Subgroups — #31022810

Order 17152.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22566392	C₂	1	1	yes	maximal, characteristic, complemented
2	#22566391	C₂	1	1	yes	maximal, characteristic, complemented
3	#22566370	C₂	1	1	yes	maximal, characteristic
4	#22566367	C₂	1	1	yes	maximal, characteristic
5	#22566304	C₂	1	1	yes	maximal, characteristic, complemented
6	#22566303	C₂	1	1	yes	maximal, characteristic, complemented
7	#22566302	C₂	1	1	yes	maximal, characteristic, complemented
8	#22566295	C₂	1	1	yes	maximal, characteristic, complemented
9	#22566290	C₂	1	1	yes	maximal, characteristic
10	#22566287	C₂	1	1	yes	maximal, characteristic
11	#22566229	C₂	1	1	yes	maximal, characteristic
12	#22566222	C₂	1	1	yes	maximal, characteristic
13	#22566116	C₂	1	1	yes	maximal, characteristic
14	#22566115	C₂	1	1	yes	maximal, characteristic
15	#22566084	C₂	1	1	yes	maximal, characteristic, complemented
16	#22563515	C₂	1	1	yes	maximal, characteristic, complemented
17	#22563515	C₂	1	1	yes	maximal, characteristic, complemented
18	#22563513	C₂	1	1	yes	maximal, characteristic, complemented
19	#22563508	C₂	1	1	yes	maximal, characteristic
20	#22563508	C₂	1	1	yes	maximal, characteristic
21	#22563499	C₂	1	1	yes	maximal, characteristic, complemented
22	#22563486	C₂	1	1	yes	maximal, characteristic
23	#22563480	C₂	1	1	yes	maximal, characteristic
24	#125×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	#22562766	C₂	1	1	yes	maximal, characteristic, complemented
26	#22562759	C₂	1	1	yes	maximal, characteristic
27	#22562757	C₂	1	1	yes	maximal, characteristic
28	#22562701	C₂	1	1	yes	maximal, characteristic
29	#22562682	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×Q₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2634	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14524038	C₂²	1	1	yes	characteristic
33	C₂×#14524037	C₂²	1	1	yes	characteristic
34	C₂×#14524033	C₂²	1	1	yes	characteristic
35	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
36	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
37	C₂×#14524008	C₂²	1	1	yes	characteristic
38	C₂×#14524001	C₂²	1	1	yes	characteristic
39	C₆₇⋊#401	C₂²	1	1	yes	characteristic
40	C₆₇⋊#401	C₂²	1	1	yes	characteristic
41	#16863338	C₂²	1	1	yes	characteristic
42	#16863338	C₂²	1	1	yes	characteristic
43	#16863338	C₂²	1	1	yes	characteristic
44	#16863338	C₂²	1	1	yes	characteristic
45	#16863338	C₂²	1	1	yes	characteristic
46	#16863338	C₂²	1	1	yes	characteristic
47	#16863337	C₂²	1	1	yes	characteristic
48	#16863337	C₂²	1	1	yes	characteristic
49	#16863337	C₂²	1	1	yes	characteristic
50	#16863337	C₂²	1	1	yes	characteristic
51	#16863336	C₂²	1	1	yes	characteristic
52	#16863336	C₂²	1	1	yes	characteristic
53	#16863336	C₂²	1	1	yes	characteristic
54	#16863335	C₂²	1	1	yes	characteristic
55	#16863335	C₂²	1	1	yes	characteristic
56	#16863334	C₂²	1	1	yes	characteristic
57	#16863333	C₂²	1	1	yes	characteristic
58	#16863331	C₂²	1	1	yes	characteristic
59	#16863330	C₂²	1	1	yes	characteristic
60	#16863330	C₂²	1	1	yes	characteristic
61	#16863330	C₂²	1	1	yes	characteristic
62	#16863330	C₂²	1	1	yes	characteristic
63	#16863329	C₂²	1	1	yes	characteristic
64	#16863329	C₂²	1	1	yes	characteristic
65	#16863329	C₂²	1	1	yes	characteristic
66	#16863329	C₂²	1	1	yes	characteristic
67	#16863329	C₂²	1	1	yes	characteristic
68	#16863329	C₂²	1	1	yes	characteristic
69	#16863328	C₂²	1	1	yes	characteristic
70	#16863328	C₂²	1	1	yes	characteristic
71	#16863328	C₂²	1	1	yes	characteristic
72	#16863328	C₂²	1	1	yes	characteristic
73	#16863327	C₂²	1	1	yes	characteristic
74	#16863327	C₂²	1	1	yes	characteristic
75	#16863326	C₂²	1	1	yes	characteristic
76	#16863326	C₂²	1	1	yes	characteristic
77	#16863325	C₂²	1	1	yes	characteristic
78	#16863325	C₂²	1	1	yes	characteristic
79	#16863323	C₂²	1	1	yes	characteristic
80	#16863323	C₂²	1	1	yes	characteristic
81	#16863322	C₂²	1	1	yes	characteristic
82	#16863322	C₂²	1	1	yes	characteristic
83	#16863318	C₂²	1	1	yes	characteristic
84	#16863318	C₂²	1	1	yes	characteristic
85	#16863318	C₂²	1	1	yes	characteristic
86	#16863318	C₂²	1	1	yes	characteristic
87	#16863318	C₂²	1	1	yes	characteristic
88	#16863318	C₂²	1	1	yes	characteristic
89	#16863317	C₂²	1	1	yes	characteristic
90	#16863317	C₂²	1	1	yes	characteristic
91	#16863317	C₂²	1	1	yes	characteristic
92	#16863315	C₂²	1	1	yes	characteristic
93	#16863309	C₂²	1	1	yes	characteristic
94	#16863307	C₂²	1	1	yes	characteristic
95	#16863300	C₂²	1	1	yes	characteristic
96	#16863300	C₂²	1	1	yes	characteristic
97	#16863295	C₂²	1	1	yes	characteristic
98	#16863295	C₂²	1	1	yes	characteristic
99	#16863293	C₂²	1	1	yes	characteristic
100	#16863293	C₂²	1	1	yes	characteristic
101	#16863291	C₂²	1	1	yes	characteristic
102	#16863291	C₂²	1	1	yes	characteristic
103	#16863288	C₂²	1	1	yes	characteristic
104	#16863288	C₂²	1	1	yes	characteristic
105	#16863287	C₂²	1	1	yes	characteristic
106	#16863287	C₂²	1	1	yes	characteristic
107	#16863286	C₂²	1	1	yes	characteristic
108	#16863286	C₂²	1	1	yes	characteristic
109	#16863285	C₂²	1	1	yes	characteristic
110	#16863285	C₂²	1	1	yes	characteristic
111	#16863285	C₂²	1	1	yes	characteristic
112	#16863285	C₂²	1	1	yes	characteristic
113	#16863283	C₂²	1	1	yes	characteristic
114	#16863283	C₂²	1	1	yes	characteristic
115	#16863282	C₂²	1	1	yes	characteristic
116	#16863282	C₂²	1	1	yes	characteristic
117	#16863282	C₂²	1	1	yes	characteristic
118	#16863282	C₂²	1	1	yes	characteristic
119	#16863282	C₂²	1	1	yes	characteristic
120	#16863282	C₂²	1	1	yes	characteristic
121	#16863281	C₂²	1	1	yes	characteristic
122	#16863281	C₂²	1	1	yes	characteristic
123	#16863280	C₂²	1	1	yes	characteristic
124	#16863280	C₂²	1	1	yes	characteristic
125	#16863279	C₂²	1	1	yes	characteristic
126	#16863279	C₂²	1	1	yes	characteristic
127	#16863278	C₂²	1	1	yes	characteristic
128	#16863278	C₂²	1	1	yes	characteristic
129	#16863278	C₂²	1	1	yes	characteristic
130	#16863278	C₂²	1	1	yes	characteristic
131	#16863263	C₂²	1	1	yes	characteristic
132	#16863262	C₂²	1	1	yes	characteristic
133	#16863260	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	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
148	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
151	#16863247	C₂²	1	1	yes	characteristic
152	#16863247	C₂²	1	1	yes	characteristic
153	#16863247	C₂²	1	1	yes	characteristic
154	#16863247	C₂²	1	1	yes	characteristic
155	#16863247	C₂²	1	1	yes	characteristic
156	#16863247	C₂²	1	1	yes	characteristic
157	#16863247	C₂²	1	1	yes	characteristic
158	#16863247	C₂²	1	1	yes	characteristic
159	#16863247	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	#16863243	C₂²	1	1	yes	characteristic
164	#16863243	C₂²	1	1	yes	characteristic
165	#16863243	C₂²	1	1	yes	characteristic
166	#16863241	C₂²	1	1	yes	characteristic
167	#16863241	C₂²	1	1	yes	characteristic
168	#16863241	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×#125×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	#400×C₆₇	C₂²	1	1	yes	characteristic
176	#400×C₆₇	C₂²	1	1	yes	characteristic
177	#400×C₆₇	C₂²	1	1	yes	characteristic
178	#398×C₆₇	C₂²	1	1	yes	characteristic
179	#398×C₆₇	C₂²	1	1	yes	characteristic
180	#395×C₆₇	C₂²	1	1	yes	characteristic
181	#395×C₆₇	C₂²	1	1	yes	characteristic
182	#387×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	#383×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
188	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
189	#14524038	—	2	4	no	—
190	#14524037	—	2	4	no	—
191	#14524033	—	2	4	no	—
192	Q₈×Dic₆₇	—	2	4	no	—
193	Q₈×Dic₆₇	—	2	4	no	—
194	#14524008	—	2	4	no	—
195	#14524001	—	2	4	no	—
196	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
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×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×Dic₆₇⋊C₄	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×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×(C₂×D₆₇)⋊C₄	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×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₄×Dic₆₇	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	C₆₇⋊#95	C₂³	1	1	yes	characteristic
269	C₆₇⋊#95	C₂³	1	1	yes	characteristic
270	C₆₇⋊#95	C₂³	1	1	yes	characteristic
271	C₆₇⋊#95	C₂³	1	1	yes	characteristic
272	C₆₇⋊#95	C₂³	1	1	yes	characteristic
273	C₆₇⋊#95	C₂³	1	1	yes	characteristic
274	C₆₇⋊#95	C₂³	1	1	yes	characteristic
275	C₆₇⋊#95	C₂³	1	1	yes	characteristic
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	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
315	#125×C₆₇	—	2	4	no	—
316	C₄×Q₈×C₆₇	—	2	4	no	—
317	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₂×C₄⋊C₄×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	#95×C₆₇	C₂³	1	1	yes	characteristic
334	#95×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	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
352	C₂×Dic₁₃₄	—	2	2	no	—
353	C₂×Dic₁₃₄	—	4	1	no	—
354	C₂×Dic₁₃₄	—	4	1	no	—
355	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
356	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
358	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
361	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
362	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
363	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
364	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
365	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
366	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
367	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
369	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×D₆₇	—	2	2	no	—
371	C₂×C₄×D₆₇	—	2	2	no	—
372	C₂×C₄×D₆₇	—	2	2	no	—
373	C₄⋊Dic₆₇	—	2	2	no	—
374	C₄⋊Dic₆₇	—	2	2	no	—
375	C₄⋊Dic₆₇	—	2	2	no	—
376	C₄⋊Dic₆₇	—	2	2	no	—
377	C₄⋊Dic₆₇	—	2	2	no	—
378	C₄⋊Dic₆₇	—	2	2	no	—
379	C₄⋊Dic₆₇	—	2	2	no	—
380	C₄⋊Dic₆₇	—	2	2	no	—
381	C₄⋊Dic₆₇	—	2	2	no	—
382	C₄⋊Dic₆₇	—	4	1	no	—
383	C₄⋊Dic₆₇	—	4	1	no	—
384	C₄⋊Dic₆₇	—	4	1	no	—
385	C₄⋊Dic₆₇	—	4	1	no	—
386	C₄⋊Dic₆₇	—	4	1	no	—
387	C₄⋊Dic₆₇	—	4	1	no	—
388	Dic₆₇⋊C₄	—	2	2	no	—
389	Dic₆₇⋊C₄	—	2	2	no	—
390	Dic₆₇⋊C₄	—	2	2	no	—
391	Dic₆₇⋊C₄	—	2	2	no	—
392	Dic₆₇⋊C₄	—	2	2	no	—
393	Dic₆₇⋊C₄	—	2	2	no	—
394	Dic₆₇⋊C₄	—	2	2	no	—
395	Dic₆₇⋊C₄	—	2	2	no	—
396	Dic₆₇⋊C₄	—	2	2	no	—
397	Dic₆₇⋊C₄	—	2	2	no	—
398	Dic₆₇⋊C₄	—	4	1	no	—
399	Dic₆₇⋊C₄	—	4	1	no	—
400	Dic₆₇⋊C₄	—	4	1	no	—
401	Dic₆₇⋊C₄	—	4	1	no	—
402	Dic₆₇⋊C₄	—	4	1	no	—
403	Dic₆₇⋊C₄	—	4	1	no	—
404	Dic₆₇⋊C₄	—	4	1	no	—
405	Dic₆₇⋊C₄	—	4	1	no	—
406	Dic₆₇⋊C₄	—	4	1	no	—
407	Dic₆₇⋊C₄	—	4	1	no	—
408	(C₂×D₆₇)⋊C₄	—	2	2	no	—
409	(C₂×D₆₇)⋊C₄	—	2	2	no	—
410	(C₂×D₆₇)⋊C₄	—	2	2	no	—
411	(C₂×D₆₇)⋊C₄	—	2	2	no	—
412	(C₂×D₆₇)⋊C₄	—	2	2	no	—
413	(C₂×D₆₇)⋊C₄	—	2	2	no	—
414	(C₂×D₆₇)⋊C₄	—	2	2	no	—
415	(C₂×D₆₇)⋊C₄	—	2	2	no	—
416	(C₂×D₆₇)⋊C₄	—	4	1	no	—
417	(C₂×D₆₇)⋊C₄	—	4	1	no	—
418	(C₂×D₆₇)⋊C₄	—	4	1	no	—
419	(C₂×D₆₇)⋊C₄	—	4	1	no	—
420	(C₂×D₆₇)⋊C₄	—	4	1	no	—
421	(C₂×D₆₇)⋊C₄	—	4	1	no	—
422	C₄×Dic₆₇	—	2	2	no	—
423	C₄×Dic₆₇	—	2	2	no	—
424	C₄×Dic₆₇	—	2	2	no	—
425	C₄×Dic₆₇	—	2	2	no	—
426	C₄×Dic₆₇	—	2	2	no	—
427	C₄×Dic₆₇	—	2	2	no	—
428	C₄×Dic₆₇	—	2	2	no	—
429	C₄×Dic₆₇	—	2	2	no	—
430	C₄×Dic₆₇	—	2	2	no	—
431	C₄×Dic₆₇	—	2	2	no	—
432	C₄×Dic₆₇	—	2	2	no	—
433	C₄×Dic₆₇	—	2	2	no	—
434	C₄×Dic₆₇	—	2	2	no	—
435	C₄×Dic₆₇	—	2	2	no	—
436	C₄×Dic₆₇	—	2	2	no	—
437	C₄×Dic₆₇	—	4	1	no	—
438	C₄×Dic₆₇	—	4	1	no	—
439	C₄×Dic₆₇	—	4	1	no	—
440	C₄×Dic₆₇	—	4	1	no	—
441	C₄×Dic₆₇	—	4	1	no	—
442	C₄×Dic₆₇	—	4	1	no	—
443	C₄×Dic₆₇	#41	1	4	yes	—
444	C₄×Dic₆₇	#41	1	4	yes	—
445	C₂×Q₈×C₆₇	—	2	2	no	—
446	C₂×Q₈×C₆₇	—	2	2	no	—
447	C₂×Q₈×C₆₇	—	2	2	no	—
448	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₆₇	—	2	2	no	—
464	C₄⋊C₄×C₆₇	—	2	2	no	—
465	C₄⋊C₄×C₆₇	—	2	2	no	—
466	C₄⋊C₄×C₆₇	—	2	2	no	—
467	C₄⋊C₄×C₆₇	—	2	2	no	—
468	C₄⋊C₄×C₆₇	—	2	2	no	—
469	C₄⋊C₄×C₆₇	—	2	2	no	—
470	C₄⋊C₄×C₆₇	—	2	2	no	—
471	C₄⋊C₄×C₆₇	—	2	2	no	—
472	C₄⋊C₄×C₆₇	—	2	2	no	—
473	C₄⋊C₄×C₆₇	—	2	2	no	—
474	C₄⋊C₄×C₆₇	—	2	2	no	—
475	C₄⋊C₄×C₆₇	—	2	2	no	—
476	C₄²×C₆₇	—	2	2	no	—
477	C₄²×C₆₇	—	2	2	no	—
478	C₄²×C₆₇	#41	1	4	yes	—
479	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
480	C₂²×D₆₇	—	2	1	no	—
481	C₂²×D₆₇	—	2	1	no	—
482	C₂²×D₆₇	—	2	1	no	—
483	C₂²×D₆₇	—	2	1	no	—
484	C₂²×D₆₇	—	2	1	no	—
485	C₂²×D₆₇	—	2	1	no	—
486	C₂²×D₆₇	—	2	1	no	—
487	Q₈×C₆₇	—	2	8	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	1	no	—
516	C₂×C₄×C₆₇	—	2	1	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	2	1	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	C₂×#41	1	2	yes	—
529	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
530	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
531	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
532	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
533	C₂×Dic₆₇	—	2	1	no	—
534	C₂×Dic₆₇	—	2	1	no	—
535	C₂×Dic₆₇	—	2	1	no	—
536	C₂×Dic₆₇	—	2	1	no	—
537	C₂×Dic₆₇	—	2	1	no	—
538	C₂×Dic₆₇	—	2	1	no	—
539	C₂×Dic₆₇	—	2	1	no	—
540	C₂×Dic₆₇	—	2	1	no	—
541	C₂×Dic₆₇	—	2	1	no	—
542	C₂×Dic₆₇	—	2	1	no	—
543	C₂×Dic₆₇	—	2	1	no	—
544	C₂×Dic₆₇	—	2	1	no	—
545	C₂×Dic₆₇	—	2	1	no	—
546	C₂×Dic₆₇	—	2	1	no	—
547	C₂×Dic₆₇	—	2	1	no	—
548	C₂×Dic₆₇	—	2	1	no	—
549	C₂×Dic₆₇	—	2	1	no	—
550	C₂×Dic₆₇	—	2	1	no	—
551	C₂×Dic₆₇	—	2	1	no	—
552	C₂×Dic₆₇	—	2	1	no	—
553	C₂×Dic₆₇	—	2	1	no	—
554	C₂×Dic₆₇	—	2	1	no	—
555	C₂×Dic₆₇	—	2	1	no	—
556	C₂×Dic₆₇	—	2	1	no	—
557	C₂×Dic₆₇	—	2	1	no	—
558	C₂×Dic₆₇	—	2	1	no	—
559	C₂×Dic₆₇	—	2	1	no	—
560	C₂×Dic₆₇	—	2	1	no	—
561	C₂×Dic₆₇	—	2	1	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	C₂×#41	1	2	yes	—
573	C₂×Dic₆₇	C₂×#41	1	2	yes	—
574	C₂×Dic₆₇	C₂×#41	1	2	yes	—
575	C₂×Dic₆₇	C₂×#41	1	2	yes	—
576	C₂×Dic₆₇	2₋¹⁺⁴	1	2	yes	—
577	C₂×Dic₆₇	2₋¹⁺⁴	1	2	yes	—
578	C₄×D₆₇	—	4	4	no	—
579	Dic₁₃₄	—	4	4	no	—
580	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
581	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
582	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
583	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
584	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
585	C₂²×C₆₇	#585	1	1	yes	characteristic
586	C₂²×C₆₇	#585	1	1	yes	characteristic
587	C₂×D₆₇	—	4	1	no	—
588	C₂×D₆₇	—	4	1	no	—
589	C₂×D₆₇	—	4	1	no	—
590	C₂×D₆₇	—	4	1	no	—
591	C₂×D₆₇	—	4	1	no	—
592	C₂×D₆₇	—	4	1	no	—
593	C₂×D₆₇	—	4	1	no	—
594	C₄×C₆₇	—	2	2	no	—
595	C₄×C₆₇	—	2	2	no	—
596	C₄×C₆₇	—	2	2	no	—
597	C₄×C₆₇	—	2	2	no	—
598	C₄×C₆₇	—	2	2	no	—
599	C₄×C₆₇	—	4	1	no	—
600	C₄×C₆₇	—	4	1	no	—
601	C₄×C₆₇	—	4	1	no	—
602	C₄×C₆₇	—	4	1	no	—
603	C₄×C₆₇	—	4	1	no	—
604	C₄×C₆₇	—	4	1	no	—
605	C₄×C₆₇	—	4	1	no	—
606	C₄×C₆₇	—	4	1	no	—
607	C₄×C₆₇	—	4	1	no	—
608	C₄×C₆₇	—	4	1	no	—
609	Dic₆₇	—	2	2	no	—
610	Dic₆₇	—	2	2	no	—
611	Dic₆₇	—	2	2	no	—
612	Dic₆₇	—	4	1	no	—
613	Dic₆₇	—	4	1	no	—
614	Dic₆₇	—	4	1	no	—
615	Dic₆₇	—	4	1	no	—
616	Dic₆₇	—	4	1	no	—
617	Dic₆₇	—	4	1	no	—
618	Dic₆₇	—	4	1	no	—
619	Dic₆₇	—	4	1	no	—
620	Dic₆₇	—	4	1	no	—
621	Dic₆₇	—	4	1	no	—
622	Dic₆₇	—	4	1	no	—
623	Dic₆₇	#541	1	4	yes	—
624	#34604	—	67	1	no	maximal, Sylow
625	C₂×C₆₇	#3444	1	1	yes	characteristic
626	C₂×C₆₇	C₂×#541	1	1	yes	characteristic
627	C₂×C₆₇	#3455	1	1	yes	characteristic
628	C₂×C₆₇	#3461	1	1	yes	characteristic
629	C₂×C₆₇	#3461	1	1	yes	characteristic
630	C₂×C₆₇	#3461	1	1	yes	characteristic
631	C₂×C₆₇	#3461	1	1	yes	characteristic
632	D₆₇	—	8	1	no	—
633	#2666	—	67	1	no	—
634	#2666	—	67	1	no	—
635	#2664	—	67	1	no	—
636	#2664	—	67	1	no	—
637	#2655	—	67	1	no	—
638	#2655	—	67	1	no	—
639	#2655	—	67	1	no	—
640	#2655	—	67	1	no	—
641	#2654	—	67	1	no	—
642	#2654	—	67	1	no	—
643	#2650	—	67	1	no	—
644	#2650	—	67	1	no	—
645	#2637	—	67	1	no	—
646	#2637	—	67	1	no	—
647	#2634	—	67	1	no	—
648	#2634	D₆₇	1	1	yes	characteristic, complemented
649	#2402	—	67	1	no	—
650	#2402	—	67	1	no	—
651	#2402	—	67	1	no	—
652	#2401	—	67	1	no	—
653	#2401	—	67	1	no	—
654	#2399	—	67	1	no	—
655	#2396	—	67	1	no	—
656	#2396	—	67	1	no	—
657	C₄×#125	—	67	1	no	—
658	C₄×#125	—	67	1	no	—
659	C₄×#126	—	67	1	no	—
660	C₄×#126	—	67	1	no	—
661	#2298	—	67	1	no	—
662	#2295	—	67	1	no	—
663	C₄²×Q₈	—	67	1	no	—
664	C₆₇	#34604	1	1	yes	characteristic, complemented, Sylow
665	C₂×#126	—	67	1	no	—
666	C₂×#126	—	67	1	no	—
667	C₂×#125	—	67	1	no	—
668	C₂×#125	C₂×D₆₇	1	1	yes	characteristic
669	C₂×C₄×Q₈	—	67	1	no	—
670	C₂×C₄×Q₈	—	67	1	no	—
671	C₂×C₄×Q₈	—	67	1	no	—
672	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
673	C₂×#117	—	67	1	no	—
674	#401	—	67	1	no	—
675	#401	—	67	1	no	—
676	#400	—	67	1	no	—
677	#400	—	67	1	no	—
678	#400	—	67	1	no	—
679	#400	—	67	1	no	—
680	#400	—	67	1	no	—
681	#400	—	67	1	no	—
682	#400	—	67	1	no	—
683	#400	—	67	1	no	—
684	#400	—	67	1	no	—
685	#400	—	67	1	no	—
686	#400	—	67	1	no	—
687	#400	—	67	1	no	—
688	#400	—	67	1	no	—
689	#400	—	67	1	no	—
690	#400	—	67	1	no	—
691	#400	—	67	1	no	—
692	#400	C₂×D₆₇	1	1	yes	characteristic
693	#400	C₂×D₆₇	1	1	yes	characteristic
694	#400	C₂×D₆₇	1	1	yes	characteristic
695	#400	C₂×D₆₇	1	1	yes	characteristic
696	#399	—	67	1	no	—
697	#399	—	67	1	no	—
698	#398	—	67	1	no	—
699	#398	—	67	1	no	—
700	#398	—	67	1	no	—
701	#398	—	67	1	no	—
702	#398	—	67	1	no	—
703	#398	—	67	1	no	—
704	#398	—	67	1	no	—
705	#398	—	67	1	no	—
706	#398	—	67	1	no	—
707	#398	—	67	1	no	—
708	#398	—	67	1	no	—
709	#398	—	67	1	no	—
710	#398	—	67	1	no	—
711	#398	—	67	1	no	—
712	#398	—	67	1	no	—
713	#398	—	67	1	no	—
714	#398	—	67	1	no	—
715	#398	—	67	1	no	—
716	#398	C₂×D₆₇	1	1	yes	characteristic
717	#398	C₂×D₆₇	1	1	yes	characteristic
718	#397	—	67	1	no	—
719	#397	—	67	1	no	—
720	#397	—	67	1	no	—
721	#397	—	67	1	no	—
722	#397	—	67	1	no	—
723	#397	—	67	1	no	—
724	#396	—	67	1	no	—
725	#396	—	67	1	no	—
726	#396	—	67	1	no	—
727	#396	—	67	1	no	—
728	#396	—	67	1	no	—
729	#396	—	67	1	no	—
730	#395	—	67	1	no	—
731	#395	—	67	1	no	—
732	#395	—	67	1	no	—
733	#395	—	67	1	no	—
734	#395	C₂×D₆₇	1	1	yes	characteristic
735	#395	C₂×D₆₇	1	1	yes	characteristic
736	#393	—	67	1	no	—
737	#393	—	67	1	no	—
738	#391	—	67	1	no	—
739	#391	—	67	1	no	—
740	#389	—	67	1	no	—
741	#389	—	67	1	no	—
742	#389	—	67	1	no	—
743	#389	—	67	1	no	—
744	#389	—	67	1	no	—
745	#389	—	67	1	no	—
746	#388	—	67	1	no	—
747	#388	—	67	1	no	—
748	#388	—	67	1	no	—
749	#388	—	67	1	no	—
750	#388	—	67	1	no	—
751	#388	—	67	1	no	—
752	#388	—	67	1	no	—
753	#388	—	67	1	no	—
754	#388	—	67	1	no	—
755	#388	—	67	1	no	—
756	#387	—	67	1	no	—
757	#387	—	67	1	no	—
758	#387	—	67	1	no	—
759	#387	—	67	1	no	—
760	#387	—	67	1	no	—
761	#387	—	67	1	no	—
762	#387	—	67	1	no	—
763	#387	—	67	1	no	—
764	#387	—	67	1	no	—
765	#387	—	67	1	no	—
766	#387	—	67	1	no	—
767	#387	—	67	1	no	—
768	#387	—	67	1	no	—
769	#387	—	67	1	no	—
770	#387	—	67	1	no	—
771	#387	—	67	1	no	—
772	#387	—	67	1	no	—
773	#387	—	67	1	no	—
774	#387	C₂×D₆₇	1	1	yes	characteristic
775	#387	C₂×D₆₇	1	1	yes	characteristic
776	#387	C₂×D₆₇	1	1	yes	characteristic
777	#387	C₂×D₆₇	1	1	yes	characteristic
778	#383	—	67	1	no	—
779	#383	C₂×D₆₇	1	1	yes	characteristic
780	#382	—	67	1	no	—
781	#382	—	67	1	no	—
782	C₄×C₄⋊C₄	—	67	1	no	—
783	C₄×C₄⋊C₄	—	67	1	no	—
784	C₄×C₄⋊C₄	—	67	1	no	—
785	C₄×C₄⋊C₄	—	67	1	no	—
786	C₄×C₄⋊C₄	—	67	1	no	—
787	C₄×C₄⋊C₄	—	67	1	no	—
788	C₄×C₄⋊C₄	—	67	1	no	—
789	C₄×C₄⋊C₄	—	67	1	no	—
790	C₄×C₄⋊C₄	—	67	1	no	—
791	C₄×C₄⋊C₄	—	67	1	no	—
792	C₄×C₄⋊C₄	—	67	1	no	—
793	C₄×C₄⋊C₄	—	67	1	no	—
794	C₄×C₄⋊C₄	—	67	1	no	—
795	C₄×C₄⋊C₄	—	67	1	no	—
796	C₄×C₄⋊C₄	—	67	1	no	—
797	C₄×C₄⋊C₄	—	67	1	no	—
798	C₄×C₄⋊C₄	—	67	1	no	—
799	C₄×C₄⋊C₄	—	67	1	no	—
800	C₄×C₄⋊C₄	—	67	1	no	—
801	C₄×C₄⋊C₄	—	67	1	no	—
802	C₄×C₄⋊C₄	—	67	1	no	—
803	C₄×C₄⋊C₄	—	67	1	no	—
804	C₄×C₄⋊C₄	—	67	1	no	—
805	C₄×C₄⋊C₄	—	67	1	no	—
806	C₄×C₄⋊C₄	—	67	1	no	—
807	C₄×C₄⋊C₄	—	67	1	no	—
808	C₄×C₂²⋊C₄	—	67	1	no	—
809	C₄×C₂²⋊C₄	—	67	1	no	—
810	C₄×C₂²⋊C₄	—	67	1	no	—
811	C₄×C₂²⋊C₄	—	67	1	no	—
812	C₄×C₂²⋊C₄	—	67	1	no	—
813	C₄×C₂²⋊C₄	—	67	1	no	—
814	#376	—	67	1	no	—
815	#376	—	67	1	no	—
816	#376	—	67	1	no	—
817	C₄³	—	67	1	no	—
818	C₄³	—	67	1	no	—
819	C₄³	—	67	1	no	—
820	C₂²×Q₈	—	67	1	no	—
821	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
822	C₂³×C₄	—	67	1	no	—
823	#126	—	134	4	no	—
824	#126	—	134	4	no	—
825	#125	—	2	4	no	—
826	#125	—	134	4	no	—
827	C₄×Q₈	—	2	4	no	—
828	C₄×Q₈	—	134	4	no	—
829	C₄×Q₈	—	134	4	no	—
830	C₄×Q₈	—	134	4	no	—
831	#117	—	134	4	no	—
832	C₂×C₄⋊C₄	—	67	1	no	—
833	C₂×C₄⋊C₄	—	67	1	no	—
834	C₂×C₄⋊C₄	—	67	1	no	—
835	C₂×C₄⋊C₄	—	67	1	no	—
836	C₂×C₄⋊C₄	—	67	1	no	—
837	C₂×C₄⋊C₄	—	67	1	no	—
838	C₂×C₄⋊C₄	—	67	1	no	—
839	C₂×C₄⋊C₄	—	67	1	no	—
840	C₂×C₄⋊C₄	—	67	1	no	—
841	C₂×C₄⋊C₄	—	67	1	no	—
842	C₂×C₄⋊C₄	—	67	1	no	—
843	C₂×C₄⋊C₄	—	67	1	no	—
844	C₂×C₄⋊C₄	—	67	1	no	—
845	C₂×C₄⋊C₄	—	67	1	no	—
846	C₂×C₄⋊C₄	—	67	1	no	—
847	C₂×C₄⋊C₄	—	67	1	no	—
848	C₂×C₄⋊C₄	—	67	1	no	—
849	C₂×C₄⋊C₄	—	67	1	no	—
850	C₂×C₄⋊C₄	—	67	1	no	—
851	C₂×C₄⋊C₄	—	67	1	no	—
852	C₂×C₄⋊C₄	—	67	1	no	—
853	C₂×C₄⋊C₄	—	67	1	no	—
854	C₂×C₄⋊C₄	—	67	1	no	—
855	C₂×C₄⋊C₄	—	67	1	no	—
856	C₂×C₄⋊C₄	—	67	1	no	—
857	C₂×C₄⋊C₄	—	67	1	no	—
858	C₂×C₄⋊C₄	—	67	1	no	—
859	C₂×C₄⋊C₄	—	67	1	no	—
860	C₂×C₄⋊C₄	—	67	1	no	—
861	C₂×C₄⋊C₄	—	67	1	no	—
862	C₂×C₄⋊C₄	—	67	1	no	—
863	C₂×C₄⋊C₄	—	67	1	no	—
864	C₂×C₄⋊C₄	—	67	1	no	—
865	C₂×C₄⋊C₄	—	67	1	no	—
866	C₂×C₄⋊C₄	—	67	1	no	—
867	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
880	C₂×C₂²⋊C₄	—	67	1	no	—
881	C₂×C₂²⋊C₄	—	67	1	no	—
882	C₂×C₂²⋊C₄	—	67	1	no	—
883	C₂×C₂²⋊C₄	—	67	1	no	—
884	C₂×C₂²⋊C₄	—	67	1	no	—
885	C₂×C₂²⋊C₄	—	67	1	no	—
886	C₂×C₂²⋊C₄	—	67	1	no	—
887	C₂×C₂²⋊C₄	—	67	1	no	—
888	C₂×C₂²⋊C₄	—	67	1	no	—
889	C₂×C₂²⋊C₄	—	67	1	no	—
890	C₂×C₂²⋊C₄	—	67	1	no	—
891	C₂×C₂²⋊C₄	—	67	1	no	—
892	C₂×C₂²⋊C₄	—	67	1	no	—
893	C₂×C₂²⋊C₄	—	67	1	no	—
894	C₂×C₄²	—	67	1	no	—
895	C₂×C₄²	—	67	1	no	—
896	C₂×C₄²	—	67	1	no	—
897	C₂×C₄²	—	67	1	no	—
898	C₂×C₄²	—	67	1	no	—
899	C₂×C₄²	—	67	1	no	—
900	C₂×C₄²	—	67	1	no	—
901	C₂×C₄²	—	67	1	no	—
902	C₂×C₄²	—	67	1	no	—
903	C₂×C₄²	—	67	1	no	—
904	C₂×C₄²	—	67	1	no	—
905	C₂×C₄²	—	67	1	no	—
906	C₂×C₄²	—	67	1	no	—
907	C₂×C₄²	—	67	1	no	—
908	C₂×C₄²	—	67	1	no	—
909	C₂×C₄²	—	67	1	no	—
910	C₂×C₄²	—	67	1	no	—
911	C₂×C₄²	—	67	1	no	—
912	C₂×C₄²	—	67	1	no	—
913	C₂×C₄²	—	67	1	no	—
914	C₂×C₄²	—	67	1	no	—
915	C₂×C₄²	—	67	1	no	—
916	C₂×C₄²	—	67	1	no	—
917	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
918	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
919	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
920	#95	—	67	1	no	—
921	#95	—	67	1	no	—
922	#95	—	67	1	no	—
923	#95	—	67	1	no	—
924	#95	—	67	1	no	—
925	#95	—	67	1	no	—
926	#95	—	67	1	no	—
927	#95	—	67	1	no	—
928	#95	—	67	1	no	—
929	#95	—	67	1	no	—
930	#95	—	67	1	no	—
931	#95	—	67	1	no	—
932	#95	—	67	1	no	—
933	#95	—	67	1	no	—
934	#95	—	67	1	no	—
935	#95	—	67	1	no	—
936	#95	—	67	1	no	—
937	#95	—	67	1	no	—
938	#95	—	67	1	no	—
939	#95	—	67	1	no	—
940	#95	—	67	1	no	—
941	#95	—	67	1	no	—
942	#95	—	67	1	no	—
943	#95	—	67	1	no	—
944	#95	—	67	1	no	—
945	#95	—	67	1	no	—
946	#95	—	67	1	no	—
947	#95	—	67	1	no	—
948	#95	—	67	1	no	—
949	#95	—	67	1	no	—
950	#95	—	67	1	no	—
951	#95	—	67	1	no	—
952	#95	—	67	1	no	—
953	#95	—	67	1	no	—
954	#95	—	67	1	no	—
955	#95	—	67	1	no	—
956	#95	—	67	1	no	—
957	#95	—	67	1	no	—
958	#95	—	67	1	no	—
959	#95	—	67	1	no	—
960	#95	—	67	1	no	—
961	#95	—	67	1	no	—
962	#95	—	67	1	no	—
963	#95	—	67	1	no	—
964	#95	—	67	1	no	—
965	#95	—	67	1	no	—
966	#95	C₂²×D₆₇	1	1	yes	characteristic
967	#95	C₂²×D₆₇	1	1	yes	characteristic
968	#95	C₂²×D₆₇	1	1	yes	characteristic
969	#95	C₂²×D₆₇	1	1	yes	characteristic
970	#95	C₂²×D₆₇	1	1	yes	characteristic
971	#95	C₂²×D₆₇	1	1	yes	characteristic
972	#95	C₂²×D₆₇	1	1	yes	characteristic
973	#95	C₂²×D₆₇	1	1	yes	characteristic
974	#95	C₂²×D₆₇	1	1	yes	characteristic
975	#95	C₂²×D₆₇	1	1	yes	characteristic
976	#95	C₂²×D₆₇	1	1	yes	characteristic
977	#95	C₂²×D₆₇	1	1	yes	characteristic
978	#95	C₂²×D₆₇	1	1	yes	characteristic
979	#95	C₂²×D₆₇	1	1	yes	characteristic
980	#95	C₂²×D₆₇	1	1	yes	characteristic
981	#95	C₂²×D₆₇	1	1	yes	characteristic
982	#95	C₂²×D₆₇	1	1	yes	characteristic
983	#95	C₂²×D₆₇	1	1	yes	characteristic
984	C₂⁴	—	67	1	no	—
985	C₂×Q₈	—	2	2	no	—
986	C₂×Q₈	—	2	2	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	268	1	no	—
989	C₂×Q₈	—	268	1	no	—
990	C₂×Q₈	—	134	2	no	—
991	C₂²×C₄	—	67	1	no	—
992	C₂²×C₄	—	67	1	no	—
993	C₂²×C₄	—	67	1	no	—
994	C₂²×C₄	—	67	1	no	—
995	C₂²×C₄	—	67	1	no	—
996	C₂²×C₄	—	67	1	no	—
997	C₂²×C₄	—	67	1	no	—
998	C₂²×C₄	—	67	1	no	—
999	C₂²×C₄	—	67	1	no	—
1000	C₂²×C₄	—	67	1	no	—
1001	C₂²×C₄	—	67	1	no	—
1002	C₂²×C₄	—	67	1	no	—
1003	C₂²×C₄	—	67	1	no	—
1004	C₂²×C₄	—	67	1	no	—
1005	C₂²×C₄	—	67	1	no	—
1006	C₂²×C₄	—	134	2	no	—
1007	C₂²×C₄	—	134	2	no	—
1008	C₂²×C₄	—	134	2	no	—
1009	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1010	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1011	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1012	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1013	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1014	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1015	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1016	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1017	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1023	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	268	1	no	—
1038	C₄⋊C₄	—	268	1	no	—
1039	C₄⋊C₄	—	268	1	no	—
1040	C₄⋊C₄	—	268	1	no	—
1041	C₄⋊C₄	—	268	1	no	—
1042	C₄⋊C₄	—	268	1	no	—
1043	C₄⋊C₄	—	268	1	no	—
1044	C₄⋊C₄	—	268	1	no	—
1045	C₄⋊C₄	—	268	1	no	—
1046	C₄⋊C₄	—	268	1	no	—
1047	C₄⋊C₄	—	268	1	no	—
1048	C₄⋊C₄	—	268	1	no	—
1049	C₄⋊C₄	—	268	1	no	—
1050	C₄⋊C₄	—	268	1	no	—
1051	C₄⋊C₄	—	268	1	no	—
1052	C₄⋊C₄	—	268	1	no	—
1053	C₄⋊C₄	—	134	2	no	—
1054	C₄⋊C₄	—	134	2	no	—
1055	C₄⋊C₄	—	134	2	no	—
1056	C₄⋊C₄	—	134	2	no	—
1057	C₄⋊C₄	—	134	2	no	—
1058	C₄⋊C₄	—	134	2	no	—
1059	C₄⋊C₄	—	134	2	no	—
1060	C₄⋊C₄	—	134	2	no	—
1061	C₄⋊C₄	—	134	2	no	—
1062	C₄⋊C₄	—	134	2	no	—
1063	C₄⋊C₄	—	134	2	no	—
1064	C₄⋊C₄	—	134	2	no	—
1065	C₄⋊C₄	—	134	2	no	—
1066	C₄⋊C₄	—	134	2	no	—
1067	C₄⋊C₄	—	134	2	no	—
1068	C₄⋊C₄	—	134	2	no	—
1069	C₄⋊C₄	—	134	2	no	—
1070	C₄⋊C₄	—	134	2	no	—
1071	C₄⋊C₄	—	134	2	no	—
1072	C₂²⋊C₄	—	268	1	no	—
1073	C₂²⋊C₄	—	268	1	no	—
1074	C₂²⋊C₄	—	268	1	no	—
1075	C₂²⋊C₄	—	268	1	no	—
1076	C₂²⋊C₄	—	268	1	no	—
1077	C₂²⋊C₄	—	268	1	no	—
1078	C₂²⋊C₄	—	134	2	no	—
1079	C₂²⋊C₄	—	134	2	no	—
1080	C₂²⋊C₄	—	134	2	no	—
1081	C₂²⋊C₄	—	134	2	no	—
1082	C₂²⋊C₄	—	134	2	no	—
1083	C₂²⋊C₄	—	134	2	no	—
1084	C₂²⋊C₄	—	134	2	no	—
1085	C₂²⋊C₄	—	134	2	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	268	1	no	—
1089	C₄²	—	268	1	no	—
1090	C₄²	—	268	1	no	—
1091	C₄²	—	268	1	no	—
1092	C₄²	—	268	1	no	—
1093	C₄²	—	268	1	no	—
1094	C₄²	—	67	4	no	—
1095	C₄²	—	67	4	no	—
1096	C₄²	—	134	2	no	—
1097	C₄²	—	134	2	no	—
1098	C₄²	—	134	2	no	—
1099	C₄²	—	134	2	no	—
1100	C₄²	—	134	2	no	—
1101	C₄²	—	134	2	no	—
1102	C₄²	—	134	2	no	—
1103	C₄²	—	134	2	no	—
1104	C₄²	—	134	2	no	—
1105	C₄²	—	134	2	no	—
1106	C₄²	—	134	2	no	—
1107	C₄²	—	134	2	no	—
1108	C₄²	—	134	2	no	—
1109	C₄²	—	134	2	no	—
1110	C₄²	—	134	2	no	—
1111	C₄²	#11761627	1	4	yes	—
1112	C₂³	—	134	1	no	—
1113	C₂³	—	134	1	no	—
1114	C₂³	—	134	1	no	—
1115	C₂³	—	134	1	no	—
1116	C₂³	—	134	1	no	—
1117	C₂³	—	134	1	no	—
1118	C₂³	—	134	1	no	—
1119	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1120	Q₈	—	2	8	no	—
1121	Q₈	—	268	4	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	268	4	no	—
1163	C₂×C₄	—	67	2	no	—
1164	C₂×C₄	—	67	2	no	—
1165	C₂×C₄	—	67	2	no	—
1166	C₂×C₄	—	67	2	no	—
1167	C₂×C₄	—	67	2	no	—
1168	C₂×C₄	—	67	2	no	—
1169	C₂×C₄	—	134	1	no	—
1170	C₂×C₄	—	134	1	no	—
1171	C₂×C₄	—	134	1	no	—
1172	C₂×C₄	—	134	1	no	—
1173	C₂×C₄	—	134	1	no	—
1174	C₂×C₄	—	134	1	no	—
1175	C₂×C₄	—	134	1	no	—
1176	C₂×C₄	—	134	1	no	—
1177	C₂×C₄	—	134	1	no	—
1178	C₂×C₄	—	134	1	no	—
1179	C₂×C₄	—	134	1	no	—
1180	C₂×C₄	—	134	1	no	—
1181	C₂×C₄	—	134	1	no	—
1182	C₂×C₄	—	134	1	no	—
1183	C₂×C₄	—	134	1	no	—
1184	C₂×C₄	—	134	1	no	—
1185	C₂×C₄	—	134	1	no	—
1186	C₂×C₄	—	134	1	no	—
1187	C₂×C₄	—	134	1	no	—
1188	C₂×C₄	—	134	1	no	—
1189	C₂×C₄	—	134	1	no	—
1190	C₂×C₄	—	134	1	no	—
1191	C₂×C₄	—	134	1	no	—
1192	C₂×C₄	—	134	1	no	—
1193	C₂×C₄	—	134	1	no	—
1194	C₂×C₄	—	134	1	no	—
1195	C₂×C₄	—	134	1	no	—
1196	C₂×C₄	—	134	1	no	—
1197	C₂×C₄	—	134	1	no	—
1198	C₂×C₄	—	134	1	no	—
1199	C₂×C₄	—	134	1	no	—
1200	C₂×C₄	—	134	1	no	—
1201	C₂×C₄	—	134	1	no	—
1202	C₂×C₄	—	134	1	no	—
1203	C₂×C₄	—	134	1	no	—
1204	C₂×C₄	—	134	1	no	—
1205	C₂×C₄	—	134	1	no	—
1206	C₂×C₄	—	134	1	no	—
1207	C₂×C₄	—	134	1	no	—
1208	C₂×C₄	#41×D₆₇	1	2	yes	—
1209	C₂×C₄	#41×D₆₇	1	2	yes	—
1210	C₂×C₄	C₂×#11761627	1	2	yes	—
1211	C₂×C₄	C₂×#11761627	1	2	yes	—
1212	C₂×C₄	C₂×#11761627	1	2	yes	—
1213	C₂²	—	268	1	no	—
1214	C₂²	—	268	1	no	—
1215	C₂²	—	268	1	no	—
1216	C₂²	—	268	1	no	—
1217	C₂²	—	268	1	no	—
1218	C₂²	—	268	1	no	—
1219	C₂²	—	268	1	no	—
1220	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1221	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1222	C₂²	C₂²×#11761627	1	1	yes	characteristic
1223	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1224	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1225	C₂²	#16864233	1	1	yes	characteristic
1226	C₂²	#16864233	1	1	yes	characteristic
1227	C₄	—	2	2	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	268	1	no	—
1243	C₄	—	268	1	no	—
1244	C₄	—	268	1	no	—
1245	C₄	—	268	1	no	—
1246	C₄	—	268	1	no	—
1247	C₄	—	268	1	no	—
1248	C₄	—	268	1	no	—
1249	C₄	—	268	1	no	—
1250	C₄	—	268	1	no	—
1251	C₄	—	268	1	no	—
1252	C₄	—	268	1	no	—
1253	C₄	—	67	4	no	—
1254	C₄	—	134	2	no	—
1255	C₄	—	134	2	no	—
1256	C₄	—	134	2	no	—
1257	C₂	—	536	1	no	—
1258	C₂	#22573501	1	1	yes	characteristic
1259	C₂	#541×D₆₇	1	1	yes	characteristic
1260	C₂	#22573600	1	1	yes	characteristic
1261	C₂	#22573633	1	1	yes	characteristic
1262	C₂	#22573633	1	1	yes	characteristic
1263	C₂	#22573641	1	1	yes	characteristic
1264	C₂	#22573641	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2634	C₂
prime radical	C₂³×D₆₇	C₂⁴
hypercenter	#2634	D₆₇
hypocenter	C₆₇	#34604
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2634

Complements

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

N	H ≅ G/N	type
1. #22566392	C₂	semidirect
2. #22566391	C₂	semidirect
5. #22566304	C₂	semidirect
6. #22566303	C₂	semidirect
7. #22566302	C₂	semidirect
8. #22566295	C₂	semidirect
15. #22566084	C₂	semidirect
16. #22563515	C₂	semidirect
17. #22563515	C₂	semidirect
18. #22563513	C₂	semidirect
21. #22563499	C₂	semidirect
24. #125×Dic₆₇	C₂	semidirect
25. #22562766	C₂	semidirect
29. #22562682	C₂	semidirect
30. C₄×Q₈×Dic₆₇	C₂	semidirect
31. C₆₇×#2634	C₂	semidirect
648. #2634	D₆₇	semidirect
664. C₆₇	#34604	semidirect

Maximal subgroups

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

subgroup	index
#22566392	2
#22566391	2
#22566370	2
#22566367	2
#22566304	2
#22566303	2
#22566302	2
#22566295	2
#22566290	2
#22566287	2
#22566229	2
#22566222	2
#22566116	2
#22566115	2
#22566084	2
#22563515	2
#22563513	2
#22563508	2
#22563499	2
#22563486	2
#22563480	2
#125×Dic₆₇	2
#22562766	2
#22562759	2
#22562757	2
#22562701	2
#22562682	2
C₄×Q₈×Dic₆₇	2
C₆₇×#2634	2
#34604	67