Subgroups — #31064214

Order 17152.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568503	C₂	1	1	yes	maximal, characteristic
2	#22568494	C₂	1	1	yes	maximal, characteristic, complemented
3	#22567979	C₂	1	1	yes	maximal, characteristic, complemented
4	#22567843	C₂	1	1	yes	maximal, characteristic, complemented
5	#22567715	C₂	1	1	yes	maximal, characteristic, complemented
6	#22567638	C₂	1	1	yes	maximal, characteristic, complemented
7	#22567635	C₂	1	1	yes	maximal, characteristic, complemented
8	#22567626	C₂	1	1	yes	maximal, characteristic, complemented
9	#22567541	C₂	1	1	yes	maximal, characteristic, complemented
10	#22567400	C₂	1	1	yes	maximal, characteristic, complemented
11	#22567288	C₂	1	1	yes	maximal, characteristic, complemented
12	#22567192	C₂	1	1	yes	maximal, characteristic, complemented
13	#22567057	C₂	1	1	yes	maximal, characteristic, complemented
14	#22567050	C₂	1	1	yes	maximal, characteristic, complemented
15	#22566785	C₂	1	1	yes	maximal, characteristic, complemented
16	#22566704	C₂	1	1	yes	maximal, characteristic, complemented
17	#22566629	C₂	1	1	yes	maximal, characteristic, complemented
18	#22566488	C₂	1	1	yes	maximal, characteristic, complemented
19	#22566026	C₂	1	1	yes	maximal, characteristic, complemented
20	#22565992	C₂	1	1	yes	maximal, characteristic, complemented
21	#22565099	C₂	1	1	yes	maximal, characteristic
22	#22564598	C₂	1	1	yes	maximal, characteristic, complemented
23	#22564531	C₂	1	1	yes	maximal, characteristic, complemented
24	#22564452	C₂	1	1	yes	maximal, characteristic, complemented
25	#22564332	C₂	1	1	yes	maximal, characteristic
26	#22563911	C₂	1	1	yes	maximal, characteristic, complemented
27	#22563661	C₂	1	1	yes	maximal, characteristic, complemented
28	#22562944	C₂	1	1	yes	maximal, characteristic, complemented
29	#22562836	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16863271	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2561	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×Dic₆₇	C₂²	1	1	yes	characteristic
33	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14524036	C₂²	1	1	yes	characteristic
35	C₂×#14524029	C₂²	1	1	yes	characteristic
36	C₂×#14524027	C₂²	1	1	yes	characteristic
37	C₂×#14524027	C₂²	1	1	yes	characteristic
38	C₂×#14524026	C₂²	1	1	yes	characteristic
39	C₂×#14524020	C₂²	1	1	yes	characteristic
40	C₂×#14524020	C₂²	1	1	yes	characteristic
41	C₂×#14524020	C₂²	1	1	yes	characteristic
42	C₂×#14524020	C₂²	1	1	yes	characteristic
43	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
44	C₂×#14524012	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
49	C₆₇⋊#401	C₂²	1	1	yes	characteristic, complemented
50	#16863338	C₂²	1	1	yes	characteristic, complemented
51	#16863338	C₂²	1	1	yes	characteristic, complemented
52	#16863338	C₂²	1	1	yes	characteristic, complemented
53	#16863338	C₂²	1	1	yes	characteristic, complemented
54	#16863337	C₂²	1	1	yes	characteristic, complemented
55	#16863337	C₂²	1	1	yes	characteristic, complemented
56	#16863336	C₂²	1	1	yes	characteristic, complemented
57	#16863336	C₂²	1	1	yes	characteristic, complemented
58	#16863336	C₂²	1	1	yes	characteristic, complemented
59	#16863333	C₂²	1	1	yes	characteristic, complemented
60	#16863333	C₂²	1	1	yes	characteristic, complemented
61	#16863330	C₂²	1	1	yes	characteristic, complemented
62	#16863330	C₂²	1	1	yes	characteristic, complemented
63	#16863329	C₂²	1	1	yes	characteristic, complemented
64	#16863329	C₂²	1	1	yes	characteristic, complemented
65	#16863328	C₂²	1	1	yes	characteristic, complemented
66	#16863328	C₂²	1	1	yes	characteristic, complemented
67	#16863328	C₂²	1	1	yes	characteristic, complemented
68	#16863328	C₂²	1	1	yes	characteristic, complemented
69	#16863328	C₂²	1	1	yes	characteristic, complemented
70	#16863328	C₂²	1	1	yes	characteristic, complemented
71	#16863325	C₂²	1	1	yes	characteristic, complemented
72	#16863324	C₂²	1	1	yes	characteristic
73	#16863324	C₂²	1	1	yes	characteristic
74	#16863324	C₂²	1	1	yes	characteristic
75	#16863323	C₂²	1	1	yes	characteristic, complemented
76	#16863323	C₂²	1	1	yes	characteristic, complemented
77	#16863321	C₂²	1	1	yes	characteristic
78	#16863319	C₂²	1	1	yes	characteristic
79	#16863319	C₂²	1	1	yes	characteristic
80	#16863319	C₂²	1	1	yes	characteristic
81	#16863318	C₂²	1	1	yes	characteristic, complemented
82	#16863318	C₂²	1	1	yes	characteristic, complemented
83	#16863317	C₂²	1	1	yes	characteristic, complemented
84	#16863317	C₂²	1	1	yes	characteristic, complemented
85	#16863317	C₂²	1	1	yes	characteristic, complemented
86	#16863317	C₂²	1	1	yes	characteristic, complemented
87	#16863312	C₂²	1	1	yes	characteristic
88	#16863312	C₂²	1	1	yes	characteristic
89	#16863312	C₂²	1	1	yes	characteristic
90	#16863311	C₂²	1	1	yes	characteristic
91	#16863309	C₂²	1	1	yes	characteristic, complemented
92	#16863308	C₂²	1	1	yes	characteristic
93	#16863303	C₂²	1	1	yes	characteristic, complemented
94	#16863303	C₂²	1	1	yes	characteristic, complemented
95	#16863303	C₂²	1	1	yes	characteristic, complemented
96	#16863300	C₂²	1	1	yes	characteristic, complemented
97	#16863296	C₂²	1	1	yes	characteristic
98	#16863295	C₂²	1	1	yes	characteristic, complemented
99	#16863295	C₂²	1	1	yes	characteristic, complemented
100	#16863294	C₂²	1	1	yes	characteristic, complemented
101	#16863294	C₂²	1	1	yes	characteristic, complemented
102	#16863292	C₂²	1	1	yes	characteristic, complemented
103	#16863290	C₂²	1	1	yes	characteristic
104	#16863289	C₂²	1	1	yes	characteristic
105	#16863289	C₂²	1	1	yes	characteristic
106	#16863288	C₂²	1	1	yes	characteristic, complemented
107	#16863287	C₂²	1	1	yes	characteristic, complemented
108	#16863287	C₂²	1	1	yes	characteristic, complemented
109	#16863285	C₂²	1	1	yes	characteristic, complemented
110	#16863284	C₂²	1	1	yes	characteristic
111	#16863284	C₂²	1	1	yes	characteristic
112	#16863284	C₂²	1	1	yes	characteristic
113	#16863284	C₂²	1	1	yes	characteristic
114	#16863283	C₂²	1	1	yes	characteristic, complemented
115	#16863282	C₂²	1	1	yes	characteristic, complemented
116	#16863282	C₂²	1	1	yes	characteristic, complemented
117	#16863282	C₂²	1	1	yes	characteristic, complemented
118	#16863282	C₂²	1	1	yes	characteristic, complemented
119	#16863281	C₂²	1	1	yes	characteristic, complemented
120	#16863280	C₂²	1	1	yes	characteristic, complemented
121	#16863280	C₂²	1	1	yes	characteristic, complemented
122	#16863278	C₂²	1	1	yes	characteristic, complemented
123	#16863273	C₂²	1	1	yes	characteristic
124	#16863273	C₂²	1	1	yes	characteristic
125	#16863273	C₂²	1	1	yes	characteristic
126	#16863273	C₂²	1	1	yes	characteristic
127	#16863273	C₂²	1	1	yes	characteristic
128	#16863273	C₂²	1	1	yes	characteristic
129	#16863272	C₂²	1	1	yes	characteristic
130	#16863272	C₂²	1	1	yes	characteristic
131	#16863271	C₂²	1	1	yes	characteristic
132	#16863271	C₂²	1	1	yes	characteristic
133	#16863271	C₂²	1	1	yes	characteristic
134	#16863271	C₂²	1	1	yes	characteristic
135	#16863271	C₂²	1	1	yes	characteristic
136	#16863271	C₂²	1	1	yes	characteristic
137	#16863271	C₂²	1	1	yes	characteristic
138	#16863271	C₂²	1	1	yes	characteristic
139	#16863271	C₂²	1	1	yes	characteristic
140	#16863271	C₂²	1	1	yes	characteristic
141	#16863271	C₂²	1	1	yes	characteristic
142	#16863271	C₂²	1	1	yes	characteristic
143	#16863271	C₂²	1	1	yes	characteristic
144	#16863271	C₂²	1	1	yes	characteristic
145	#16863271	C₂²	1	1	yes	characteristic
146	#16863271	C₂²	1	1	yes	characteristic
147	#16863268	C₂²	1	1	yes	characteristic
148	#16863268	C₂²	1	1	yes	characteristic
149	#16863268	C₂²	1	1	yes	characteristic
150	#16863268	C₂²	1	1	yes	characteristic
151	#16863266	C₂²	1	1	yes	characteristic, complemented
152	#16863263	C₂²	1	1	yes	characteristic, complemented
153	#16863263	C₂²	1	1	yes	characteristic, complemented
154	#16863260	C₂²	1	1	yes	characteristic, complemented
155	#16863260	C₂²	1	1	yes	characteristic, complemented
156	#16863259	C₂²	1	1	yes	characteristic
157	#16863258	C₂²	1	1	yes	characteristic, complemented
158	#16863257	C₂²	1	1	yes	characteristic
159	#16863257	C₂²	1	1	yes	characteristic
160	#16863256	C₂²	1	1	yes	characteristic
161	#16863255	C₂²	1	1	yes	characteristic, complemented
162	#16863254	C₂²	1	1	yes	characteristic
163	#16863254	C₂²	1	1	yes	characteristic
164	#16863254	C₂²	1	1	yes	characteristic
165	#16863254	C₂²	1	1	yes	characteristic
166	#16863253	C₂²	1	1	yes	characteristic, complemented
167	#16863252	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
170	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
171	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
172	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
173	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
174	#397×C₆₇	C₂²	1	1	yes	characteristic
175	#397×C₆₇	C₂²	1	1	yes	characteristic
176	#393×C₆₇	C₂²	1	1	yes	characteristic
177	#393×C₆₇	C₂²	1	1	yes	characteristic
178	#388×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	#381×C₆₇	C₂²	1	1	yes	characteristic
183	#381×C₆₇	C₂²	1	1	yes	characteristic
184	#379×C₆₇	C₂²	1	1	yes	characteristic
185	#379×C₆₇	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊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	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
191	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
192	C₂³×Dic₆₇	—	4	2	no	—
193	C₂³×Dic₆₇	—	4	2	no	—
194	C₂³×Dic₆₇	—	4	2	no	—
195	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
196	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
197	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
199	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
204	#14524043	—	4	2	no	—
205	#14524036	—	4	2	no	—
206	#14524029	—	4	2	no	—
207	#14524027	—	4	2	no	—
208	#14524027	—	4	2	no	—
209	#14524026	—	4	2	no	—
210	#14524020	—	4	2	no	—
211	#14524020	—	4	2	no	—
212	#14524020	—	4	2	no	—
213	#14524020	—	4	2	no	—
214	#14524019	—	4	2	no	—
215	#14524012	—	4	2	no	—
216	C₄×C₂²⋊D₆₇	—	2	4	no	—
217	C₂×C₄⋊Dic₆₇	—	4	2	no	—
218	C₂×C₄⋊Dic₆₇	—	4	2	no	—
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×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₆₇	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×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₆₇	—	4	2	no	—
255	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊Dic₆₇	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×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×(C₂×D₆₇)⋊C₄	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	C₂×C₄×Dic₆₇	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	C₆₇⋊#95	C₂³	1	1	yes	characteristic
321	C₆₇⋊#95	C₂³	1	1	yes	characteristic
322	C₆₇⋊#95	C₂³	1	1	yes	characteristic
323	C₆₇⋊#95	C₂³	1	1	yes	characteristic
324	C₆₇⋊#95	C₂³	1	1	yes	characteristic
325	C₆₇⋊#95	C₂³	1	1	yes	characteristic
326	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
327	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
328	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂²⋊Q₈×C₆₇	—	2	4	no	—
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
353	#95×C₆₇	C₂³	1	1	yes	characteristic
354	#95×C₆₇	C₂³	1	1	yes	characteristic
355	#95×C₆₇	C₂³	1	1	yes	characteristic
356	#95×C₆₇	C₂³	1	1	yes	characteristic
357	#95×C₆₇	C₂³	1	1	yes	characteristic
358	#95×C₆₇	C₂³	1	1	yes	characteristic
359	#95×C₆₇	C₂³	1	1	yes	characteristic
360	#95×C₆₇	C₂³	1	1	yes	characteristic
361	#95×C₆₇	C₂³	1	1	yes	characteristic
362	#95×C₆₇	C₂³	1	1	yes	characteristic
363	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
364	C₂×Dic₁₃₄	—	2	2	no	—
365	C₂×Dic₁₃₄	—	4	1	no	—
366	C₂×Dic₁₃₄	—	4	1	no	—
367	C₂×Dic₁₃₄	—	4	1	no	—
368	C₂×Dic₁₃₄	—	4	1	no	—
369	C₂×Dic₁₃₄	—	4	1	no	—
370	C₂×C₂²⋊D₆₇	—	2	2	no	—
371	C₂×C₂²⋊D₆₇	—	2	2	no	—
372	C₂×C₂²⋊D₆₇	—	2	2	no	—
373	C₂×C₂²⋊D₆₇	—	2	2	no	—
374	C₂×C₂²⋊D₆₇	—	2	2	no	—
375	C₂×C₂²⋊D₆₇	—	4	1	no	—
376	C₂×C₂²⋊D₆₇	—	4	1	no	—
377	C₂×C₂²⋊D₆₇	—	4	1	no	—
378	C₂×C₂²⋊D₆₇	—	4	1	no	—
379	C₂²×Dic₆₇	—	2	2	no	—
380	C₂²×Dic₆₇	—	2	2	no	—
381	C₂²×Dic₆₇	—	2	2	no	—
382	C₂²×Dic₆₇	—	2	2	no	—
383	C₂²×Dic₆₇	—	2	2	no	—
384	C₂²×Dic₆₇	—	2	2	no	—
385	C₂²×Dic₆₇	—	2	2	no	—
386	C₂²×Dic₆₇	—	2	2	no	—
387	C₂²×Dic₆₇	—	2	2	no	—
388	C₂²×Dic₆₇	—	4	1	no	—
389	C₂²×Dic₆₇	—	4	1	no	—
390	C₂²×Dic₆₇	—	4	1	no	—
391	C₂²×Dic₆₇	—	4	1	no	—
392	C₂²×Dic₆₇	—	4	1	no	—
393	C₂²×Dic₆₇	—	4	1	no	—
394	C₂²×Dic₆₇	—	4	1	no	—
395	C₂²×Dic₆₇	—	4	1	no	—
396	C₂²×Dic₆₇	—	4	1	no	—
397	C₂²×Dic₆₇	—	4	1	no	—
398	C₂²×Dic₆₇	—	4	1	no	—
399	C₂²×Dic₆₇	—	4	1	no	—
400	C₂²×Dic₆₇	—	4	1	no	—
401	C₂²×Dic₆₇	—	4	1	no	—
402	C₂²×Dic₆₇	—	4	1	no	—
403	C₂²×Dic₆₇	—	4	16	no	—
404	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×D₆₇	—	2	2	no	—
420	C₂×C₄×D₆₇	—	4	1	no	—
421	C₂×C₄×D₆₇	—	4	1	no	—
422	C₄⋊Dic₆₇	—	2	2	no	—
423	C₄⋊Dic₆₇	—	2	2	no	—
424	C₄⋊Dic₆₇	—	2	2	no	—
425	C₄⋊Dic₆₇	—	4	1	no	—
426	C₄⋊Dic₆₇	—	4	1	no	—
427	C₄⋊Dic₆₇	—	4	1	no	—
428	C₄⋊Dic₆₇	—	4	1	no	—
429	C₄⋊Dic₆₇	—	4	1	no	—
430	C₄⋊Dic₆₇	—	4	1	no	—
431	C₄⋊Dic₆₇	—	4	1	no	—
432	C₄⋊Dic₆₇	—	4	1	no	—
433	C₄⋊Dic₆₇	—	4	1	no	—
434	C₄⋊Dic₆₇	—	4	1	no	—
435	C₄⋊Dic₆₇	—	4	1	no	—
436	C₄⋊Dic₆₇	—	4	1	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	Dic₆₇⋊C₄	—	2	2	no	—
443	Dic₆₇⋊C₄	—	2	2	no	—
444	Dic₆₇⋊C₄	—	4	1	no	—
445	Dic₆₇⋊C₄	—	4	1	no	—
446	Dic₆₇⋊C₄	—	4	1	no	—
447	Dic₆₇⋊C₄	—	4	1	no	—
448	Dic₆₇⋊C₄	—	4	1	no	—
449	Dic₆₇⋊C₄	—	4	1	no	—
450	Dic₆₇⋊C₄	—	4	1	no	—
451	Dic₆₇⋊C₄	—	4	1	no	—
452	Dic₆₇⋊C₄	—	4	1	no	—
453	Dic₆₇⋊C₄	—	4	1	no	—
454	Dic₆₇⋊C₄	—	4	1	no	—
455	Dic₆₇⋊C₄	—	4	1	no	—
456	Dic₆₇⋊C₄	—	4	1	no	—
457	C₂²⋊Dic₆₇	—	2	2	no	—
458	C₂²⋊Dic₆₇	—	2	2	no	—
459	C₂²⋊Dic₆₇	—	2	2	no	—
460	C₂²⋊Dic₆₇	—	2	2	no	—
461	C₂²⋊Dic₆₇	—	2	2	no	—
462	C₂²⋊Dic₆₇	—	2	2	no	—
463	C₂²⋊Dic₆₇	—	2	2	no	—
464	C₂²⋊Dic₆₇	—	4	1	no	—
465	C₂²⋊Dic₆₇	—	4	1	no	—
466	C₂²⋊Dic₆₇	—	4	1	no	—
467	C₂²⋊Dic₆₇	—	4	1	no	—
468	C₂²⋊Dic₆₇	—	4	1	no	—
469	C₂²⋊Dic₆₇	—	4	1	no	—
470	(C₂×D₆₇)⋊C₄	—	2	2	no	—
471	(C₂×D₆₇)⋊C₄	—	2	2	no	—
472	(C₂×D₆₇)⋊C₄	—	4	1	no	—
473	(C₂×D₆₇)⋊C₄	—	4	1	no	—
474	(C₂×D₆₇)⋊C₄	—	4	1	no	—
475	(C₂×D₆₇)⋊C₄	—	4	1	no	—
476	(C₂×D₆₇)⋊C₄	—	4	1	no	—
477	(C₂×D₆₇)⋊C₄	—	4	1	no	—
478	(C₂×D₆₇)⋊C₄	—	4	1	no	—
479	(C₂×D₆₇)⋊C₄	—	4	1	no	—
480	(C₂×D₆₇)⋊C₄	—	4	1	no	—
481	C₄×Dic₆₇	—	2	2	no	—
482	C₄×Dic₆₇	—	4	1	no	—
483	C₄×Dic₆₇	—	4	1	no	—
484	C₄×Dic₆₇	—	4	1	no	—
485	C₄×Dic₆₇	—	4	1	no	—
486	C₂⁴×C₆₇	—	2	2	no	—
487	C₂⁴×C₆₇	—	2	2	no	—
488	C₂⁴×C₆₇	—	2	2	no	—
489	C₂⁴×C₆₇	—	2	2	no	—
490	C₂⁴×C₆₇	—	2	2	no	—
491	C₂⁴×C₆₇	—	4	1	no	—
492	C₂⁴×C₆₇	—	4	1	no	—
493	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
494	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂×Q₈×C₆₇	—	2	2	no	—
497	C₂×Q₈×C₆₇	—	4	1	no	—
498	C₂×Q₈×C₆₇	—	4	1	no	—
499	C₂²×C₄×C₆₇	—	2	2	no	—
500	C₂²×C₄×C₆₇	—	2	2	no	—
501	C₂²×C₄×C₆₇	—	2	2	no	—
502	C₂²×C₄×C₆₇	—	4	1	no	—
503	C₂²×C₄×C₆₇	—	4	1	no	—
504	C₂²×C₄×C₆₇	#41	1	4	yes	—
505	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
511	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
515	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
516	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
517	C₄⋊C₄×C₆₇	—	2	2	no	—
518	C₄⋊C₄×C₆₇	—	2	2	no	—
519	C₄⋊C₄×C₆₇	—	2	2	no	—
520	C₂²⋊C₄×C₆₇	—	2	2	no	—
521	C₂²⋊C₄×C₆₇	—	2	2	no	—
522	C₂²⋊C₄×C₆₇	—	2	2	no	—
523	C₂²⋊C₄×C₆₇	—	2	2	no	—
524	C₂²⋊C₄×C₆₇	—	2	2	no	—
525	C₂²⋊C₄×C₆₇	—	2	2	no	—
526	C₂²⋊C₄×C₆₇	—	2	2	no	—
527	C₂²⋊C₄×C₆₇	—	2	2	no	—
528	C₂²⋊C₄×C₆₇	—	2	2	no	—
529	C₂²⋊C₄×C₆₇	—	2	2	no	—
530	C₂²⋊C₄×C₆₇	—	2	2	no	—
531	C₂²⋊C₄×C₆₇	—	2	2	no	—
532	C₂²⋊C₄×C₆₇	—	4	1	no	—
533	C₂²⋊C₄×C₆₇	—	4	1	no	—
534	C₂²⋊C₄×C₆₇	—	4	1	no	—
535	C₂²⋊C₄×C₆₇	—	4	1	no	—
536	C₄²×C₆₇	—	4	1	no	—
537	C₄²×C₆₇	—	4	1	no	—
538	C₂³×C₆₇	—	2	1	no	—
539	C₂³×C₆₇	—	2	1	no	—
540	C₂³×C₆₇	—	2	1	no	—
541	C₂³×C₆₇	—	2	1	no	—
542	C₂³×C₆₇	—	2	8	no	—
543	C₂³×C₆₇	—	2	1	no	—
544	C₂³×C₆₇	—	2	1	no	—
545	C₂³×C₆₇	—	2	1	no	—
546	C₂³×C₆₇	—	2	1	no	—
547	C₂³×C₆₇	—	2	1	no	—
548	C₂³×C₆₇	—	2	1	no	—
549	C₂³×C₆₇	—	2	1	no	—
550	C₂³×C₆₇	—	2	1	no	—
551	C₂³×C₆₇	—	2	1	no	—
552	C₂³×C₆₇	—	2	1	no	—
553	C₂³×C₆₇	—	2	1	no	—
554	C₂³×C₆₇	—	2	1	no	—
555	C₂³×C₆₇	—	4	4	no	—
556	C₂³×C₆₇	—	4	4	no	—
557	C₂³×C₆₇	—	4	4	no	—
558	C₂³×C₆₇	—	4	4	no	—
559	C₂³×C₆₇	—	4	4	no	—
560	C₂³×C₆₇	—	4	4	no	—
561	C₂³×C₆₇	C₂×#41	1	2	yes	—
562	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
563	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
564	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
565	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
566	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
567	C₂²×D₆₇	—	2	1	no	—
568	C₂²×D₆₇	—	2	1	no	—
569	C₂²×D₆₇	—	2	1	no	—
570	C₂²×D₆₇	—	2	1	no	—
571	C₂²×D₆₇	—	2	1	no	—
572	C₂²×D₆₇	—	2	1	no	—
573	C₂²×D₆₇	—	2	1	no	—
574	Q₈×C₆₇	—	8	2	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	2	1	no	—
577	C₂×C₄×C₆₇	—	2	1	no	—
578	C₂×C₄×C₆₇	—	2	1	no	—
579	C₂×C₄×C₆₇	—	2	1	no	—
580	C₂×C₄×C₆₇	—	2	1	no	—
581	C₂×C₄×C₆₇	—	2	1	no	—
582	C₂×C₄×C₆₇	—	2	1	no	—
583	C₂×C₄×C₆₇	—	2	1	no	—
584	C₂×C₄×C₆₇	—	2	1	no	—
585	C₂×C₄×C₆₇	—	2	1	no	—
586	C₂×C₄×C₆₇	—	2	1	no	—
587	C₂×C₄×C₆₇	—	2	1	no	—
588	C₂×C₄×C₆₇	—	2	1	no	—
589	C₂×C₄×C₆₇	—	2	1	no	—
590	C₂×C₄×C₆₇	—	2	1	no	—
591	C₂×C₄×C₆₇	—	2	1	no	—
592	C₂×C₄×C₆₇	—	2	1	no	—
593	C₂×C₄×C₆₇	—	2	1	no	—
594	C₂×C₄×C₆₇	—	2	1	no	—
595	C₂×C₄×C₆₇	—	2	1	no	—
596	C₂×C₄×C₆₇	—	2	1	no	—
597	C₂×C₄×C₆₇	—	2	1	no	—
598	C₂×C₄×C₆₇	—	2	1	no	—
599	C₂×C₄×C₆₇	—	2	1	no	—
600	C₂×C₄×C₆₇	—	2	1	no	—
601	C₂×C₄×C₆₇	—	2	1	no	—
602	C₂×C₄×C₆₇	—	2	1	no	—
603	C₂×C₄×C₆₇	—	2	1	no	—
604	C₂×C₄×C₆₇	—	2	1	no	—
605	C₂×C₄×C₆₇	—	2	1	no	—
606	C₂×C₄×C₆₇	—	2	1	no	—
607	C₂×C₄×C₆₇	—	2	1	no	—
608	C₂×C₄×C₆₇	—	2	1	no	—
609	C₂×C₄×C₆₇	—	4	4	no	—
610	C₂×C₄×C₆₇	—	4	4	no	—
611	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
612	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
613	C₂²⋊D₆₇	—	4	4	no	—
614	C₂²⋊D₆₇	—	8	2	no	—
615	C₂²⋊D₆₇	—	8	2	no	—
616	C₂×Dic₆₇	—	2	1	no	—
617	C₂×Dic₆₇	—	2	1	no	—
618	C₂×Dic₆₇	—	2	1	no	—
619	C₂×Dic₆₇	—	2	1	no	—
620	C₂×Dic₆₇	—	2	1	no	—
621	C₂×Dic₆₇	—	2	1	no	—
622	C₂×Dic₆₇	—	2	1	no	—
623	C₂×Dic₆₇	—	2	1	no	—
624	C₂×Dic₆₇	—	2	1	no	—
625	C₂×Dic₆₇	—	2	1	no	—
626	C₂×Dic₆₇	—	2	1	no	—
627	C₂×Dic₆₇	—	2	1	no	—
628	C₂×Dic₆₇	—	2	1	no	—
629	C₂×Dic₆₇	—	2	1	no	—
630	C₂×Dic₆₇	—	2	1	no	—
631	C₂×Dic₆₇	—	2	1	no	—
632	C₂×Dic₆₇	—	2	1	no	—
633	C₂×Dic₆₇	—	2	1	no	—
634	C₂×Dic₆₇	—	2	1	no	—
635	C₂×Dic₆₇	—	2	1	no	—
636	C₂×Dic₆₇	—	2	1	no	—
637	C₂×Dic₆₇	—	2	1	no	—
638	C₂×Dic₆₇	—	2	1	no	—
639	C₂×Dic₆₇	—	2	1	no	—
640	C₂×Dic₆₇	—	2	1	no	—
641	C₂×Dic₆₇	—	2	1	no	—
642	C₂×Dic₆₇	—	2	1	no	—
643	C₂×Dic₆₇	—	2	1	no	—
644	C₂×Dic₆₇	—	2	1	no	—
645	C₂×Dic₆₇	—	2	1	no	—
646	C₂×Dic₆₇	—	2	1	no	—
647	C₂×Dic₆₇	—	2	1	no	—
648	C₂×Dic₆₇	—	2	1	no	—
649	C₂×Dic₆₇	—	2	1	no	—
650	C₂×Dic₆₇	—	2	1	no	—
651	C₂×Dic₆₇	—	2	1	no	—
652	C₂×Dic₆₇	—	2	1	no	—
653	C₂×Dic₆₇	—	2	1	no	—
654	C₂×Dic₆₇	—	2	1	no	—
655	C₂×Dic₆₇	—	2	1	no	—
656	C₂×Dic₆₇	—	2	1	no	—
657	C₂×Dic₆₇	—	2	1	no	—
658	C₂×Dic₆₇	—	2	1	no	—
659	C₂×Dic₆₇	—	2	1	no	—
660	C₂×Dic₆₇	—	4	4	no	—
661	C₂×Dic₆₇	—	4	4	no	—
662	C₂×Dic₆₇	—	4	4	no	—
663	C₂×Dic₆₇	—	4	4	no	—
664	C₂×Dic₆₇	—	4	4	no	—
665	C₂×Dic₆₇	—	4	4	no	—
666	C₂×Dic₆₇	—	8	2	no	—
667	C₂×Dic₆₇	—	8	2	no	—
668	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
669	C₄×D₆₇	—	8	2	no	—
670	Dic₁₃₄	—	8	2	no	—
671	Dic₁₃₄	—	8	2	no	—
672	C₂²×C₆₇	—	2	2	no	—
673	C₂²×C₆₇	—	2	2	no	—
674	C₂²×C₆₇	—	2	2	no	—
675	C₂²×C₆₇	—	2	2	no	—
676	C₂²×C₆₇	—	2	2	no	—
677	C₂²×C₆₇	—	2	2	no	—
678	C₂²×C₆₇	—	2	2	no	—
679	C₂²×C₆₇	—	2	2	no	—
680	C₂²×C₆₇	—	2	2	no	—
681	C₂²×C₆₇	—	2	2	no	—
682	C₂²×C₆₇	—	2	2	no	—
683	C₂²×C₆₇	—	2	2	no	—
684	C₂²×C₆₇	—	4	16	no	—
685	C₂²×C₆₇	—	4	1	no	—
686	C₂²×C₆₇	—	4	1	no	—
687	C₂²×C₆₇	—	4	1	no	—
688	C₂²×C₆₇	—	4	1	no	—
689	C₂²×C₆₇	—	4	1	no	—
690	C₂²×C₆₇	—	4	1	no	—
691	C₂²×C₆₇	—	4	1	no	—
692	C₂²×C₆₇	—	4	1	no	—
693	C₂²×C₆₇	#542	1	4	yes	—
694	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
695	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
699	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
700	C₂²×C₆₇	#585	1	1	yes	characteristic
701	C₂×D₆₇	—	4	1	no	—
702	C₂×D₆₇	—	4	1	no	—
703	C₂×D₆₇	—	4	1	no	—
704	C₂×D₆₇	—	4	1	no	—
705	C₂×D₆₇	—	4	1	no	—
706	C₂×D₆₇	—	4	1	no	—
707	C₂×D₆₇	—	4	1	no	—
708	C₄×C₆₇	—	2	2	no	—
709	C₄×C₆₇	—	2	2	no	—
710	C₄×C₆₇	—	4	1	no	—
711	C₄×C₆₇	—	4	1	no	—
712	C₄×C₆₇	—	4	1	no	—
713	C₄×C₆₇	—	4	1	no	—
714	C₄×C₆₇	—	4	1	no	—
715	C₄×C₆₇	—	4	1	no	—
716	C₄×C₆₇	—	4	1	no	—
717	C₄×C₆₇	—	4	1	no	—
718	C₄×C₆₇	—	4	1	no	—
719	C₄×C₆₇	—	4	1	no	—
720	Dic₆₇	—	2	2	no	—
721	Dic₆₇	—	4	1	no	—
722	Dic₆₇	—	4	1	no	—
723	Dic₆₇	—	4	1	no	—
724	Dic₆₇	—	4	1	no	—
725	Dic₆₇	—	4	1	no	—
726	Dic₆₇	—	4	1	no	—
727	Dic₆₇	—	4	1	no	—
728	Dic₆₇	—	4	1	no	—
729	Dic₆₇	—	4	1	no	—
730	Dic₆₇	—	4	1	no	—
731	Dic₆₇	—	4	1	no	—
732	Dic₆₇	—	4	1	no	—
733	Dic₆₇	—	4	1	no	—
734	Dic₆₇	—	4	1	no	—
735	#36778	—	67	1	no	maximal, Sylow
736	C₂×C₆₇	—	2	4	no	—
737	C₂×C₆₇	—	4	2	no	—
738	C₂×C₆₇	—	4	2	no	—
739	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
740	C₂×C₆₇	#3492	1	1	yes	characteristic
741	C₂×C₆₇	#3505	1	1	yes	characteristic
742	C₂×C₆₇	#3532	1	1	yes	characteristic
743	C₂×C₆₇	#3535	1	1	yes	characteristic
744	C₂×C₆₇	#3535	1	1	yes	characteristic
745	C₂×C₆₇	#3538	1	1	yes	characteristic
746	D₆₇	—	8	1	no	—
747	#2849	—	67	1	no	—
748	#2848	—	67	1	no	—
749	#2790	—	67	1	no	—
750	#2779	—	67	1	no	—
751	#2770	—	67	1	no	—
752	#2765	—	67	1	no	—
753	#2764	—	67	1	no	—
754	#2763	—	67	1	no	—
755	#2757	—	67	1	no	—
756	#2746	—	67	1	no	—
757	#2739	—	67	1	no	—
758	#2729	—	67	1	no	—
759	#2718	—	67	1	no	—
760	#2717	—	67	1	no	—
761	#2698	—	67	1	no	—
762	#2692	—	67	1	no	—
763	#2687	—	67	1	no	—
764	#2674	—	67	1	no	—
765	#2627	—	67	1	no	—
766	#2623	—	67	1	no	—
767	#2561	D₆₇	1	1	yes	characteristic, complemented
768	#2534	—	67	1	no	—
769	#2493	—	67	1	no	—
770	#2488	—	67	1	no	—
771	#2480	—	67	1	no	—
772	#2472	—	67	1	no	—
773	#2440	—	67	1	no	—
774	#2417	—	67	1	no	—
775	#2329	—	67	1	no	—
776	#2318	—	67	1	no	—
777	C₂×#385	—	67	1	no	—
778	C₆₇	#36778	1	1	yes	characteristic, complemented, Sylow
779	C₂⁴×C₄	—	67	1	no	—
780	C₂×C₄⋊Q₈	—	67	1	no	—
781	C₂×#126	—	67	1	no	—
782	C₂×#124	—	67	1	no	—
783	C₂×#123	—	67	1	no	—
784	C₂×#123	—	67	1	no	—
785	C₂×#123	—	67	1	no	—
786	C₂×C₂²⋊Q₈	—	67	1	no	—
787	C₂×C₂²⋊Q₈	—	67	1	no	—
788	C₂×C₂²⋊Q₈	—	67	1	no	—
789	C₂×C₂²⋊Q₈	—	67	1	no	—
790	C₂×C₂²⋊Q₈	—	67	1	no	—
791	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
792	C₂×#120	—	67	1	no	—
793	C₂×C₄×D₄	—	67	1	no	—
794	C₂²×C₄⋊C₄	—	67	1	no	—
795	C₂²×C₄⋊C₄	—	67	1	no	—
796	C₂²×C₂²⋊C₄	—	67	1	no	—
797	C₂²×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
798	#401	—	67	1	no	—
799	#400	—	67	1	no	—
800	#400	—	67	1	no	—
801	#400	—	67	1	no	—
802	#400	—	67	1	no	—
803	#400	—	67	1	no	—
804	#400	—	67	1	no	—
805	#400	—	67	1	no	—
806	#400	—	67	1	no	—
807	#400	—	67	1	no	—
808	#399	—	67	1	no	—
809	#399	—	67	1	no	—
810	#398	—	67	1	no	—
811	#398	—	67	1	no	—
812	#398	—	67	1	no	—
813	#398	—	67	1	no	—
814	#398	—	67	1	no	—
815	#398	—	67	1	no	—
816	#398	—	67	1	no	—
817	#398	—	67	1	no	—
818	#398	—	67	1	no	—
819	#398	—	67	1	no	—
820	#397	—	67	1	no	—
821	#397	—	67	1	no	—
822	#397	—	67	1	no	—
823	#397	—	67	1	no	—
824	#397	—	67	1	no	—
825	#397	—	67	1	no	—
826	#397	—	67	1	no	—
827	#397	C₂×D₆₇	1	1	yes	characteristic
828	#397	C₂×D₆₇	1	1	yes	characteristic
829	#396	—	67	1	no	—
830	#396	—	67	1	no	—
831	#396	—	67	1	no	—
832	#396	—	67	1	no	—
833	#396	—	67	1	no	—
834	#395	—	67	1	no	—
835	#395	—	67	1	no	—
836	#395	—	67	1	no	—
837	#395	—	67	1	no	—
838	#394	—	67	1	no	—
839	#394	—	67	1	no	—
840	#394	—	67	1	no	—
841	#394	—	67	1	no	—
842	#393	—	67	1	no	—
843	#393	—	67	1	no	—
844	#393	C₂×D₆₇	1	1	yes	characteristic
845	#393	C₂×D₆₇	1	1	yes	characteristic
846	#391	—	67	1	no	—
847	#391	—	67	1	no	—
848	#391	—	67	1	no	—
849	#391	—	67	1	no	—
850	#390	—	67	1	no	—
851	#389	—	67	1	no	—
852	#389	—	67	1	no	—
853	#389	—	67	1	no	—
854	#389	—	67	1	no	—
855	#389	—	67	1	no	—
856	#388	—	67	1	no	—
857	#388	—	67	1	no	—
858	#388	—	67	1	no	—
859	#388	—	67	1	no	—
860	#388	—	67	1	no	—
861	#388	—	67	1	no	—
862	#388	—	67	1	no	—
863	#388	—	67	1	no	—
864	#388	—	67	1	no	—
865	#388	—	67	1	no	—
866	#388	—	67	1	no	—
867	#388	C₂×D₆₇	1	1	yes	characteristic
868	#388	C₂×D₆₇	1	1	yes	characteristic
869	#388	C₂×D₆₇	1	1	yes	characteristic
870	#388	C₂×D₆₇	1	1	yes	characteristic
871	#387	—	67	1	no	—
872	#387	—	67	1	no	—
873	#387	—	67	1	no	—
874	#387	—	67	1	no	—
875	#387	—	67	1	no	—
876	#387	—	67	1	no	—
877	#387	—	67	1	no	—
878	#387	—	67	1	no	—
879	#387	—	67	1	no	—
880	#386	—	67	1	no	—
881	#386	—	67	1	no	—
882	#386	—	67	1	no	—
883	#386	—	67	1	no	—
884	#386	—	67	1	no	—
885	#386	—	67	1	no	—
886	#386	—	67	1	no	—
887	#386	—	67	1	no	—
888	#385	—	67	1	no	—
889	#385	—	67	1	no	—
890	#385	—	67	1	no	—
891	#385	—	67	1	no	—
892	#385	—	67	1	no	—
893	#385	—	67	1	no	—
894	#385	—	67	1	no	—
895	#385	—	67	1	no	—
896	#385	—	67	1	no	—
897	#385	—	67	1	no	—
898	#385	—	67	1	no	—
899	#385	—	67	1	no	—
900	#385	—	67	1	no	—
901	#385	—	67	1	no	—
902	#385	—	67	1	no	—
903	#385	—	67	1	no	—
904	#385	—	67	1	no	—
905	#385	—	67	1	no	—
906	#385	—	67	1	no	—
907	#385	—	67	1	no	—
908	#384	—	67	1	no	—
909	#383	—	67	1	no	—
910	#383	—	67	1	no	—
911	#382	—	67	1	no	—
912	#382	—	67	1	no	—
913	#381	—	67	1	no	—
914	#381	—	67	1	no	—
915	#381	—	67	1	no	—
916	#381	—	67	1	no	—
917	#381	C₂×D₆₇	1	1	yes	characteristic
918	#381	C₂×D₆₇	1	1	yes	characteristic
919	#380	—	67	1	no	—
920	#380	—	67	1	no	—
921	#380	—	67	1	no	—
922	#380	—	67	1	no	—
923	#380	—	67	1	no	—
924	#380	—	67	1	no	—
925	#380	—	67	1	no	—
926	#379	—	67	1	no	—
927	#379	C₂×D₆₇	1	1	yes	characteristic
928	#379	C₂×D₆₇	1	1	yes	characteristic
929	C₄×C₂²⋊C₄	—	67	1	no	—
930	C₄×C₂²⋊C₄	—	67	1	no	—
931	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
932	C₂×#95	—	67	1	no	—
933	C₂×#95	—	67	1	no	—
934	C₂⁵	C₂²×D₆₇	1	1	yes	characteristic
935	C₂²×Q₈	—	67	1	no	—
936	C₂²×Q₈	—	67	1	no	—
937	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
938	C₂²×D₄	—	67	1	no	—
939	C₂²×D₄	—	67	1	no	—
940	C₂²×D₄	—	67	1	no	—
941	C₂³×C₄	—	268	2	no	—
942	C₂³×C₄	—	268	2	no	—
943	C₂³×C₄	—	268	2	no	—
944	C₂³×C₄	—	67	1	no	—
945	C₂³×C₄	—	67	1	no	—
946	C₂³×C₄	—	67	1	no	—
947	C₂³×C₄	—	67	1	no	—
948	C₂³×C₄	—	67	1	no	—
949	C₂³×C₄	—	67	1	no	—
950	C₂³×C₄	—	67	1	no	—
951	C₂³×C₄	—	67	1	no	—
952	C₂³×C₄	—	67	1	no	—
953	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
954	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
955	C₄⋊Q₈	—	268	2	no	—
956	#126	—	268	2	no	—
957	#124	—	268	2	no	—
958	#123	—	268	2	no	—
959	#123	—	268	2	no	—
960	#123	—	268	2	no	—
961	C₂²⋊Q₈	—	2	4	no	—
962	C₂²⋊Q₈	—	268	2	no	—
963	C₂²⋊Q₈	—	268	2	no	—
964	C₂²⋊Q₈	—	268	2	no	—
965	C₂²⋊Q₈	—	268	2	no	—
966	C₂²⋊Q₈	—	268	2	no	—
967	#120	—	268	2	no	—
968	C₄×D₄	—	134	4	no	—
969	C₂×C₄⋊C₄	—	268	2	no	—
970	C₂×C₄⋊C₄	—	268	2	no	—
971	C₂×C₄⋊C₄	—	67	1	no	—
972	C₂×C₄⋊C₄	—	67	1	no	—
973	C₂×C₄⋊C₄	—	67	1	no	—
974	C₂×C₄⋊C₄	—	67	1	no	—
975	C₂×C₄⋊C₄	—	67	1	no	—
976	C₂×C₄⋊C₄	—	67	1	no	—
977	C₂×C₄⋊C₄	—	67	1	no	—
978	C₂×C₄⋊C₄	—	67	1	no	—
979	C₂×C₄⋊C₄	—	67	1	no	—
980	C₂×C₄⋊C₄	—	67	1	no	—
981	C₂×C₄⋊C₄	—	67	1	no	—
982	C₂×C₄⋊C₄	—	67	1	no	—
983	C₂×C₄⋊C₄	—	67	1	no	—
984	C₂×C₄⋊C₄	—	67	1	no	—
985	C₂×C₄⋊C₄	—	67	1	no	—
986	C₂×C₄⋊C₄	—	67	1	no	—
987	C₂×C₄⋊C₄	—	67	1	no	—
988	C₂×C₄⋊C₄	—	67	1	no	—
989	C₂×C₄⋊C₄	—	67	1	no	—
990	C₂×C₄⋊C₄	—	67	1	no	—
991	C₂×C₄⋊C₄	—	67	1	no	—
992	C₂×C₄⋊C₄	—	67	1	no	—
993	C₂×C₄⋊C₄	—	67	1	no	—
994	C₂×C₄⋊C₄	—	67	1	no	—
995	C₂×C₄⋊C₄	—	67	1	no	—
996	C₂×C₄⋊C₄	—	67	1	no	—
997	C₂×C₄⋊C₄	—	67	1	no	—
998	C₂×C₄⋊C₄	—	67	1	no	—
999	C₂×C₄⋊C₄	—	67	1	no	—
1000	C₂×C₄⋊C₄	—	67	1	no	—
1001	C₂×C₄⋊C₄	—	67	1	no	—
1002	C₂×C₄⋊C₄	—	67	1	no	—
1003	C₂×C₄⋊C₄	—	67	1	no	—
1004	C₂×C₄⋊C₄	—	67	1	no	—
1005	C₂×C₄⋊C₄	—	67	1	no	—
1006	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	—	2	4	no	—
1010	C₂×C₂²⋊C₄	—	268	2	no	—
1011	C₂×C₂²⋊C₄	—	67	1	no	—
1012	C₂×C₂²⋊C₄	—	67	1	no	—
1013	C₂×C₂²⋊C₄	—	67	1	no	—
1014	C₂×C₂²⋊C₄	—	67	1	no	—
1015	C₂×C₂²⋊C₄	—	67	1	no	—
1016	C₂×C₂²⋊C₄	—	67	1	no	—
1017	C₂×C₂²⋊C₄	—	67	1	no	—
1018	C₂×C₂²⋊C₄	—	67	1	no	—
1019	C₂×C₂²⋊C₄	—	67	1	no	—
1020	C₂×C₂²⋊C₄	—	67	1	no	—
1021	C₂×C₂²⋊C₄	—	67	1	no	—
1022	C₂×C₂²⋊C₄	—	67	1	no	—
1023	C₂×C₂²⋊C₄	—	67	1	no	—
1024	C₂×C₂²⋊C₄	—	67	1	no	—
1025	C₂×C₂²⋊C₄	—	67	1	no	—
1026	C₂×C₂²⋊C₄	—	67	1	no	—
1027	C₂×C₂²⋊C₄	—	67	1	no	—
1028	C₂×C₂²⋊C₄	—	67	1	no	—
1029	C₂×C₂²⋊C₄	—	67	1	no	—
1030	C₂×C₂²⋊C₄	—	67	1	no	—
1031	C₂×C₂²⋊C₄	—	67	1	no	—
1032	C₂×C₂²⋊C₄	—	67	1	no	—
1033	C₂×C₂²⋊C₄	—	67	1	no	—
1034	C₂×C₂²⋊C₄	—	67	1	no	—
1035	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1051	C₂×C₄²	—	67	1	no	—
1052	C₂×C₄²	—	67	1	no	—
1053	C₂×C₄²	—	67	1	no	—
1054	C₂×C₄²	—	67	1	no	—
1055	C₂×C₄²	—	67	1	no	—
1056	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1057	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1058	#95	—	67	1	no	—
1059	#95	—	67	1	no	—
1060	#95	—	67	1	no	—
1061	#95	—	67	1	no	—
1062	#95	—	67	1	no	—
1063	#95	—	67	1	no	—
1064	#95	—	67	1	no	—
1065	#95	—	67	1	no	—
1066	#95	—	67	1	no	—
1067	#95	—	67	1	no	—
1068	#95	—	67	1	no	—
1069	#95	—	67	1	no	—
1070	#95	—	67	1	no	—
1071	#95	—	67	1	no	—
1072	#95	—	67	1	no	—
1073	#95	—	67	1	no	—
1074	#95	—	67	1	no	—
1075	#95	—	67	1	no	—
1076	#95	—	67	1	no	—
1077	#95	—	67	1	no	—
1078	#95	—	67	1	no	—
1079	#95	—	67	1	no	—
1080	#95	—	67	1	no	—
1081	#95	—	67	1	no	—
1082	#95	—	67	1	no	—
1083	#95	—	67	1	no	—
1084	#95	—	67	1	no	—
1085	#95	—	67	1	no	—
1086	#95	—	67	1	no	—
1087	#95	—	67	1	no	—
1088	#95	—	67	1	no	—
1089	#95	—	67	1	no	—
1090	#95	—	67	1	no	—
1091	#95	—	67	1	no	—
1092	#95	—	67	1	no	—
1093	#95	—	67	1	no	—
1094	#95	—	67	1	no	—
1095	#95	—	67	1	no	—
1096	#95	—	67	1	no	—
1097	#95	—	67	1	no	—
1098	#95	—	67	1	no	—
1099	#95	—	67	1	no	—
1100	#95	C₂²×D₆₇	1	1	yes	characteristic
1101	#95	C₂²×D₆₇	1	1	yes	characteristic
1102	#95	C₂²×D₆₇	1	1	yes	characteristic
1103	#95	C₂²×D₆₇	1	1	yes	characteristic
1104	#95	C₂²×D₆₇	1	1	yes	characteristic
1105	#95	C₂²×D₆₇	1	1	yes	characteristic
1106	#95	C₂²×D₆₇	1	1	yes	characteristic
1107	#95	C₂²×D₆₇	1	1	yes	characteristic
1108	#95	C₂²×D₆₇	1	1	yes	characteristic
1109	#95	C₂²×D₆₇	1	1	yes	characteristic
1110	C₂⁴	—	2	2	no	—
1111	C₂⁴	—	2	2	no	—
1112	C₂⁴	—	2	2	no	—
1113	C₂⁴	—	2	2	no	—
1114	C₂⁴	—	2	2	no	—
1115	C₂⁴	—	4	1	no	—
1116	C₂⁴	—	4	1	no	—
1117	C₂⁴	—	67	1	no	—
1118	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1119	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1120	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1121	C₂×Q₈	—	2	2	no	—
1122	C₂×Q₈	—	4	1	no	—
1123	C₂×Q₈	—	4	1	no	—
1124	C₂×Q₈	—	268	1	no	—
1125	C₂×Q₈	—	268	1	no	—
1126	C₂×Q₈	—	268	1	no	—
1127	C₂×Q₈	—	268	1	no	—
1128	C₂×Q₈	—	268	1	no	—
1129	C₂×Q₈	—	134	2	no	—
1130	C₂×D₄	—	268	1	no	—
1131	C₂×D₄	—	268	1	no	—
1132	C₂×D₄	—	268	1	no	—
1133	C₂×D₄	—	268	1	no	—
1134	C₂×D₄	—	134	2	no	—
1135	C₂×D₄	—	134	2	no	—
1136	C₂×D₄	—	134	2	no	—
1137	C₂×D₄	—	134	2	no	—
1138	C₂×D₄	—	134	2	no	—
1139	C₂²×C₄	—	2	2	no	—
1140	C₂²×C₄	—	2	2	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	4	1	no	—
1143	C₂²×C₄	—	4	1	no	—
1144	C₂²×C₄	—	268	1	no	—
1145	C₂²×C₄	—	268	1	no	—
1146	C₂²×C₄	—	268	16	no	—
1147	C₂²×C₄	—	268	1	no	—
1148	C₂²×C₄	—	268	1	no	—
1149	C₂²×C₄	—	268	1	no	—
1150	C₂²×C₄	—	268	1	no	—
1151	C₂²×C₄	—	268	1	no	—
1152	C₂²×C₄	—	268	1	no	—
1153	C₂²×C₄	—	268	1	no	—
1154	C₂²×C₄	—	268	1	no	—
1155	C₂²×C₄	—	268	1	no	—
1156	C₂²×C₄	—	268	1	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	—	67	1	no	—
1163	C₂²×C₄	—	67	1	no	—
1164	C₂²×C₄	—	67	1	no	—
1165	C₂²×C₄	—	67	1	no	—
1166	C₂²×C₄	—	67	1	no	—
1167	C₂²×C₄	—	67	1	no	—
1168	C₂²×C₄	—	67	1	no	—
1169	C₂²×C₄	—	67	1	no	—
1170	C₂²×C₄	—	67	1	no	—
1171	C₂²×C₄	—	67	1	no	—
1172	C₂²×C₄	—	67	1	no	—
1173	C₂²×C₄	—	67	1	no	—
1174	C₂²×C₄	—	67	1	no	—
1175	C₂²×C₄	—	67	1	no	—
1176	C₂²×C₄	—	67	1	no	—
1177	C₂²×C₄	—	134	2	no	—
1178	C₂²×C₄	—	134	2	no	—
1179	C₂²×C₄	—	134	2	no	—
1180	C₂²×C₄	—	134	2	no	—
1181	C₂²×C₄	—	134	2	no	—
1182	C₂²×C₄	—	134	2	no	—
1183	C₂²×C₄	—	134	2	no	—
1184	C₂²×C₄	—	134	2	no	—
1185	C₂²×C₄	—	134	2	no	—
1186	C₂²×C₄	—	134	2	no	—
1187	C₂²×C₄	#11761627	1	4	yes	—
1188	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1189	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1190	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1191	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1192	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1193	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1194	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1195	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1196	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1197	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1198	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1199	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	2	no	—
1203	C₄⋊C₄	—	268	1	no	—
1204	C₄⋊C₄	—	268	1	no	—
1205	C₄⋊C₄	—	268	1	no	—
1206	C₄⋊C₄	—	268	1	no	—
1207	C₄⋊C₄	—	268	1	no	—
1208	C₄⋊C₄	—	268	1	no	—
1209	C₄⋊C₄	—	268	1	no	—
1210	C₄⋊C₄	—	268	1	no	—
1211	C₄⋊C₄	—	268	1	no	—
1212	C₄⋊C₄	—	268	1	no	—
1213	C₄⋊C₄	—	268	1	no	—
1214	C₄⋊C₄	—	268	1	no	—
1215	C₄⋊C₄	—	268	1	no	—
1216	C₄⋊C₄	—	268	1	no	—
1217	C₄⋊C₄	—	268	1	no	—
1218	C₄⋊C₄	—	268	1	no	—
1219	C₄⋊C₄	—	268	1	no	—
1220	C₄⋊C₄	—	268	1	no	—
1221	C₄⋊C₄	—	268	1	no	—
1222	C₄⋊C₄	—	268	1	no	—
1223	C₄⋊C₄	—	268	1	no	—
1224	C₄⋊C₄	—	268	1	no	—
1225	C₄⋊C₄	—	268	1	no	—
1226	C₄⋊C₄	—	268	1	no	—
1227	C₄⋊C₄	—	268	1	no	—
1228	C₄⋊C₄	—	268	1	no	—
1229	C₄⋊C₄	—	268	1	no	—
1230	C₄⋊C₄	—	268	1	no	—
1231	C₄⋊C₄	—	268	1	no	—
1232	C₄⋊C₄	—	268	1	no	—
1233	C₄⋊C₄	—	134	2	no	—
1234	C₄⋊C₄	—	134	2	no	—
1235	C₄⋊C₄	—	134	2	no	—
1236	C₄⋊C₄	—	134	2	no	—
1237	C₄⋊C₄	—	134	2	no	—
1238	C₂²⋊C₄	—	2	2	no	—
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	2	no	—
1245	C₂²⋊C₄	—	2	2	no	—
1246	C₂²⋊C₄	—	2	2	no	—
1247	C₂²⋊C₄	—	2	2	no	—
1248	C₂²⋊C₄	—	2	2	no	—
1249	C₂²⋊C₄	—	2	2	no	—
1250	C₂²⋊C₄	—	4	1	no	—
1251	C₂²⋊C₄	—	4	1	no	—
1252	C₂²⋊C₄	—	4	1	no	—
1253	C₂²⋊C₄	—	4	1	no	—
1254	C₂²⋊C₄	—	268	1	no	—
1255	C₂²⋊C₄	—	268	1	no	—
1256	C₂²⋊C₄	—	268	1	no	—
1257	C₂²⋊C₄	—	268	1	no	—
1258	C₂²⋊C₄	—	268	1	no	—
1259	C₂²⋊C₄	—	268	1	no	—
1260	C₂²⋊C₄	—	268	1	no	—
1261	C₂²⋊C₄	—	268	1	no	—
1262	C₂²⋊C₄	—	268	1	no	—
1263	C₂²⋊C₄	—	268	1	no	—
1264	C₂²⋊C₄	—	268	1	no	—
1265	C₂²⋊C₄	—	268	1	no	—
1266	C₂²⋊C₄	—	268	1	no	—
1267	C₂²⋊C₄	—	268	1	no	—
1268	C₂²⋊C₄	—	268	1	no	—
1269	C₂²⋊C₄	—	134	2	no	—
1270	C₂²⋊C₄	—	134	2	no	—
1271	C₂²⋊C₄	—	134	2	no	—
1272	C₂²⋊C₄	—	134	2	no	—
1273	C₂²⋊C₄	—	134	2	no	—
1274	C₂²⋊C₄	—	134	2	no	—
1275	C₂²⋊C₄	—	134	2	no	—
1276	C₂²⋊C₄	—	134	2	no	—
1277	C₂²⋊C₄	—	134	2	no	—
1278	C₄²	—	4	1	no	—
1279	C₄²	—	4	1	no	—
1280	C₄²	—	268	1	no	—
1281	C₄²	—	268	1	no	—
1282	C₄²	—	268	1	no	—
1283	C₄²	—	268	1	no	—
1284	C₄²	—	134	2	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	8	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	2	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	2	1	no	—
1301	C₂³	—	2	1	no	—
1302	C₂³	—	4	4	no	—
1303	C₂³	—	4	4	no	—
1304	C₂³	—	4	4	no	—
1305	C₂³	—	4	4	no	—
1306	C₂³	—	4	4	no	—
1307	C₂³	—	4	4	no	—
1308	C₂³	—	134	1	no	—
1309	C₂³	—	134	1	no	—
1310	C₂³	—	134	1	no	—
1311	C₂³	—	134	1	no	—
1312	C₂³	—	134	1	no	—
1313	C₂³	—	134	1	no	—
1314	C₂³	—	134	1	no	—
1315	C₂³	C₂×#11761627	1	2	yes	—
1316	C₂³	#14524089	1	2	yes	—
1317	C₂³	#14524089	1	2	yes	—
1318	C₂³	#14524090	1	2	yes	—
1319	C₂³	#14524090	1	2	yes	—
1320	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1321	Q₈	—	8	2	no	—
1322	Q₈	—	536	2	no	—
1323	Q₈	—	536	2	no	—
1324	D₄	—	268	4	no	—
1325	D₄	—	536	2	no	—
1326	D₄	—	536	2	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	4	4	no	—
1362	C₂×C₄	—	4	4	no	—
1363	C₂×C₄	—	268	4	no	—
1364	C₂×C₄	—	268	4	no	—
1365	C₂×C₄	—	268	4	no	—
1366	C₂×C₄	—	268	4	no	—
1367	C₂×C₄	—	268	4	no	—
1368	C₂×C₄	—	268	4	no	—
1369	C₂×C₄	—	536	2	no	—
1370	C₂×C₄	—	536	2	no	—
1371	C₂×C₄	—	536	2	no	—
1372	C₂×C₄	—	67	2	no	—
1373	C₂×C₄	—	134	1	no	—
1374	C₂×C₄	—	134	1	no	—
1375	C₂×C₄	—	134	1	no	—
1376	C₂×C₄	—	134	1	no	—
1377	C₂×C₄	—	134	1	no	—
1378	C₂×C₄	—	134	1	no	—
1379	C₂×C₄	—	134	1	no	—
1380	C₂×C₄	—	134	1	no	—
1381	C₂×C₄	—	134	1	no	—
1382	C₂×C₄	—	134	1	no	—
1383	C₂×C₄	—	134	1	no	—
1384	C₂×C₄	—	134	1	no	—
1385	C₂×C₄	—	134	1	no	—
1386	C₂×C₄	—	134	1	no	—
1387	C₂×C₄	—	134	1	no	—
1388	C₂×C₄	—	134	1	no	—
1389	C₂×C₄	—	134	1	no	—
1390	C₂×C₄	—	134	1	no	—
1391	C₂×C₄	—	134	1	no	—
1392	C₂×C₄	—	134	1	no	—
1393	C₂×C₄	—	134	1	no	—
1394	C₂×C₄	—	134	1	no	—
1395	C₂×C₄	—	134	1	no	—
1396	C₂×C₄	—	134	1	no	—
1397	C₂×C₄	—	134	1	no	—
1398	C₂×C₄	—	134	1	no	—
1399	C₂×C₄	—	134	1	no	—
1400	C₂×C₄	—	134	1	no	—
1401	C₂×C₄	—	134	1	no	—
1402	C₂×C₄	—	134	1	no	—
1403	C₂×C₄	—	134	1	no	—
1404	C₂×C₄	—	134	1	no	—
1405	C₂×C₄	—	134	1	no	—
1406	C₂×C₄	—	134	1	no	—
1407	C₂×C₄	—	134	1	no	—
1408	C₂×C₄	—	134	1	no	—
1409	C₂×C₄	—	134	1	no	—
1410	C₂×C₄	—	134	1	no	—
1411	C₂×C₄	—	134	1	no	—
1412	C₂×C₄	—	134	1	no	—
1413	C₂×C₄	—	134	1	no	—
1414	C₂×C₄	—	134	1	no	—
1415	C₂×C₄	—	134	1	no	—
1416	C₂×C₄	—	134	1	no	—
1417	C₂×C₄	C₂×#11761627	1	2	yes	—
1418	C₂×C₄	C₂×#11761627	1	2	yes	—
1419	C₂²	—	2	2	no	—
1420	C₂²	—	2	2	no	—
1421	C₂²	—	2	2	no	—
1422	C₂²	—	2	2	no	—
1423	C₂²	—	2	2	no	—
1424	C₂²	—	2	2	no	—
1425	C₂²	—	2	2	no	—
1426	C₂²	—	2	2	no	—
1427	C₂²	—	2	2	no	—
1428	C₂²	—	2	2	no	—
1429	C₂²	—	2	2	no	—
1430	C₂²	—	2	2	no	—
1431	C₂²	—	4	16	no	—
1432	C₂²	—	4	1	no	—
1433	C₂²	—	4	1	no	—
1434	C₂²	—	4	1	no	—
1435	C₂²	—	4	1	no	—
1436	C₂²	—	4	1	no	—
1437	C₂²	—	4	1	no	—
1438	C₂²	—	4	1	no	—
1439	C₂²	—	4	1	no	—
1440	C₂²	—	268	1	no	—
1441	C₂²	—	268	1	no	—
1442	C₂²	—	268	1	no	—
1443	C₂²	—	268	1	no	—
1444	C₂²	—	268	1	no	—
1445	C₂²	—	268	1	no	—
1446	C₂²	—	268	1	no	—
1447	C₂²	#16864015	1	4	yes	—
1448	C₂²	C₂²×#11761627	1	1	yes	characteristic
1449	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1450	C₂²	C₂×#14524089	1	1	yes	characteristic
1451	C₂²	C₂×#14524089	1	1	yes	characteristic
1452	C₂²	C₂×#14524090	1	1	yes	characteristic
1453	C₂²	C₂×#14524090	1	1	yes	characteristic
1454	C₂²	#16864231	1	1	yes	characteristic
1455	C₄	—	2	2	no	—
1456	C₄	—	2	2	no	—
1457	C₄	—	4	1	no	—
1458	C₄	—	4	1	no	—
1459	C₄	—	4	1	no	—
1460	C₄	—	4	1	no	—
1461	C₄	—	4	1	no	—
1462	C₄	—	4	1	no	—
1463	C₄	—	4	1	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	4	1	no	—
1467	C₄	—	268	1	no	—
1468	C₄	—	268	1	no	—
1469	C₄	—	268	1	no	—
1470	C₄	—	268	1	no	—
1471	C₄	—	268	1	no	—
1472	C₄	—	268	1	no	—
1473	C₄	—	268	1	no	—
1474	C₄	—	268	1	no	—
1475	C₄	—	268	1	no	—
1476	C₄	—	268	1	no	—
1477	C₄	—	268	1	no	—
1478	C₄	—	268	1	no	—
1479	C₄	—	268	1	no	—
1480	C₄	—	268	1	no	—
1481	C₄	—	134	2	no	—
1482	C₂	—	2	4	no	—
1483	C₂	—	4	2	no	—
1484	C₂	—	4	2	no	—
1485	C₂	—	536	1	no	—
1486	C₂	C₂×#16864015	1	1	yes	characteristic
1487	C₂	#22573915	1	1	yes	characteristic
1488	C₂	#22574046	1	1	yes	characteristic
1489	C₂	#22574365	1	1	yes	characteristic
1490	C₂	#22574414	1	1	yes	characteristic
1491	C₂	#22574414	1	1	yes	characteristic
1492	C₂	#22574449	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2561	C₂
prime radical	C₂×#14524012	C₂²
hypercenter	#2561	D₆₇
hypocenter	C₆₇	#36778
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2561

Complements

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

N	H ≅ G/N	type
2. #22568494	C₂	semidirect
3. #22567979	C₂	semidirect
4. #22567843	C₂	semidirect
5. #22567715	C₂	semidirect
6. #22567638	C₂	semidirect
7. #22567635	C₂	semidirect
8. #22567626	C₂	semidirect
9. #22567541	C₂	semidirect
10. #22567400	C₂	semidirect
11. #22567288	C₂	semidirect
12. #22567192	C₂	semidirect
13. #22567057	C₂	semidirect
14. #22567050	C₂	semidirect
15. #22566785	C₂	semidirect
16. #22566704	C₂	semidirect
17. #22566629	C₂	semidirect
18. #22566488	C₂	semidirect
19. #22566026	C₂	semidirect
20. #22565992	C₂	semidirect
22. #22564598	C₂	semidirect
23. #22564531	C₂	semidirect
24. #22564452	C₂	semidirect
26. #22563911	C₂	semidirect
27. #22563661	C₂	semidirect
28. #22562944	C₂	semidirect
29. #22562836	C₂	semidirect
30. C₂×#16863271	C₂	semidirect
31. C₆₇×#2561	C₂	semidirect
33. C₂×#14524043	C₂²	semidirect
43. C₂×#14524019	C₂²	semidirect
49. C₆₇⋊#401	C₂²	semidirect
50. #16863338	C₂²	semidirect
51. #16863338	C₂²	semidirect
52. #16863338	C₂²	semidirect
53. #16863338	C₂²	semidirect
54. #16863337	C₂²	semidirect
55. #16863337	C₂²	semidirect
56. #16863336	C₂²	semidirect
57. #16863336	C₂²	semidirect
58. #16863336	C₂²	semidirect
59. #16863333	C₂²	semidirect
60. #16863333	C₂²	semidirect
61. #16863330	C₂²	semidirect
62. #16863330	C₂²	semidirect
63. #16863329	C₂²	semidirect
64. #16863329	C₂²	semidirect
65. #16863328	C₂²	semidirect
66. #16863328	C₂²	semidirect
67. #16863328	C₂²	semidirect
68. #16863328	C₂²	semidirect
69. #16863328	C₂²	semidirect
70. #16863328	C₂²	semidirect
71. #16863325	C₂²	semidirect
75. #16863323	C₂²	semidirect
76. #16863323	C₂²	semidirect
81. #16863318	C₂²	semidirect
82. #16863318	C₂²	semidirect
83. #16863317	C₂²	semidirect
84. #16863317	C₂²	semidirect
85. #16863317	C₂²	semidirect
86. #16863317	C₂²	semidirect
91. #16863309	C₂²	semidirect
93. #16863303	C₂²	semidirect
94. #16863303	C₂²	semidirect
95. #16863303	C₂²	semidirect
96. #16863300	C₂²	semidirect
98. #16863295	C₂²	semidirect
99. #16863295	C₂²	semidirect
100. #16863294	C₂²	semidirect
101. #16863294	C₂²	semidirect
102. #16863292	C₂²	semidirect
106. #16863288	C₂²	semidirect
107. #16863287	C₂²	semidirect
108. #16863287	C₂²	semidirect
109. #16863285	C₂²	semidirect
114. #16863283	C₂²	semidirect
115. #16863282	C₂²	semidirect
116. #16863282	C₂²	semidirect
117. #16863282	C₂²	semidirect
118. #16863282	C₂²	semidirect
119. #16863281	C₂²	semidirect
120. #16863280	C₂²	semidirect
121. #16863280	C₂²	semidirect
122. #16863278	C₂²	semidirect
151. #16863266	C₂²	semidirect
152. #16863263	C₂²	semidirect
153. #16863263	C₂²	semidirect
154. #16863260	C₂²	semidirect
155. #16863260	C₂²	semidirect
157. #16863258	C₂²	semidirect
161. #16863255	C₂²	semidirect
166. #16863253	C₂²	semidirect
767. #2561	D₆₇	semidirect
778. C₆₇	#36778	semidirect

Maximal subgroups

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

subgroup	index
#22568503	2
#22568494	2
#22567979	2
#22567843	2
#22567715	2
#22567638	2
#22567635	2
#22567626	2
#22567541	2
#22567400	2
#22567288	2
#22567192	2
#22567057	2
#22567050	2
#22566785	2
#22566704	2
#22566629	2
#22566488	2
#22566026	2
#22565992	2
#22565099	2
#22564598	2
#22564531	2
#22564452	2
#22564332	2
#22563911	2
#22563661	2
#22562944	2
#22562836	2
C₂×#16863271	2
C₆₇×#2561	2
#36778	67