Subgroups — #31063483

Order 17152.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568558	C₂	1	1	yes	maximal, characteristic, complemented
2	#22568514	C₂	1	1	yes	maximal, characteristic, complemented
3	#22568181	C₂	1	1	yes	maximal, characteristic, complemented
4	#22568179	C₂	1	1	yes	maximal, characteristic, complemented
5	#22567953	C₂	1	1	yes	maximal, characteristic, complemented
6	#22567951	C₂	1	1	yes	maximal, characteristic, complemented
7	#22567696	C₂	1	1	yes	maximal, characteristic, complemented
8	#22567694	C₂	1	1	yes	maximal, characteristic, complemented
9	#22567625	C₂	1	1	yes	maximal, characteristic, complemented
10	#22567620	C₂	1	1	yes	maximal, characteristic, complemented
11	#22567198	C₂	1	1	yes	maximal, characteristic, complemented
12	#22567187	C₂	1	1	yes	maximal, characteristic, complemented
13	#22567095	C₂	1	1	yes	maximal, characteristic, complemented
14	#22567089	C₂	1	1	yes	maximal, characteristic, complemented
15	#22566869	C₂	1	1	yes	maximal, characteristic, complemented
16	#22566868	C₂	1	1	yes	maximal, characteristic, complemented
17	#22566861	C₂	1	1	yes	maximal, characteristic, complemented
18	#22566324	C₂	1	1	yes	maximal, characteristic, complemented
19	#22566178	C₂	1	1	yes	maximal, characteristic, complemented
20	#22565219	C₂	1	1	yes	maximal, characteristic, complemented
21	#22565214	C₂	1	1	yes	maximal, characteristic, complemented
22	#22563935	C₂	1	1	yes	maximal, characteristic, complemented
23	#22563928	C₂	1	1	yes	maximal, characteristic, complemented
24	#22563877	C₂	1	1	yes	maximal, characteristic
25	#22563872	C₂	1	1	yes	maximal, characteristic
26	#22563871	C₂	1	1	yes	maximal, characteristic
27	#22563871	C₂	1	1	yes	maximal, characteristic
28	#22562820	C₂	1	1	yes	maximal, characteristic
29	#22562803	C₂	1	1	yes	maximal, characteristic
30	#388×D₆₇	C₂	1	1	yes	maximal, characteristic
31	C₆₇×#2704	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14524033	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14524023	C₂²	1	1	yes	characteristic
36	C₂×#14524023	C₂²	1	1	yes	characteristic
37	C₂×#14524021	C₂²	1	1	yes	characteristic
38	C₂×#14524021	C₂²	1	1	yes	characteristic
39	C₂×#14524021	C₂²	1	1	yes	characteristic
40	C₂×#14524020	C₂²	1	1	yes	characteristic
41	C₂×#14524019	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
43	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
49	#16863338	C₂²	1	1	yes	characteristic, complemented
50	#16863338	C₂²	1	1	yes	characteristic, complemented
51	#16863338	C₂²	1	1	yes	characteristic, complemented
52	#16863337	C₂²	1	1	yes	characteristic, complemented
53	#16863337	C₂²	1	1	yes	characteristic, complemented
54	#16863337	C₂²	1	1	yes	characteristic, complemented
55	#16863335	C₂²	1	1	yes	characteristic, complemented
56	#16863334	C₂²	1	1	yes	characteristic, complemented
57	#16863332	C₂²	1	1	yes	characteristic
58	#16863332	C₂²	1	1	yes	characteristic
59	#16863331	C₂²	1	1	yes	characteristic
60	#16863331	C₂²	1	1	yes	characteristic
61	#16863330	C₂²	1	1	yes	characteristic, complemented
62	#16863329	C₂²	1	1	yes	characteristic, complemented
63	#16863329	C₂²	1	1	yes	characteristic, complemented
64	#16863329	C₂²	1	1	yes	characteristic, complemented
65	#16863329	C₂²	1	1	yes	characteristic, complemented
66	#16863329	C₂²	1	1	yes	characteristic, complemented
67	#16863328	C₂²	1	1	yes	characteristic, complemented
68	#16863327	C₂²	1	1	yes	characteristic, complemented
69	#16863327	C₂²	1	1	yes	characteristic, complemented
70	#16863327	C₂²	1	1	yes	characteristic, complemented
71	#16863327	C₂²	1	1	yes	characteristic, complemented
72	#16863326	C₂²	1	1	yes	characteristic, complemented
73	#16863326	C₂²	1	1	yes	characteristic, complemented
74	#16863320	C₂²	1	1	yes	characteristic
75	#16863319	C₂²	1	1	yes	characteristic
76	#16863319	C₂²	1	1	yes	characteristic
77	#16863318	C₂²	1	1	yes	characteristic
78	#16863318	C₂²	1	1	yes	characteristic
79	#16863318	C₂²	1	1	yes	characteristic
80	#16863317	C₂²	1	1	yes	characteristic, complemented
81	#16863317	C₂²	1	1	yes	characteristic, complemented
82	#16863317	C₂²	1	1	yes	characteristic, complemented
83	#16863317	C₂²	1	1	yes	characteristic, complemented
84	#16863316	C₂²	1	1	yes	characteristic, complemented
85	#16863316	C₂²	1	1	yes	characteristic, complemented
86	#16863316	C₂²	1	1	yes	characteristic, complemented
87	#16863309	C₂²	1	1	yes	characteristic
88	#16863308	C₂²	1	1	yes	characteristic
89	#16863308	C₂²	1	1	yes	characteristic
90	#16863307	C₂²	1	1	yes	characteristic
91	#16863303	C₂²	1	1	yes	characteristic, complemented
92	#16863302	C₂²	1	1	yes	characteristic, complemented
93	#16863302	C₂²	1	1	yes	characteristic, complemented
94	#16863300	C₂²	1	1	yes	characteristic, complemented
95	#16863300	C₂²	1	1	yes	characteristic, complemented
96	#16863295	C₂²	1	1	yes	characteristic, complemented
97	#16863293	C₂²	1	1	yes	characteristic, complemented
98	#16863293	C₂²	1	1	yes	characteristic, complemented
99	#16863293	C₂²	1	1	yes	characteristic, complemented
100	#16863293	C₂²	1	1	yes	characteristic, complemented
101	#16863293	C₂²	1	1	yes	characteristic, complemented
102	#16863292	C₂²	1	1	yes	characteristic, complemented
103	#16863292	C₂²	1	1	yes	characteristic, complemented
104	#16863292	C₂²	1	1	yes	characteristic, complemented
105	#16863291	C₂²	1	1	yes	characteristic, complemented
106	#16863291	C₂²	1	1	yes	characteristic, complemented
107	#16863291	C₂²	1	1	yes	characteristic, complemented
108	#16863290	C₂²	1	1	yes	characteristic
109	#16863290	C₂²	1	1	yes	characteristic
110	#16863289	C₂²	1	1	yes	characteristic
111	#16863289	C₂²	1	1	yes	characteristic
112	#16863288	C₂²	1	1	yes	characteristic
113	#16863288	C₂²	1	1	yes	characteristic
114	#16863287	C₂²	1	1	yes	characteristic
115	#16863287	C₂²	1	1	yes	characteristic
116	#16863286	C₂²	1	1	yes	characteristic
117	#16863286	C₂²	1	1	yes	characteristic
118	#16863285	C₂²	1	1	yes	characteristic
119	#16863285	C₂²	1	1	yes	characteristic
120	#16863284	C₂²	1	1	yes	characteristic
121	#16863284	C₂²	1	1	yes	characteristic
122	#16863277	C₂²	1	1	yes	characteristic, complemented
123	#16863277	C₂²	1	1	yes	characteristic, complemented
124	#16863277	C₂²	1	1	yes	characteristic, complemented
125	#16863277	C₂²	1	1	yes	characteristic, complemented
126	#16863271	C₂²	1	1	yes	characteristic
127	#16863271	C₂²	1	1	yes	characteristic
128	#16863270	C₂²	1	1	yes	characteristic
129	#16863270	C₂²	1	1	yes	characteristic
130	#16863270	C₂²	1	1	yes	characteristic
131	#16863270	C₂²	1	1	yes	characteristic
132	#16863270	C₂²	1	1	yes	characteristic
133	#16863269	C₂²	1	1	yes	characteristic
134	#16863269	C₂²	1	1	yes	characteristic
135	#16863269	C₂²	1	1	yes	characteristic
136	#16863268	C₂²	1	1	yes	characteristic
137	#16863268	C₂²	1	1	yes	characteristic
138	#16863267	C₂²	1	1	yes	characteristic
139	#16863267	C₂²	1	1	yes	characteristic
140	#16863267	C₂²	1	1	yes	characteristic
141	#16863267	C₂²	1	1	yes	characteristic
142	#16863267	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	#16863267	C₂²	1	1	yes	characteristic
148	#16863267	C₂²	1	1	yes	characteristic
149	#16863265	C₂²	1	1	yes	characteristic, complemented
150	#16863262	C₂²	1	1	yes	characteristic, complemented
151	#16863261	C₂²	1	1	yes	characteristic, complemented
152	#16863260	C₂²	1	1	yes	characteristic, complemented
153	#16863255	C₂²	1	1	yes	characteristic
154	#16863255	C₂²	1	1	yes	characteristic
155	#16863255	C₂²	1	1	yes	characteristic
156	#16863255	C₂²	1	1	yes	characteristic
157	#16863255	C₂²	1	1	yes	characteristic
158	#16863255	C₂²	1	1	yes	characteristic
159	#16863254	C₂²	1	1	yes	characteristic
160	#16863253	C₂²	1	1	yes	characteristic
161	#16863253	C₂²	1	1	yes	characteristic
162	#16863253	C₂²	1	1	yes	characteristic
163	#16863253	C₂²	1	1	yes	characteristic
164	#16863253	C₂²	1	1	yes	characteristic
165	#16863253	C₂²	1	1	yes	characteristic
166	#16863251	C₂²	1	1	yes	characteristic
167	#16863251	C₂²	1	1	yes	characteristic
168	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
169	#16863243	C₂²	1	1	yes	characteristic
170	#95×D₆₇	C₂²	1	1	yes	characteristic
171	#95×D₆₇	C₂²	1	1	yes	characteristic
172	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
173	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
174	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
175	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
176	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
177	#396×C₆₇	C₂²	1	1	yes	characteristic
178	#396×C₆₇	C₂²	1	1	yes	characteristic
179	#395×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	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
183	#388×C₆₇	C₂²	1	1	yes	characteristic
184	#388×C₆₇	C₂²	1	1	yes	characteristic
185	#385×C₆₇	C₂²	1	1	yes	characteristic
186	#380×C₆₇	C₂²	1	1	yes	characteristic
187	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
191	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
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	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
200	#14524041	—	4	2	no	—
201	#14524035	—	4	2	no	—
202	#14524033	—	4	2	no	—
203	#14524023	—	4	2	no	—
204	#14524023	—	4	2	no	—
205	#14524021	—	4	2	no	—
206	#14524021	—	4	2	no	—
207	#14524021	—	4	2	no	—
208	#14524020	—	4	2	no	—
209	#14524019	—	4	2	no	—
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×Dic₆₇⋊C₄	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×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
247	C₄⋊C₄×D₆₇	—	4	2	no	—
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×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
254	C₂×(C₂×D₆₇)⋊C₄	—	4	2	no	—
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×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
275	C₂²⋊C₄×D₆₇	—	4	2	no	—
276	C₂²⋊C₄×D₆₇	—	4	2	no	—
277	C₂²⋊C₄×D₆₇	—	4	2	no	—
278	C₂²⋊C₄×D₆₇	Q₈	1	8	yes	complemented
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	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
285	C₄²×D₆₇	—	4	2	no	—
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	C₆₇⋊#95	C₂³	1	1	yes	characteristic
321	C₆₇⋊#95	C₂³	1	1	yes	characteristic
322	C₆₇⋊#95	C₂³	1	1	yes	characteristic
323	C₆₇⋊#95	C₂³	1	1	yes	characteristic
324	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
325	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
326	#125×C₆₇	—	4	2	no	—
327	C₂²⋊Q₈×C₆₇	—	4	2	no	—
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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊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×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₄²×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	#95×C₆₇	C₂³	1	1	yes	characteristic
358	#95×C₆₇	C₂³	1	1	yes	characteristic
359	#95×C₆₇	C₂³	1	1	yes	characteristic
360	#95×C₆₇	C₂³	1	1	yes	characteristic
361	C₂³×D₆₇	—	2	2	no	—
362	C₂³×D₆₇	—	2	2	no	—
363	C₂³×D₆₇	—	4	1	no	—
364	C₂³×D₆₇	—	4	1	no	—
365	C₂³×D₆₇	—	4	1	no	—
366	C₂³×D₆₇	—	4	1	no	—
367	C₂³×D₆₇	C₂×Q₈	1	4	yes	—
368	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
369	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×Dic₁₃₄	—	2	2	no	—
371	C₂×Dic₁₃₄	—	4	1	no	—
372	C₂×Dic₁₃₄	—	4	1	no	—
373	C₂×Dic₁₃₄	—	4	1	no	—
374	C₂×Dic₁₃₄	—	4	1	no	—
375	C₂×Dic₁₃₄	—	4	1	no	—
376	C₂×Dic₁₃₄	—	4	1	no	—
377	C₂×Dic₁₃₄	—	4	1	no	—
378	C₂×Dic₁₃₄	—	4	1	no	—
379	C₂²×Dic₆₇	—	4	1	no	—
380	C₂²×Dic₆₇	—	4	1	no	—
381	C₂²×Dic₆₇	—	4	1	no	—
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	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
400	C₂×C₄×D₆₇	—	2	2	no	—
401	C₂×C₄×D₆₇	—	2	2	no	—
402	C₂×C₄×D₆₇	—	4	1	no	—
403	C₂×C₄×D₆₇	—	4	1	no	—
404	C₂×C₄×D₆₇	—	4	1	no	—
405	C₂×C₄×D₆₇	—	4	1	no	—
406	C₂×C₄×D₆₇	—	4	1	no	—
407	C₂×C₄×D₆₇	—	4	1	no	—
408	C₂×C₄×D₆₇	—	4	1	no	—
409	C₂×C₄×D₆₇	—	4	1	no	—
410	C₂×C₄×D₆₇	—	4	1	no	—
411	C₂×C₄×D₆₇	—	4	1	no	—
412	C₂×C₄×D₆₇	—	4	1	no	—
413	C₂×C₄×D₆₇	—	4	1	no	—
414	C₂×C₄×D₆₇	—	4	1	no	—
415	C₂×C₄×D₆₇	—	4	1	no	—
416	C₂×C₄×D₆₇	—	4	1	no	—
417	C₂×C₄×D₆₇	—	4	1	no	—
418	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
419	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
420	C₄⋊Dic₆₇	—	2	2	no	—
421	C₄⋊Dic₆₇	—	4	1	no	—
422	C₄⋊Dic₆₇	—	4	1	no	—
423	C₄⋊Dic₆₇	—	4	1	no	—
424	C₄⋊Dic₆₇	—	4	1	no	—
425	C₄⋊Dic₆₇	—	4	1	no	—
426	C₄⋊Dic₆₇	—	4	1	no	—
427	C₄⋊Dic₆₇	—	4	1	no	—
428	C₄⋊Dic₆₇	—	4	1	no	—
429	C₄⋊Dic₆₇	—	4	1	no	—
430	C₄⋊Dic₆₇	—	4	1	no	—
431	Dic₆₇⋊C₄	—	2	2	no	—
432	Dic₆₇⋊C₄	—	2	2	no	—
433	Dic₆₇⋊C₄	—	2	2	no	—
434	Dic₆₇⋊C₄	—	2	2	no	—
435	Dic₆₇⋊C₄	—	2	2	no	—
436	Dic₆₇⋊C₄	—	4	1	no	—
437	Dic₆₇⋊C₄	—	4	1	no	—
438	Dic₆₇⋊C₄	—	4	1	no	—
439	Dic₆₇⋊C₄	—	4	1	no	—
440	Dic₆₇⋊C₄	—	4	1	no	—
441	Dic₆₇⋊C₄	—	4	1	no	—
442	Dic₆₇⋊C₄	—	4	1	no	—
443	Dic₆₇⋊C₄	—	4	1	no	—
444	Dic₆₇⋊C₄	—	4	1	no	—
445	Dic₆₇⋊C₄	—	4	1	no	—
446	Dic₆₇⋊C₄	—	4	1	no	—
447	Dic₆₇⋊C₄	—	4	1	no	—
448	Dic₆₇⋊C₄	—	4	1	no	—
449	Dic₆₇⋊C₄	—	4	1	no	—
450	Dic₆₇⋊C₄	—	4	1	no	—
451	Dic₆₇⋊C₄	—	4	1	no	—
452	Dic₆₇⋊C₄	—	4	1	no	—
453	Dic₆₇⋊C₄	—	4	1	no	—
454	Dic₆₇⋊C₄	—	4	1	no	—
455	Dic₆₇⋊C₄	—	4	1	no	—
456	Dic₆₇⋊C₄	—	4	1	no	—
457	C₂²⋊Dic₆₇	—	2	2	no	—
458	C₂²⋊Dic₆₇	—	4	1	no	—
459	C₂²⋊Dic₆₇	—	4	1	no	—
460	C₂²⋊Dic₆₇	—	4	1	no	—
461	C₂²⋊Dic₆₇	—	4	1	no	—
462	C₂²⋊Dic₆₇	C₂×Q₈	1	4	yes	—
463	(C₂×D₆₇)⋊C₄	—	2	2	no	—
464	(C₂×D₆₇)⋊C₄	—	2	2	no	—
465	(C₂×D₆₇)⋊C₄	—	2	2	no	—
466	(C₂×D₆₇)⋊C₄	—	2	2	no	—
467	(C₂×D₆₇)⋊C₄	—	2	2	no	—
468	(C₂×D₆₇)⋊C₄	—	2	2	no	—
469	(C₂×D₆₇)⋊C₄	—	2	2	no	—
470	(C₂×D₆₇)⋊C₄	—	2	2	no	—
471	(C₂×D₆₇)⋊C₄	—	2	2	no	—
472	(C₂×D₆₇)⋊C₄	—	2	2	no	—
473	(C₂×D₆₇)⋊C₄	—	4	1	no	—
474	(C₂×D₆₇)⋊C₄	—	4	1	no	—
475	(C₂×D₆₇)⋊C₄	—	4	1	no	—
476	(C₂×D₆₇)⋊C₄	—	4	1	no	—
477	(C₂×D₆₇)⋊C₄	—	4	1	no	—
478	(C₂×D₆₇)⋊C₄	—	4	1	no	—
479	(C₂×D₆₇)⋊C₄	—	4	1	no	—
480	(C₂×D₆₇)⋊C₄	—	4	1	no	—
481	(C₂×D₆₇)⋊C₄	C₂×Q₈	1	4	yes	—
482	(C₂×D₆₇)⋊C₄	C₂×Q₈	1	4	yes	—
483	C₄×Dic₆₇	—	2	2	no	—
484	C₄×Dic₆₇	—	4	1	no	—
485	C₄×Dic₆₇	—	4	1	no	—
486	C₄×Dic₆₇	—	4	1	no	—
487	C₄×Dic₆₇	—	4	1	no	—
488	C₄×Dic₆₇	—	4	1	no	—
489	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
490	C₂×Q₈×C₆₇	—	2	2	no	—
491	C₂×Q₈×C₆₇	—	4	1	no	—
492	C₂×Q₈×C₆₇	—	4	1	no	—
493	C₂²×C₄×C₆₇	—	4	1	no	—
494	C₂²×C₄×C₆₇	—	4	1	no	—
495	C₂²×C₄×C₆₇	—	4	1	no	—
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	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
510	C₄⋊C₄×C₆₇	—	2	2	no	—
511	C₄⋊C₄×C₆₇	—	2	2	no	—
512	C₄⋊C₄×C₆₇	—	4	1	no	—
513	C₄⋊C₄×C₆₇	—	4	1	no	—
514	C₄⋊C₄×C₆₇	—	4	1	no	—
515	C₄⋊C₄×C₆₇	—	4	1	no	—
516	C₄⋊C₄×C₆₇	—	4	1	no	—
517	C₄⋊C₄×C₆₇	—	4	1	no	—
518	C₄⋊C₄×C₆₇	—	4	1	no	—
519	C₄⋊C₄×C₆₇	—	4	1	no	—
520	C₄⋊C₄×C₆₇	—	4	1	no	—
521	C₄⋊C₄×C₆₇	—	4	1	no	—
522	C₄⋊C₄×C₆₇	—	4	1	no	—
523	C₄⋊C₄×C₆₇	—	4	1	no	—
524	C₄⋊C₄×C₆₇	—	4	1	no	—
525	C₂²⋊C₄×C₆₇	—	2	2	no	—
526	C₂²⋊C₄×C₆₇	—	4	1	no	—
527	C₂²⋊C₄×C₆₇	—	4	1	no	—
528	C₂²⋊C₄×C₆₇	—	4	1	no	—
529	C₂²⋊C₄×C₆₇	—	4	1	no	—
530	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
531	C₄²×C₆₇	—	2	2	no	—
532	C₄²×C₆₇	—	4	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	no	—
538	C₂³×C₆₇	—	2	1	no	—
539	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
540	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
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	—	2	8	no	—
552	C₂²×D₆₇	—	4	4	no	—
553	C₂²×D₆₇	—	4	4	no	—
554	C₂²×D₆₇	—	8	2	no	—
555	C₂²×D₆₇	—	8	2	no	—
556	C₂²×D₆₇	—	8	2	no	—
557	C₂²×D₆₇	—	8	2	no	—
558	C₂²×D₆₇	C₂²×Q₈	1	2	yes	—
559	C₂²×D₆₇	C₂²×Q₈	1	2	yes	—
560	C₂²×D₆₇	H(5,𝔽₂)	1	2	yes	—
561	C₂²×D₆₇	2₋¹⁺⁴	1	2	yes	—
562	Q₈×C₆₇	—	8	2	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	—	2	1	no	—
600	C₂×C₄×C₆₇	—	2	1	no	—
601	C₂×C₄×C₆₇	—	2	1	no	—
602	C₂×C₄×C₆₇	—	8	2	no	—
603	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
604	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
605	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
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	—	8	2	no	—
646	C₂×Dic₆₇	C₂²×Q₈	1	2	yes	—
647	C₂×Dic₆₇	C₂²×Q₈	1	2	yes	—
648	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
649	C₄×D₆₇	—	4	4	no	—
650	C₄×D₆₇	—	4	4	no	—
651	C₄×D₆₇	—	4	4	no	—
652	C₄×D₆₇	—	4	4	no	—
653	C₄×D₆₇	—	8	2	no	—
654	C₄×D₆₇	—	8	2	no	—
655	C₄×D₆₇	—	8	2	no	—
656	C₄×D₆₇	—	8	2	no	—
657	Dic₁₃₄	—	8	2	no	—
658	Dic₁₃₄	—	8	2	no	—
659	Dic₁₃₄	—	8	2	no	—
660	C₂²×C₆₇	—	2	2	no	—
661	C₂²×C₆₇	—	2	2	no	—
662	C₂²×C₆₇	—	2	2	no	—
663	C₂²×C₆₇	—	4	1	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	4	1	no	—
666	C₂²×C₆₇	—	4	1	no	—
667	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
668	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
670	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
672	C₂²×C₆₇	#585	1	1	yes	characteristic
673	C₂²×C₆₇	#585	1	1	yes	characteristic
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	—	2	2	no	—
680	C₂×D₆₇	—	2	2	no	—
681	C₂×D₆₇	—	2	2	no	—
682	C₂×D₆₇	—	2	2	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	—	8	8	no	—
688	C₂×D₆₇	#544	1	4	yes	—
689	C₄×C₆₇	—	2	2	no	—
690	C₄×C₆₇	—	2	2	no	—
691	C₄×C₆₇	—	2	2	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	C₄×C₆₇	—	4	1	no	—
702	C₄×C₆₇	—	4	1	no	—
703	Dic₆₇	—	2	2	no	—
704	Dic₆₇	—	2	2	no	—
705	Dic₆₇	—	2	2	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	Dic₆₇	—	4	1	no	—
716	Dic₆₇	—	4	1	no	—
717	#36750	—	67	1	no	maximal, Sylow
718	C₂×C₆₇	—	4	2	no	—
719	C₂×C₆₇	C₂×#544	1	1	yes	characteristic
720	C₂×C₆₇	#3501	1	1	yes	characteristic
721	C₂×C₆₇	#3501	1	1	yes	characteristic
722	C₂×C₆₇	#3534	1	1	yes	characteristic
723	C₂×C₆₇	#3536	1	1	yes	characteristic
724	C₂×C₆₇	#3558	1	1	yes	characteristic
725	C₂×C₆₇	#3564	1	1	yes	characteristic
726	D₆₇	—	2	4	no	—
727	D₆₇	—	4	2	no	—
728	#2857	—	67	1	no	—
729	#2851	—	67	1	no	—
730	#2807	—	67	1	no	—
731	#2807	—	67	1	no	—
732	#2788	—	67	1	no	—
733	#2788	—	67	1	no	—
734	#2768	—	67	1	no	—
735	#2768	—	67	1	no	—
736	#2763	—	67	1	no	—
737	#2763	—	67	1	no	—
738	#2729	—	67	1	no	—
739	#2729	—	67	1	no	—
740	#2720	—	67	1	no	—
741	#2720	—	67	1	no	—
742	#2704	—	67	1	no	—
743	#2704	—	67	1	no	—
744	#2704	—	67	1	no	—
745	#2704	D₆₇	1	1	yes	characteristic, complemented
746	#2659	—	67	1	no	—
747	#2646	—	67	1	no	—
748	#2549	—	67	1	no	—
749	#2549	—	67	1	no	—
750	#2442	—	67	1	no	—
751	#2442	—	67	1	no	—
752	#2437	—	67	1	no	—
753	#2437	—	67	1	no	—
754	#2437	—	67	1	no	—
755	#2437	—	67	1	no	—
756	#2315	—	67	1	no	—
757	#2312	—	67	1	no	—
758	C₂×#388	—	67	1	no	—
759	C₆₇	#36750	1	1	yes	characteristic, complemented, Sylow
760	C₂×C₄⋊Q₈	—	67	1	no	—
761	C₂×#125	—	67	1	no	—
762	C₂×#125	—	67	1	no	—
763	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
764	C₂×C₂²⋊Q₈	—	67	1	no	—
765	C₂×C₂²⋊Q₈	—	67	1	no	—
766	C₂×C₂²⋊Q₈	—	67	1	no	—
767	C₂×C₂²⋊Q₈	—	67	1	no	—
768	C₂×C₂²⋊Q₈	—	67	1	no	—
769	C₂×C₂²⋊Q₈	—	67	1	no	—
770	C₂×C₂²⋊Q₈	—	67	1	no	—
771	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
772	C₂²×C₄⋊C₄	—	67	1	no	—
773	C₂²×C₂²⋊C₄	—	67	1	no	—
774	C₂²×C₂²⋊C₄	—	67	1	no	—
775	C₂²×C₂²⋊C₄	—	67	1	no	—
776	C₂²×C₂²⋊C₄	—	67	1	no	—
777	C₂²×C₂²⋊C₄	—	67	1	no	—
778	C₂²×C₄²	—	67	1	no	—
779	#400	—	67	1	no	—
780	#400	—	67	1	no	—
781	#400	—	67	1	no	—
782	#400	—	67	1	no	—
783	#400	—	67	1	no	—
784	#400	—	67	1	no	—
785	#400	—	67	1	no	—
786	#400	—	67	1	no	—
787	#399	—	67	1	no	—
788	#399	—	67	1	no	—
789	#399	—	67	1	no	—
790	#399	—	67	1	no	—
791	#398	—	67	1	no	—
792	#398	—	67	1	no	—
793	#398	—	67	1	no	—
794	#398	—	67	1	no	—
795	#398	—	67	1	no	—
796	#398	—	67	1	no	—
797	#398	—	67	1	no	—
798	#398	—	67	1	no	—
799	#398	—	67	1	no	—
800	#398	—	67	1	no	—
801	#398	—	67	1	no	—
802	#398	—	67	1	no	—
803	#398	—	67	1	no	—
804	#398	C₂×D₆₇	1	1	yes	characteristic, complemented
805	#398	C₂×D₆₇	1	1	yes	characteristic, complemented
806	#398	C₂×D₆₇	1	1	yes	characteristic, complemented
807	#396	—	67	1	no	—
808	#396	—	67	1	no	—
809	#396	—	67	1	no	—
810	#396	—	67	1	no	—
811	#396	—	67	1	no	—
812	#396	—	67	1	no	—
813	#396	C₂×D₆₇	1	1	yes	characteristic
814	#396	C₂×D₆₇	1	1	yes	characteristic
815	#395	—	67	1	no	—
816	#395	—	67	1	no	—
817	#395	—	67	1	no	—
818	#395	—	67	1	no	—
819	#395	—	67	1	no	—
820	#395	—	67	1	no	—
821	#395	—	67	1	no	—
822	#395	C₂×D₆₇	1	1	yes	characteristic, complemented
823	#393	—	67	1	no	—
824	#393	—	67	1	no	—
825	#393	—	67	1	no	—
826	#393	—	67	1	no	—
827	#391	—	67	1	no	—
828	#391	—	67	1	no	—
829	#391	—	67	1	no	—
830	#391	—	67	1	no	—
831	#391	—	67	1	no	—
832	#391	C₂×D₆₇	1	1	yes	characteristic, complemented
833	#389	—	67	1	no	—
834	#389	—	67	1	no	—
835	#389	—	67	1	no	—
836	#389	—	67	1	no	—
837	#389	—	67	1	no	—
838	#389	—	67	1	no	—
839	#389	—	67	1	no	—
840	#389	—	67	1	no	—
841	#389	—	67	1	no	—
842	#389	—	67	1	no	—
843	#389	—	67	1	no	—
844	#389	—	67	1	no	—
845	#389	C₂×D₆₇	1	1	yes	characteristic, complemented
846	#389	C₂×D₆₇	1	1	yes	characteristic, complemented
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	—	67	1	no	—
854	#388	—	67	1	no	—
855	#388	—	67	1	no	—
856	#388	—	67	1	no	—
857	#388	—	67	1	no	—
858	#388	—	67	1	no	—
859	#388	—	67	1	no	—
860	#388	—	67	1	no	—
861	#388	C₂×D₆₇	1	1	yes	characteristic
862	#388	C₂×D₆₇	1	1	yes	characteristic
863	#387	—	67	1	no	—
864	#387	—	67	1	no	—
865	#387	—	67	1	no	—
866	#387	—	67	1	no	—
867	#385	—	67	1	no	—
868	#385	—	67	1	no	—
869	#385	—	67	1	no	—
870	#385	—	67	1	no	—
871	#385	—	67	1	no	—
872	#385	—	67	1	no	—
873	#385	—	67	1	no	—
874	#385	—	67	1	no	—
875	#385	—	67	1	no	—
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	#385	—	67	1	no	—
889	#385	—	67	1	no	—
890	#385	C₂×D₆₇	1	1	yes	characteristic
891	#384	—	67	1	no	—
892	#382	—	67	1	no	—
893	#382	—	67	1	no	—
894	#382	—	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	—	67	1	no	—
901	#380	—	67	1	no	—
902	#380	—	67	1	no	—
903	#380	—	67	1	no	—
904	#380	—	67	1	no	—
905	#380	—	67	1	no	—
906	#380	—	67	1	no	—
907	#380	—	67	1	no	—
908	#380	C₂×D₆₇	1	1	yes	characteristic
909	#379	—	67	1	no	—
910	#379	—	67	1	no	—
911	C₄×C₂²⋊C₄	—	67	1	no	—
912	C₄×C₂²⋊C₄	—	67	1	no	—
913	C₂×#95	—	67	1	no	—
914	C₂×#95	—	67	1	no	—
915	C₂⁵	—	67	1	no	—
916	C₂²×Q₈	—	67	1	no	—
917	C₂²×Q₈	—	67	1	no	—
918	C₂²×Q₈	—	67	1	no	—
919	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
920	C₂³×C₄	—	67	1	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	—	67	1	no	—
928	C₂³×C₄	—	67	1	no	—
929	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
930	C₄⋊Q₈	—	268	2	no	—
931	#125	—	4	2	no	—
932	#125	—	268	2	no	—
933	#125	—	268	2	no	—
934	C₂²⋊Q₈	—	4	2	no	—
935	C₂²⋊Q₈	—	268	2	no	—
936	C₂²⋊Q₈	—	268	2	no	—
937	C₂²⋊Q₈	—	268	2	no	—
938	C₂²⋊Q₈	—	268	2	no	—
939	C₂²⋊Q₈	—	268	2	no	—
940	C₂²⋊Q₈	—	268	2	no	—
941	C₂²⋊Q₈	—	268	2	no	—
942	C₂×C₄⋊C₄	—	268	2	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	—	67	1	no	—
973	C₂×C₄⋊C₄	—	67	1	no	—
974	C₂×C₄⋊C₄	—	67	1	no	—
975	C₂×C₄⋊C₄	—	67	1	no	—
976	C₂×C₄⋊C₄	—	67	1	no	—
977	C₂×C₄⋊C₄	—	67	1	no	—
978	C₂×C₄⋊C₄	—	67	1	no	—
979	C₂×C₄⋊C₄	—	67	1	no	—
980	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
982	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
983	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
985	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	—	268	2	no	—
996	C₂×C₂²⋊C₄	—	268	2	no	—
997	C₂×C₂²⋊C₄	—	268	2	no	—
998	C₂×C₂²⋊C₄	—	268	2	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	—	67	8	no	—
1015	C₂×C₂²⋊C₄	—	67	1	no	—
1016	C₂×C₂²⋊C₄	—	67	1	no	—
1017	C₂×C₂²⋊C₄	—	67	1	no	—
1018	C₂×C₂²⋊C₄	—	67	1	no	—
1019	C₂×C₂²⋊C₄	—	67	1	no	—
1020	C₂×C₂²⋊C₄	—	67	1	no	—
1021	C₂×C₂²⋊C₄	—	67	1	no	—
1022	C₂×C₂²⋊C₄	—	67	1	no	—
1023	C₂×C₂²⋊C₄	—	67	1	no	—
1024	C₂×C₂²⋊C₄	—	67	1	no	—
1025	C₂×C₂²⋊C₄	—	67	1	no	—
1026	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1032	C₂×C₄²	—	268	2	no	—
1033	C₂×C₄²	—	67	1	no	—
1034	C₂×C₄²	—	67	1	no	—
1035	C₂×C₄²	—	67	1	no	—
1036	C₂×C₄²	—	67	1	no	—
1037	C₂×C₄²	—	67	1	no	—
1038	C₂×C₄²	—	67	1	no	—
1039	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1040	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
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	—	67	1	no	—
1075	#95	—	67	1	no	—
1076	#95	—	67	1	no	—
1077	#95	—	67	1	no	—
1078	#95	—	67	1	no	—
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	#95	C₂²×D₆₇	1	1	yes	characteristic
1085	#95	C₂²×D₆₇	1	1	yes	characteristic
1086	#95	C₂²×D₆₇	1	1	yes	characteristic
1087	#95	C₂²×D₆₇	1	1	yes	characteristic
1088	#95	C₂²×D₆₇	1	1	yes	characteristic
1089	C₂⁴	—	268	1	no	—
1090	C₂⁴	—	268	1	no	—
1091	C₂⁴	—	268	1	no	—
1092	C₂⁴	—	268	1	no	—
1093	C₂⁴	—	67	4	no	—
1094	C₂⁴	—	67	1	no	—
1095	C₂⁴	—	67	1	no	—
1096	C₂⁴	—	134	2	no	—
1097	C₂⁴	—	134	2	no	—
1098	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1099	C₂×Q₈	—	2	2	no	—
1100	C₂×Q₈	—	4	1	no	—
1101	C₂×Q₈	—	4	1	no	—
1102	C₂×Q₈	—	268	1	no	—
1103	C₂×Q₈	—	268	1	no	—
1104	C₂×Q₈	—	268	1	no	—
1105	C₂×Q₈	—	268	1	no	—
1106	C₂×Q₈	—	268	1	no	—
1107	C₂×Q₈	—	268	1	no	—
1108	C₂×Q₈	—	268	1	no	—
1109	C₂×Q₈	—	268	1	no	—
1110	C₂×Q₈	—	134	2	no	—
1111	C₂²×C₄	—	4	1	no	—
1112	C₂²×C₄	—	4	1	no	—
1113	C₂²×C₄	—	4	1	no	—
1114	C₂²×C₄	—	268	1	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	—	268	1	no	—
1121	C₂²×C₄	—	268	1	no	—
1122	C₂²×C₄	—	268	1	no	—
1123	C₂²×C₄	—	268	1	no	—
1124	C₂²×C₄	—	268	1	no	—
1125	C₂²×C₄	—	268	1	no	—
1126	C₂²×C₄	—	268	1	no	—
1127	C₂²×C₄	—	268	1	no	—
1128	C₂²×C₄	—	268	1	no	—
1129	C₂²×C₄	—	268	1	no	—
1130	C₂²×C₄	—	268	1	no	—
1131	C₂²×C₄	—	268	1	no	—
1132	C₂²×C₄	—	268	1	no	—
1133	C₂²×C₄	—	67	4	no	—
1134	C₂²×C₄	—	67	4	no	—
1135	C₂²×C₄	—	67	1	no	—
1136	C₂²×C₄	—	67	1	no	—
1137	C₂²×C₄	—	67	1	no	—
1138	C₂²×C₄	—	67	1	no	—
1139	C₂²×C₄	—	67	1	no	—
1140	C₂²×C₄	—	67	1	no	—
1141	C₂²×C₄	—	67	1	no	—
1142	C₂²×C₄	—	67	1	no	—
1143	C₂²×C₄	—	67	1	no	—
1144	C₂²×C₄	—	67	1	no	—
1145	C₂²×C₄	—	67	1	no	—
1146	C₂²×C₄	—	67	1	no	—
1147	C₂²×C₄	—	67	1	no	—
1148	C₂²×C₄	—	67	1	no	—
1149	C₂²×C₄	—	134	2	no	—
1150	C₂²×C₄	—	134	2	no	—
1151	C₂²×C₄	—	134	2	no	—
1152	C₂²×C₄	—	134	2	no	—
1153	C₂²×C₄	—	134	2	no	—
1154	C₂²×C₄	—	134	2	no	—
1155	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1156	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1157	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1158	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1159	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1160	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1161	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1162	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1163	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1164	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1165	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1166	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1167	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1168	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1169	C₄⋊C₄	—	2	2	no	—
1170	C₄⋊C₄	—	2	2	no	—
1171	C₄⋊C₄	—	4	1	no	—
1172	C₄⋊C₄	—	4	1	no	—
1173	C₄⋊C₄	—	4	1	no	—
1174	C₄⋊C₄	—	4	1	no	—
1175	C₄⋊C₄	—	4	1	no	—
1176	C₄⋊C₄	—	4	1	no	—
1177	C₄⋊C₄	—	4	1	no	—
1178	C₄⋊C₄	—	4	1	no	—
1179	C₄⋊C₄	—	4	1	no	—
1180	C₄⋊C₄	—	4	1	no	—
1181	C₄⋊C₄	—	4	1	no	—
1182	C₄⋊C₄	—	4	1	no	—
1183	C₄⋊C₄	—	4	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	—	268	1	no	—
1190	C₄⋊C₄	—	268	1	no	—
1191	C₄⋊C₄	—	268	1	no	—
1192	C₄⋊C₄	—	268	1	no	—
1193	C₄⋊C₄	—	268	1	no	—
1194	C₄⋊C₄	—	268	1	no	—
1195	C₄⋊C₄	—	268	1	no	—
1196	C₄⋊C₄	—	268	1	no	—
1197	C₄⋊C₄	—	268	1	no	—
1198	C₄⋊C₄	—	268	1	no	—
1199	C₄⋊C₄	—	268	1	no	—
1200	C₄⋊C₄	—	268	1	no	—
1201	C₄⋊C₄	—	268	1	no	—
1202	C₄⋊C₄	—	268	1	no	—
1203	C₄⋊C₄	—	268	1	no	—
1204	C₄⋊C₄	—	268	1	no	—
1205	C₄⋊C₄	—	268	1	no	—
1206	C₄⋊C₄	—	268	1	no	—
1207	C₄⋊C₄	—	268	1	no	—
1208	C₄⋊C₄	—	268	1	no	—
1209	C₄⋊C₄	—	268	1	no	—
1210	C₄⋊C₄	—	268	1	no	—
1211	C₄⋊C₄	—	268	1	no	—
1212	C₄⋊C₄	—	268	1	no	—
1213	C₄⋊C₄	—	268	1	no	—
1214	C₄⋊C₄	—	268	1	no	—
1215	C₄⋊C₄	—	134	2	no	—
1216	C₄⋊C₄	—	134	2	no	—
1217	C₄⋊C₄	—	134	2	no	—
1218	C₄⋊C₄	—	134	2	no	—
1219	C₄⋊C₄	—	134	2	no	—
1220	C₄⋊C₄	—	134	2	no	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	4	1	no	—
1223	C₂²⋊C₄	—	4	1	no	—
1224	C₂²⋊C₄	—	4	1	no	—
1225	C₂²⋊C₄	—	4	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	—	268	1	no	—
1231	C₂²⋊C₄	—	268	1	no	—
1232	C₂²⋊C₄	—	268	1	no	—
1233	C₂²⋊C₄	—	268	1	no	—
1234	C₂²⋊C₄	—	268	1	no	—
1235	C₂²⋊C₄	—	268	1	no	—
1236	C₂²⋊C₄	—	268	1	no	—
1237	C₂²⋊C₄	—	268	1	no	—
1238	C₂²⋊C₄	—	67	4	no	—
1239	C₂²⋊C₄	—	67	4	no	—
1240	C₂²⋊C₄	—	67	4	no	—
1241	C₂²⋊C₄	—	134	2	no	—
1242	C₂²⋊C₄	—	134	2	no	—
1243	C₂²⋊C₄	—	134	2	no	—
1244	C₂²⋊C₄	—	134	2	no	—
1245	C₂²⋊C₄	—	134	2	no	—
1246	C₂²⋊C₄	—	134	2	no	—
1247	C₂²⋊C₄	—	134	2	no	—
1248	C₂²⋊C₄	—	134	2	no	—
1249	C₂²⋊C₄	—	134	2	no	—
1250	C₂²⋊C₄	—	134	2	no	—
1251	C₂²⋊C₄	—	134	2	no	—
1252	C₂²⋊C₄	Q₈×D₆₇	1	4	yes	—
1253	C₄²	—	2	2	no	—
1254	C₄²	—	4	1	no	—
1255	C₄²	—	268	1	no	—
1256	C₄²	—	268	1	no	—
1257	C₄²	—	268	1	no	—
1258	C₄²	—	268	1	no	—
1259	C₄²	—	268	1	no	—
1260	C₄²	—	134	2	no	—
1261	C₂³	—	2	1	no	—
1262	C₂³	—	2	1	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	2	1	no	—
1265	C₂³	—	2	1	no	—
1266	C₂³	—	2	1	no	—
1267	C₂³	—	268	4	no	—
1268	C₂³	—	268	4	no	—
1269	C₂³	—	536	2	no	—
1270	C₂³	—	536	2	no	—
1271	C₂³	—	536	2	no	—
1272	C₂³	—	536	2	no	—
1273	C₂³	—	67	2	no	—
1274	C₂³	—	67	2	no	—
1275	C₂³	—	67	2	no	—
1276	C₂³	—	67	2	no	—
1277	C₂³	—	134	8	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	—	134	1	no	—
1286	C₂³	—	134	1	no	—
1287	C₂³	—	134	1	no	—
1288	C₂³	C₂×Q₈×D₆₇	1	2	yes	—
1289	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1290	Q₈	—	8	2	no	—
1291	Q₈	—	536	2	no	—
1292	Q₈	—	536	2	no	—
1293	Q₈	—	536	2	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	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	8	2	no	—
1334	C₂×C₄	—	268	4	no	—
1335	C₂×C₄	—	268	4	no	—
1336	C₂×C₄	—	268	4	no	—
1337	C₂×C₄	—	268	4	no	—
1338	C₂×C₄	—	536	2	no	—
1339	C₂×C₄	—	536	2	no	—
1340	C₂×C₄	—	536	2	no	—
1341	C₂×C₄	—	536	2	no	—
1342	C₂×C₄	—	536	2	no	—
1343	C₂×C₄	—	67	2	no	—
1344	C₂×C₄	—	67	2	no	—
1345	C₂×C₄	—	67	2	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	—	134	1	no	—
1378	C₂×C₄	—	134	1	no	—
1379	C₂×C₄	—	134	1	no	—
1380	C₂×C₄	—	134	1	no	—
1381	C₂×C₄	—	134	1	no	—
1382	C₂×C₄	—	134	1	no	—
1383	C₂×C₄	—	134	1	no	—
1384	C₂×C₄	—	134	1	no	—
1385	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1386	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1387	C₂×C₄	#14524088	1	2	yes	—
1388	C₂²	—	2	2	no	—
1389	C₂²	—	2	2	no	—
1390	C₂²	—	2	2	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	1	no	—
1393	C₂²	—	4	1	no	—
1394	C₂²	—	4	1	no	—
1395	C₂²	—	268	1	no	—
1396	C₂²	—	268	1	no	—
1397	C₂²	—	268	1	no	—
1398	C₂²	—	268	1	no	—
1399	C₂²	—	536	8	no	—
1400	C₂²	—	67	4	no	—
1401	C₂²	—	134	2	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	—	134	2	no	—
1409	C₂²	—	134	2	no	—
1410	C₂²	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1411	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1412	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1413	C₂²	C₂×#14524088	1	1	yes	characteristic
1414	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1415	C₂²	#16864232	1	1	yes	characteristic
1416	C₂²	#16864233	1	1	yes	characteristic
1417	C₄	—	2	2	no	—
1418	C₄	—	2	2	no	—
1419	C₄	—	2	2	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	—	4	1	no	—
1429	C₄	—	4	1	no	—
1430	C₄	—	4	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	—	268	1	no	—
1442	C₄	—	134	2	no	—
1443	C₄	—	134	2	no	—
1444	C₄	—	134	2	no	—
1445	C₂	—	4	2	no	—
1446	C₂	—	268	2	no	—
1447	C₂	—	134	4	no	—
1448	C₂	#544×D₆₇	1	1	yes	characteristic
1449	C₂	#22574004	1	1	yes	characteristic
1450	C₂	#22574008	1	1	yes	characteristic
1451	C₂	#22574391	1	1	yes	characteristic
1452	C₂	#22574427	1	1	yes	characteristic
1453	C₂	#22574731	1	1	yes	characteristic
1454	C₂	#22574822	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2704	C₂
prime radical	C₂⁴×D₆₇	C₂³
hypercenter	#2704	D₆₇
hypocenter	C₆₇	#36750
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2704

Complements

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

N	H ≅ G/N	type
1. #22568558	C₂	semidirect
2. #22568514	C₂	semidirect
3. #22568181	C₂	semidirect
4. #22568179	C₂	semidirect
5. #22567953	C₂	semidirect
6. #22567951	C₂	semidirect
7. #22567696	C₂	semidirect
8. #22567694	C₂	semidirect
9. #22567625	C₂	semidirect
10. #22567620	C₂	semidirect
11. #22567198	C₂	semidirect
12. #22567187	C₂	semidirect
13. #22567095	C₂	semidirect
14. #22567089	C₂	semidirect
15. #22566869	C₂	semidirect
16. #22566868	C₂	semidirect
17. #22566861	C₂	semidirect
18. #22566324	C₂	semidirect
19. #22566178	C₂	semidirect
20. #22565219	C₂	semidirect
21. #22565214	C₂	semidirect
22. #22563935	C₂	semidirect
23. #22563928	C₂	semidirect
31. C₆₇×#2704	C₂	semidirect
32. C₂×#14524041	C₂²	semidirect
33. C₂×#14524035	C₂²	semidirect
34. C₂×#14524033	C₂²	semidirect
49. #16863338	C₂²	semidirect
50. #16863338	C₂²	semidirect
51. #16863338	C₂²	semidirect
52. #16863337	C₂²	semidirect
53. #16863337	C₂²	semidirect
54. #16863337	C₂²	semidirect
55. #16863335	C₂²	semidirect
56. #16863334	C₂²	semidirect
61. #16863330	C₂²	semidirect
62. #16863329	C₂²	semidirect
63. #16863329	C₂²	semidirect
64. #16863329	C₂²	semidirect
65. #16863329	C₂²	semidirect
66. #16863329	C₂²	semidirect
67. #16863328	C₂²	semidirect
68. #16863327	C₂²	semidirect
69. #16863327	C₂²	semidirect
70. #16863327	C₂²	semidirect
71. #16863327	C₂²	semidirect
72. #16863326	C₂²	semidirect
73. #16863326	C₂²	semidirect
80. #16863317	C₂²	semidirect
81. #16863317	C₂²	semidirect
82. #16863317	C₂²	semidirect
83. #16863317	C₂²	semidirect
84. #16863316	C₂²	semidirect
85. #16863316	C₂²	semidirect
86. #16863316	C₂²	semidirect
91. #16863303	C₂²	semidirect
92. #16863302	C₂²	semidirect
93. #16863302	C₂²	semidirect
94. #16863300	C₂²	semidirect
95. #16863300	C₂²	semidirect
96. #16863295	C₂²	semidirect
97. #16863293	C₂²	semidirect
98. #16863293	C₂²	semidirect
99. #16863293	C₂²	semidirect
100. #16863293	C₂²	semidirect
101. #16863293	C₂²	semidirect
102. #16863292	C₂²	semidirect
103. #16863292	C₂²	semidirect
104. #16863292	C₂²	semidirect
105. #16863291	C₂²	semidirect
106. #16863291	C₂²	semidirect
107. #16863291	C₂²	semidirect
122. #16863277	C₂²	semidirect
123. #16863277	C₂²	semidirect
124. #16863277	C₂²	semidirect
125. #16863277	C₂²	semidirect
149. #16863265	C₂²	semidirect
150. #16863262	C₂²	semidirect
151. #16863261	C₂²	semidirect
152. #16863260	C₂²	semidirect
172. C₂×#125×C₆₇	C₂²	semidirect
174. #398×C₆₇	C₂²	semidirect
175. #398×C₆₇	C₂²	semidirect
176. #398×C₆₇	C₂²	semidirect
179. #395×C₆₇	C₂²	semidirect
180. #391×C₆₇	C₂²	semidirect
181. #389×C₆₇	C₂²	semidirect
182. #389×C₆₇	C₂²	semidirect
278. C₂²⋊C₄×D₆₇	Q₈	semidirect
745. #2704	D₆₇	semidirect
759. C₆₇	#36750	semidirect
763. C₂×#125	C₂×D₆₇	semidirect
804. #398	C₂×D₆₇	semidirect
805. #398	C₂×D₆₇	semidirect
806. #398	C₂×D₆₇	semidirect
822. #395	C₂×D₆₇	semidirect
832. #391	C₂×D₆₇	semidirect
845. #389	C₂×D₆₇	semidirect
846. #389	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568558	2
#22568514	2
#22568181	2
#22568179	2
#22567953	2
#22567951	2
#22567696	2
#22567694	2
#22567625	2
#22567620	2
#22567198	2
#22567187	2
#22567095	2
#22567089	2
#22566869	2
#22566868	2
#22566861	2
#22566324	2
#22566178	2
#22565219	2
#22565214	2
#22563935	2
#22563928	2
#22563877	2
#22563872	2
#22563871	2
#22562820	2
#22562803	2
#388×D₆₇	2
C₆₇×#2704	2
#36750	67