Subgroups — #31063543

Order 17152.

1588 conjugacy classes of subgroups.

The subgroup lattice has 1366 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	#22568550	C₂	1	1	yes	maximal, characteristic, complemented
3	#22568182	C₂	1	1	yes	maximal, characteristic, complemented
4	#22568173	C₂	1	1	yes	maximal, characteristic, complemented
5	#22568006	C₂	1	1	yes	maximal, characteristic, complemented
6	#22567991	C₂	1	1	yes	maximal, characteristic, complemented
7	#22567961	C₂	1	1	yes	maximal, characteristic, complemented
8	#22567417	C₂	1	1	yes	maximal, characteristic
9	#22567337	C₂	1	1	yes	maximal, characteristic, complemented
10	#22567227	C₂	1	1	yes	maximal, characteristic
11	#22567197	C₂	1	1	yes	maximal, characteristic, complemented
12	#22567094	C₂	1	1	yes	maximal, characteristic, complemented
13	#22567082	C₂	1	1	yes	maximal, characteristic, complemented
14	#22566985	C₂	1	1	yes	maximal, characteristic, complemented
15	#22566874	C₂	1	1	yes	maximal, characteristic, complemented
16	#22566703	C₂	1	1	yes	maximal, characteristic
17	#22566700	C₂	1	1	yes	maximal, characteristic
18	#22566523	C₂	1	1	yes	maximal, characteristic, complemented
19	#22566409	C₂	1	1	yes	maximal, characteristic, complemented
20	#22566385	C₂	1	1	yes	maximal, characteristic, complemented
21	#22565912	C₂	1	1	yes	maximal, characteristic, complemented
22	#22565872	C₂	1	1	yes	maximal, characteristic, complemented
23	#22565867	C₂	1	1	yes	maximal, characteristic, complemented
24	#22565224	C₂	1	1	yes	maximal, characteristic, complemented
25	#22565218	C₂	1	1	yes	maximal, characteristic, complemented
26	#22563921	C₂	1	1	yes	maximal, characteristic, complemented
27	#22563884	C₂	1	1	yes	maximal, characteristic, complemented
28	#22562853	C₂	1	1	yes	maximal, characteristic
29	#22562840	C₂	1	1	yes	maximal, characteristic
30	#22562650	C₂	1	1	yes	maximal, characteristic
31	C₆₇×#2605	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14524042	C₂²	1	1	yes	characteristic
33	C₂×#14524041	C₂²	1	1	yes	characteristic
34	C₂×#14524034	C₂²	1	1	yes	characteristic
35	C₂×#14524033	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×#14524019	C₂²	1	1	yes	characteristic
40	C₂×#14524019	C₂²	1	1	yes	characteristic
41	C₂×#14524019	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
43	C₂×#14524000	C₂²	1	1	yes	characteristic
44	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
45	#16863338	C₂²	1	1	yes	characteristic
46	#16863337	C₂²	1	1	yes	characteristic
47	#16863337	C₂²	1	1	yes	characteristic
48	#16863334	C₂²	1	1	yes	characteristic
49	#16863333	C₂²	1	1	yes	characteristic
50	#16863333	C₂²	1	1	yes	characteristic
51	#16863333	C₂²	1	1	yes	characteristic
52	#16863331	C₂²	1	1	yes	characteristic
53	#16863331	C₂²	1	1	yes	characteristic
54	#16863331	C₂²	1	1	yes	characteristic
55	#16863330	C₂²	1	1	yes	characteristic
56	#16863330	C₂²	1	1	yes	characteristic
57	#16863330	C₂²	1	1	yes	characteristic
58	#16863330	C₂²	1	1	yes	characteristic
59	#16863330	C₂²	1	1	yes	characteristic
60	#16863330	C₂²	1	1	yes	characteristic
61	#16863329	C₂²	1	1	yes	characteristic
62	#16863329	C₂²	1	1	yes	characteristic
63	#16863328	C₂²	1	1	yes	characteristic
64	#16863328	C₂²	1	1	yes	characteristic
65	#16863328	C₂²	1	1	yes	characteristic
66	#16863328	C₂²	1	1	yes	characteristic
67	#16863328	C₂²	1	1	yes	characteristic
68	#16863327	C₂²	1	1	yes	characteristic
69	#16863327	C₂²	1	1	yes	characteristic
70	#16863326	C₂²	1	1	yes	characteristic
71	#16863320	C₂²	1	1	yes	characteristic
72	#16863320	C₂²	1	1	yes	characteristic
73	#16863318	C₂²	1	1	yes	characteristic
74	#16863318	C₂²	1	1	yes	characteristic
75	#16863318	C₂²	1	1	yes	characteristic
76	#16863318	C₂²	1	1	yes	characteristic
77	#16863317	C₂²	1	1	yes	characteristic
78	#16863317	C₂²	1	1	yes	characteristic
79	#16863317	C₂²	1	1	yes	characteristic
80	#16863317	C₂²	1	1	yes	characteristic
81	#16863317	C₂²	1	1	yes	characteristic
82	#16863317	C₂²	1	1	yes	characteristic
83	#16863316	C₂²	1	1	yes	characteristic
84	#16863315	C₂²	1	1	yes	characteristic
85	#16863309	C₂²	1	1	yes	characteristic
86	#16863309	C₂²	1	1	yes	characteristic
87	#16863309	C₂²	1	1	yes	characteristic
88	#16863307	C₂²	1	1	yes	characteristic
89	#16863303	C₂²	1	1	yes	characteristic
90	#16863303	C₂²	1	1	yes	characteristic
91	#16863302	C₂²	1	1	yes	characteristic
92	#16863302	C₂²	1	1	yes	characteristic
93	#16863302	C₂²	1	1	yes	characteristic
94	#16863300	C₂²	1	1	yes	characteristic
95	#16863300	C₂²	1	1	yes	characteristic
96	#16863298	C₂²	1	1	yes	characteristic
97	#16863298	C₂²	1	1	yes	characteristic
98	#16863295	C₂²	1	1	yes	characteristic
99	#16863295	C₂²	1	1	yes	characteristic
100	#16863295	C₂²	1	1	yes	characteristic
101	#16863294	C₂²	1	1	yes	characteristic
102	#16863294	C₂²	1	1	yes	characteristic
103	#16863294	C₂²	1	1	yes	characteristic
104	#16863294	C₂²	1	1	yes	characteristic
105	#16863294	C₂²	1	1	yes	characteristic
106	#16863293	C₂²	1	1	yes	characteristic
107	#16863293	C₂²	1	1	yes	characteristic
108	#16863293	C₂²	1	1	yes	characteristic
109	#16863293	C₂²	1	1	yes	characteristic
110	#16863293	C₂²	1	1	yes	characteristic
111	#16863293	C₂²	1	1	yes	characteristic
112	#16863293	C₂²	1	1	yes	characteristic
113	#16863293	C₂²	1	1	yes	characteristic
114	#16863293	C₂²	1	1	yes	characteristic
115	#16863288	C₂²	1	1	yes	characteristic
116	#16863288	C₂²	1	1	yes	characteristic
117	#16863286	C₂²	1	1	yes	characteristic
118	#16863286	C₂²	1	1	yes	characteristic
119	#16863285	C₂²	1	1	yes	characteristic
120	#16863285	C₂²	1	1	yes	characteristic
121	#16863285	C₂²	1	1	yes	characteristic
122	#16863285	C₂²	1	1	yes	characteristic
123	#16863283	C₂²	1	1	yes	characteristic
124	#16863283	C₂²	1	1	yes	characteristic
125	#16863283	C₂²	1	1	yes	characteristic
126	#16863282	C₂²	1	1	yes	characteristic
127	#16863281	C₂²	1	1	yes	characteristic
128	#16863280	C₂²	1	1	yes	characteristic
129	#16863280	C₂²	1	1	yes	characteristic
130	#16863279	C₂²	1	1	yes	characteristic
131	#16863279	C₂²	1	1	yes	characteristic
132	#16863279	C₂²	1	1	yes	characteristic
133	#16863279	C₂²	1	1	yes	characteristic
134	#16863279	C₂²	1	1	yes	characteristic
135	#16863279	C₂²	1	1	yes	characteristic
136	#16863279	C₂²	1	1	yes	characteristic
137	#16863278	C₂²	1	1	yes	characteristic
138	#16863278	C₂²	1	1	yes	characteristic
139	#16863274	C₂²	1	1	yes	characteristic
140	#16863274	C₂²	1	1	yes	characteristic
141	#16863274	C₂²	1	1	yes	characteristic
142	#16863274	C₂²	1	1	yes	characteristic
143	#16863270	C₂²	1	1	yes	characteristic
144	#16863270	C₂²	1	1	yes	characteristic
145	#16863270	C₂²	1	1	yes	characteristic
146	#16863270	C₂²	1	1	yes	characteristic
147	#16863270	C₂²	1	1	yes	characteristic
148	#16863270	C₂²	1	1	yes	characteristic
149	#16863270	C₂²	1	1	yes	characteristic
150	#16863270	C₂²	1	1	yes	characteristic
151	#16863267	C₂²	1	1	yes	characteristic
152	#16863267	C₂²	1	1	yes	characteristic
153	#16863265	C₂²	1	1	yes	characteristic
154	#16863265	C₂²	1	1	yes	characteristic
155	#16863262	C₂²	1	1	yes	characteristic
156	#16863258	C₂²	1	1	yes	characteristic
157	#16863258	C₂²	1	1	yes	characteristic
158	#16863258	C₂²	1	1	yes	characteristic
159	#16863255	C₂²	1	1	yes	characteristic
160	#16863255	C₂²	1	1	yes	characteristic
161	#16863255	C₂²	1	1	yes	characteristic
162	#16863255	C₂²	1	1	yes	characteristic
163	#16863255	C₂²	1	1	yes	characteristic
164	#16863253	C₂²	1	1	yes	characteristic
165	#16863253	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
167	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
168	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
169	#16863243	C₂²	1	1	yes	characteristic
170	#16863242	C₂²	1	1	yes	characteristic
171	#95×D₆₇	C₂²	1	1	yes	characteristic
172	#400×C₆₇	C₂²	1	1	yes	characteristic
173	#400×C₆₇	C₂²	1	1	yes	characteristic
174	#395×C₆₇	C₂²	1	1	yes	characteristic
175	#395×C₆₇	C₂²	1	1	yes	characteristic
176	#391×C₆₇	C₂²	1	1	yes	characteristic
177	#391×C₆₇	C₂²	1	1	yes	characteristic
178	#391×C₆₇	C₂²	1	1	yes	characteristic
179	#391×C₆₇	C₂²	1	1	yes	characteristic
180	#387×C₆₇	C₂²	1	1	yes	characteristic
181	#387×C₆₇	C₂²	1	1	yes	characteristic
182	#387×C₆₇	C₂²	1	1	yes	characteristic
183	#387×C₆₇	C₂²	1	1	yes	characteristic
184	#383×C₆₇	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
186	#376×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
190	C₂²×D₂₆₈	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	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	#14524042	—	4	2	no	—
198	#14524041	—	4	2	no	—
199	#14524034	—	4	2	no	—
200	#14524033	—	4	2	no	—
201	#14524023	—	4	2	no	—
202	#14524021	—	4	2	no	—
203	#14524021	—	4	2	no	—
204	#14524019	—	4	2	no	—
205	#14524019	—	4	2	no	—
206	#14524019	—	4	2	no	—
207	C₄×D₂₆₈	Q₈	1	8	yes	complemented
208	#14524000	—	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×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₆₇	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	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×Dic₆₇⋊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×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×(C₂×D₆₇)⋊C₄	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	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
283	C₄²×D₆₇	—	4	2	no	—
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×Q₈×C₆₇	C₂³	1	1	yes	characteristic
322	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
333	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
335	#95×C₆₇	C₂³	1	1	yes	characteristic
336	#95×C₆₇	C₂³	1	1	yes	characteristic
337	#95×C₆₇	C₂³	1	1	yes	characteristic
338	#95×C₆₇	C₂³	1	1	yes	characteristic
339	#95×C₆₇	C₂³	1	1	yes	characteristic
340	#95×C₆₇	C₂³	1	1	yes	characteristic
341	#95×C₆₇	C₂³	1	1	yes	characteristic
342	#95×C₆₇	C₂³	1	1	yes	characteristic
343	#95×C₆₇	C₂³	1	1	yes	characteristic
344	#95×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	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
356	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×Dic₁₃₄	—	2	2	no	—
358	C₂×Dic₁₃₄	—	4	1	no	—
359	C₂×Dic₁₃₄	—	4	1	no	—
360	C₂×Dic₁₃₄	—	4	1	no	—
361	C₂×Dic₁₃₄	—	4	1	no	—
362	C₂×Dic₁₃₄	—	4	1	no	—
363	C₂×Dic₁₃₄	—	4	1	no	—
364	C₂×Dic₁₃₄	—	4	1	no	—
365	C₂×Dic₁₃₄	—	4	1	no	—
366	C₂×D₂₆₈	—	4	1	no	—
367	C₂×D₂₆₈	—	4	1	no	—
368	C₂×D₂₆₈	C₂×Q₈	1	4	yes	—
369	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×D₆₇	—	2	2	no	—
384	C₂×C₄×D₆₇	—	2	2	no	—
385	C₂×C₄×D₆₇	—	2	2	no	—
386	C₂×C₄×D₆₇	—	4	1	no	—
387	C₂×C₄×D₆₇	—	4	1	no	—
388	C₂×C₄×D₆₇	—	4	1	no	—
389	C₂×C₄×D₆₇	—	4	1	no	—
390	C₂×C₄×D₆₇	—	4	1	no	—
391	C₂×C₄×D₆₇	—	4	1	no	—
392	C₂×C₄×D₆₇	—	4	1	no	—
393	C₂×C₄×D₆₇	—	4	1	no	—
394	C₂×C₄×D₆₇	—	4	1	no	—
395	C₂×C₄×D₆₇	—	4	1	no	—
396	C₂×C₄×D₆₇	—	4	1	no	—
397	C₂×C₄×D₆₇	—	4	1	no	—
398	C₂×C₄×D₆₇	—	4	1	no	—
399	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
400	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
401	C₄⋊Dic₆₇	—	2	2	no	—
402	C₄⋊Dic₆₇	—	4	1	no	—
403	C₄⋊Dic₆₇	—	4	1	no	—
404	C₄⋊Dic₆₇	—	4	1	no	—
405	C₄⋊Dic₆₇	—	4	1	no	—
406	C₄⋊Dic₆₇	—	4	1	no	—
407	C₄⋊Dic₆₇	—	4	1	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	C₄⋊Dic₆₇	C₂×Q₈	1	4	yes	—
419	Dic₆₇⋊C₄	—	2	2	no	—
420	Dic₆₇⋊C₄	—	2	2	no	—
421	Dic₆₇⋊C₄	—	2	2	no	—
422	Dic₆₇⋊C₄	—	2	2	no	—
423	Dic₆₇⋊C₄	—	2	2	no	—
424	Dic₆₇⋊C₄	—	2	2	no	—
425	Dic₆₇⋊C₄	—	2	2	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	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	(C₂×D₆₇)⋊C₄	—	2	2	no	—
446	(C₂×D₆₇)⋊C₄	—	2	2	no	—
447	(C₂×D₆₇)⋊C₄	—	2	2	no	—
448	(C₂×D₆₇)⋊C₄	—	4	1	no	—
449	(C₂×D₆₇)⋊C₄	—	4	1	no	—
450	(C₂×D₆₇)⋊C₄	—	4	1	no	—
451	(C₂×D₆₇)⋊C₄	—	4	1	no	—
452	(C₂×D₆₇)⋊C₄	—	4	1	no	—
453	(C₂×D₆₇)⋊C₄	—	4	1	no	—
454	(C₂×D₆₇)⋊C₄	—	4	1	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	C₂×Q₈	1	4	yes	—
466	(C₂×D₆₇)⋊C₄	C₂×Q₈	1	4	yes	—
467	C₄×Dic₆₇	—	2	2	no	—
468	C₄×Dic₆₇	—	2	2	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	C₂×Q₈×C₆₇	—	2	2	no	—
476	C₂×Q₈×C₆₇	—	2	2	no	—
477	C₂×Q₈×C₆₇	—	4	1	no	—
478	C₂×Q₈×C₆₇	—	4	1	no	—
479	C₂×Q₈×C₆₇	—	4	1	no	—
480	C₂×Q₈×C₆₇	—	4	1	no	—
481	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
483	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
486	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
487	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	—	2	2	no	—
497	C₄⋊C₄×C₆₇	—	2	2	no	—
498	C₄⋊C₄×C₆₇	—	2	2	no	—
499	C₄⋊C₄×C₆₇	—	2	2	no	—
500	C₄⋊C₄×C₆₇	—	4	1	no	—
501	C₄⋊C₄×C₆₇	—	4	1	no	—
502	C₄⋊C₄×C₆₇	—	4	1	no	—
503	C₄⋊C₄×C₆₇	—	4	1	no	—
504	C₄²×C₆₇	—	4	1	no	—
505	C₄²×C₆₇	—	4	1	no	—
506	C₄²×C₆₇	—	4	1	no	—
507	C₄²×C₆₇	—	4	1	no	—
508	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
509	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
510	C₂²×D₆₇	—	2	1	no	—
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	—	2	1	no	—
518	C₂²×D₆₇	—	2	1	no	—
519	C₂²×D₆₇	—	2	1	no	—
520	C₂²×D₆₇	—	2	1	no	—
521	C₂²×D₆₇	—	2	1	no	—
522	C₂²×D₆₇	C₂²×Q₈	1	2	yes	—
523	C₂²×D₆₇	C₂²×Q₈	1	2	yes	—
524	Q₈×C₆₇	—	8	2	no	—
525	Q₈×C₆₇	—	8	2	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	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	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	C₂²×Q₈	1	2	yes	—
567	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
568	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
569	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
570	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
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	—	2	1	no	—
600	C₂×Dic₆₇	—	2	1	no	—
601	C₂×Dic₆₇	—	2	1	no	—
602	C₂×Dic₆₇	—	2	1	no	—
603	C₂×Dic₆₇	—	2	1	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	C₂²×Q₈	1	2	yes	—
611	C₂×Dic₆₇	C₂²×Q₈	1	2	yes	—
612	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
613	D₂₆₈	—	4	4	no	—
614	C₄×D₆₇	—	4	4	no	—
615	C₄×D₆₇	—	4	4	no	—
616	C₄×D₆₇	—	4	4	no	—
617	C₄×D₆₇	—	4	4	no	—
618	C₄×D₆₇	—	8	2	no	—
619	C₄×D₆₇	—	8	2	no	—
620	Dic₁₃₄	—	8	2	no	—
621	Dic₁₃₄	—	8	2	no	—
622	Dic₁₃₄	—	8	2	no	—
623	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
624	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
627	C₂²×C₆₇	#585	1	1	yes	characteristic
628	C₂²×C₆₇	#585	1	1	yes	characteristic
629	C₂²×C₆₇	#585	1	1	yes	characteristic
630	C₂×D₆₇	—	2	2	no	—
631	C₂×D₆₇	—	2	2	no	—
632	C₂×D₆₇	—	2	2	no	—
633	C₂×D₆₇	—	2	2	no	—
634	C₂×D₆₇	—	2	2	no	—
635	C₂×D₆₇	—	2	2	no	—
636	C₂×D₆₇	—	4	1	no	—
637	C₂×D₆₇	—	4	1	no	—
638	C₂×D₆₇	—	4	1	no	—
639	C₂×D₆₇	—	4	1	no	—
640	C₂×D₆₇	—	4	1	no	—
641	C₂×D₆₇	—	4	1	no	—
642	C₂×D₆₇	—	4	1	no	—
643	C₂×D₆₇	—	4	1	no	—
644	C₄×C₆₇	—	2	2	no	—
645	C₄×C₆₇	—	2	2	no	—
646	C₄×C₆₇	—	2	2	no	—
647	C₄×C₆₇	—	2	2	no	—
648	C₄×C₆₇	—	2	2	no	—
649	C₄×C₆₇	—	4	1	no	—
650	C₄×C₆₇	—	4	1	no	—
651	C₄×C₆₇	—	4	1	no	—
652	C₄×C₆₇	—	4	1	no	—
653	C₄×C₆₇	—	4	1	no	—
654	C₄×C₆₇	—	4	1	no	—
655	C₄×C₆₇	—	4	1	no	—
656	C₄×C₆₇	—	4	1	no	—
657	C₄×C₆₇	—	4	1	no	—
658	C₄×C₆₇	—	4	1	no	—
659	Dic₆₇	—	2	2	no	—
660	Dic₆₇	—	2	2	no	—
661	Dic₆₇	—	2	2	no	—
662	Dic₆₇	—	4	1	no	—
663	Dic₆₇	—	4	1	no	—
664	Dic₆₇	—	4	1	no	—
665	Dic₆₇	—	4	1	no	—
666	Dic₆₇	—	4	1	no	—
667	Dic₆₇	—	4	1	no	—
668	Dic₆₇	—	4	1	no	—
669	Dic₆₇	—	4	1	no	—
670	Dic₆₇	—	4	1	no	—
671	Dic₆₇	—	4	1	no	—
672	Dic₆₇	—	4	1	no	—
673	#36753	—	67	1	no	maximal, Sylow
674	C₂×C₆₇	#3458	1	1	yes	characteristic
675	C₂×C₆₇	#3501	1	1	yes	characteristic
676	C₂×C₆₇	#3503	1	1	yes	characteristic
677	C₂×C₆₇	#3535	1	1	yes	characteristic
678	C₂×C₆₇	#3542	1	1	yes	characteristic
679	C₂×C₆₇	#3557	1	1	yes	characteristic
680	C₂×C₆₇	#3562	1	1	yes	characteristic
681	D₆₇	—	4	2	no	—
682	D₆₇	—	4	2	no	—
683	#2857	—	67	1	no	—
684	#2855	—	67	1	no	—
685	#2807	—	67	1	no	—
686	#2806	—	67	1	no	—
687	#2792	—	67	1	no	—
688	#2791	—	67	1	no	—
689	#2788	—	67	1	no	—
690	#2748	—	67	1	no	—
691	#2742	—	67	1	no	—
692	#2732	—	67	1	no	—
693	#2729	—	67	1	no	—
694	#2720	—	67	1	no	—
695	#2720	—	67	1	no	—
696	#2713	—	67	1	no	—
697	#2704	—	67	1	no	—
698	#2692	—	67	1	no	—
699	#2692	—	67	1	no	—
700	#2677	—	67	1	no	—
701	#2667	—	67	1	no	—
702	#2665	—	67	1	no	—
703	#2612	—	67	1	no	—
704	#2607	—	67	1	no	—
705	#2606	—	67	1	no	—
706	#2605	D₆₇	1	1	yes	characteristic, complemented
707	#2550	—	67	1	no	—
708	#2549	—	67	1	no	—
709	#2441	—	67	1	no	—
710	#2438	—	67	1	no	—
711	#2319	—	67	1	no	—
712	#2318	—	67	1	no	—
713	#2290	—	67	1	no	—
714	C₆₇	#36753	1	1	yes	characteristic, complemented, Sylow
715	C₂×C₄⋊Q₈	—	67	1	no	—
716	C₂×C₄⋊Q₈	—	67	1	no	—
717	C₂×#125	—	67	1	no	—
718	C₂×#125	—	67	1	no	—
719	C₂×C₂²⋊Q₈	—	67	1	no	—
720	C₂×C₂²⋊Q₈	—	67	1	no	—
721	C₂×C₂²⋊Q₈	—	67	1	no	—
722	C₂×C₂²⋊Q₈	—	67	1	no	—
723	C₂×C₂²⋊Q₈	—	67	1	no	—
724	C₂×C₂²⋊Q₈	—	67	1	no	—
725	C₂×C₄×D₄	—	67	1	no	—
726	C₂×#117	—	67	1	no	—
727	C₂²×C₄²	—	67	1	no	—
728	#400	—	67	1	no	—
729	#400	—	67	1	no	—
730	#400	—	67	1	no	—
731	#400	—	67	1	no	—
732	#400	C₂×D₆₇	1	1	yes	characteristic
733	#400	C₂×D₆₇	1	1	yes	characteristic
734	#399	—	67	1	no	—
735	#399	—	67	1	no	—
736	#399	—	67	1	no	—
737	#399	—	67	1	no	—
738	#399	—	67	1	no	—
739	#399	—	67	1	no	—
740	#398	—	67	1	no	—
741	#398	—	67	1	no	—
742	#398	—	67	1	no	—
743	#398	—	67	1	no	—
744	#398	—	67	1	no	—
745	#398	—	67	1	no	—
746	#398	—	67	1	no	—
747	#398	—	67	1	no	—
748	#398	—	67	1	no	—
749	#398	—	67	1	no	—
750	#398	—	67	1	no	—
751	#398	—	67	1	no	—
752	#398	—	67	1	no	—
753	#398	—	67	1	no	—
754	#398	—	67	1	no	—
755	#398	—	67	1	no	—
756	#396	—	67	1	no	—
757	#396	—	67	1	no	—
758	#396	—	67	1	no	—
759	#396	—	67	1	no	—
760	#396	—	67	1	no	—
761	#396	—	67	1	no	—
762	#395	—	67	1	no	—
763	#395	—	67	1	no	—
764	#395	—	67	1	no	—
765	#395	—	67	1	no	—
766	#395	—	67	1	no	—
767	#395	—	67	1	no	—
768	#395	—	67	1	no	—
769	#395	—	67	1	no	—
770	#395	C₂×D₆₇	1	1	yes	characteristic
771	#395	C₂×D₆₇	1	1	yes	characteristic
772	#393	—	67	1	no	—
773	#393	—	67	1	no	—
774	#393	—	67	1	no	—
775	#393	—	67	1	no	—
776	#391	—	67	1	no	—
777	#391	—	67	1	no	—
778	#391	—	67	1	no	—
779	#391	—	67	1	no	—
780	#391	—	67	1	no	—
781	#391	—	67	1	no	—
782	#391	—	67	1	no	—
783	#391	C₂×D₆₇	1	1	yes	characteristic
784	#391	C₂×D₆₇	1	1	yes	characteristic
785	#391	C₂×D₆₇	1	1	yes	characteristic
786	#391	C₂×D₆₇	1	1	yes	characteristic
787	#390	—	67	1	no	—
788	#390	—	67	1	no	—
789	#389	—	67	1	no	—
790	#389	—	67	1	no	—
791	#389	—	67	1	no	—
792	#389	—	67	1	no	—
793	#389	—	67	1	no	—
794	#389	—	67	1	no	—
795	#389	—	67	1	no	—
796	#389	—	67	1	no	—
797	#389	—	67	1	no	—
798	#389	—	67	1	no	—
799	#389	—	67	1	no	—
800	#389	—	67	1	no	—
801	#389	—	67	1	no	—
802	#389	—	67	1	no	—
803	#389	—	67	1	no	—
804	#389	—	67	1	no	—
805	#389	—	67	1	no	—
806	#388	—	67	1	no	—
807	#388	—	67	1	no	—
808	#388	—	67	1	no	—
809	#388	—	67	1	no	—
810	#388	—	67	1	no	—
811	#388	—	67	1	no	—
812	#388	—	67	1	no	—
813	#388	—	67	1	no	—
814	#387	—	67	1	no	—
815	#387	—	67	1	no	—
816	#387	—	67	1	no	—
817	#387	—	67	1	no	—
818	#387	—	67	1	no	—
819	#387	—	67	1	no	—
820	#387	—	67	1	no	—
821	#387	—	67	1	no	—
822	#387	—	67	1	no	—
823	#387	—	67	1	no	—
824	#387	—	67	1	no	—
825	#387	—	67	1	no	—
826	#387	—	67	1	no	—
827	#387	—	67	1	no	—
828	#387	—	67	1	no	—
829	#387	—	67	1	no	—
830	#387	C₂×D₆₇	1	1	yes	characteristic
831	#387	C₂×D₆₇	1	1	yes	characteristic
832	#387	C₂×D₆₇	1	1	yes	characteristic
833	#387	C₂×D₆₇	1	1	yes	characteristic
834	#386	—	67	1	no	—
835	#386	—	67	1	no	—
836	#386	—	67	1	no	—
837	#386	—	67	1	no	—
838	#385	—	67	1	no	—
839	#385	—	67	1	no	—
840	#385	—	67	1	no	—
841	#385	—	67	1	no	—
842	#385	—	67	1	no	—
843	#385	—	67	1	no	—
844	#385	—	67	1	no	—
845	#385	—	67	1	no	—
846	#385	—	67	1	no	—
847	#385	—	67	1	no	—
848	#384	—	67	1	no	—
849	#384	—	67	1	no	—
850	#383	C₂×D₆₇	1	1	yes	characteristic
851	#382	—	67	1	no	—
852	#381	—	67	1	no	—
853	#381	—	67	1	no	—
854	#381	—	67	1	no	—
855	#380	—	67	1	no	—
856	#380	—	67	1	no	—
857	#380	—	67	1	no	—
858	#380	—	67	1	no	—
859	#380	—	67	1	no	—
860	#380	—	67	1	no	—
861	#380	—	67	1	no	—
862	C₄×C₄⋊C₄	—	67	1	no	—
863	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
864	C₄×C₂²⋊C₄	—	67	1	no	—
865	C₄×C₂²⋊C₄	—	67	1	no	—
866	C₄×C₂²⋊C₄	—	67	1	no	—
867	#376	—	67	1	no	—
868	#376	C₂×D₆₇	1	1	yes	characteristic
869	C₂×#95	—	67	1	no	—
870	C₂²×Q₈	—	67	1	no	—
871	C₂²×Q₈	—	67	1	no	—
872	C₂²×Q₈	—	67	1	no	—
873	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
874	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
875	C₂²×D₄	—	67	1	no	—
876	C₂³×C₄	—	67	1	no	—
877	C₂³×C₄	—	67	1	no	—
878	C₂³×C₄	—	67	1	no	—
879	C₂³×C₄	—	67	1	no	—
880	C₂³×C₄	—	67	1	no	—
881	C₂³×C₄	—	67	1	no	—
882	C₄⋊Q₈	—	268	2	no	—
883	C₄⋊Q₈	—	268	2	no	—
884	#125	—	268	2	no	—
885	#125	—	268	2	no	—
886	C₂²⋊Q₈	—	268	2	no	—
887	C₂²⋊Q₈	—	268	2	no	—
888	C₂²⋊Q₈	—	268	2	no	—
889	C₂²⋊Q₈	—	268	2	no	—
890	C₂²⋊Q₈	—	268	2	no	—
891	C₂²⋊Q₈	—	268	2	no	—
892	C₄×D₄	—	67	8	no	—
893	#117	—	268	2	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	—	67	1	no	—
909	C₂×C₄⋊C₄	—	67	1	no	—
910	C₂×C₄⋊C₄	—	67	1	no	—
911	C₂×C₄⋊C₄	—	67	1	no	—
912	C₂×C₄⋊C₄	—	67	1	no	—
913	C₂×C₄⋊C₄	—	67	1	no	—
914	C₂×C₄⋊C₄	—	67	1	no	—
915	C₂×C₄⋊C₄	—	67	1	no	—
916	C₂×C₄⋊C₄	—	67	1	no	—
917	C₂×C₄⋊C₄	—	67	1	no	—
918	C₂×C₄⋊C₄	—	67	1	no	—
919	C₂×C₄⋊C₄	—	67	1	no	—
920	C₂×C₄⋊C₄	—	67	1	no	—
921	C₂×C₄⋊C₄	—	67	1	no	—
922	C₂×C₄⋊C₄	—	67	1	no	—
923	C₂×C₄⋊C₄	—	67	1	no	—
924	C₂×C₄⋊C₄	—	67	1	no	—
925	C₂×C₄⋊C₄	—	67	1	no	—
926	C₂×C₄⋊C₄	—	67	1	no	—
927	C₂×C₄⋊C₄	—	67	1	no	—
928	C₂×C₄⋊C₄	—	67	1	no	—
929	C₂×C₄⋊C₄	—	67	1	no	—
930	C₂×C₄⋊C₄	—	67	1	no	—
931	C₂×C₄⋊C₄	—	67	1	no	—
932	C₂×C₄⋊C₄	—	67	1	no	—
933	C₂×C₄⋊C₄	—	67	1	no	—
934	C₂×C₄⋊C₄	—	67	1	no	—
935	C₂×C₄⋊C₄	—	67	1	no	—
936	C₂×C₄⋊C₄	—	67	1	no	—
937	C₂×C₄⋊C₄	—	67	1	no	—
938	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
946	C₂×C₂²⋊C₄	—	67	1	no	—
947	C₂×C₂²⋊C₄	—	67	1	no	—
948	C₂×C₂²⋊C₄	—	67	1	no	—
949	C₂×C₂²⋊C₄	—	67	1	no	—
950	C₂×C₂²⋊C₄	—	67	1	no	—
951	C₂×C₂²⋊C₄	—	67	1	no	—
952	C₂×C₂²⋊C₄	—	67	1	no	—
953	C₂×C₂²⋊C₄	—	67	1	no	—
954	C₂×C₂²⋊C₄	—	67	1	no	—
955	C₂×C₂²⋊C₄	—	67	1	no	—
956	C₂×C₂²⋊C₄	—	67	1	no	—
957	C₂×C₂²⋊C₄	—	67	1	no	—
958	C₂×C₂²⋊C₄	—	67	1	no	—
959	C₂×C₂²⋊C₄	—	67	1	no	—
960	C₂×C₂²⋊C₄	—	67	1	no	—
961	C₂×C₂²⋊C₄	—	67	1	no	—
962	C₂×C₂²⋊C₄	—	67	1	no	—
963	C₂×C₂²⋊C₄	—	67	1	no	—
964	C₂×C₂²⋊C₄	—	67	1	no	—
965	C₂×C₂²⋊C₄	—	67	1	no	—
966	C₂×C₂²⋊C₄	—	67	1	no	—
967	C₂×C₂²⋊C₄	—	67	1	no	—
968	C₂×C₄²	—	268	2	no	—
969	C₂×C₄²	—	67	1	no	—
970	C₂×C₄²	—	67	1	no	—
971	C₂×C₄²	—	67	1	no	—
972	C₂×C₄²	—	67	1	no	—
973	C₂×C₄²	—	67	1	no	—
974	C₂×C₄²	—	67	1	no	—
975	C₂×C₄²	—	67	1	no	—
976	C₂×C₄²	—	67	1	no	—
977	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
978	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
979	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
980	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
981	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
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	#95	C₂²×D₆₇	1	1	yes	characteristic
1031	#95	C₂²×D₆₇	1	1	yes	characteristic
1032	#95	C₂²×D₆₇	1	1	yes	characteristic
1033	#95	C₂²×D₆₇	1	1	yes	characteristic
1034	#95	C₂²×D₆₇	1	1	yes	characteristic
1035	#95	C₂²×D₆₇	1	1	yes	characteristic
1036	#95	C₂²×D₆₇	1	1	yes	characteristic
1037	#95	C₂²×D₆₇	1	1	yes	characteristic
1038	C₂⁴	—	67	1	no	—
1039	C₂⁴	—	67	1	no	—
1040	C₂×Q₈	—	2	2	no	—
1041	C₂×Q₈	—	2	2	no	—
1042	C₂×Q₈	—	4	1	no	—
1043	C₂×Q₈	—	4	1	no	—
1044	C₂×Q₈	—	4	1	no	—
1045	C₂×Q₈	—	4	1	no	—
1046	C₂×Q₈	—	268	1	no	—
1047	C₂×Q₈	—	268	1	no	—
1048	C₂×Q₈	—	268	1	no	—
1049	C₂×Q₈	—	268	1	no	—
1050	C₂×Q₈	—	268	1	no	—
1051	C₂×Q₈	—	268	1	no	—
1052	C₂×Q₈	—	268	1	no	—
1053	C₂×Q₈	—	268	1	no	—
1054	C₂×Q₈	—	134	2	no	—
1055	C₂×D₄	—	268	1	no	—
1056	C₂×D₄	—	268	1	no	—
1057	C₂×D₄	—	67	4	no	—
1058	C₂²×C₄	—	268	1	no	—
1059	C₂²×C₄	—	268	1	no	—
1060	C₂²×C₄	—	268	1	no	—
1061	C₂²×C₄	—	268	1	no	—
1062	C₂²×C₄	—	268	1	no	—
1063	C₂²×C₄	—	268	1	no	—
1064	C₂²×C₄	—	268	1	no	—
1065	C₂²×C₄	—	268	1	no	—
1066	C₂²×C₄	—	268	1	no	—
1067	C₂²×C₄	—	268	1	no	—
1068	C₂²×C₄	—	268	1	no	—
1069	C₂²×C₄	—	268	1	no	—
1070	C₂²×C₄	—	268	1	no	—
1071	C₂²×C₄	—	67	4	no	—
1072	C₂²×C₄	—	67	4	no	—
1073	C₂²×C₄	—	67	1	no	—
1074	C₂²×C₄	—	67	1	no	—
1075	C₂²×C₄	—	67	1	no	—
1076	C₂²×C₄	—	67	1	no	—
1077	C₂²×C₄	—	67	1	no	—
1078	C₂²×C₄	—	67	1	no	—
1079	C₂²×C₄	—	67	1	no	—
1080	C₂²×C₄	—	67	1	no	—
1081	C₂²×C₄	—	67	1	no	—
1082	C₂²×C₄	—	67	1	no	—
1083	C₂²×C₄	—	67	1	no	—
1084	C₂²×C₄	—	67	1	no	—
1085	C₂²×C₄	—	67	1	no	—
1086	C₂²×C₄	—	67	1	no	—
1087	C₂²×C₄	—	134	2	no	—
1088	C₂²×C₄	—	134	2	no	—
1089	C₂²×C₄	—	134	2	no	—
1090	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1091	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1092	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1093	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1094	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1095	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1096	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1097	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1098	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1099	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1100	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1101	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1102	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1103	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1104	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1105	C₄⋊C₄	—	2	2	no	—
1106	C₄⋊C₄	—	2	2	no	—
1107	C₄⋊C₄	—	2	2	no	—
1108	C₄⋊C₄	—	2	2	no	—
1109	C₄⋊C₄	—	4	1	no	—
1110	C₄⋊C₄	—	4	1	no	—
1111	C₄⋊C₄	—	4	1	no	—
1112	C₄⋊C₄	—	4	1	no	—
1113	C₄⋊C₄	—	268	1	no	—
1114	C₄⋊C₄	—	268	1	no	—
1115	C₄⋊C₄	—	268	1	no	—
1116	C₄⋊C₄	—	268	1	no	—
1117	C₄⋊C₄	—	268	1	no	—
1118	C₄⋊C₄	—	268	1	no	—
1119	C₄⋊C₄	—	268	1	no	—
1120	C₄⋊C₄	—	268	1	no	—
1121	C₄⋊C₄	—	268	1	no	—
1122	C₄⋊C₄	—	268	1	no	—
1123	C₄⋊C₄	—	268	1	no	—
1124	C₄⋊C₄	—	268	1	no	—
1125	C₄⋊C₄	—	268	1	no	—
1126	C₄⋊C₄	—	268	1	no	—
1127	C₄⋊C₄	—	268	1	no	—
1128	C₄⋊C₄	—	268	1	no	—
1129	C₄⋊C₄	—	268	1	no	—
1130	C₄⋊C₄	—	268	1	no	—
1131	C₄⋊C₄	—	268	1	no	—
1132	C₄⋊C₄	—	268	1	no	—
1133	C₄⋊C₄	—	268	1	no	—
1134	C₄⋊C₄	—	268	1	no	—
1135	C₄⋊C₄	—	268	1	no	—
1136	C₄⋊C₄	—	268	1	no	—
1137	C₄⋊C₄	—	268	1	no	—
1138	C₄⋊C₄	—	268	1	no	—
1139	C₄⋊C₄	—	268	1	no	—
1140	C₄⋊C₄	—	268	1	no	—
1141	C₄⋊C₄	—	268	1	no	—
1142	C₄⋊C₄	—	268	1	no	—
1143	C₄⋊C₄	—	268	1	no	—
1144	C₄⋊C₄	—	268	1	no	—
1145	C₄⋊C₄	—	268	1	no	—
1146	C₄⋊C₄	—	268	1	no	—
1147	C₄⋊C₄	—	268	1	no	—
1148	C₄⋊C₄	—	67	4	no	—
1149	C₄⋊C₄	—	134	2	no	—
1150	C₄⋊C₄	—	134	2	no	—
1151	C₄⋊C₄	—	134	2	no	—
1152	C₄⋊C₄	—	134	2	no	—
1153	C₄⋊C₄	—	134	2	no	—
1154	C₄⋊C₄	—	134	2	no	—
1155	C₄⋊C₄	—	134	2	no	—
1156	C₄⋊C₄	—	134	2	no	—
1157	C₂²⋊C₄	—	268	1	no	—
1158	C₂²⋊C₄	—	268	1	no	—
1159	C₂²⋊C₄	—	268	1	no	—
1160	C₂²⋊C₄	—	268	1	no	—
1161	C₂²⋊C₄	—	268	1	no	—
1162	C₂²⋊C₄	—	268	1	no	—
1163	C₂²⋊C₄	—	268	1	no	—
1164	C₂²⋊C₄	—	268	1	no	—
1165	C₂²⋊C₄	—	268	1	no	—
1166	C₂²⋊C₄	—	268	1	no	—
1167	C₂²⋊C₄	—	268	1	no	—
1168	C₂²⋊C₄	—	268	1	no	—
1169	C₂²⋊C₄	—	268	1	no	—
1170	C₂²⋊C₄	—	268	1	no	—
1171	C₂²⋊C₄	—	268	1	no	—
1172	C₂²⋊C₄	—	268	1	no	—
1173	C₂²⋊C₄	—	268	1	no	—
1174	C₂²⋊C₄	—	67	4	no	—
1175	C₂²⋊C₄	—	67	4	no	—
1176	C₂²⋊C₄	—	134	2	no	—
1177	C₂²⋊C₄	—	134	2	no	—
1178	C₂²⋊C₄	—	134	2	no	—
1179	C₄²	—	4	1	no	—
1180	C₄²	—	4	1	no	—
1181	C₄²	—	4	1	no	—
1182	C₄²	—	4	1	no	—
1183	C₄²	—	268	1	no	—
1184	C₄²	—	268	1	no	—
1185	C₄²	—	268	1	no	—
1186	C₄²	—	268	1	no	—
1187	C₄²	—	268	1	no	—
1188	C₄²	—	268	1	no	—
1189	C₄²	—	134	2	no	—
1190	C₄²	—	134	2	no	—
1191	C₄²	Q₈×D₆₇	1	4	yes	—
1192	C₂³	—	67	2	no	—
1193	C₂³	—	67	2	no	—
1194	C₂³	—	134	1	no	—
1195	C₂³	—	134	1	no	—
1196	C₂³	—	134	1	no	—
1197	C₂³	—	134	1	no	—
1198	C₂³	—	134	1	no	—
1199	C₂³	—	134	1	no	—
1200	C₂³	—	134	1	no	—
1201	C₂³	—	134	1	no	—
1202	C₂³	—	134	1	no	—
1203	C₂³	—	134	1	no	—
1204	C₂³	—	134	1	no	—
1205	C₂³	—	134	1	no	—
1206	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1207	Q₈	—	8	2	no	—
1208	Q₈	—	8	2	no	—
1209	Q₈	—	536	2	no	—
1210	Q₈	—	536	2	no	—
1211	Q₈	—	536	2	no	—
1212	D₄	—	268	4	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	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	268	4	no	—
1254	C₂×C₄	—	268	4	no	—
1255	C₂×C₄	—	268	4	no	—
1256	C₂×C₄	—	268	4	no	—
1257	C₂×C₄	—	536	2	no	—
1258	C₂×C₄	—	536	2	no	—
1259	C₂×C₄	—	67	2	no	—
1260	C₂×C₄	—	67	2	no	—
1261	C₂×C₄	—	67	2	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	—	134	1	no	—
1280	C₂×C₄	—	134	1	no	—
1281	C₂×C₄	—	134	1	no	—
1282	C₂×C₄	—	134	1	no	—
1283	C₂×C₄	—	134	1	no	—
1284	C₂×C₄	—	134	1	no	—
1285	C₂×C₄	—	134	1	no	—
1286	C₂×C₄	—	134	1	no	—
1287	C₂×C₄	—	134	1	no	—
1288	C₂×C₄	—	134	1	no	—
1289	C₂×C₄	—	134	1	no	—
1290	C₂×C₄	—	134	1	no	—
1291	C₂×C₄	—	134	1	no	—
1292	C₂×C₄	—	134	1	no	—
1293	C₂×C₄	—	134	1	no	—
1294	C₂×C₄	—	134	1	no	—
1295	C₂×C₄	—	134	1	no	—
1296	C₂×C₄	—	134	1	no	—
1297	C₂×C₄	—	134	1	no	—
1298	C₂×C₄	—	134	1	no	—
1299	C₂×C₄	—	134	1	no	—
1300	C₂×C₄	—	134	1	no	—
1301	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1302	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1303	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1304	C₂×C₄	#14524089	1	2	yes	—
1305	C₂×C₄	#14524090	1	2	yes	—
1306	C₂²	—	268	1	no	—
1307	C₂²	—	268	1	no	—
1308	C₂²	—	268	1	no	—
1309	C₂²	—	268	1	no	—
1310	C₂²	—	268	1	no	—
1311	C₂²	—	268	1	no	—
1312	C₂²	—	268	1	no	—
1313	C₂²	—	268	1	no	—
1314	C₂²	—	134	2	no	—
1315	C₂²	—	134	2	no	—
1316	C₂²	—	134	2	no	—
1317	C₂²	—	134	2	no	—
1318	C₂²	—	134	2	no	—
1319	C₂²	—	134	2	no	—
1320	C₂²	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1321	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1322	C₂²	C₂×#14524089	1	1	yes	characteristic
1323	C₂²	C₂×#14524090	1	1	yes	characteristic
1324	C₂²	#16864232	1	1	yes	characteristic
1325	C₂²	#16864232	1	1	yes	characteristic
1326	C₂²	#16864233	1	1	yes	characteristic
1327	C₄	—	2	2	no	—
1328	C₄	—	2	2	no	—
1329	C₄	—	2	2	no	—
1330	C₄	—	2	2	no	—
1331	C₄	—	2	2	no	—
1332	C₄	—	4	1	no	—
1333	C₄	—	4	1	no	—
1334	C₄	—	4	1	no	—
1335	C₄	—	4	1	no	—
1336	C₄	—	4	1	no	—
1337	C₄	—	4	1	no	—
1338	C₄	—	4	1	no	—
1339	C₄	—	4	1	no	—
1340	C₄	—	4	1	no	—
1341	C₄	—	4	1	no	—
1342	C₄	—	268	1	no	—
1343	C₄	—	268	1	no	—
1344	C₄	—	268	1	no	—
1345	C₄	—	268	1	no	—
1346	C₄	—	268	1	no	—
1347	C₄	—	268	1	no	—
1348	C₄	—	268	1	no	—
1349	C₄	—	268	1	no	—
1350	C₄	—	268	1	no	—
1351	C₄	—	268	1	no	—
1352	C₄	—	268	1	no	—
1353	C₄	—	134	2	no	—
1354	C₄	—	134	2	no	—
1355	C₄	—	134	2	no	—
1356	C₂	—	268	2	no	—
1357	C₂	—	268	2	no	—
1358	C₂	#22573612	1	1	yes	characteristic
1359	C₂	#22574011	1	1	yes	characteristic
1360	C₂	#22574021	1	1	yes	characteristic
1361	C₂	#22574405	1	1	yes	characteristic
1362	C₂	#22574518	1	1	yes	characteristic
1363	C₂	#22574712	1	1	yes	characteristic
1364	C₂	#22574804	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2605	C₂
prime radical	C₂²×D₂₆₈	C₂³
hypercenter	#2605	D₆₇
hypocenter	C₆₇	#36753
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2605

Complements

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

N	H ≅ G/N	type
1. #22568558	C₂	semidirect
2. #22568550	C₂	semidirect
3. #22568182	C₂	semidirect
4. #22568173	C₂	semidirect
5. #22568006	C₂	semidirect
6. #22567991	C₂	semidirect
7. #22567961	C₂	semidirect
9. #22567337	C₂	semidirect
11. #22567197	C₂	semidirect
12. #22567094	C₂	semidirect
13. #22567082	C₂	semidirect
14. #22566985	C₂	semidirect
15. #22566874	C₂	semidirect
18. #22566523	C₂	semidirect
19. #22566409	C₂	semidirect
20. #22566385	C₂	semidirect
21. #22565912	C₂	semidirect
22. #22565872	C₂	semidirect
23. #22565867	C₂	semidirect
24. #22565224	C₂	semidirect
25. #22565218	C₂	semidirect
26. #22563921	C₂	semidirect
27. #22563884	C₂	semidirect
31. C₆₇×#2605	C₂	semidirect
207. C₄×D₂₆₈	Q₈	semidirect
706. #2605	D₆₇	semidirect
714. C₆₇	#36753	semidirect

Maximal subgroups

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

subgroup	index
#22568558	2
#22568550	2
#22568182	2
#22568173	2
#22568006	2
#22567991	2
#22567961	2
#22567417	2
#22567337	2
#22567227	2
#22567197	2
#22567094	2
#22567082	2
#22566985	2
#22566874	2
#22566703	2
#22566700	2
#22566523	2
#22566409	2
#22566385	2
#22565912	2
#22565872	2
#22565867	2
#22565224	2
#22565218	2
#22563921	2
#22563884	2
#22562853	2
#22562840	2
#22562650	2
C₆₇×#2605	2
#36753	67