Subgroups — #31063181

Order 17152.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568500	C₂	1	1	yes	maximal, characteristic
2	#22568493	C₂	1	1	yes	maximal, characteristic, complemented
3	#22567424	C₂	1	1	yes	maximal, characteristic, complemented
4	#22567408	C₂	1	1	yes	maximal, characteristic, complemented
5	#22567312	C₂	1	1	yes	maximal, characteristic, complemented
6	#22567297	C₂	1	1	yes	maximal, characteristic, complemented
7	#22567286	C₂	1	1	yes	maximal, characteristic, complemented
8	#22567278	C₂	1	1	yes	maximal, characteristic, complemented
9	#22567248	C₂	1	1	yes	maximal, characteristic, complemented
10	#22567245	C₂	1	1	yes	maximal, characteristic, complemented
11	#22566863	C₂	1	1	yes	maximal, characteristic, complemented
12	#22566775	C₂	1	1	yes	maximal, characteristic
13	#22566738	C₂	1	1	yes	maximal, characteristic, complemented
14	#22566735	C₂	1	1	yes	maximal, characteristic, complemented
15	#22566655	C₂	1	1	yes	maximal, characteristic, complemented
16	#22566629	C₂	1	1	yes	maximal, characteristic, complemented
17	#22566599	C₂	1	1	yes	maximal, characteristic
18	#22566408	C₂	1	1	yes	maximal, characteristic, complemented
19	#22566365	C₂	1	1	yes	maximal, characteristic, complemented
20	#22565763	C₂	1	1	yes	maximal, characteristic, complemented
21	#22565628	C₂	1	1	yes	maximal, characteristic, complemented
22	#22565626	C₂	1	1	yes	maximal, characteristic, complemented
23	#22565544	C₂	1	1	yes	maximal, characteristic, complemented
24	#22564436	C₂	1	1	yes	maximal, characteristic, complemented
25	#22564431	C₂	1	1	yes	maximal, characteristic, complemented
26	#22564373	C₂	1	1	yes	maximal, characteristic, complemented
27	#22564306	C₂	1	1	yes	maximal, characteristic, complemented
28	#22563006	C₂	1	1	yes	maximal, characteristic, complemented
29	#22562964	C₂	1	1	yes	maximal, characteristic, complemented
30	#22562591	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2702	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic
33	C₂×#14524038	C₂²	1	1	yes	characteristic
34	C₂×#14524033	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14524027	C₂²	1	1	yes	characteristic
36	C₂×#14524025	C₂²	1	1	yes	characteristic
37	C₂×#14524025	C₂²	1	1	yes	characteristic
38	C₂×#14524019	C₂²	1	1	yes	characteristic
39	C₂×#14524019	C₂²	1	1	yes	characteristic
40	C₂×#14524011	C₂²	1	1	yes	characteristic
41	C₂×#14524001	C₂²	1	1	yes	characteristic
42	C₂×#14524001	C₂²	1	1	yes	characteristic
43	#16863338	C₂²	1	1	yes	characteristic, complemented
44	#16863338	C₂²	1	1	yes	characteristic, complemented
45	#16863336	C₂²	1	1	yes	characteristic, complemented
46	#16863335	C₂²	1	1	yes	characteristic, complemented
47	#16863335	C₂²	1	1	yes	characteristic, complemented
48	#16863334	C₂²	1	1	yes	characteristic, complemented
49	#16863333	C₂²	1	1	yes	characteristic
50	#16863332	C₂²	1	1	yes	characteristic, complemented
51	#16863332	C₂²	1	1	yes	characteristic, complemented
52	#16863331	C₂²	1	1	yes	characteristic
53	#16863331	C₂²	1	1	yes	characteristic
54	#16863329	C₂²	1	1	yes	characteristic, complemented
55	#16863329	C₂²	1	1	yes	characteristic, complemented
56	#16863329	C₂²	1	1	yes	characteristic, complemented
57	#16863328	C₂²	1	1	yes	characteristic, complemented
58	#16863328	C₂²	1	1	yes	characteristic, complemented
59	#16863328	C₂²	1	1	yes	characteristic, complemented
60	#16863328	C₂²	1	1	yes	characteristic, complemented
61	#16863327	C₂²	1	1	yes	characteristic, complemented
62	#16863326	C₂²	1	1	yes	characteristic, complemented
63	#16863325	C₂²	1	1	yes	characteristic
64	#16863325	C₂²	1	1	yes	characteristic
65	#16863325	C₂²	1	1	yes	characteristic
66	#16863324	C₂²	1	1	yes	characteristic
67	#16863324	C₂²	1	1	yes	characteristic
68	#16863324	C₂²	1	1	yes	characteristic, complemented
69	#16863324	C₂²	1	1	yes	characteristic, complemented
70	#16863323	C₂²	1	1	yes	characteristic
71	#16863323	C₂²	1	1	yes	characteristic
72	#16863322	C₂²	1	1	yes	characteristic
73	#16863320	C₂²	1	1	yes	characteristic
74	#16863319	C₂²	1	1	yes	characteristic
75	#16863319	C₂²	1	1	yes	characteristic
76	#16863319	C₂²	1	1	yes	characteristic
77	#16863319	C₂²	1	1	yes	characteristic
78	#16863318	C₂²	1	1	yes	characteristic
79	#16863318	C₂²	1	1	yes	characteristic
80	#16863315	C₂²	1	1	yes	characteristic, complemented
81	#16863312	C₂²	1	1	yes	characteristic
82	#16863312	C₂²	1	1	yes	characteristic
83	#16863311	C₂²	1	1	yes	characteristic
84	#16863311	C₂²	1	1	yes	characteristic
85	#16863303	C₂²	1	1	yes	characteristic, complemented
86	#16863299	C₂²	1	1	yes	characteristic
87	#16863296	C₂²	1	1	yes	characteristic
88	#16863296	C₂²	1	1	yes	characteristic
89	#16863295	C₂²	1	1	yes	characteristic, complemented
90	#16863295	C₂²	1	1	yes	characteristic, complemented
91	#16863294	C₂²	1	1	yes	characteristic, complemented
92	#16863293	C₂²	1	1	yes	characteristic, complemented
93	#16863293	C₂²	1	1	yes	characteristic, complemented
94	#16863293	C₂²	1	1	yes	characteristic, complemented
95	#16863292	C₂²	1	1	yes	characteristic, complemented
96	#16863291	C₂²	1	1	yes	characteristic, complemented
97	#16863290	C₂²	1	1	yes	characteristic
98	#16863290	C₂²	1	1	yes	characteristic, complemented
99	#16863289	C₂²	1	1	yes	characteristic
100	#16863289	C₂²	1	1	yes	characteristic
101	#16863288	C₂²	1	1	yes	characteristic
102	#16863288	C₂²	1	1	yes	characteristic
103	#16863287	C₂²	1	1	yes	characteristic
104	#16863287	C₂²	1	1	yes	characteristic
105	#16863287	C₂²	1	1	yes	characteristic
106	#16863287	C₂²	1	1	yes	characteristic
107	#16863286	C₂²	1	1	yes	characteristic
108	#16863286	C₂²	1	1	yes	characteristic
109	#16863285	C₂²	1	1	yes	characteristic
110	#16863285	C₂²	1	1	yes	characteristic
111	#16863285	C₂²	1	1	yes	characteristic
112	#16863284	C₂²	1	1	yes	characteristic
113	#16863284	C₂²	1	1	yes	characteristic, complemented
114	#16863284	C₂²	1	1	yes	characteristic, complemented
115	#16863284	C₂²	1	1	yes	characteristic, complemented
116	#16863283	C₂²	1	1	yes	characteristic, complemented
117	#16863283	C₂²	1	1	yes	characteristic, complemented
118	#16863282	C₂²	1	1	yes	characteristic, complemented
119	#16863282	C₂²	1	1	yes	characteristic, complemented
120	#16863281	C₂²	1	1	yes	characteristic, complemented
121	#16863280	C₂²	1	1	yes	characteristic, complemented
122	#16863279	C₂²	1	1	yes	characteristic, complemented
123	#16863279	C₂²	1	1	yes	characteristic, complemented
124	#16863279	C₂²	1	1	yes	characteristic, complemented
125	#16863279	C₂²	1	1	yes	characteristic, complemented
126	#16863278	C₂²	1	1	yes	characteristic, complemented
127	#16863277	C₂²	1	1	yes	characteristic, complemented
128	#16863277	C₂²	1	1	yes	characteristic, complemented
129	#16863277	C₂²	1	1	yes	characteristic, complemented
130	#16863276	C₂²	1	1	yes	characteristic
131	#16863276	C₂²	1	1	yes	characteristic
132	#16863273	C₂²	1	1	yes	characteristic
133	#16863272	C₂²	1	1	yes	characteristic
134	#16863272	C₂²	1	1	yes	characteristic
135	#16863271	C₂²	1	1	yes	characteristic
136	#16863271	C₂²	1	1	yes	characteristic, complemented
137	#16863271	C₂²	1	1	yes	characteristic, complemented
138	#16863270	C₂²	1	1	yes	characteristic
139	#16863270	C₂²	1	1	yes	characteristic
140	#16863269	C₂²	1	1	yes	characteristic
141	#16863268	C₂²	1	1	yes	characteristic
142	#16863268	C₂²	1	1	yes	characteristic
143	#16863267	C₂²	1	1	yes	characteristic
144	#16863267	C₂²	1	1	yes	characteristic
145	#16863267	C₂²	1	1	yes	characteristic
146	#16863267	C₂²	1	1	yes	characteristic
147	#16863263	C₂²	1	1	yes	characteristic, complemented
148	#16863258	C₂²	1	1	yes	characteristic
149	#16863258	C₂²	1	1	yes	characteristic
150	#16863258	C₂²	1	1	yes	characteristic
151	#16863258	C₂²	1	1	yes	characteristic
152	#16863256	C₂²	1	1	yes	characteristic
153	#16863256	C₂²	1	1	yes	characteristic
154	#16863254	C₂²	1	1	yes	characteristic, complemented
155	#16863253	C₂²	1	1	yes	characteristic
156	#16863253	C₂²	1	1	yes	characteristic
157	#16863253	C₂²	1	1	yes	characteristic
158	#16863253	C₂²	1	1	yes	characteristic
159	#16863251	C₂²	1	1	yes	characteristic
160	#16863251	C₂²	1	1	yes	characteristic
161	#16863251	C₂²	1	1	yes	characteristic
162	#16863251	C₂²	1	1	yes	characteristic
163	#16863251	C₂²	1	1	yes	characteristic
164	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
166	#16863247	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
170	#16863243	C₂²	1	1	yes	characteristic
171	#16863243	C₂²	1	1	yes	characteristic
172	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
173	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
174	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
175	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
176	#396×C₆₇	C₂²	1	1	yes	characteristic, complemented
177	#394×C₆₇	C₂²	1	1	yes	characteristic
178	#394×C₆₇	C₂²	1	1	yes	characteristic
179	#393×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
181	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
182	#388×C₆₇	C₂²	1	1	yes	characteristic
183	#388×C₆₇	C₂²	1	1	yes	characteristic
184	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
185	#386×C₆₇	C₂²	1	1	yes	characteristic
186	#380×C₆₇	C₂²	1	1	yes	characteristic
187	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
188	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
189	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
190	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
191	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₆₇	—	2	4	no	—
193	C₂²×C₄×D₆₇	—	4	2	no	—
194	C₂²×C₄×D₆₇	—	4	2	no	—
195	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
199	#14524038	—	4	2	no	—
200	#14524033	—	4	2	no	—
201	#14524027	—	4	2	no	—
202	#14524025	—	2	4	no	—
203	#14524025	—	4	2	no	—
204	#14524019	—	2	4	no	—
205	#14524019	—	4	2	no	—
206	#14524011	—	4	2	no	—
207	#14524001	—	4	2	no	—
208	#14524001	—	4	2	no	—
209	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
222	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
251	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
282	C₆₇⋊#95	C₂³	1	1	yes	characteristic
283	C₆₇⋊#95	C₂³	1	1	yes	characteristic
284	C₆₇⋊#95	C₂³	1	1	yes	characteristic
285	C₆₇⋊#95	C₂³	1	1	yes	characteristic
286	C₆₇⋊#95	C₂³	1	1	yes	characteristic
287	C₆₇⋊#95	C₂³	1	1	yes	characteristic
288	C₆₇⋊#95	C₂³	1	1	yes	characteristic
289	C₆₇⋊#95	C₂³	1	1	yes	characteristic
290	C₆₇⋊#95	C₂³	1	1	yes	characteristic
291	C₆₇⋊#95	C₂³	1	1	yes	characteristic
292	C₆₇⋊#95	C₂³	1	1	yes	characteristic
293	C₆₇⋊#95	C₂³	1	1	yes	characteristic
294	C₆₇⋊#95	C₂³	1	1	yes	characteristic
295	C₆₇⋊#95	C₂³	1	1	yes	characteristic
296	C₆₇⋊#95	C₂³	1	1	yes	characteristic
297	C₆₇⋊#95	C₂³	1	1	yes	characteristic
298	C₆₇⋊#95	C₂³	1	1	yes	characteristic
299	C₆₇⋊#95	C₂³	1	1	yes	characteristic
300	C₆₇⋊#95	C₂³	1	1	yes	characteristic
301	C₆₇⋊#95	C₂³	1	1	yes	characteristic
302	C₆₇⋊#95	C₂³	1	1	yes	characteristic
303	C₆₇⋊#95	C₂³	1	1	yes	characteristic
304	C₆₇⋊#95	C₂³	1	1	yes	characteristic
305	C₆₇⋊#95	C₂³	1	1	yes	characteristic
306	C₆₇⋊#95	C₂³	1	1	yes	characteristic
307	C₆₇⋊#95	C₂³	1	1	yes	characteristic
308	C₆₇⋊#95	C₂³	1	1	yes	characteristic
309	C₆₇⋊#95	C₂³	1	1	yes	characteristic
310	C₆₇⋊#95	C₂³	1	1	yes	characteristic
311	C₆₇⋊#95	C₂³	1	1	yes	characteristic
312	C₆₇⋊#95	C₂³	1	1	yes	characteristic
313	C₆₇⋊#95	C₂³	1	1	yes	characteristic
314	C₆₇⋊#95	C₂³	1	1	yes	characteristic
315	C₆₇⋊#95	C₂³	1	1	yes	characteristic
316	C₆₇⋊#95	C₂³	1	1	yes	characteristic
317	C₆₇⋊#95	C₂³	1	1	yes	characteristic
318	C₆₇⋊#95	C₂³	1	1	yes	characteristic
319	C₆₇⋊#95	C₂³	1	1	yes	characteristic
320	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
323	#126×C₆₇	—	4	2	no	—
324	C₂²⋊Q₈×C₆₇	—	4	2	no	—
325	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
347	#95×C₆₇	C₂³	1	1	yes	characteristic
348	#95×C₆₇	C₂³	1	1	yes	characteristic
349	#95×C₆₇	C₂³	1	1	yes	characteristic
350	#95×C₆₇	C₂³	1	1	yes	characteristic
351	#95×C₆₇	C₂³	1	1	yes	characteristic
352	#95×C₆₇	C₂³	1	1	yes	characteristic
353	#95×C₆₇	C₂³	1	1	yes	characteristic
354	#95×C₆₇	C₂³	1	1	yes	characteristic
355	#95×C₆₇	C₂³	1	1	yes	characteristic
356	#95×C₆₇	C₂³	1	1	yes	characteristic
357	C₂³×D₆₇	—	2	2	no	—
358	C₂³×D₆₇	—	2	2	no	—
359	C₂³×D₆₇	—	2	2	no	—
360	C₂³×D₆₇	—	4	1	no	—
361	C₂³×D₆₇	—	4	1	no	—
362	C₂³×D₆₇	—	4	1	no	—
363	C₂³×D₆₇	—	4	1	no	—
364	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
365	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×C₂²⋊D₆₇	—	2	2	no	—
367	C₂×C₂²⋊D₆₇	—	2	2	no	—
368	C₂×C₂²⋊D₆₇	—	4	1	no	—
369	C₂×C₂²⋊D₆₇	—	4	1	no	—
370	C₂×C₂²⋊D₆₇	—	4	1	no	—
371	C₂×C₂²⋊D₆₇	—	4	1	no	—
372	C₂²×Dic₆₇	—	2	2	no	—
373	C₂²×Dic₆₇	—	4	1	no	—
374	C₂²×Dic₆₇	—	4	1	no	—
375	C₂²×Dic₆₇	—	4	1	no	—
376	C₂²×Dic₆₇	—	4	1	no	—
377	C₂²×Dic₆₇	—	4	1	no	—
378	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×D₆₇	—	2	2	no	—
393	C₂×C₄×D₆₇	—	2	2	no	—
394	C₂×C₄×D₆₇	—	2	2	no	—
395	C₂×C₄×D₆₇	—	2	2	no	—
396	C₂×C₄×D₆₇	—	2	2	no	—
397	C₂×C₄×D₆₇	—	2	2	no	—
398	C₂×C₄×D₆₇	—	2	2	no	—
399	C₂×C₄×D₆₇	—	4	16	no	—
400	C₂×C₄×D₆₇	—	4	1	no	—
401	C₂×C₄×D₆₇	—	4	1	no	—
402	C₂×C₄×D₆₇	—	4	1	no	—
403	C₂×C₄×D₆₇	—	4	1	no	—
404	C₂×C₄×D₆₇	#41	1	4	yes	—
405	C₄⋊Dic₆₇	—	2	2	no	—
406	C₄⋊Dic₆₇	—	2	2	no	—
407	C₄⋊Dic₆₇	—	2	2	no	—
408	C₄⋊Dic₆₇	—	4	1	no	—
409	C₄⋊Dic₆₇	—	4	1	no	—
410	C₄⋊Dic₆₇	—	4	1	no	—
411	C₄⋊Dic₆₇	—	4	1	no	—
412	C₄⋊Dic₆₇	—	4	1	no	—
413	C₄⋊Dic₆₇	—	4	1	no	—
414	C₄⋊Dic₆₇	—	4	1	no	—
415	C₄⋊Dic₆₇	—	4	1	no	—
416	C₄⋊Dic₆₇	—	4	1	no	—
417	C₄⋊Dic₆₇	—	4	1	no	—
418	Dic₆₇⋊C₄	—	2	2	no	—
419	Dic₆₇⋊C₄	—	2	2	no	—
420	Dic₆₇⋊C₄	—	2	2	no	—
421	Dic₆₇⋊C₄	—	2	2	no	—
422	Dic₆₇⋊C₄	—	4	1	no	—
423	Dic₆₇⋊C₄	—	4	1	no	—
424	Dic₆₇⋊C₄	—	4	1	no	—
425	Dic₆₇⋊C₄	—	4	1	no	—
426	Dic₆₇⋊C₄	—	4	1	no	—
427	Dic₆₇⋊C₄	—	4	1	no	—
428	Dic₆₇⋊C₄	—	4	1	no	—
429	Dic₆₇⋊C₄	—	4	1	no	—
430	Dic₆₇⋊C₄	—	4	1	no	—
431	Dic₆₇⋊C₄	—	4	1	no	—
432	Dic₆₇⋊C₄	—	4	1	no	—
433	Dic₆₇⋊C₄	—	4	1	no	—
434	Dic₆₇⋊C₄	—	4	1	no	—
435	Dic₆₇⋊C₄	—	4	1	no	—
436	C₂²⋊Dic₆₇	—	2	2	no	—
437	C₂²⋊Dic₆₇	—	2	2	no	—
438	C₂²⋊Dic₆₇	—	4	1	no	—
439	C₂²⋊Dic₆₇	—	4	1	no	—
440	C₂²⋊Dic₆₇	—	4	1	no	—
441	C₂²⋊Dic₆₇	—	4	1	no	—
442	C₂²⋊Dic₆₇	—	4	1	no	—
443	C₂²⋊Dic₆₇	—	4	1	no	—
444	C₂²⋊Dic₆₇	—	4	1	no	—
445	C₂²⋊Dic₆₇	—	4	1	no	—
446	C₂²⋊Dic₆₇	—	4	1	no	—
447	(C₂×D₆₇)⋊C₄	—	2	2	no	—
448	(C₂×D₆₇)⋊C₄	—	2	2	no	—
449	(C₂×D₆₇)⋊C₄	—	2	2	no	—
450	(C₂×D₆₇)⋊C₄	—	2	2	no	—
451	(C₂×D₆₇)⋊C₄	—	2	2	no	—
452	(C₂×D₆₇)⋊C₄	—	2	2	no	—
453	(C₂×D₆₇)⋊C₄	—	2	2	no	—
454	(C₂×D₆₇)⋊C₄	—	2	2	no	—
455	(C₂×D₆₇)⋊C₄	—	4	1	no	—
456	(C₂×D₆₇)⋊C₄	—	4	1	no	—
457	(C₂×D₆₇)⋊C₄	—	4	1	no	—
458	(C₂×D₆₇)⋊C₄	—	4	1	no	—
459	(C₂×D₆₇)⋊C₄	—	4	1	no	—
460	(C₂×D₆₇)⋊C₄	—	4	1	no	—
461	(C₂×D₆₇)⋊C₄	—	4	1	no	—
462	(C₂×D₆₇)⋊C₄	—	4	1	no	—
463	(C₂×D₆₇)⋊C₄	—	4	1	no	—
464	(C₂×D₆₇)⋊C₄	—	4	1	no	—
465	(C₂×D₆₇)⋊C₄	—	4	1	no	—
466	(C₂×D₆₇)⋊C₄	—	4	1	no	—
467	(C₂×D₆₇)⋊C₄	—	4	1	no	—
468	(C₂×D₆₇)⋊C₄	—	4	1	no	—
469	C₄×Dic₆₇	—	4	1	no	—
470	C₄×Dic₆₇	—	4	1	no	—
471	C₄×Dic₆₇	—	4	1	no	—
472	C₄×Dic₆₇	—	4	1	no	—
473	C₄×Dic₆₇	—	4	1	no	—
474	C₄×Dic₆₇	—	4	1	no	—
475	C₄×Dic₆₇	—	4	1	no	—
476	C₄×Dic₆₇	—	4	1	no	—
477	C₄×Dic₆₇	—	4	1	no	—
478	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
479	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
480	C₂×Q₈×C₆₇	—	2	2	no	—
481	C₂×Q₈×C₆₇	—	4	1	no	—
482	C₂×Q₈×C₆₇	—	4	1	no	—
483	C₂×D₄×C₆₇	—	2	2	no	—
484	C₂×D₄×C₆₇	—	4	1	no	—
485	C₂×D₄×C₆₇	—	4	1	no	—
486	C₂²×C₄×C₆₇	—	2	2	no	—
487	C₂²×C₄×C₆₇	—	2	2	no	—
488	C₂²×C₄×C₆₇	—	4	1	no	—
489	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
490	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
494	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₄⋊C₄×C₆₇	—	2	2	no	—
503	C₄⋊C₄×C₆₇	—	2	2	no	—
504	C₄⋊C₄×C₆₇	—	2	2	no	—
505	C₄⋊C₄×C₆₇	—	4	1	no	—
506	C₄⋊C₄×C₆₇	—	4	1	no	—
507	C₄⋊C₄×C₆₇	—	4	1	no	—
508	C₄⋊C₄×C₆₇	—	4	1	no	—
509	C₄⋊C₄×C₆₇	—	4	1	no	—
510	C₄⋊C₄×C₆₇	—	4	1	no	—
511	C₂²⋊C₄×C₆₇	—	2	2	no	—
512	C₂²⋊C₄×C₆₇	—	2	2	no	—
513	C₂²⋊C₄×C₆₇	—	2	2	no	—
514	C₂²⋊C₄×C₆₇	—	2	2	no	—
515	C₂²⋊C₄×C₆₇	—	4	1	no	—
516	C₂²⋊C₄×C₆₇	—	4	1	no	—
517	C₂²⋊C₄×C₆₇	—	4	1	no	—
518	C₂²⋊C₄×C₆₇	—	4	1	no	—
519	C₂²⋊C₄×C₆₇	—	4	1	no	—
520	C₂²⋊C₄×C₆₇	—	4	1	no	—
521	C₂²⋊C₄×C₆₇	—	4	1	no	—
522	C₄²×C₆₇	—	4	1	no	—
523	C₄²×C₆₇	—	4	1	no	—
524	C₂³×C₆₇	—	2	1	no	—
525	C₂³×C₆₇	—	2	1	no	—
526	C₂³×C₆₇	—	2	1	no	—
527	C₂³×C₆₇	—	2	1	no	—
528	C₂³×C₆₇	—	2	1	no	—
529	C₂³×C₆₇	—	2	1	no	—
530	C₂³×C₆₇	—	2	1	no	—
531	C₂³×C₆₇	—	2	1	no	—
532	C₂³×C₆₇	—	2	1	no	—
533	C₂³×C₆₇	—	2	1	no	—
534	C₂³×C₆₇	—	2	1	no	—
535	C₂³×C₆₇	—	2	1	no	—
536	C₂³×C₆₇	—	2	1	no	—
537	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
538	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
539	C₂²×D₆₇	—	2	1	no	—
540	C₂²×D₆₇	—	2	1	no	—
541	C₂²×D₆₇	—	2	1	no	—
542	C₂²×D₆₇	—	2	1	no	—
543	C₂²×D₆₇	—	2	1	no	—
544	C₂²×D₆₇	—	2	1	no	—
545	C₂²×D₆₇	—	2	1	no	—
546	C₂²×D₆₇	—	2	1	no	—
547	C₂²×D₆₇	—	2	1	no	—
548	C₂²×D₆₇	—	2	1	no	—
549	C₂²×D₆₇	—	2	1	no	—
550	C₂²×D₆₇	—	2	1	no	—
551	C₂²×D₆₇	—	4	4	no	—
552	C₂²×D₆₇	—	4	4	no	—
553	C₂²×D₆₇	—	4	4	no	—
554	C₂²×D₆₇	—	4	4	no	—
555	C₂²×D₆₇	—	4	4	no	—
556	C₂²×D₆₇	—	4	4	no	—
557	C₂²×D₆₇	—	4	4	no	—
558	C₂²×D₆₇	C₂×#41	1	2	yes	—
559	C₂²×D₆₇	H(5,𝔽₂)	1	2	yes	—
560	Q₈×C₆₇	—	8	2	no	—
561	D₄×C₆₇	—	8	2	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	2	1	no	—
567	C₂×C₄×C₆₇	—	2	1	no	—
568	C₂×C₄×C₆₇	—	2	1	no	—
569	C₂×C₄×C₆₇	—	2	1	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	1	no	—
574	C₂×C₄×C₆₇	—	2	1	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	2	1	no	—
577	C₂×C₄×C₆₇	—	2	1	no	—
578	C₂×C₄×C₆₇	—	2	1	no	—
579	C₂×C₄×C₆₇	—	2	1	no	—
580	C₂×C₄×C₆₇	—	2	1	no	—
581	C₂×C₄×C₆₇	—	2	1	no	—
582	C₂×C₄×C₆₇	—	2	1	no	—
583	C₂×C₄×C₆₇	—	2	1	no	—
584	C₂×C₄×C₆₇	—	2	1	no	—
585	C₂×C₄×C₆₇	—	2	1	no	—
586	C₂×C₄×C₆₇	—	2	1	no	—
587	C₂×C₄×C₆₇	—	2	1	no	—
588	C₂×C₄×C₆₇	—	2	1	no	—
589	C₂×C₄×C₆₇	—	2	1	no	—
590	C₂×C₄×C₆₇	—	2	1	no	—
591	C₂×C₄×C₆₇	—	2	1	no	—
592	C₂×C₄×C₆₇	—	2	1	no	—
593	C₂×C₄×C₆₇	—	2	1	no	—
594	C₂×C₄×C₆₇	—	2	1	no	—
595	C₂×C₄×C₆₇	—	2	1	no	—
596	C₂×C₄×C₆₇	—	2	1	no	—
597	C₂×C₄×C₆₇	—	2	1	no	—
598	C₂×C₄×C₆₇	—	2	1	no	—
599	C₂×C₄×C₆₇	—	4	4	no	—
600	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
601	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
602	C₂²⋊D₆₇	—	8	2	no	—
603	C₂²⋊D₆₇	—	8	2	no	—
604	C₂×Dic₆₇	—	2	1	no	—
605	C₂×Dic₆₇	—	2	1	no	—
606	C₂×Dic₆₇	—	2	1	no	—
607	C₂×Dic₆₇	—	2	1	no	—
608	C₂×Dic₆₇	—	2	1	no	—
609	C₂×Dic₆₇	—	2	1	no	—
610	C₂×Dic₆₇	—	2	1	no	—
611	C₂×Dic₆₇	—	2	1	no	—
612	C₂×Dic₆₇	—	2	1	no	—
613	C₂×Dic₆₇	—	2	1	no	—
614	C₂×Dic₆₇	—	2	1	no	—
615	C₂×Dic₆₇	—	2	1	no	—
616	C₂×Dic₆₇	—	2	1	no	—
617	C₂×Dic₆₇	—	2	1	no	—
618	C₂×Dic₆₇	—	2	1	no	—
619	C₂×Dic₆₇	—	2	1	no	—
620	C₂×Dic₆₇	—	2	1	no	—
621	C₂×Dic₆₇	—	2	1	no	—
622	C₂×Dic₆₇	—	2	1	no	—
623	C₂×Dic₆₇	—	2	1	no	—
624	C₂×Dic₆₇	—	2	1	no	—
625	C₂×Dic₆₇	—	2	1	no	—
626	C₂×Dic₆₇	—	2	1	no	—
627	C₂×Dic₆₇	—	2	1	no	—
628	C₂×Dic₆₇	—	2	1	no	—
629	C₂×Dic₆₇	—	2	1	no	—
630	C₂×Dic₆₇	—	2	1	no	—
631	C₂×Dic₆₇	—	2	1	no	—
632	C₂×Dic₆₇	—	2	1	no	—
633	C₂×Dic₆₇	—	2	1	no	—
634	C₂×Dic₆₇	—	2	1	no	—
635	C₂×Dic₆₇	—	2	1	no	—
636	C₂×Dic₆₇	—	2	1	no	—
637	C₂×Dic₆₇	—	2	1	no	—
638	C₂×Dic₆₇	—	2	1	no	—
639	C₂×Dic₆₇	—	2	1	no	—
640	C₂×Dic₆₇	—	2	1	no	—
641	C₂×Dic₆₇	—	2	1	no	—
642	C₂×Dic₆₇	—	2	1	no	—
643	C₂×Dic₆₇	—	2	1	no	—
644	C₂×Dic₆₇	—	2	1	no	—
645	C₂×Dic₆₇	—	4	4	no	—
646	C₂×Dic₆₇	—	8	2	no	—
647	C₂×Dic₆₇	C₂×#41	1	2	yes	—
648	C₄×D₆₇	—	2	8	no	—
649	C₄×D₆₇	—	4	4	no	—
650	C₄×D₆₇	—	4	4	no	—
651	C₄×D₆₇	—	4	4	no	—
652	C₂²×C₆₇	—	2	2	no	—
653	C₂²×C₆₇	—	2	2	no	—
654	C₂²×C₆₇	—	2	2	no	—
655	C₂²×C₆₇	—	4	1	no	—
656	C₂²×C₆₇	—	4	1	no	—
657	C₂²×C₆₇	—	4	1	no	—
658	C₂²×C₆₇	—	4	1	no	—
659	C₂²×C₆₇	—	4	1	no	—
660	C₂²×C₆₇	—	4	1	no	—
661	C₂²×C₆₇	—	4	1	no	—
662	C₂²×C₆₇	—	4	1	no	—
663	C₂²×C₆₇	—	4	1	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	4	1	no	—
666	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
667	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
670	C₂²×C₆₇	#585	1	1	yes	characteristic
671	C₂²×C₆₇	#585	1	1	yes	characteristic
672	C₂²×C₆₇	#585	1	1	yes	characteristic
673	C₂×D₆₇	—	2	2	no	—
674	C₂×D₆₇	—	2	2	no	—
675	C₂×D₆₇	—	2	2	no	—
676	C₂×D₆₇	—	2	2	no	—
677	C₂×D₆₇	—	2	2	no	—
678	C₂×D₆₇	—	2	2	no	—
679	C₂×D₆₇	—	4	16	no	—
680	C₂×D₆₇	—	4	1	no	—
681	C₂×D₆₇	—	4	1	no	—
682	C₂×D₆₇	—	4	1	no	—
683	C₂×D₆₇	—	4	1	no	—
684	C₂×D₆₇	—	4	1	no	—
685	C₂×D₆₇	—	4	1	no	—
686	C₂×D₆₇	—	4	1	no	—
687	C₂×D₆₇	—	4	1	no	—
688	C₄×C₆₇	—	2	2	no	—
689	C₄×C₆₇	—	2	2	no	—
690	C₄×C₆₇	—	4	1	no	—
691	C₄×C₆₇	—	4	1	no	—
692	C₄×C₆₇	—	4	1	no	—
693	C₄×C₆₇	—	4	1	no	—
694	C₄×C₆₇	—	4	1	no	—
695	C₄×C₆₇	—	4	1	no	—
696	C₄×C₆₇	—	4	1	no	—
697	C₄×C₆₇	—	4	1	no	—
698	C₄×C₆₇	—	4	1	no	—
699	C₄×C₆₇	—	4	1	no	—
700	C₄×C₆₇	—	4	1	no	—
701	Dic₆₇	—	2	2	no	—
702	Dic₆₇	—	4	1	no	—
703	Dic₆₇	—	4	1	no	—
704	Dic₆₇	—	4	1	no	—
705	Dic₆₇	—	4	1	no	—
706	Dic₆₇	—	4	1	no	—
707	Dic₆₇	—	4	1	no	—
708	Dic₆₇	—	4	1	no	—
709	Dic₆₇	—	4	1	no	—
710	Dic₆₇	—	4	1	no	—
711	Dic₆₇	—	4	1	no	—
712	Dic₆₇	—	4	1	no	—
713	Dic₆₇	—	4	1	no	—
714	Dic₆₇	—	4	1	no	—
715	#36736	—	67	1	no	maximal, Sylow
716	C₂×C₆₇	—	4	2	no	—
717	C₂×C₆₇	—	8	1	no	—
718	C₂×C₆₇	#3455	1	1	yes	characteristic
719	C₂×C₆₇	#3490	1	1	yes	characteristic
720	C₂×C₆₇	#3495	1	1	yes	characteristic
721	C₂×C₆₇	#3533	1	1	yes	characteristic
722	C₂×C₆₇	#3535	1	1	yes	characteristic
723	C₂×C₆₇	#3539	1	1	yes	characteristic
724	C₂×C₆₇	#3541	1	1	yes	characteristic
725	D₆₇	—	4	2	no	—
726	D₆₇	—	4	2	no	—
727	#2849	—	67	1	no	—
728	#2848	—	67	1	no	—
729	#2748	—	67	1	no	—
730	#2747	—	67	1	no	—
731	#2740	—	67	1	no	—
732	#2739	—	67	1	no	—
733	#2738	—	67	1	no	—
734	#2738	—	67	1	no	—
735	#2735	—	67	1	no	—
736	#2735	—	67	1	no	—
737	#2704	—	67	1	no	—
738	#2702	D₆₇	1	1	yes	characteristic, complemented
739	#2697	—	67	1	no	—
740	#2695	—	67	1	no	—
741	#2694	—	67	1	no	—
742	#2689	—	67	1	no	—
743	#2687	—	67	1	no	—
744	#2685	—	67	1	no	—
745	#2667	—	67	1	no	—
746	#2663	—	67	1	no	—
747	#2597	—	67	1	no	—
748	#2587	—	67	1	no	—
749	#2587	—	67	1	no	—
750	#2578	—	67	1	no	—
751	#2479	—	67	1	no	—
752	#2478	—	67	1	no	—
753	#2475	—	67	1	no	—
754	#2470	—	67	1	no	—
755	#2335	—	67	1	no	—
756	#2332	—	67	1	no	—
757	#2280	—	67	1	no	—
758	C₆₇	#36736	1	1	yes	characteristic, complemented, Sylow
759	C₂⁴×C₄	—	67	1	no	—
760	C₂×#126	—	67	1	no	—
761	C₂×#126	C₂×D₆₇	1	1	yes	characteristic, complemented
762	C₂×#125	—	67	1	no	—
763	C₂×#123	—	67	1	no	—
764	C₂×#123	—	67	1	no	—
765	C₂×#123	—	67	1	no	—
766	C₂×C₂²⋊Q₈	—	67	1	no	—
767	C₂×C₂²⋊Q₈	—	67	1	no	—
768	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
769	C₂×#120	—	67	1	no	—
770	C₂×#117	—	67	1	no	—
771	C₂×#117	—	67	1	no	—
772	#400	—	67	1	no	—
773	#400	—	67	1	no	—
774	#400	—	67	1	no	—
775	#400	—	67	1	no	—
776	#400	—	67	1	no	—
777	#400	—	67	1	no	—
778	#400	C₂×D₆₇	1	1	yes	characteristic, complemented
779	#399	—	67	1	no	—
780	#399	—	67	1	no	—
781	#399	—	67	1	no	—
782	#399	—	67	1	no	—
783	#399	—	67	1	no	—
784	#398	—	67	1	no	—
785	#398	—	67	1	no	—
786	#398	—	67	1	no	—
787	#398	—	67	1	no	—
788	#398	—	67	1	no	—
789	#398	—	67	1	no	—
790	#398	—	67	1	no	—
791	#398	—	67	1	no	—
792	#398	—	67	1	no	—
793	#398	C₂×D₆₇	1	1	yes	characteristic, complemented
794	#397	—	67	1	no	—
795	#397	—	67	1	no	—
796	#397	—	67	1	no	—
797	#397	—	67	1	no	—
798	#397	—	67	1	no	—
799	#397	—	67	1	no	—
800	#397	—	67	1	no	—
801	#397	—	67	1	no	—
802	#397	—	67	1	no	—
803	#397	—	67	1	no	—
804	#396	—	67	1	no	—
805	#396	—	67	1	no	—
806	#396	—	67	1	no	—
807	#396	—	67	1	no	—
808	#396	—	67	1	no	—
809	#396	—	67	1	no	—
810	#396	—	67	1	no	—
811	#396	C₂×D₆₇	1	1	yes	characteristic, complemented
812	#395	—	67	1	no	—
813	#394	—	67	1	no	—
814	#394	—	67	1	no	—
815	#394	—	67	1	no	—
816	#394	—	67	1	no	—
817	#394	C₂×D₆₇	1	1	yes	characteristic
818	#394	C₂×D₆₇	1	1	yes	characteristic
819	#393	C₂×D₆₇	1	1	yes	characteristic, complemented
820	#391	—	67	1	no	—
821	#391	C₂×D₆₇	1	1	yes	characteristic, complemented
822	#390	—	67	1	no	—
823	#390	—	67	1	no	—
824	#390	—	67	1	no	—
825	#389	—	67	1	no	—
826	#389	—	67	1	no	—
827	#389	—	67	1	no	—
828	#389	—	67	1	no	—
829	#389	—	67	1	no	—
830	#389	—	67	1	no	—
831	#389	—	67	1	no	—
832	#389	—	67	1	no	—
833	#389	C₂×D₆₇	1	1	yes	characteristic, complemented
834	#388	—	67	1	no	—
835	#388	—	67	1	no	—
836	#388	—	67	1	no	—
837	#388	—	67	1	no	—
838	#388	—	67	1	no	—
839	#388	—	67	1	no	—
840	#388	—	67	1	no	—
841	#388	—	67	1	no	—
842	#388	—	67	1	no	—
843	#388	—	67	1	no	—
844	#388	—	67	1	no	—
845	#388	—	67	1	no	—
846	#388	—	67	1	no	—
847	#388	—	67	1	no	—
848	#388	—	67	1	no	—
849	#388	—	67	1	no	—
850	#388	—	67	1	no	—
851	#388	—	67	1	no	—
852	#388	—	67	1	no	—
853	#388	C₂×D₆₇	1	1	yes	characteristic
854	#388	C₂×D₆₇	1	1	yes	characteristic
855	#388	C₂×D₆₇	1	1	yes	characteristic, complemented
856	#387	—	67	1	no	—
857	#387	—	67	1	no	—
858	#387	—	67	1	no	—
859	#387	—	67	1	no	—
860	#387	—	67	1	no	—
861	#387	—	67	1	no	—
862	#387	—	67	1	no	—
863	#387	—	67	1	no	—
864	#387	—	67	1	no	—
865	#387	—	67	1	no	—
866	#387	—	67	1	no	—
867	#387	—	67	1	no	—
868	#387	—	67	1	no	—
869	#387	—	67	1	no	—
870	#386	—	67	1	no	—
871	#386	—	67	1	no	—
872	#386	—	67	1	no	—
873	#386	—	67	1	no	—
874	#386	—	67	1	no	—
875	#386	C₂×D₆₇	1	1	yes	characteristic
876	#385	—	67	1	no	—
877	#385	—	67	1	no	—
878	#385	—	67	1	no	—
879	#385	—	67	1	no	—
880	#385	—	67	1	no	—
881	#385	—	67	1	no	—
882	#385	—	67	1	no	—
883	#385	—	67	1	no	—
884	#385	—	67	1	no	—
885	#385	—	67	1	no	—
886	#385	—	67	1	no	—
887	#385	—	67	1	no	—
888	#383	—	67	1	no	—
889	#381	—	67	1	no	—
890	#381	—	67	1	no	—
891	#381	—	67	1	no	—
892	#381	—	67	1	no	—
893	#380	—	67	1	no	—
894	#380	—	67	1	no	—
895	#380	—	67	1	no	—
896	#380	—	67	1	no	—
897	#380	—	67	1	no	—
898	#380	—	67	1	no	—
899	#380	—	67	1	no	—
900	#380	C₂×D₆₇	1	1	yes	characteristic
901	#379	—	67	1	no	—
902	#379	—	67	1	no	—
903	#379	—	67	1	no	—
904	#379	—	67	1	no	—
905	#379	—	67	1	no	—
906	C₄×C₄⋊C₄	—	67	1	no	—
907	C₄×C₄⋊C₄	—	67	1	no	—
908	C₄×C₄⋊C₄	—	67	1	no	—
909	C₄×C₂²⋊C₄	—	67	1	no	—
910	C₄×C₂²⋊C₄	—	67	1	no	—
911	C₄×C₂²⋊C₄	—	67	1	no	—
912	C₄×C₂²⋊C₄	—	67	1	no	—
913	C₄×C₂²⋊C₄	—	67	1	no	—
914	C₂⁵	—	67	1	no	—
915	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
916	C₂²×D₄	—	67	1	no	—
917	C₂²×D₄	—	67	1	no	—
918	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
919	C₂³×C₄	—	268	2	no	—
920	C₂³×C₄	—	268	2	no	—
921	C₂³×C₄	—	67	1	no	—
922	C₂³×C₄	—	67	1	no	—
923	C₂³×C₄	—	67	1	no	—
924	C₂³×C₄	—	67	1	no	—
925	C₂³×C₄	—	67	1	no	—
926	C₂³×C₄	—	67	1	no	—
927	C₂³×C₄	—	134	4	no	—
928	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
929	#126	—	4	2	no	—
930	#126	—	268	2	no	—
931	#125	—	268	2	no	—
932	#123	—	268	2	no	—
933	#123	—	268	2	no	—
934	#123	—	134	4	no	—
935	C₂²⋊Q₈	—	4	2	no	—
936	C₂²⋊Q₈	—	268	2	no	—
937	C₂²⋊Q₈	—	134	4	no	—
938	#120	—	268	2	no	—
939	#117	—	268	2	no	—
940	#117	—	268	2	no	—
941	C₂×C₄⋊C₄	—	67	1	no	—
942	C₂×C₄⋊C₄	—	67	1	no	—
943	C₂×C₄⋊C₄	—	67	1	no	—
944	C₂×C₄⋊C₄	—	67	1	no	—
945	C₂×C₄⋊C₄	—	67	1	no	—
946	C₂×C₄⋊C₄	—	67	1	no	—
947	C₂×C₄⋊C₄	—	67	1	no	—
948	C₂×C₄⋊C₄	—	67	1	no	—
949	C₂×C₄⋊C₄	—	67	1	no	—
950	C₂×C₄⋊C₄	—	67	1	no	—
951	C₂×C₄⋊C₄	—	67	1	no	—
952	C₂×C₄⋊C₄	—	67	1	no	—
953	C₂×C₄⋊C₄	—	67	1	no	—
954	C₂×C₄⋊C₄	—	67	1	no	—
955	C₂×C₄⋊C₄	—	67	1	no	—
956	C₂×C₄⋊C₄	—	67	1	no	—
957	C₂×C₄⋊C₄	—	67	1	no	—
958	C₂×C₄⋊C₄	—	67	1	no	—
959	C₂×C₄⋊C₄	—	67	1	no	—
960	C₂×C₄⋊C₄	—	67	1	no	—
961	C₂×C₄⋊C₄	—	67	1	no	—
962	C₂×C₄⋊C₄	—	67	1	no	—
963	C₂×C₄⋊C₄	—	67	1	no	—
964	C₂×C₄⋊C₄	—	67	1	no	—
965	C₂×C₄⋊C₄	—	67	1	no	—
966	C₂×C₄⋊C₄	—	67	1	no	—
967	C₂×C₄⋊C₄	—	67	1	no	—
968	C₂×C₄⋊C₄	—	67	1	no	—
969	C₂×C₄⋊C₄	—	67	1	no	—
970	C₂×C₄⋊C₄	—	67	1	no	—
971	C₂×C₄⋊C₄	—	67	1	no	—
972	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
980	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
981	C₂×C₂²⋊C₄	—	67	1	no	—
982	C₂×C₂²⋊C₄	—	67	1	no	—
983	C₂×C₂²⋊C₄	—	67	1	no	—
984	C₂×C₂²⋊C₄	—	67	1	no	—
985	C₂×C₂²⋊C₄	—	67	1	no	—
986	C₂×C₂²⋊C₄	—	67	1	no	—
987	C₂×C₂²⋊C₄	—	67	1	no	—
988	C₂×C₂²⋊C₄	—	67	1	no	—
989	C₂×C₂²⋊C₄	—	67	1	no	—
990	C₂×C₂²⋊C₄	—	67	1	no	—
991	C₂×C₂²⋊C₄	—	67	1	no	—
992	C₂×C₂²⋊C₄	—	67	1	no	—
993	C₂×C₂²⋊C₄	—	67	1	no	—
994	C₂×C₂²⋊C₄	—	67	1	no	—
995	C₂×C₂²⋊C₄	—	67	1	no	—
996	C₂×C₂²⋊C₄	—	67	1	no	—
997	C₂×C₂²⋊C₄	—	67	1	no	—
998	C₂×C₂²⋊C₄	—	67	1	no	—
999	C₂×C₂²⋊C₄	—	67	1	no	—
1000	C₂×C₂²⋊C₄	—	67	1	no	—
1001	C₂×C₂²⋊C₄	—	67	1	no	—
1002	C₂×C₂²⋊C₄	—	67	1	no	—
1003	C₂×C₂²⋊C₄	—	67	1	no	—
1004	C₂×C₂²⋊C₄	—	67	1	no	—
1005	C₂×C₂²⋊C₄	—	67	1	no	—
1006	C₂×C₂²⋊C₄	—	67	1	no	—
1007	C₂×C₂²⋊C₄	—	67	1	no	—
1008	C₂×C₂²⋊C₄	—	67	1	no	—
1009	C₂×C₂²⋊C₄	—	67	1	no	—
1010	C₂×C₂²⋊C₄	—	67	1	no	—
1011	C₂×C₂²⋊C₄	—	67	1	no	—
1012	C₂×C₂²⋊C₄	—	67	1	no	—
1013	C₂×C₂²⋊C₄	—	67	1	no	—
1014	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1015	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1016	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1018	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1025	C₂×C₄²	—	67	1	no	—
1026	C₂×C₄²	—	67	1	no	—
1027	C₂×C₄²	—	67	1	no	—
1028	C₂×C₄²	—	67	1	no	—
1029	C₂×C₄²	—	67	1	no	—
1030	C₂×C₄²	—	67	1	no	—
1031	C₂×C₄²	—	67	1	no	—
1032	C₂×C₄²	—	67	1	no	—
1033	C₂×C₄²	—	67	1	no	—
1034	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1035	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1036	#95	—	67	1	no	—
1037	#95	—	67	1	no	—
1038	#95	—	67	1	no	—
1039	#95	—	67	1	no	—
1040	#95	—	67	1	no	—
1041	#95	—	67	1	no	—
1042	#95	—	67	1	no	—
1043	#95	—	67	1	no	—
1044	#95	—	67	1	no	—
1045	#95	—	67	1	no	—
1046	#95	—	67	1	no	—
1047	#95	—	67	1	no	—
1048	#95	—	67	1	no	—
1049	#95	—	67	1	no	—
1050	#95	—	67	1	no	—
1051	#95	—	67	1	no	—
1052	#95	—	67	1	no	—
1053	#95	—	67	1	no	—
1054	#95	—	67	1	no	—
1055	#95	—	67	1	no	—
1056	#95	—	67	1	no	—
1057	#95	—	67	1	no	—
1058	#95	—	67	1	no	—
1059	#95	—	67	1	no	—
1060	#95	—	67	1	no	—
1061	#95	—	67	1	no	—
1062	#95	—	67	1	no	—
1063	#95	—	67	1	no	—
1064	#95	—	67	1	no	—
1065	#95	—	67	1	no	—
1066	#95	—	67	1	no	—
1067	#95	—	67	1	no	—
1068	#95	—	67	1	no	—
1069	#95	—	67	1	no	—
1070	#95	—	67	1	no	—
1071	#95	—	67	1	no	—
1072	#95	—	67	1	no	—
1073	#95	—	67	1	no	—
1074	#95	C₂²×D₆₇	1	1	yes	characteristic
1075	#95	C₂²×D₆₇	1	1	yes	characteristic
1076	#95	C₂²×D₆₇	1	1	yes	characteristic
1077	#95	C₂²×D₆₇	1	1	yes	characteristic
1078	#95	C₂²×D₆₇	1	1	yes	characteristic
1079	#95	C₂²×D₆₇	1	1	yes	characteristic
1080	#95	C₂²×D₆₇	1	1	yes	characteristic
1081	#95	C₂²×D₆₇	1	1	yes	characteristic
1082	#95	C₂²×D₆₇	1	1	yes	characteristic
1083	#95	C₂²×D₆₇	1	1	yes	characteristic
1084	C₂⁴	—	268	1	no	—
1085	C₂⁴	—	268	1	no	—
1086	C₂⁴	—	268	1	no	—
1087	C₂⁴	—	268	1	no	—
1088	C₂⁴	—	67	1	no	—
1089	C₂⁴	—	67	1	no	—
1090	C₂⁴	—	134	2	no	—
1091	C₂⁴	—	134	2	no	—
1092	C₂⁴	—	134	2	no	—
1093	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1094	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1095	C₂×Q₈	—	2	2	no	—
1096	C₂×Q₈	—	4	1	no	—
1097	C₂×Q₈	—	4	1	no	—
1098	C₂×D₄	—	2	2	no	—
1099	C₂×D₄	—	4	1	no	—
1100	C₂×D₄	—	4	1	no	—
1101	C₂×D₄	—	268	1	no	—
1102	C₂×D₄	—	268	1	no	—
1103	C₂×D₄	—	268	1	no	—
1104	C₂×D₄	—	268	1	no	—
1105	C₂×D₄	—	134	2	no	—
1106	C₂×D₄	—	134	2	no	—
1107	C₂²×C₄	—	2	2	no	—
1108	C₂²×C₄	—	2	2	no	—
1109	C₂²×C₄	—	4	1	no	—
1110	C₂²×C₄	—	268	1	no	—
1111	C₂²×C₄	—	268	1	no	—
1112	C₂²×C₄	—	268	1	no	—
1113	C₂²×C₄	—	268	1	no	—
1114	C₂²×C₄	—	268	16	no	—
1115	C₂²×C₄	—	268	1	no	—
1116	C₂²×C₄	—	268	1	no	—
1117	C₂²×C₄	—	268	1	no	—
1118	C₂²×C₄	—	268	1	no	—
1119	C₂²×C₄	—	268	1	no	—
1120	C₂²×C₄	—	67	4	no	—
1121	C₂²×C₄	—	67	1	no	—
1122	C₂²×C₄	—	67	1	no	—
1123	C₂²×C₄	—	67	1	no	—
1124	C₂²×C₄	—	67	1	no	—
1125	C₂²×C₄	—	67	1	no	—
1126	C₂²×C₄	—	67	1	no	—
1127	C₂²×C₄	—	67	1	no	—
1128	C₂²×C₄	—	67	1	no	—
1129	C₂²×C₄	—	67	1	no	—
1130	C₂²×C₄	—	67	1	no	—
1131	C₂²×C₄	—	67	1	no	—
1132	C₂²×C₄	—	67	1	no	—
1133	C₂²×C₄	—	67	1	no	—
1134	C₂²×C₄	—	67	1	no	—
1135	C₂²×C₄	—	134	2	no	—
1136	C₂²×C₄	—	134	2	no	—
1137	C₂²×C₄	—	134	2	no	—
1138	C₂²×C₄	—	134	2	no	—
1139	C₂²×C₄	—	134	2	no	—
1140	C₂²×C₄	—	134	2	no	—
1141	C₂²×C₄	—	134	2	no	—
1142	C₂²×C₄	—	134	2	no	—
1143	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1144	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1145	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1147	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1148	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1151	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1152	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1153	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1154	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1155	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1156	C₄⋊C₄	—	2	2	no	—
1157	C₄⋊C₄	—	2	2	no	—
1158	C₄⋊C₄	—	2	2	no	—
1159	C₄⋊C₄	—	4	1	no	—
1160	C₄⋊C₄	—	4	1	no	—
1161	C₄⋊C₄	—	4	1	no	—
1162	C₄⋊C₄	—	4	1	no	—
1163	C₄⋊C₄	—	4	1	no	—
1164	C₄⋊C₄	—	4	1	no	—
1165	C₄⋊C₄	—	268	1	no	—
1166	C₄⋊C₄	—	268	1	no	—
1167	C₄⋊C₄	—	268	1	no	—
1168	C₄⋊C₄	—	268	1	no	—
1169	C₄⋊C₄	—	268	1	no	—
1170	C₄⋊C₄	—	268	1	no	—
1171	C₄⋊C₄	—	268	1	no	—
1172	C₄⋊C₄	—	268	1	no	—
1173	C₄⋊C₄	—	268	1	no	—
1174	C₄⋊C₄	—	268	1	no	—
1175	C₄⋊C₄	—	268	1	no	—
1176	C₄⋊C₄	—	268	1	no	—
1177	C₄⋊C₄	—	268	1	no	—
1178	C₄⋊C₄	—	268	1	no	—
1179	C₄⋊C₄	—	268	1	no	—
1180	C₄⋊C₄	—	268	1	no	—
1181	C₄⋊C₄	—	268	1	no	—
1182	C₄⋊C₄	—	268	1	no	—
1183	C₄⋊C₄	—	268	1	no	—
1184	C₄⋊C₄	—	268	1	no	—
1185	C₄⋊C₄	—	268	1	no	—
1186	C₄⋊C₄	—	268	1	no	—
1187	C₄⋊C₄	—	268	1	no	—
1188	C₄⋊C₄	—	268	1	no	—
1189	C₄⋊C₄	—	134	2	no	—
1190	C₄⋊C₄	—	134	2	no	—
1191	C₄⋊C₄	—	134	2	no	—
1192	C₄⋊C₄	—	134	2	no	—
1193	C₄⋊C₄	—	134	2	no	—
1194	C₄⋊C₄	—	134	2	no	—
1195	C₄⋊C₄	—	134	2	no	—
1196	C₂²⋊C₄	—	2	2	no	—
1197	C₂²⋊C₄	—	2	2	no	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	4	1	no	—
1201	C₂²⋊C₄	—	4	1	no	—
1202	C₂²⋊C₄	—	4	1	no	—
1203	C₂²⋊C₄	—	4	1	no	—
1204	C₂²⋊C₄	—	4	1	no	—
1205	C₂²⋊C₄	—	4	1	no	—
1206	C₂²⋊C₄	—	4	1	no	—
1207	C₂²⋊C₄	—	268	1	no	—
1208	C₂²⋊C₄	—	268	1	no	—
1209	C₂²⋊C₄	—	268	1	no	—
1210	C₂²⋊C₄	—	268	1	no	—
1211	C₂²⋊C₄	—	268	1	no	—
1212	C₂²⋊C₄	—	268	1	no	—
1213	C₂²⋊C₄	—	268	1	no	—
1214	C₂²⋊C₄	—	268	1	no	—
1215	C₂²⋊C₄	—	268	1	no	—
1216	C₂²⋊C₄	—	268	1	no	—
1217	C₂²⋊C₄	—	268	1	no	—
1218	C₂²⋊C₄	—	268	1	no	—
1219	C₂²⋊C₄	—	268	1	no	—
1220	C₂²⋊C₄	—	268	1	no	—
1221	C₂²⋊C₄	—	268	1	no	—
1222	C₂²⋊C₄	—	268	1	no	—
1223	C₂²⋊C₄	—	268	1	no	—
1224	C₂²⋊C₄	—	268	1	no	—
1225	C₂²⋊C₄	—	268	1	no	—
1226	C₂²⋊C₄	—	268	1	no	—
1227	C₂²⋊C₄	—	268	1	no	—
1228	C₂²⋊C₄	—	268	1	no	—
1229	C₂²⋊C₄	—	268	1	no	—
1230	C₂²⋊C₄	—	134	2	no	—
1231	C₂²⋊C₄	—	134	2	no	—
1232	C₂²⋊C₄	—	134	2	no	—
1233	C₂²⋊C₄	—	134	2	no	—
1234	C₂²⋊C₄	—	134	2	no	—
1235	C₂²⋊C₄	—	134	2	no	—
1236	C₂²⋊C₄	—	134	2	no	—
1237	C₂²⋊C₄	—	134	2	no	—
1238	C₂²⋊C₄	—	134	2	no	—
1239	C₂²⋊C₄	—	134	2	no	—
1240	C₄²	—	4	1	no	—
1241	C₄²	—	4	1	no	—
1242	C₄²	—	268	1	no	—
1243	C₄²	—	268	1	no	—
1244	C₄²	—	268	1	no	—
1245	C₄²	—	268	1	no	—
1246	C₄²	—	268	1	no	—
1247	C₄²	—	268	1	no	—
1248	C₄²	—	268	1	no	—
1249	C₄²	—	268	1	no	—
1250	C₄²	—	268	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	1	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	1	no	—
1259	C₂³	—	2	1	no	—
1260	C₂³	—	2	1	no	—
1261	C₂³	—	2	1	no	—
1262	C₂³	—	2	1	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	268	4	no	—
1265	C₂³	—	268	4	no	—
1266	C₂³	—	268	4	no	—
1267	C₂³	—	268	4	no	—
1268	C₂³	—	268	4	no	—
1269	C₂³	—	268	4	no	—
1270	C₂³	—	268	4	no	—
1271	C₂³	—	67	2	no	—
1272	C₂³	—	67	2	no	—
1273	C₂³	—	134	1	no	—
1274	C₂³	—	134	1	no	—
1275	C₂³	—	134	1	no	—
1276	C₂³	—	134	1	no	—
1277	C₂³	—	134	1	no	—
1278	C₂³	—	134	1	no	—
1279	C₂³	—	134	1	no	—
1280	C₂³	—	134	1	no	—
1281	C₂³	—	134	1	no	—
1282	C₂³	—	134	1	no	—
1283	C₂³	—	134	1	no	—
1284	C₂³	—	134	1	no	—
1285	C₂³	#14524090	1	2	yes	—
1286	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1287	Q₈	—	8	2	no	—
1288	D₄	—	8	2	no	—
1289	D₄	—	536	2	no	—
1290	D₄	—	536	2	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	4	4	no	—
1329	C₂×C₄	—	268	4	no	—
1330	C₂×C₄	—	268	4	no	—
1331	C₂×C₄	—	268	4	no	—
1332	C₂×C₄	—	268	4	no	—
1333	C₂×C₄	—	536	2	no	—
1334	C₂×C₄	—	67	2	no	—
1335	C₂×C₄	—	134	8	no	—
1336	C₂×C₄	—	134	1	no	—
1337	C₂×C₄	—	134	1	no	—
1338	C₂×C₄	—	134	1	no	—
1339	C₂×C₄	—	134	1	no	—
1340	C₂×C₄	—	134	1	no	—
1341	C₂×C₄	—	134	1	no	—
1342	C₂×C₄	—	134	1	no	—
1343	C₂×C₄	—	134	1	no	—
1344	C₂×C₄	—	134	1	no	—
1345	C₂×C₄	—	134	1	no	—
1346	C₂×C₄	—	134	1	no	—
1347	C₂×C₄	—	134	1	no	—
1348	C₂×C₄	—	134	1	no	—
1349	C₂×C₄	—	134	1	no	—
1350	C₂×C₄	—	134	1	no	—
1351	C₂×C₄	—	134	1	no	—
1352	C₂×C₄	—	134	1	no	—
1353	C₂×C₄	—	134	1	no	—
1354	C₂×C₄	—	134	1	no	—
1355	C₂×C₄	—	134	1	no	—
1356	C₂×C₄	—	134	1	no	—
1357	C₂×C₄	—	134	1	no	—
1358	C₂×C₄	—	134	1	no	—
1359	C₂×C₄	—	134	1	no	—
1360	C₂×C₄	—	134	1	no	—
1361	C₂×C₄	—	134	1	no	—
1362	C₂×C₄	—	134	1	no	—
1363	C₂×C₄	—	134	1	no	—
1364	C₂×C₄	—	134	1	no	—
1365	C₂×C₄	—	134	1	no	—
1366	C₂×C₄	—	134	1	no	—
1367	C₂×C₄	—	134	1	no	—
1368	C₂×C₄	—	134	1	no	—
1369	C₂×C₄	—	134	1	no	—
1370	C₂×C₄	—	134	1	no	—
1371	C₂×C₄	—	134	1	no	—
1372	C₂×C₄	—	134	1	no	—
1373	C₂×C₄	—	134	1	no	—
1374	C₂×C₄	—	134	1	no	—
1375	C₂×C₄	—	134	1	no	—
1376	C₂×C₄	—	134	1	no	—
1377	C₂×C₄	#41×D₆₇	1	2	yes	—
1378	C₂×C₄	#14524088	1	2	yes	—
1379	C₂²	—	2	2	no	—
1380	C₂²	—	2	2	no	—
1381	C₂²	—	2	2	no	—
1382	C₂²	—	4	1	no	—
1383	C₂²	—	4	1	no	—
1384	C₂²	—	4	1	no	—
1385	C₂²	—	4	1	no	—
1386	C₂²	—	4	1	no	—
1387	C₂²	—	4	1	no	—
1388	C₂²	—	4	1	no	—
1389	C₂²	—	4	1	no	—
1390	C₂²	—	4	1	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	1	no	—
1393	C₂²	—	268	16	no	—
1394	C₂²	—	268	1	no	—
1395	C₂²	—	268	1	no	—
1396	C₂²	—	268	1	no	—
1397	C₂²	—	268	1	no	—
1398	C₂²	—	268	1	no	—
1399	C₂²	—	268	1	no	—
1400	C₂²	—	268	1	no	—
1401	C₂²	—	268	1	no	—
1402	C₂²	—	134	2	no	—
1403	C₂²	—	134	2	no	—
1404	C₂²	—	134	2	no	—
1405	C₂²	—	134	2	no	—
1406	C₂²	—	134	2	no	—
1407	C₂²	—	134	2	no	—
1408	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1409	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1410	C₂²	C₂×#14524088	1	1	yes	characteristic
1411	C₂²	C₂×#14524090	1	1	yes	characteristic
1412	C₂²	#16864231	1	1	yes	characteristic
1413	C₂²	#16864233	1	1	yes	characteristic
1414	C₂²	#16864233	1	1	yes	characteristic
1415	C₄	—	2	2	no	—
1416	C₄	—	2	2	no	—
1417	C₄	—	4	1	no	—
1418	C₄	—	4	1	no	—
1419	C₄	—	4	1	no	—
1420	C₄	—	4	1	no	—
1421	C₄	—	4	1	no	—
1422	C₄	—	4	1	no	—
1423	C₄	—	4	1	no	—
1424	C₄	—	4	1	no	—
1425	C₄	—	4	1	no	—
1426	C₄	—	4	1	no	—
1427	C₄	—	4	1	no	—
1428	C₄	—	268	1	no	—
1429	C₄	—	268	1	no	—
1430	C₄	—	268	1	no	—
1431	C₄	—	268	1	no	—
1432	C₄	—	268	1	no	—
1433	C₄	—	268	1	no	—
1434	C₄	—	268	1	no	—
1435	C₄	—	268	1	no	—
1436	C₄	—	268	1	no	—
1437	C₄	—	268	1	no	—
1438	C₄	—	268	1	no	—
1439	C₄	—	268	1	no	—
1440	C₄	—	268	1	no	—
1441	C₄	—	134	2	no	—
1442	C₂	—	4	2	no	—
1443	C₂	—	8	1	no	—
1444	C₂	—	268	2	no	—
1445	C₂	—	268	2	no	—
1446	C₂	#22573596	1	1	yes	characteristic
1447	C₂	#22573891	1	1	yes	characteristic
1448	C₂	#22573950	1	1	yes	characteristic
1449	C₂	#22574385	1	1	yes	characteristic
1450	C₂	#22574407	1	1	yes	characteristic
1451	C₂	#22574462	1	1	yes	characteristic
1452	C₂	#22574488	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2702	C₂
prime radical	C₂×#14524011	C₂²
hypercenter	#2702	D₆₇
hypocenter	C₆₇	#36736
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2702

Complements

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

N	H ≅ G/N	type
2. #22568493	C₂	semidirect
3. #22567424	C₂	semidirect
4. #22567408	C₂	semidirect
5. #22567312	C₂	semidirect
6. #22567297	C₂	semidirect
7. #22567286	C₂	semidirect
8. #22567278	C₂	semidirect
9. #22567248	C₂	semidirect
10. #22567245	C₂	semidirect
11. #22566863	C₂	semidirect
13. #22566738	C₂	semidirect
14. #22566735	C₂	semidirect
15. #22566655	C₂	semidirect
16. #22566629	C₂	semidirect
18. #22566408	C₂	semidirect
19. #22566365	C₂	semidirect
20. #22565763	C₂	semidirect
21. #22565628	C₂	semidirect
22. #22565626	C₂	semidirect
23. #22565544	C₂	semidirect
24. #22564436	C₂	semidirect
25. #22564431	C₂	semidirect
26. #22564373	C₂	semidirect
27. #22564306	C₂	semidirect
28. #22563006	C₂	semidirect
29. #22562964	C₂	semidirect
30. #22562591	C₂	semidirect
31. C₆₇×#2702	C₂	semidirect
34. C₂×#14524033	C₂²	semidirect
43. #16863338	C₂²	semidirect
44. #16863338	C₂²	semidirect
45. #16863336	C₂²	semidirect
46. #16863335	C₂²	semidirect
47. #16863335	C₂²	semidirect
48. #16863334	C₂²	semidirect
50. #16863332	C₂²	semidirect
51. #16863332	C₂²	semidirect
54. #16863329	C₂²	semidirect
55. #16863329	C₂²	semidirect
56. #16863329	C₂²	semidirect
57. #16863328	C₂²	semidirect
58. #16863328	C₂²	semidirect
59. #16863328	C₂²	semidirect
60. #16863328	C₂²	semidirect
61. #16863327	C₂²	semidirect
62. #16863326	C₂²	semidirect
68. #16863324	C₂²	semidirect
69. #16863324	C₂²	semidirect
80. #16863315	C₂²	semidirect
85. #16863303	C₂²	semidirect
89. #16863295	C₂²	semidirect
90. #16863295	C₂²	semidirect
91. #16863294	C₂²	semidirect
92. #16863293	C₂²	semidirect
93. #16863293	C₂²	semidirect
94. #16863293	C₂²	semidirect
95. #16863292	C₂²	semidirect
96. #16863291	C₂²	semidirect
98. #16863290	C₂²	semidirect
113. #16863284	C₂²	semidirect
114. #16863284	C₂²	semidirect
115. #16863284	C₂²	semidirect
116. #16863283	C₂²	semidirect
117. #16863283	C₂²	semidirect
118. #16863282	C₂²	semidirect
119. #16863282	C₂²	semidirect
120. #16863281	C₂²	semidirect
121. #16863280	C₂²	semidirect
122. #16863279	C₂²	semidirect
123. #16863279	C₂²	semidirect
124. #16863279	C₂²	semidirect
125. #16863279	C₂²	semidirect
126. #16863278	C₂²	semidirect
127. #16863277	C₂²	semidirect
128. #16863277	C₂²	semidirect
129. #16863277	C₂²	semidirect
136. #16863271	C₂²	semidirect
137. #16863271	C₂²	semidirect
147. #16863263	C₂²	semidirect
154. #16863254	C₂²	semidirect
164. C₄×Dic₆₇⋊C₄	C₂²	semidirect
165. C₄×C₄⋊Dic₆₇	C₂²	semidirect
166. #16863247	C₂²	semidirect
169. C₂²⋊C₄×Dic₆₇	C₂²	semidirect
172. C₂×#126×C₆₇	C₂²	semidirect
174. #400×C₆₇	C₂²	semidirect
175. #398×C₆₇	C₂²	semidirect
176. #396×C₆₇	C₂²	semidirect
179. #393×C₆₇	C₂²	semidirect
180. #391×C₆₇	C₂²	semidirect
181. #389×C₆₇	C₂²	semidirect
184. #388×C₆₇	C₂²	semidirect
738. #2702	D₆₇	semidirect
758. C₆₇	#36736	semidirect
761. C₂×#126	C₂×D₆₇	semidirect
778. #400	C₂×D₆₇	semidirect
793. #398	C₂×D₆₇	semidirect
811. #396	C₂×D₆₇	semidirect
819. #393	C₂×D₆₇	semidirect
821. #391	C₂×D₆₇	semidirect
833. #389	C₂×D₆₇	semidirect
855. #388	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568500	2
#22568493	2
#22567424	2
#22567408	2
#22567312	2
#22567297	2
#22567286	2
#22567278	2
#22567248	2
#22567245	2
#22566863	2
#22566775	2
#22566738	2
#22566735	2
#22566655	2
#22566629	2
#22566599	2
#22566408	2
#22566365	2
#22565763	2
#22565628	2
#22565626	2
#22565544	2
#22564436	2
#22564431	2
#22564373	2
#22564306	2
#22563006	2
#22562964	2
#22562591	2
C₆₇×#2702	2
#36736	67