Subgroups — #31026642

Order 17152.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22565853	C₂	1	1	yes	maximal, characteristic, complemented
2	#22565842	C₂	1	1	yes	maximal, characteristic, complemented
3	#22565809	C₂	1	1	yes	maximal, characteristic
4	#22565781	C₂	1	1	yes	maximal, characteristic, complemented
5	#22565719	C₂	1	1	yes	maximal, characteristic, complemented
6	#22565641	C₂	1	1	yes	maximal, characteristic, complemented
7	#22565534	C₂	1	1	yes	maximal, characteristic, complemented
8	#22565351	C₂	1	1	yes	maximal, characteristic
9	#22565069	C₂	1	1	yes	maximal, characteristic, complemented
10	#22565009	C₂	1	1	yes	maximal, characteristic, complemented
11	#22564951	C₂	1	1	yes	maximal, characteristic, complemented
12	#22564914	C₂	1	1	yes	maximal, characteristic
13	#22564431	C₂	1	1	yes	maximal, characteristic, complemented
14	#22564371	C₂	1	1	yes	maximal, characteristic
15	#22564224	C₂	1	1	yes	maximal, characteristic, complemented
16	#22563508	C₂	1	1	yes	maximal, characteristic, complemented
17	#22563499	C₂	1	1	yes	maximal, characteristic, complemented
18	#22563491	C₂	1	1	yes	maximal, characteristic
19	#22563484	C₂	1	1	yes	maximal, characteristic, complemented
20	#22562763	C₂	1	1	yes	maximal, characteristic, complemented
21	#126×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#22562759	C₂	1	1	yes	maximal, characteristic, complemented
23	#22562750	C₂	1	1	yes	maximal, characteristic
24	#22562743	C₂	1	1	yes	maximal, characteristic, complemented
25	#22562703	C₂	1	1	yes	maximal, characteristic, complemented
26	#22562682	C₂	1	1	yes	maximal, characteristic, complemented
27	#22562680	C₂	1	1	yes	maximal, characteristic, complemented
28	#22562651	C₂	1	1	yes	maximal, characteristic
29	C₄×Q₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#14524001	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2469	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14524038	C₂²	1	1	yes	characteristic
33	C₂×#14524036	C₂²	1	1	yes	characteristic
34	C₂×#14524029	C₂²	1	1	yes	characteristic
35	C₂×#14524021	C₂²	1	1	yes	characteristic
36	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
37	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
38	C₂×#14524008	C₂²	1	1	yes	characteristic
39	C₂×#14524008	C₂²	1	1	yes	characteristic
40	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×#14524001	C₂²	1	1	yes	characteristic
42	C₂×#14524001	C₂²	1	1	yes	characteristic
43	C₂×#14523999	C₂²	1	1	yes	characteristic
44	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
45	C₆₇⋊#401	C₂²	1	1	yes	characteristic
46	#16863338	C₂²	1	1	yes	characteristic
47	#16863338	C₂²	1	1	yes	characteristic
48	#16863338	C₂²	1	1	yes	characteristic
49	#16863337	C₂²	1	1	yes	characteristic
50	#16863336	C₂²	1	1	yes	characteristic
51	#16863332	C₂²	1	1	yes	characteristic
52	#16863329	C₂²	1	1	yes	characteristic
53	#16863329	C₂²	1	1	yes	characteristic
54	#16863329	C₂²	1	1	yes	characteristic
55	#16863328	C₂²	1	1	yes	characteristic
56	#16863326	C₂²	1	1	yes	characteristic
57	#16863326	C₂²	1	1	yes	characteristic
58	#16863325	C₂²	1	1	yes	characteristic
59	#16863323	C₂²	1	1	yes	characteristic
60	#16863323	C₂²	1	1	yes	characteristic
61	#16863322	C₂²	1	1	yes	characteristic
62	#16863321	C₂²	1	1	yes	characteristic
63	#16863319	C₂²	1	1	yes	characteristic
64	#16863318	C₂²	1	1	yes	characteristic
65	#16863317	C₂²	1	1	yes	characteristic
66	#16863317	C₂²	1	1	yes	characteristic
67	#16863316	C₂²	1	1	yes	characteristic
68	#16863315	C₂²	1	1	yes	characteristic
69	#16863312	C₂²	1	1	yes	characteristic
70	#16863312	C₂²	1	1	yes	characteristic
71	#16863308	C₂²	1	1	yes	characteristic
72	#16863307	C₂²	1	1	yes	characteristic
73	#16863302	C₂²	1	1	yes	characteristic
74	#16863301	C₂²	1	1	yes	characteristic
75	#16863300	C₂²	1	1	yes	characteristic
76	#16863300	C₂²	1	1	yes	characteristic
77	#16863300	C₂²	1	1	yes	characteristic
78	#16863300	C₂²	1	1	yes	characteristic
79	#16863296	C₂²	1	1	yes	characteristic
80	#16863295	C₂²	1	1	yes	characteristic
81	#16863293	C₂²	1	1	yes	characteristic
82	#16863293	C₂²	1	1	yes	characteristic
83	#16863291	C₂²	1	1	yes	characteristic
84	#16863290	C₂²	1	1	yes	characteristic
85	#16863290	C₂²	1	1	yes	characteristic
86	#16863290	C₂²	1	1	yes	characteristic
87	#16863289	C₂²	1	1	yes	characteristic
88	#16863289	C₂²	1	1	yes	characteristic
89	#16863289	C₂²	1	1	yes	characteristic
90	#16863289	C₂²	1	1	yes	characteristic
91	#16863289	C₂²	1	1	yes	characteristic
92	#16863288	C₂²	1	1	yes	characteristic
93	#16863287	C₂²	1	1	yes	characteristic
94	#16863287	C₂²	1	1	yes	characteristic
95	#16863286	C₂²	1	1	yes	characteristic
96	#16863286	C₂²	1	1	yes	characteristic
97	#16863284	C₂²	1	1	yes	characteristic
98	#16863284	C₂²	1	1	yes	characteristic
99	#16863283	C₂²	1	1	yes	characteristic
100	#16863283	C₂²	1	1	yes	characteristic
101	#16863283	C₂²	1	1	yes	characteristic
102	#16863283	C₂²	1	1	yes	characteristic
103	#16863282	C₂²	1	1	yes	characteristic
104	#16863282	C₂²	1	1	yes	characteristic
105	#16863282	C₂²	1	1	yes	characteristic
106	#16863282	C₂²	1	1	yes	characteristic
107	#16863281	C₂²	1	1	yes	characteristic
108	#16863280	C₂²	1	1	yes	characteristic
109	#16863280	C₂²	1	1	yes	characteristic
110	#16863280	C₂²	1	1	yes	characteristic
111	#16863280	C₂²	1	1	yes	characteristic
112	#16863280	C₂²	1	1	yes	characteristic
113	#16863279	C₂²	1	1	yes	characteristic
114	#16863278	C₂²	1	1	yes	characteristic
115	#16863278	C₂²	1	1	yes	characteristic
116	#16863278	C₂²	1	1	yes	characteristic
117	#16863277	C₂²	1	1	yes	characteristic
118	#16863277	C₂²	1	1	yes	characteristic
119	#16863277	C₂²	1	1	yes	characteristic
120	#16863277	C₂²	1	1	yes	characteristic
121	#16863272	C₂²	1	1	yes	characteristic
122	#16863272	C₂²	1	1	yes	characteristic
123	#16863270	C₂²	1	1	yes	characteristic
124	#16863270	C₂²	1	1	yes	characteristic
125	#16863267	C₂²	1	1	yes	characteristic
126	#16863267	C₂²	1	1	yes	characteristic
127	#16863264	C₂²	1	1	yes	characteristic
128	#16863263	C₂²	1	1	yes	characteristic
129	#16863263	C₂²	1	1	yes	characteristic
130	#16863260	C₂²	1	1	yes	characteristic
131	#16863255	C₂²	1	1	yes	characteristic
132	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
133	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
134	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
135	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
136	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
137	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
138	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
139	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
140	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
141	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
142	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
143	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
144	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
145	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
146	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
147	#16863247	C₂²	1	1	yes	characteristic
148	#16863247	C₂²	1	1	yes	characteristic
149	#16863247	C₂²	1	1	yes	characteristic
150	#16863247	C₂²	1	1	yes	characteristic
151	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
152	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
153	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
154	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
155	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
156	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
157	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
158	#16863243	C₂²	1	1	yes	characteristic
159	#16863243	C₂²	1	1	yes	characteristic
160	#16863243	C₂²	1	1	yes	characteristic
161	#16863243	C₂²	1	1	yes	characteristic
162	#16863243	C₂²	1	1	yes	characteristic
163	#16863241	C₂²	1	1	yes	characteristic
164	#16863241	C₂²	1	1	yes	characteristic
165	#16863241	C₂²	1	1	yes	characteristic
166	#16863241	C₂²	1	1	yes	characteristic
167	#16863241	C₂²	1	1	yes	characteristic
168	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
169	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
170	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
171	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
172	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
173	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
174	#400×C₆₇	C₂²	1	1	yes	characteristic
175	#396×C₆₇	C₂²	1	1	yes	characteristic
176	#395×C₆₇	C₂²	1	1	yes	characteristic
177	#393×C₆₇	C₂²	1	1	yes	characteristic
178	#389×C₆₇	C₂²	1	1	yes	characteristic
179	#388×C₆₇	C₂²	1	1	yes	characteristic
180	#388×C₆₇	C₂²	1	1	yes	characteristic
181	#388×C₆₇	C₂²	1	1	yes	characteristic
182	#388×C₆₇	C₂²	1	1	yes	characteristic
183	#387×C₆₇	C₂²	1	1	yes	characteristic
184	#387×C₆₇	C₂²	1	1	yes	characteristic
185	#387×C₆₇	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
189	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
190	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
194	#14524038	—	2	4	no	—
195	#14524036	—	2	4	no	—
196	#14524029	—	2	4	no	—
197	#14524021	—	2	4	no	—
198	Q₈×Dic₆₇	—	2	4	no	—
199	Q₈×Dic₆₇	—	2	4	no	—
200	#14524008	—	2	4	no	—
201	#14524008	—	2	4	no	—
202	(C₂²⋊D₆₇)⋊C₄	—	2	4	no	—
203	#14524001	—	2	4	no	—
204	#14524001	—	2	4	no	—
205	#14523999	—	2	4	no	—
206	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
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×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×Dic₆₇⋊C₄	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×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
238	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
260	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
275	C₄²×D₆₇	—	2	4	no	—
276	C₆₇⋊#95	C₂³	1	1	yes	characteristic
277	C₆₇⋊#95	C₂³	1	1	yes	characteristic
278	C₆₇⋊#95	C₂³	1	1	yes	characteristic
279	C₆₇⋊#95	C₂³	1	1	yes	characteristic
280	C₆₇⋊#95	C₂³	1	1	yes	characteristic
281	C₆₇⋊#95	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	#126×C₆₇	—	2	4	no	—
322	C₄×Q₈×C₆₇	—	2	4	no	—
323	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₂²⋊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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
345	#95×C₆₇	C₂³	1	1	yes	characteristic
346	#95×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	C₂⁴	1	1	yes	characteristic
358	C₂×Dic₁₃₄	—	2	2	no	—
359	C₂×Dic₁₃₄	—	2	2	no	—
360	C₂×Dic₁₃₄	—	2	2	no	—
361	C₂×Dic₁₃₄	—	2	2	no	—
362	C₂×Dic₁₃₄	—	4	1	no	—
363	C₂×Dic₁₃₄	—	4	1	no	—
364	C₂×C₂²⋊D₆₇	—	2	2	no	—
365	C₂×C₂²⋊D₆₇	—	2	2	no	—
366	C₂×C₂²⋊D₆₇	—	4	1	no	—
367	C₂²×Dic₆₇	—	2	2	no	—
368	C₂²×Dic₆₇	—	2	2	no	—
369	C₂²×Dic₆₇	—	2	2	no	—
370	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
371	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
373	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
374	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
375	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×D₆₇	—	2	2	no	—
386	C₂×C₄×D₆₇	—	2	2	no	—
387	C₂×C₄×D₆₇	—	2	2	no	—
388	C₂×C₄×D₆₇	—	2	2	no	—
389	C₂×C₄×D₆₇	—	2	2	no	—
390	C₂×C₄×D₆₇	—	2	2	no	—
391	C₂×C₄×D₆₇	—	2	2	no	—
392	C₂×C₄×D₆₇	—	2	2	no	—
393	C₂×C₄×D₆₇	—	4	1	no	—
394	C₄⋊Dic₆₇	—	2	2	no	—
395	C₄⋊Dic₆₇	—	2	2	no	—
396	C₄⋊Dic₆₇	—	2	2	no	—
397	C₄⋊Dic₆₇	—	2	2	no	—
398	C₄⋊Dic₆₇	—	2	2	no	—
399	C₄⋊Dic₆₇	—	2	2	no	—
400	C₄⋊Dic₆₇	—	2	2	no	—
401	C₄⋊Dic₆₇	—	2	2	no	—
402	C₄⋊Dic₆₇	—	2	2	no	—
403	C₄⋊Dic₆₇	—	2	2	no	—
404	C₄⋊Dic₆₇	—	4	1	no	—
405	Dic₆₇⋊C₄	—	2	2	no	—
406	Dic₆₇⋊C₄	—	2	2	no	—
407	Dic₆₇⋊C₄	—	2	2	no	—
408	Dic₆₇⋊C₄	—	2	2	no	—
409	Dic₆₇⋊C₄	—	2	2	no	—
410	Dic₆₇⋊C₄	—	2	2	no	—
411	Dic₆₇⋊C₄	—	2	2	no	—
412	Dic₆₇⋊C₄	—	2	2	no	—
413	Dic₆₇⋊C₄	—	2	2	no	—
414	Dic₆₇⋊C₄	—	2	2	no	—
415	Dic₆₇⋊C₄	—	2	2	no	—
416	Dic₆₇⋊C₄	—	2	2	no	—
417	Dic₆₇⋊C₄	—	4	1	no	—
418	Dic₆₇⋊C₄	—	4	1	no	—
419	Dic₆₇⋊C₄	—	4	1	no	—
420	C₂²⋊Dic₆₇	—	2	2	no	—
421	C₂²⋊Dic₆₇	—	2	2	no	—
422	C₂²⋊Dic₆₇	—	2	2	no	—
423	C₂²⋊Dic₆₇	—	2	2	no	—
424	C₂²⋊Dic₆₇	—	4	1	no	—
425	C₂²⋊Dic₆₇	—	4	1	no	—
426	(C₂×D₆₇)⋊C₄	—	2	2	no	—
427	(C₂×D₆₇)⋊C₄	—	2	2	no	—
428	(C₂×D₆₇)⋊C₄	—	2	2	no	—
429	(C₂×D₆₇)⋊C₄	—	2	2	no	—
430	(C₂×D₆₇)⋊C₄	—	2	2	no	—
431	(C₂×D₆₇)⋊C₄	—	2	2	no	—
432	(C₂×D₆₇)⋊C₄	—	2	2	no	—
433	(C₂×D₆₇)⋊C₄	—	2	2	no	—
434	(C₂×D₆₇)⋊C₄	—	2	2	no	—
435	(C₂×D₆₇)⋊C₄	—	4	1	no	—
436	(C₂×D₆₇)⋊C₄	#41	1	4	yes	—
437	C₄×Dic₆₇	—	2	2	no	—
438	C₄×Dic₆₇	—	2	2	no	—
439	C₄×Dic₆₇	—	2	2	no	—
440	C₄×Dic₆₇	—	2	2	no	—
441	C₄×Dic₆₇	—	2	2	no	—
442	C₄×Dic₆₇	—	2	2	no	—
443	C₄×Dic₆₇	—	2	2	no	—
444	C₄×Dic₆₇	—	2	2	no	—
445	C₄×Dic₆₇	—	2	2	no	—
446	C₄×Dic₆₇	—	2	2	no	—
447	C₄×Dic₆₇	—	2	2	no	—
448	C₄×Dic₆₇	—	2	2	no	—
449	C₄×Dic₆₇	—	2	2	no	—
450	C₄×Dic₆₇	—	2	2	no	—
451	C₄×Dic₆₇	—	2	2	no	—
452	C₄×Dic₆₇	—	2	2	no	—
453	C₄×Dic₆₇	—	2	2	no	—
454	C₄×Dic₆₇	—	2	2	no	—
455	C₄×Dic₆₇	—	2	2	no	—
456	C₄×Dic₆₇	—	4	1	no	—
457	C₄×Dic₆₇	—	4	1	no	—
458	C₄×Dic₆₇	—	4	1	no	—
459	C₄×Dic₆₇	—	4	1	no	—
460	C₄×Dic₆₇	#41	1	4	yes	—
461	C₄×Dic₆₇	#41	1	4	yes	—
462	C₄×Dic₆₇	#41	1	4	yes	—
463	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
464	C₂×Q₈×C₆₇	—	2	2	no	—
465	C₂×Q₈×C₆₇	—	2	2	no	—
466	C₂×Q₈×C₆₇	—	2	2	no	—
467	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
471	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
473	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
474	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
475	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
481	C₄⋊C₄×C₆₇	—	2	2	no	—
482	C₄⋊C₄×C₆₇	—	2	2	no	—
483	C₄⋊C₄×C₆₇	—	2	2	no	—
484	C₄⋊C₄×C₆₇	—	2	2	no	—
485	C₄⋊C₄×C₆₇	—	2	2	no	—
486	C₄⋊C₄×C₆₇	—	2	2	no	—
487	C₄⋊C₄×C₆₇	—	2	2	no	—
488	C₄⋊C₄×C₆₇	—	2	2	no	—
489	C₄⋊C₄×C₆₇	—	2	2	no	—
490	C₄⋊C₄×C₆₇	#41	1	4	yes	—
491	C₂²⋊C₄×C₆₇	—	2	2	no	—
492	C₂²⋊C₄×C₆₇	—	2	2	no	—
493	C₂²⋊C₄×C₆₇	—	2	2	no	—
494	C₂²⋊C₄×C₆₇	—	2	2	no	—
495	C₂²⋊C₄×C₆₇	—	2	2	no	—
496	C₂²⋊C₄×C₆₇	—	2	2	no	—
497	C₂²⋊C₄×C₆₇	—	2	2	no	—
498	C₄²×C₆₇	—	2	2	no	—
499	C₄²×C₆₇	—	2	2	no	—
500	C₄²×C₆₇	—	2	2	no	—
501	C₄²×C₆₇	—	2	2	no	—
502	C₄²×C₆₇	—	2	2	no	—
503	C₂³×C₆₇	—	2	1	no	—
504	C₂³×C₆₇	—	2	1	no	—
505	C₂³×C₆₇	—	2	1	no	—
506	C₂³×C₆₇	—	2	1	no	—
507	C₂³×C₆₇	—	2	1	no	—
508	C₂³×C₆₇	—	2	1	no	—
509	C₂³×C₆₇	—	2	1	no	—
510	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
511	C₂²×D₆₇	—	2	1	no	—
512	C₂²×D₆₇	—	2	1	no	—
513	C₂²×D₆₇	—	2	1	no	—
514	C₂²×D₆₇	—	2	1	no	—
515	C₂²×D₆₇	—	2	1	no	—
516	C₂²×D₆₇	—	2	1	no	—
517	C₂²×D₆₇	C₂×#41	1	2	yes	—
518	Q₈×C₆₇	—	2	8	no	—
519	C₂×C₄×C₆₇	—	2	1	no	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	1	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	1	no	—
545	C₂×C₄×C₆₇	—	2	1	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	2	1	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
555	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
556	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
557	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
558	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
559	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
560	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
561	C₂²⋊D₆₇	—	4	4	no	—
562	C₂×Dic₆₇	—	2	1	no	—
563	C₂×Dic₆₇	—	2	1	no	—
564	C₂×Dic₆₇	—	2	1	no	—
565	C₂×Dic₆₇	—	2	1	no	—
566	C₂×Dic₆₇	—	2	1	no	—
567	C₂×Dic₆₇	—	2	1	no	—
568	C₂×Dic₆₇	—	2	1	no	—
569	C₂×Dic₆₇	—	2	1	no	—
570	C₂×Dic₆₇	—	2	1	no	—
571	C₂×Dic₆₇	—	2	1	no	—
572	C₂×Dic₆₇	—	2	1	no	—
573	C₂×Dic₆₇	—	2	1	no	—
574	C₂×Dic₆₇	—	2	1	no	—
575	C₂×Dic₆₇	—	2	1	no	—
576	C₂×Dic₆₇	—	2	1	no	—
577	C₂×Dic₆₇	—	2	1	no	—
578	C₂×Dic₆₇	—	2	1	no	—
579	C₂×Dic₆₇	—	2	1	no	—
580	C₂×Dic₆₇	—	2	1	no	—
581	C₂×Dic₆₇	—	2	1	no	—
582	C₂×Dic₆₇	—	2	1	no	—
583	C₂×Dic₆₇	—	2	1	no	—
584	C₂×Dic₆₇	—	2	1	no	—
585	C₂×Dic₆₇	—	2	1	no	—
586	C₂×Dic₆₇	—	2	1	no	—
587	C₂×Dic₆₇	—	2	1	no	—
588	C₂×Dic₆₇	—	2	1	no	—
589	C₂×Dic₆₇	—	2	1	no	—
590	C₂×Dic₆₇	—	2	1	no	—
591	C₂×Dic₆₇	—	2	1	no	—
592	C₂×Dic₆₇	—	2	1	no	—
593	C₂×Dic₆₇	—	2	1	no	—
594	C₂×Dic₆₇	—	2	1	no	—
595	C₂×Dic₆₇	—	2	1	no	—
596	C₂×Dic₆₇	—	2	1	no	—
597	C₂×Dic₆₇	—	2	1	no	—
598	C₂×Dic₆₇	—	2	1	no	—
599	C₂×Dic₆₇	—	4	4	no	—
600	C₂×Dic₆₇	C₂×#41	1	2	yes	—
601	C₂×Dic₆₇	C₂×#41	1	2	yes	—
602	C₂×Dic₆₇	C₂×#41	1	2	yes	—
603	C₂×Dic₆₇	C₂×#41	1	2	yes	—
604	C₂×Dic₆₇	C₂×#41	1	2	yes	—
605	C₂×Dic₆₇	C₂×#41	1	2	yes	—
606	C₂×Dic₆₇	C₂×#41	1	2	yes	—
607	C₂×Dic₆₇	2₋¹⁺⁴	1	2	yes	—
608	C₄×D₆₇	—	2	8	no	—
609	C₄×D₆₇	—	4	4	no	—
610	C₄×D₆₇	—	4	4	no	—
611	Dic₁₃₄	—	4	4	no	—
612	Dic₁₃₄	—	4	4	no	—
613	C₂²×C₆₇	—	4	1	no	—
614	C₂²×C₆₇	—	4	1	no	—
615	C₂²×C₆₇	—	4	1	no	—
616	C₂²×C₆₇	—	4	1	no	—
617	C₂²×C₆₇	—	4	1	no	—
618	C₂²×C₆₇	—	4	1	no	—
619	C₂²×C₆₇	—	4	1	no	—
620	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
621	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
622	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
623	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
624	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
625	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
626	C₂²×C₆₇	#585	1	1	yes	characteristic
627	C₂×D₆₇	—	2	2	no	—
628	C₂×D₆₇	—	2	2	no	—
629	C₂×D₆₇	—	2	2	no	—
630	C₂×D₆₇	—	4	1	no	—
631	C₂×D₆₇	—	4	1	no	—
632	C₂×D₆₇	—	4	1	no	—
633	C₂×D₆₇	—	4	1	no	—
634	C₄×C₆₇	—	2	2	no	—
635	C₄×C₆₇	—	2	2	no	—
636	C₄×C₆₇	—	2	2	no	—
637	C₄×C₆₇	—	2	2	no	—
638	C₄×C₆₇	—	2	2	no	—
639	C₄×C₆₇	—	2	2	no	—
640	C₄×C₆₇	—	2	2	no	—
641	C₄×C₆₇	—	4	1	no	—
642	C₄×C₆₇	—	4	1	no	—
643	C₄×C₆₇	—	4	1	no	—
644	C₄×C₆₇	—	4	1	no	—
645	C₄×C₆₇	—	4	1	no	—
646	C₄×C₆₇	—	4	1	no	—
647	C₄×C₆₇	—	4	1	no	—
648	Dic₆₇	—	2	2	no	—
649	Dic₆₇	—	2	2	no	—
650	Dic₆₇	—	2	2	no	—
651	Dic₆₇	—	2	2	no	—
652	Dic₆₇	—	2	2	no	—
653	Dic₆₇	—	4	1	no	—
654	Dic₆₇	—	4	1	no	—
655	Dic₆₇	—	4	1	no	—
656	Dic₆₇	—	4	1	no	—
657	Dic₆₇	—	4	1	no	—
658	Dic₆₇	—	4	1	no	—
659	Dic₆₇	—	4	1	no	—
660	Dic₆₇	—	4	1	no	—
661	Dic₆₇	—	4	1	no	—
662	Dic₆₇	#556	1	4	yes	—
663	#34867	—	67	1	no	maximal, Sylow
664	C₂×C₆₇	—	8	1	no	—
665	C₂×C₆₇	#3444	1	1	yes	characteristic
666	C₂×C₆₇	#3444	1	1	yes	characteristic
667	C₂×C₆₇	#3461	1	1	yes	characteristic
668	C₂×C₆₇	C₂×#556	1	1	yes	characteristic
669	C₂×C₆₇	#3475	1	1	yes	characteristic
670	C₂×C₆₇	#3475	1	1	yes	characteristic
671	C₂×C₆₇	#3482	1	1	yes	characteristic
672	D₆₇	—	4	2	no	—
673	#2605	—	67	1	no	—
674	#2604	—	67	1	no	—
675	#2601	—	67	1	no	—
676	#2599	—	67	1	no	—
677	#2594	—	67	1	no	—
678	#2588	—	67	1	no	—
679	#2577	—	67	1	no	—
680	#2560	—	67	1	no	—
681	#2532	—	67	1	no	—
682	#2528	—	67	1	no	—
683	#2524	—	67	1	no	—
684	#2521	—	67	1	no	—
685	#2478	—	67	1	no	—
686	#2474	—	67	1	no	—
687	#2469	D₆₇	1	1	yes	characteristic, complemented
688	#2465	—	67	1	no	—
689	#2401	—	67	1	no	—
690	#2399	—	67	1	no	—
691	#2398	—	67	1	no	—
692	#2396	—	67	1	no	—
693	C₄×#126	—	67	1	no	—
694	C₄×#126	—	67	1	no	—
695	C₄×#126	—	67	1	no	—
696	C₄×#124	—	67	1	no	—
697	C₄×C₂²⋊Q₈	—	67	1	no	—
698	#2298	—	67	1	no	—
699	#2295	—	67	1	no	—
700	#2295	—	67	1	no	—
701	#2290	—	67	1	no	—
702	C₄²×Q₈	—	67	1	no	—
703	C₄×#117	—	67	1	no	—
704	C₆₇	#34867	1	1	yes	characteristic, complemented, Sylow
705	C₂×#126	—	67	1	no	—
706	C₂×#126	—	67	1	no	—
707	C₂×#126	C₂×D₆₇	1	1	yes	characteristic
708	C₂×#124	—	67	1	no	—
709	C₂×C₂²⋊Q₈	—	67	1	no	—
710	C₂×C₄×Q₈	—	67	1	no	—
711	C₂×C₄×Q₈	—	67	1	no	—
712	C₂×C₄×Q₈	—	67	1	no	—
713	C₂×C₄×Q₈	—	67	1	no	—
714	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
715	C₂×C₄×D₄	—	67	1	no	—
716	C₂×#117	—	67	1	no	—
717	C₂×#117	—	67	1	no	—
718	C₂×#117	—	67	1	no	—
719	C₂²×C₄²	—	67	1	no	—
720	#401	—	67	1	no	—
721	#400	—	67	1	no	—
722	#400	—	67	1	no	—
723	#400	—	67	1	no	—
724	#400	—	67	1	no	—
725	#400	—	67	1	no	—
726	#400	C₂×D₆₇	1	1	yes	characteristic
727	#399	—	67	1	no	—
728	#398	—	67	1	no	—
729	#398	—	67	1	no	—
730	#398	—	67	1	no	—
731	#398	—	67	1	no	—
732	#398	—	67	1	no	—
733	#398	—	67	1	no	—
734	#397	—	67	1	no	—
735	#397	—	67	1	no	—
736	#397	—	67	1	no	—
737	#397	—	67	1	no	—
738	#397	—	67	1	no	—
739	#396	—	67	1	no	—
740	#396	—	67	1	no	—
741	#396	C₂×D₆₇	1	1	yes	characteristic
742	#395	—	67	1	no	—
743	#395	—	67	1	no	—
744	#395	—	67	1	no	—
745	#395	—	67	1	no	—
746	#395	C₂×D₆₇	1	1	yes	characteristic
747	#394	—	67	1	no	—
748	#394	—	67	1	no	—
749	#393	—	67	1	no	—
750	#393	—	67	1	no	—
751	#393	C₂×D₆₇	1	1	yes	characteristic
752	#391	—	67	1	no	—
753	#391	—	67	1	no	—
754	#391	—	67	1	no	—
755	#391	—	67	1	no	—
756	#391	—	67	1	no	—
757	#391	—	67	1	no	—
758	#390	—	67	1	no	—
759	#389	—	67	1	no	—
760	#389	—	67	1	no	—
761	#389	—	67	1	no	—
762	#389	—	67	1	no	—
763	#389	C₂×D₆₇	1	1	yes	characteristic
764	#388	—	67	1	no	—
765	#388	—	67	1	no	—
766	#388	—	67	1	no	—
767	#388	—	67	1	no	—
768	#388	—	67	1	no	—
769	#388	—	67	1	no	—
770	#388	—	67	1	no	—
771	#388	—	67	1	no	—
772	#388	—	67	1	no	—
773	#388	—	67	1	no	—
774	#388	—	67	1	no	—
775	#388	—	67	1	no	—
776	#388	—	67	1	no	—
777	#388	—	67	1	no	—
778	#388	—	67	1	no	—
779	#388	C₂×D₆₇	1	1	yes	characteristic
780	#388	C₂×D₆₇	1	1	yes	characteristic
781	#388	C₂×D₆₇	1	1	yes	characteristic
782	#388	C₂×D₆₇	1	1	yes	characteristic
783	#387	—	67	1	no	—
784	#387	—	67	1	no	—
785	#387	—	67	1	no	—
786	#387	—	67	1	no	—
787	#387	—	67	1	no	—
788	#387	—	67	1	no	—
789	#387	—	67	1	no	—
790	#387	—	67	1	no	—
791	#387	—	67	1	no	—
792	#387	—	67	1	no	—
793	#387	—	67	1	no	—
794	#387	—	67	1	no	—
795	#387	—	67	1	no	—
796	#387	—	67	1	no	—
797	#387	—	67	1	no	—
798	#387	—	67	1	no	—
799	#387	—	67	1	no	—
800	#387	—	67	1	no	—
801	#387	—	67	1	no	—
802	#387	—	67	1	no	—
803	#387	—	67	1	no	—
804	#387	—	67	1	no	—
805	#387	C₂×D₆₇	1	1	yes	characteristic
806	#387	C₂×D₆₇	1	1	yes	characteristic
807	#387	C₂×D₆₇	1	1	yes	characteristic
808	#386	—	67	1	no	—
809	#386	—	67	1	no	—
810	#385	—	67	1	no	—
811	#385	—	67	1	no	—
812	#385	—	67	1	no	—
813	#385	—	67	1	no	—
814	#383	—	67	1	no	—
815	#383	—	67	1	no	—
816	#383	—	67	1	no	—
817	#382	—	67	1	no	—
818	#380	—	67	1	no	—
819	C₄×C₄⋊C₄	—	67	1	no	—
820	C₄×C₄⋊C₄	—	67	1	no	—
821	C₄×C₄⋊C₄	—	67	1	no	—
822	C₄×C₄⋊C₄	—	67	1	no	—
823	C₄×C₄⋊C₄	—	67	1	no	—
824	C₄×C₄⋊C₄	—	67	1	no	—
825	C₄×C₄⋊C₄	—	67	1	no	—
826	C₄×C₄⋊C₄	—	67	1	no	—
827	C₄×C₄⋊C₄	—	67	1	no	—
828	C₄×C₄⋊C₄	—	67	1	no	—
829	C₄×C₄⋊C₄	—	67	1	no	—
830	C₄×C₄⋊C₄	—	67	1	no	—
831	C₄×C₄⋊C₄	—	67	1	no	—
832	C₄×C₄⋊C₄	—	67	1	no	—
833	C₄×C₄⋊C₄	—	67	1	no	—
834	C₄×C₄⋊C₄	—	67	1	no	—
835	C₄×C₄⋊C₄	—	67	1	no	—
836	C₄×C₄⋊C₄	—	67	1	no	—
837	C₄×C₄⋊C₄	—	67	1	no	—
838	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
839	C₄×C₂²⋊C₄	—	67	1	no	—
840	C₄×C₂²⋊C₄	—	67	1	no	—
841	C₄×C₂²⋊C₄	—	67	1	no	—
842	C₄×C₂²⋊C₄	—	67	1	no	—
843	C₄×C₂²⋊C₄	—	67	1	no	—
844	C₄×C₂²⋊C₄	—	67	1	no	—
845	C₄×C₂²⋊C₄	—	67	1	no	—
846	C₄×C₂²⋊C₄	—	67	1	no	—
847	C₄×C₂²⋊C₄	—	67	1	no	—
848	C₄×C₂²⋊C₄	—	67	1	no	—
849	C₄×C₂²⋊C₄	—	67	1	no	—
850	C₄×C₂²⋊C₄	—	67	1	no	—
851	#376	—	67	1	no	—
852	#376	—	67	1	no	—
853	#376	—	67	1	no	—
854	#376	—	67	1	no	—
855	#376	—	67	1	no	—
856	C₄³	—	67	1	no	—
857	C₄³	—	67	1	no	—
858	C₄³	—	67	1	no	—
859	C₄³	—	67	1	no	—
860	C₂²×Q₈	—	67	1	no	—
861	C₂²×Q₈	—	67	1	no	—
862	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
863	C₂²×D₄	—	67	1	no	—
864	C₂³×C₄	—	67	1	no	—
865	C₂³×C₄	—	67	1	no	—
866	C₂³×C₄	—	67	1	no	—
867	C₂³×C₄	—	67	1	no	—
868	#126	—	2	4	no	—
869	#126	—	134	4	no	—
870	#126	—	134	4	no	—
871	#124	—	134	4	no	—
872	C₂²⋊Q₈	—	134	4	no	—
873	C₄×Q₈	—	2	4	no	—
874	C₄×Q₈	—	134	4	no	—
875	C₄×Q₈	—	134	4	no	—
876	C₄×Q₈	—	134	4	no	—
877	C₄×Q₈	—	134	4	no	—
878	C₄×D₄	—	134	4	no	—
879	#117	—	134	4	no	—
880	#117	—	134	4	no	—
881	#117	—	134	4	no	—
882	C₂×C₄⋊C₄	—	67	1	no	—
883	C₂×C₄⋊C₄	—	67	1	no	—
884	C₂×C₄⋊C₄	—	67	1	no	—
885	C₂×C₄⋊C₄	—	67	1	no	—
886	C₂×C₄⋊C₄	—	67	1	no	—
887	C₂×C₄⋊C₄	—	67	1	no	—
888	C₂×C₄⋊C₄	—	67	1	no	—
889	C₂×C₄⋊C₄	—	67	1	no	—
890	C₂×C₄⋊C₄	—	67	1	no	—
891	C₂×C₄⋊C₄	—	67	1	no	—
892	C₂×C₄⋊C₄	—	67	1	no	—
893	C₂×C₄⋊C₄	—	67	1	no	—
894	C₂×C₄⋊C₄	—	67	1	no	—
895	C₂×C₄⋊C₄	—	67	1	no	—
896	C₂×C₄⋊C₄	—	67	1	no	—
897	C₂×C₄⋊C₄	—	67	1	no	—
898	C₂×C₄⋊C₄	—	67	1	no	—
899	C₂×C₄⋊C₄	—	67	1	no	—
900	C₂×C₄⋊C₄	—	67	1	no	—
901	C₂×C₄⋊C₄	—	67	1	no	—
902	C₂×C₄⋊C₄	—	67	1	no	—
903	C₂×C₄⋊C₄	—	67	1	no	—
904	C₂×C₄⋊C₄	—	67	1	no	—
905	C₂×C₄⋊C₄	—	67	1	no	—
906	C₂×C₄⋊C₄	—	67	1	no	—
907	C₂×C₄⋊C₄	—	67	1	no	—
908	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
913	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
918	C₂×C₂²⋊C₄	—	67	1	no	—
919	C₂×C₂²⋊C₄	—	67	1	no	—
920	C₂×C₂²⋊C₄	—	67	1	no	—
921	C₂×C₂²⋊C₄	—	67	1	no	—
922	C₂×C₂²⋊C₄	—	67	1	no	—
923	C₂×C₂²⋊C₄	—	67	1	no	—
924	C₂×C₂²⋊C₄	—	67	1	no	—
925	C₂×C₂²⋊C₄	—	67	1	no	—
926	C₂×C₂²⋊C₄	—	67	1	no	—
927	C₂×C₂²⋊C₄	—	67	1	no	—
928	C₂×C₂²⋊C₄	—	67	1	no	—
929	C₂×C₂²⋊C₄	—	67	1	no	—
930	C₂×C₂²⋊C₄	—	67	1	no	—
931	C₂×C₂²⋊C₄	—	67	1	no	—
932	C₂×C₂²⋊C₄	—	67	1	no	—
933	C₂×C₂²⋊C₄	—	67	1	no	—
934	C₂×C₂²⋊C₄	—	67	1	no	—
935	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
936	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
937	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
938	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
939	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
941	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
942	C₂×C₄²	—	67	1	no	—
943	C₂×C₄²	—	67	1	no	—
944	C₂×C₄²	—	67	1	no	—
945	C₂×C₄²	—	67	1	no	—
946	C₂×C₄²	—	67	1	no	—
947	C₂×C₄²	—	67	1	no	—
948	C₂×C₄²	—	67	1	no	—
949	C₂×C₄²	—	67	1	no	—
950	C₂×C₄²	—	67	1	no	—
951	C₂×C₄²	—	67	1	no	—
952	C₂×C₄²	—	67	1	no	—
953	C₂×C₄²	—	67	1	no	—
954	C₂×C₄²	—	67	1	no	—
955	C₂×C₄²	—	67	1	no	—
956	C₂×C₄²	—	67	1	no	—
957	C₂×C₄²	—	67	1	no	—
958	C₂×C₄²	—	67	1	no	—
959	C₂×C₄²	—	67	1	no	—
960	C₂×C₄²	—	67	1	no	—
961	C₂×C₄²	—	67	1	no	—
962	C₂×C₄²	—	67	1	no	—
963	C₂×C₄²	—	67	1	no	—
964	C₂×C₄²	—	67	1	no	—
965	C₂×C₄²	—	67	1	no	—
966	C₂×C₄²	—	67	1	no	—
967	C₂×C₄²	—	67	1	no	—
968	C₂×C₄²	—	134	4	no	—
969	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
970	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
971	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
972	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
973	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
974	#95	—	67	1	no	—
975	#95	—	67	1	no	—
976	#95	—	67	1	no	—
977	#95	—	67	1	no	—
978	#95	—	67	1	no	—
979	#95	—	67	1	no	—
980	#95	—	67	1	no	—
981	#95	—	67	1	no	—
982	#95	—	67	1	no	—
983	#95	—	67	1	no	—
984	#95	—	67	1	no	—
985	#95	—	67	1	no	—
986	#95	—	67	1	no	—
987	#95	—	67	1	no	—
988	#95	—	67	1	no	—
989	#95	—	67	1	no	—
990	#95	—	67	1	no	—
991	#95	—	67	1	no	—
992	#95	—	67	1	no	—
993	#95	—	67	1	no	—
994	#95	—	67	1	no	—
995	#95	—	67	1	no	—
996	#95	—	67	1	no	—
997	#95	—	67	1	no	—
998	#95	—	67	1	no	—
999	#95	—	67	1	no	—
1000	#95	—	67	1	no	—
1001	#95	—	67	1	no	—
1002	#95	—	67	1	no	—
1003	#95	—	67	1	no	—
1004	#95	—	67	1	no	—
1005	#95	—	67	1	no	—
1006	#95	—	67	1	no	—
1007	#95	—	67	1	no	—
1008	#95	—	67	1	no	—
1009	#95	—	67	1	no	—
1010	#95	—	67	1	no	—
1011	#95	—	67	1	no	—
1012	#95	—	67	1	no	—
1013	#95	—	67	1	no	—
1014	#95	—	67	1	no	—
1015	#95	—	67	1	no	—
1016	#95	—	67	1	no	—
1017	#95	—	67	1	no	—
1018	#95	C₂²×D₆₇	1	1	yes	characteristic
1019	#95	C₂²×D₆₇	1	1	yes	characteristic
1020	#95	C₂²×D₆₇	1	1	yes	characteristic
1021	#95	C₂²×D₆₇	1	1	yes	characteristic
1022	#95	C₂²×D₆₇	1	1	yes	characteristic
1023	#95	C₂²×D₆₇	1	1	yes	characteristic
1024	#95	C₂²×D₆₇	1	1	yes	characteristic
1025	#95	C₂²×D₆₇	1	1	yes	characteristic
1026	#95	C₂²×D₆₇	1	1	yes	characteristic
1027	#95	C₂²×D₆₇	1	1	yes	characteristic
1028	#95	C₂²×D₆₇	1	1	yes	characteristic
1029	#95	C₂²×D₆₇	1	1	yes	characteristic
1030	C₂⁴	—	67	1	no	—
1031	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1032	C₂×Q₈	—	2	2	no	—
1033	C₂×Q₈	—	2	2	no	—
1034	C₂×Q₈	—	2	2	no	—
1035	C₂×Q₈	—	268	1	no	—
1036	C₂×Q₈	—	268	1	no	—
1037	C₂×Q₈	—	134	2	no	—
1038	C₂×Q₈	—	134	2	no	—
1039	C₂×Q₈	—	134	2	no	—
1040	C₂×Q₈	—	134	2	no	—
1041	C₂×D₄	—	268	1	no	—
1042	C₂×D₄	—	134	2	no	—
1043	C₂×D₄	—	134	2	no	—
1044	C₂²×C₄	—	268	1	no	—
1045	C₂²×C₄	—	67	1	no	—
1046	C₂²×C₄	—	67	1	no	—
1047	C₂²×C₄	—	67	1	no	—
1048	C₂²×C₄	—	67	1	no	—
1049	C₂²×C₄	—	67	1	no	—
1050	C₂²×C₄	—	67	1	no	—
1051	C₂²×C₄	—	67	1	no	—
1052	C₂²×C₄	—	67	1	no	—
1053	C₂²×C₄	—	67	1	no	—
1054	C₂²×C₄	—	67	1	no	—
1055	C₂²×C₄	—	67	1	no	—
1056	C₂²×C₄	—	67	1	no	—
1057	C₂²×C₄	—	67	1	no	—
1058	C₂²×C₄	—	67	1	no	—
1059	C₂²×C₄	—	67	1	no	—
1060	C₂²×C₄	—	134	2	no	—
1061	C₂²×C₄	—	134	2	no	—
1062	C₂²×C₄	—	134	2	no	—
1063	C₂²×C₄	—	134	2	no	—
1064	C₂²×C₄	—	134	2	no	—
1065	C₂²×C₄	—	134	2	no	—
1066	C₂²×C₄	—	134	2	no	—
1067	C₂²×C₄	—	134	2	no	—
1068	C₂²×C₄	—	134	2	no	—
1069	C₂²×C₄	—	134	2	no	—
1070	C₂²×C₄	—	134	2	no	—
1071	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1072	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1073	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1074	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1075	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1076	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1077	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1078	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1079	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1080	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1081	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1082	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1083	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1084	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	268	1	no	—
1095	C₄⋊C₄	—	268	1	no	—
1096	C₄⋊C₄	—	268	1	no	—
1097	C₄⋊C₄	—	268	1	no	—
1098	C₄⋊C₄	—	134	2	no	—
1099	C₄⋊C₄	—	134	2	no	—
1100	C₄⋊C₄	—	134	2	no	—
1101	C₄⋊C₄	—	134	2	no	—
1102	C₄⋊C₄	—	134	2	no	—
1103	C₄⋊C₄	—	134	2	no	—
1104	C₄⋊C₄	—	134	2	no	—
1105	C₄⋊C₄	—	134	2	no	—
1106	C₄⋊C₄	—	134	2	no	—
1107	C₄⋊C₄	—	134	2	no	—
1108	C₄⋊C₄	—	134	2	no	—
1109	C₄⋊C₄	—	134	2	no	—
1110	C₄⋊C₄	—	134	2	no	—
1111	C₄⋊C₄	—	134	2	no	—
1112	C₄⋊C₄	—	134	2	no	—
1113	C₄⋊C₄	—	134	2	no	—
1114	C₄⋊C₄	—	134	2	no	—
1115	C₄⋊C₄	—	134	2	no	—
1116	C₄⋊C₄	—	134	2	no	—
1117	C₄⋊C₄	—	134	2	no	—
1118	C₄⋊C₄	—	134	2	no	—
1119	C₄⋊C₄	—	134	2	no	—
1120	C₄⋊C₄	#11761627	1	4	yes	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	268	1	no	—
1129	C₂²⋊C₄	—	268	1	no	—
1130	C₂²⋊C₄	—	268	1	no	—
1131	C₂²⋊C₄	—	67	4	no	—
1132	C₂²⋊C₄	—	134	2	no	—
1133	C₂²⋊C₄	—	134	2	no	—
1134	C₂²⋊C₄	—	134	2	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	—	134	2	no	—
1144	C₂²⋊C₄	—	134	2	no	—
1145	C₄²	—	2	2	no	—
1146	C₄²	—	2	2	no	—
1147	C₄²	—	2	2	no	—
1148	C₄²	—	2	2	no	—
1149	C₄²	—	2	2	no	—
1150	C₄²	—	268	1	no	—
1151	C₄²	—	268	1	no	—
1152	C₄²	—	268	1	no	—
1153	C₄²	—	268	1	no	—
1154	C₄²	—	67	4	no	—
1155	C₄²	—	67	4	no	—
1156	C₄²	—	67	4	no	—
1157	C₄²	—	134	2	no	—
1158	C₄²	—	134	2	no	—
1159	C₄²	—	134	2	no	—
1160	C₄²	—	134	2	no	—
1161	C₄²	—	134	2	no	—
1162	C₄²	—	134	2	no	—
1163	C₄²	—	134	2	no	—
1164	C₄²	—	134	2	no	—
1165	C₄²	—	134	2	no	—
1166	C₄²	—	134	2	no	—
1167	C₄²	—	134	2	no	—
1168	C₄²	—	134	2	no	—
1169	C₄²	—	134	2	no	—
1170	C₄²	—	134	2	no	—
1171	C₄²	—	134	2	no	—
1172	C₄²	—	134	2	no	—
1173	C₄²	—	134	2	no	—
1174	C₄²	—	134	2	no	—
1175	C₄²	—	134	2	no	—
1176	C₂³	—	2	1	no	—
1177	C₂³	—	2	1	no	—
1178	C₂³	—	2	1	no	—
1179	C₂³	—	2	1	no	—
1180	C₂³	—	2	1	no	—
1181	C₂³	—	2	1	no	—
1182	C₂³	—	2	1	no	—
1183	C₂³	—	67	2	no	—
1184	C₂³	—	134	1	no	—
1185	C₂³	—	134	1	no	—
1186	C₂³	—	134	1	no	—
1187	C₂³	—	134	1	no	—
1188	C₂³	—	134	1	no	—
1189	C₂³	—	134	1	no	—
1190	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1191	Q₈	—	2	8	no	—
1192	Q₈	—	268	4	no	—
1193	Q₈	—	268	4	no	—
1194	D₄	—	268	4	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	268	4	no	—
1231	C₂×C₄	—	268	4	no	—
1232	C₂×C₄	—	268	4	no	—
1233	C₂×C₄	—	67	2	no	—
1234	C₂×C₄	—	67	2	no	—
1235	C₂×C₄	—	67	2	no	—
1236	C₂×C₄	—	67	2	no	—
1237	C₂×C₄	—	67	2	no	—
1238	C₂×C₄	—	67	2	no	—
1239	C₂×C₄	—	67	2	no	—
1240	C₂×C₄	—	67	2	no	—
1241	C₂×C₄	—	134	8	no	—
1242	C₂×C₄	—	134	1	no	—
1243	C₂×C₄	—	134	1	no	—
1244	C₂×C₄	—	134	1	no	—
1245	C₂×C₄	—	134	1	no	—
1246	C₂×C₄	—	134	1	no	—
1247	C₂×C₄	—	134	1	no	—
1248	C₂×C₄	—	134	1	no	—
1249	C₂×C₄	—	134	1	no	—
1250	C₂×C₄	—	134	1	no	—
1251	C₂×C₄	—	134	1	no	—
1252	C₂×C₄	—	134	1	no	—
1253	C₂×C₄	—	134	1	no	—
1254	C₂×C₄	—	134	1	no	—
1255	C₂×C₄	—	134	1	no	—
1256	C₂×C₄	—	134	1	no	—
1257	C₂×C₄	—	134	1	no	—
1258	C₂×C₄	—	134	1	no	—
1259	C₂×C₄	—	134	1	no	—
1260	C₂×C₄	—	134	1	no	—
1261	C₂×C₄	—	134	1	no	—
1262	C₂×C₄	—	134	1	no	—
1263	C₂×C₄	—	134	1	no	—
1264	C₂×C₄	—	134	1	no	—
1265	C₂×C₄	—	134	1	no	—
1266	C₂×C₄	—	134	1	no	—
1267	C₂×C₄	—	134	1	no	—
1268	C₂×C₄	—	134	1	no	—
1269	C₂×C₄	—	134	1	no	—
1270	C₂×C₄	—	134	1	no	—
1271	C₂×C₄	—	134	1	no	—
1272	C₂×C₄	—	134	1	no	—
1273	C₂×C₄	—	134	1	no	—
1274	C₂×C₄	—	134	1	no	—
1275	C₂×C₄	—	134	1	no	—
1276	C₂×C₄	—	134	1	no	—
1277	C₂×C₄	—	134	1	no	—
1278	C₂×C₄	—	134	1	no	—
1279	C₂×C₄	#41×D₆₇	1	2	yes	—
1280	C₂×C₄	#41×D₆₇	1	2	yes	—
1281	C₂×C₄	#41×D₆₇	1	2	yes	—
1282	C₂×C₄	#41×D₆₇	1	2	yes	—
1283	C₂×C₄	C₂×#11761627	1	2	yes	—
1284	C₂×C₄	C₂×#11761627	1	2	yes	—
1285	C₂×C₄	C₂×#11761627	1	2	yes	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	1	no	—
1288	C₂²	—	4	1	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	4	1	no	—
1292	C₂²	—	4	1	no	—
1293	C₂²	—	268	1	no	—
1294	C₂²	—	268	1	no	—
1295	C₂²	—	268	1	no	—
1296	C₂²	—	268	1	no	—
1297	C₂²	—	134	2	no	—
1298	C₂²	—	134	2	no	—
1299	C₂²	—	134	2	no	—
1300	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1301	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1302	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1303	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1304	C₂²	C₂²×#11761627	1	1	yes	characteristic
1305	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1306	C₂²	#16864233	1	1	yes	characteristic
1307	C₄	—	2	2	no	—
1308	C₄	—	2	2	no	—
1309	C₄	—	2	2	no	—
1310	C₄	—	2	2	no	—
1311	C₄	—	2	2	no	—
1312	C₄	—	2	2	no	—
1313	C₄	—	2	2	no	—
1314	C₄	—	4	1	no	—
1315	C₄	—	4	1	no	—
1316	C₄	—	4	1	no	—
1317	C₄	—	4	1	no	—
1318	C₄	—	4	1	no	—
1319	C₄	—	4	1	no	—
1320	C₄	—	4	1	no	—
1321	C₄	—	268	1	no	—
1322	C₄	—	268	1	no	—
1323	C₄	—	268	1	no	—
1324	C₄	—	268	1	no	—
1325	C₄	—	268	1	no	—
1326	C₄	—	268	1	no	—
1327	C₄	—	268	1	no	—
1328	C₄	—	268	1	no	—
1329	C₄	—	268	1	no	—
1330	C₄	—	67	4	no	—
1331	C₄	—	134	2	no	—
1332	C₄	—	134	2	no	—
1333	C₄	—	134	2	no	—
1334	C₄	—	134	2	no	—
1335	C₄	—	134	2	no	—
1336	C₂	—	8	1	no	—
1337	C₂	—	268	2	no	—
1338	C₂	#22573501	1	1	yes	characteristic
1339	C₂	#22573503	1	1	yes	characteristic
1340	C₂	#22573641	1	1	yes	characteristic
1341	C₂	#556×D₆₇	1	1	yes	characteristic
1342	C₂	#22573770	1	1	yes	characteristic
1343	C₂	#22573772	1	1	yes	characteristic
1344	C₂	#22573825	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2469	C₂
prime radical	C₂²×C₂²⋊D₆₇	C₂³
hypercenter	#2469	D₆₇
hypocenter	C₆₇	#34867
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2469

Complements

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

N	H ≅ G/N	type
1. #22565853	C₂	semidirect
2. #22565842	C₂	semidirect
4. #22565781	C₂	semidirect
5. #22565719	C₂	semidirect
6. #22565641	C₂	semidirect
7. #22565534	C₂	semidirect
9. #22565069	C₂	semidirect
10. #22565009	C₂	semidirect
11. #22564951	C₂	semidirect
13. #22564431	C₂	semidirect
15. #22564224	C₂	semidirect
16. #22563508	C₂	semidirect
17. #22563499	C₂	semidirect
19. #22563484	C₂	semidirect
20. #22562763	C₂	semidirect
21. #126×Dic₆₇	C₂	semidirect
22. #22562759	C₂	semidirect
24. #22562743	C₂	semidirect
25. #22562703	C₂	semidirect
26. #22562682	C₂	semidirect
27. #22562680	C₂	semidirect
29. C₄×Q₈×Dic₆₇	C₂	semidirect
30. C₄×#14524001	C₂	semidirect
31. C₆₇×#2469	C₂	semidirect
687. #2469	D₆₇	semidirect
704. C₆₇	#34867	semidirect

Maximal subgroups

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

subgroup	index
#22565853	2
#22565842	2
#22565809	2
#22565781	2
#22565719	2
#22565641	2
#22565534	2
#22565351	2
#22565069	2
#22565009	2
#22564951	2
#22564914	2
#22564431	2
#22564371	2
#22564224	2
#22563508	2
#22563499	2
#22563491	2
#22563484	2
#22562763	2
#126×Dic₆₇	2
#22562759	2
#22562750	2
#22562743	2
#22562703	2
#22562682	2
#22562680	2
#22562651	2
C₄×Q₈×Dic₆₇	2
C₄×#14524001	2
C₆₇×#2469	2
#34867	67