	142	1	no	—
1037	C₂²	—	142	1	no	—
1038	C₂²	—	142	1	no	—
1039	C₂²	—	142	1	no	—
1040	C₂²	—	142	1	no	—
1041	C₂²	—	142	1	no	—
1042	C₂²	—	142	1	no	—
1043	C₂²	#14556173	1	2	yes	—
1044	C₂²	C₂⁴×D₇₁	1	1	yes	characteristic
1045	C₄	—	2	1	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	71	2	no	—
1054	C₄	—	142	1	no	—
1055	C₄	—	142	1	no	—
1056	C₄	—	142	1	no	—
1057	C₄	—	142	1	no	—
1058	C₄	—	142	1	no	—
1059	C₄	—	142	1	no	—
1060	C₄	—	142	1	no	—
1061	C₄	—	142	1	no	—
1062	C₄	—	142	1	no	—
1063	C₄	—	142	1	no	—
1064	C₄	—	142	1	no	—
1065	C₂	—	2	2	no	—
1066	C₂	—	4	1	no	—
1067	C₂	—	4	1	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	284	1	no	—
1073	C₂	—	284	1	no	—
1074	C₂	—	284	1	no	—
1075	C₂	—	284	1	no	—
1076	C₂	H(5,𝔽₂)×D₇₁	1	1	yes	characteristic
1077	C₂	C₂×#14556173	1	1	yes	characteristic
1078	C₂	#17986834	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₁
commutator, socle	C₂²×C₇₁	C₂⁵
Fitting	#535×C₇₁	C₂
hypercenter	#535	D₇₁
hypocenter	C₇₁	#3542
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #17986744	C₂	semidirect
2. #17986743	C₂	semidirect
3. #17986737	C₂	semidirect
4. #17986736	C₂	semidirect
5. #17986711	C₂	semidirect
6. #17986692	C₂	semidirect
7. #17986682	C₂	semidirect
8. #17986680	C₂	semidirect
9. #17986673	C₂	semidirect
10. #17986669	C₂	semidirect
11. #17986648	C₂	semidirect
12. #17986638	C₂	semidirect
13. #17986637	C₂	semidirect
14. #17986636	C₂	semidirect
15. #17986636	C₂	semidirect
16. #17986631	C₂	semidirect
17. #17986613	C₂	semidirect
18. #17986603	C₂	semidirect
19. #17986599	C₂	semidirect
20. #17986599	C₂	semidirect
21. #17986586	C₂	semidirect
22. #17986583	C₂	semidirect
23. #17986576	C₂	semidirect
24. #17986564	C₂	semidirect
25. #17986562	C₂	semidirect
26. #17986559	C₂	semidirect
27. #17986558	C₂	semidirect
28. #17986505	C₂	semidirect
29. #17986505	C₂	semidirect
30. C₂×#14556100	C₂	semidirect
31. #535×C₇₁	C₂	semidirect
32. C₂×#11765864	C₂²	semidirect
33. C₂×#11765864	C₂²	semidirect
34. C₂×#11765864	C₂²	semidirect
35. C₂×#11765864	C₂²	semidirect
38. C₂²×C₂²⋊D₇₁	C₂²	semidirect
40. C₂×D₄×D₇₁	C₂²	semidirect
41. C₂³×Dic₇₁	C₂²	semidirect
42. #14556126	C₂²	semidirect
43. #14556124	C₂²	semidirect
44. #14556124	C₂²	semidirect
45. #14556124	C₂²	semidirect
46. #14556123	C₂²	semidirect
47. #14556123	C₂²	semidirect
48. #14556122	C₂²	semidirect
49. #14556122	C₂²	semidirect
50. #14556121	C₂²	semidirect
51. #14556121	C₂²	semidirect
52. #14556120	C₂²	semidirect
53. #14556118	C₂²	semidirect
54. #14556118	C₂²	semidirect
55. #14556117	C₂²	semidirect
56. #14556116	C₂²	semidirect
57. #14556115	C₂²	semidirect
58. #14556114	C₂²	semidirect
59. #14556114	C₂²	semidirect
60. #14556114	C₂²	semidirect
61. #14556114	C₂²	semidirect
62. #14556113	C₂²	semidirect
63. #14556113	C₂²	semidirect
65. #14556112	C₂²	semidirect
66. #14556112	C₂²	semidirect
67. #14556112	C₂²	semidirect
69. #14556111	C₂²	semidirect
70. #14556111	C₂²	semidirect
71. #14556111	C₂²	semidirect
72. #14556110	C₂²	semidirect
73. #14556110	C₂²	semidirect
74. #14556110	C₂²	semidirect
75. #14556110	C₂²	semidirect
76. #14556109	C₂²	semidirect
77. #14556109	C₂²	semidirect
78. #14556109	C₂²	semidirect
79. #14556109	C₂²	semidirect
80. #14556109	C₂²	semidirect
81. #14556109	C₂²	semidirect
82. #14556109	C₂²	semidirect
83. #14556109	C₂²	semidirect
84. #14556107	C₂²	semidirect
85. #14556106	C₂²	semidirect
86. #14556106	C₂²	semidirect
87. #14556105	C₂²	semidirect
88. #14556105	C₂²	semidirect
89. #14556105	C₂²	semidirect
90. #14556105	C₂²	semidirect
91. #14556105	C₂²	semidirect
92. #14556105	C₂²	semidirect
93. #14556104	C₂²	semidirect
94. #14556104	C₂²	semidirect
95. #14556102	C₂²	semidirect
96. #14556101	C₂²	semidirect
97. #14556101	C₂²	semidirect
98. #14556101	C₂²	semidirect
99. #14556101	C₂²	semidirect
100. #14556101	C₂²	semidirect
101. #14556101	C₂²	semidirect
106. #14556100	C₂²	semidirect
107. #14556100	C₂²	semidirect
108. #14556100	C₂²	semidirect
109. #14556100	C₂²	semidirect
110. #14556100	C₂²	semidirect
111. #14556100	C₂²	semidirect
112. #14556100	C₂²	semidirect
113. #14556100	C₂²	semidirect
114. #14556100	C₂²	semidirect
115. #14556100	C₂²	semidirect
116. #14556100	C₂²	semidirect
117. #14556100	C₂²	semidirect
118. #14556100	C₂²	semidirect
119. #14556100	C₂²	semidirect
120. #14556100	C₂²	semidirect
121. #14556100	C₂²	semidirect
122. #14556100	C₂²	semidirect
123. #14556100	C₂²	semidirect
124. #14556100	C₂²	semidirect
125. #14556100	C₂²	semidirect
126. #14556099	C₂²	semidirect
127. #14556099	C₂²	semidirect
128. #14556099	C₂²	semidirect
129. #14556099	C₂²	semidirect
131. #14556098	C₂²	semidirect
133. #14556097	C₂²	semidirect
134. #14556096	C₂²	semidirect
135. #14556096	C₂²	semidirect
136. #14556096	C₂²	semidirect
137. #14556096	C₂²	semidirect
138. #14556096	C₂²	semidirect
139. #14556096	C₂²	semidirect
140. #14556096	C₂²	semidirect
141. #14556096	C₂²	semidirect
142. C₄×Dic₁₄₂	C₂²	semidirect
143. C₄×D₂₈₄	C₂²	semidirect
144. D₄×Dic₇₁	C₂²	semidirect
145. D₄×Dic₇₁	C₂²	semidirect
146. D₄×Dic₇₁	C₂²	semidirect
147. D₄×Dic₇₁	C₂²	semidirect
148. D₄×Dic₇₁	C₂²	semidirect
149. D₄×Dic₇₁	C₂²	semidirect
150. C₄×C₂²⋊D₇₁	C₂²	semidirect
151. C₄×C₂²⋊D₇₁	C₂²	semidirect
153. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
154. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
155. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
156. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
157. (C₂²⋊D₇₁)⋊C₄	C₂²	semidirect
158. #14556085	C₂²	semidirect
159. #14556085	C₂²	semidirect
160. #14556084	C₂²	semidirect
161. #14556084	C₂²	semidirect
162. #14556084	C₂²	semidirect
163. #14556084	C₂²	semidirect
164. C₂×Dic₇₁⋊C₄	C₂²	semidirect
165. C₂×Dic₇₁⋊C₄	C₂²	semidirect
166. C₂×C₂²⋊Dic₇₁	C₂²	semidirect
167. C₂×C₂²⋊Dic₇₁	C₂²	semidirect
168. C₂×(C₂×D₇₁)⋊C₄	C₂²	semidirect
169. C₂×(C₂×D₇₁)⋊C₄	C₂²	semidirect
170. C₂²⋊C₄×D₇₁	C₂²	semidirect
171. C₂²⋊C₄×D₇₁	C₂²	semidirect
172. C₂×#41×C₇₁	C₂²	semidirect
173. C₂²×D₄×C₇₁	C₂²	semidirect
174. #127×C₇₁	C₂²	semidirect
175. #127×C₇₁	C₂²	semidirect
176. #124×C₇₁	C₂²	semidirect
177. #124×C₇₁	C₂²	semidirect
178. #121×C₇₁	C₂²	semidirect
179. #121×C₇₁	C₂²	semidirect
180. #121×C₇₁	C₂²	semidirect
181. #121×C₇₁	C₂²	semidirect
183. #120×C₇₁	C₂²	semidirect
184. #120×C₇₁	C₂²	semidirect
185. #120×C₇₁	C₂²	semidirect
186. #117×C₇₁	C₂²	semidirect
540. C₇₁	#3542	semidirect
566. #535	D₇₁	semidirect
576. C₂×#41	C₂×D₇₁	semidirect
582. C₂²×D₄	C₂×D₇₁	semidirect
588. #127	C₂×D₇₁	semidirect
589. #127	C₂×D₇₁	semidirect
606. #124	C₂×D₇₁	semidirect
607. #124	C₂×D₇₁	semidirect
676. #121	C₂×D₇₁	semidirect
677. #121	C₂×D₇₁	semidirect
678. #121	C₂×D₇₁	semidirect
679. #121	C₂×D₇₁	semidirect
693. #120	C₂×D₇₁	semidirect
694. #120	C₂×D₇₁	semidirect
695. #120	C₂×D₇₁	semidirect
718. #117	C₂×D₇₁	semidirect