Subgroups — #31025615

Order 17152.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22565062	C₂	1	1	yes	maximal, characteristic, complemented
2	#22565039	C₂	1	1	yes	maximal, characteristic, complemented
3	#22565000	C₂	1	1	yes	maximal, characteristic, complemented
4	#22564977	C₂	1	1	yes	maximal, characteristic, complemented
5	#22564929	C₂	1	1	yes	maximal, characteristic, complemented
6	#22564906	C₂	1	1	yes	maximal, characteristic, complemented
7	#22564843	C₂	1	1	yes	maximal, characteristic, complemented
8	#22564776	C₂	1	1	yes	maximal, characteristic, complemented
9	#22564709	C₂	1	1	yes	maximal, characteristic, complemented
10	#22564648	C₂	1	1	yes	maximal, characteristic, complemented
11	#22564478	C₂	1	1	yes	maximal, characteristic, complemented
12	#22564459	C₂	1	1	yes	maximal, characteristic, complemented
13	#22564339	C₂	1	1	yes	maximal, characteristic
14	#22563880	C₂	1	1	yes	maximal, characteristic, complemented
15	#22563589	C₂	1	1	yes	maximal, characteristic
16	#22563508	C₂	1	1	yes	maximal, characteristic, complemented
17	#22563484	C₂	1	1	yes	maximal, characteristic, complemented
18	#22563473	C₂	1	1	yes	maximal, characteristic, complemented
19	#22563467	C₂	1	1	yes	maximal, characteristic, complemented
20	#22562757	C₂	1	1	yes	maximal, characteristic, complemented
21	#22562748	C₂	1	1	yes	maximal, characteristic, complemented
22	#22562743	C₂	1	1	yes	maximal, characteristic, complemented
23	#22562730	C₂	1	1	yes	maximal, characteristic, complemented
24	#22562710	C₂	1	1	yes	maximal, characteristic
25	#22562703	C₂	1	1	yes	maximal, characteristic, complemented
26	#22562669	C₂	1	1	yes	maximal, characteristic, complemented
27	#22562647	C₂	1	1	yes	maximal, characteristic, complemented
28	#22562589	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#14524001	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂²⋊C₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2515	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic
33	C₂×#14524037	C₂²	1	1	yes	characteristic
34	C₂×#14524031	C₂²	1	1	yes	characteristic
35	C₂×#14524028	C₂²	1	1	yes	characteristic
36	C₂×#14524021	C₂²	1	1	yes	characteristic
37	C₂×#14524013	C₂²	1	1	yes	characteristic
38	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14524005	C₂²	1	1	yes	characteristic
40	C₂×#14524005	C₂²	1	1	yes	characteristic
41	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×#14524001	C₂²	1	1	yes	characteristic
43	C₂×#14524001	C₂²	1	1	yes	characteristic
44	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
45	C₂×#14523999	C₂²	1	1	yes	characteristic
46	C₂×#14523999	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
51	C₆₇⋊#401	C₂²	1	1	yes	characteristic, complemented
52	#16863338	C₂²	1	1	yes	characteristic, complemented
53	#16863337	C₂²	1	1	yes	characteristic, complemented
54	#16863337	C₂²	1	1	yes	characteristic, complemented
55	#16863336	C₂²	1	1	yes	characteristic, complemented
56	#16863335	C₂²	1	1	yes	characteristic, complemented
57	#16863333	C₂²	1	1	yes	characteristic
58	#16863332	C₂²	1	1	yes	characteristic
59	#16863331	C₂²	1	1	yes	characteristic, complemented
60	#16863330	C₂²	1	1	yes	characteristic, complemented
61	#16863329	C₂²	1	1	yes	characteristic, complemented
62	#16863326	C₂²	1	1	yes	characteristic, complemented
63	#16863325	C₂²	1	1	yes	characteristic
64	#16863325	C₂²	1	1	yes	characteristic, complemented
65	#16863324	C₂²	1	1	yes	characteristic
66	#16863323	C₂²	1	1	yes	characteristic
67	#16863323	C₂²	1	1	yes	characteristic, complemented
68	#16863323	C₂²	1	1	yes	characteristic, complemented
69	#16863322	C₂²	1	1	yes	characteristic
70	#16863322	C₂²	1	1	yes	characteristic
71	#16863319	C₂²	1	1	yes	characteristic
72	#16863318	C₂²	1	1	yes	characteristic
73	#16863316	C₂²	1	1	yes	characteristic, complemented
74	#16863313	C₂²	1	1	yes	characteristic
75	#16863313	C₂²	1	1	yes	characteristic
76	#16863312	C₂²	1	1	yes	characteristic
77	#16863311	C₂²	1	1	yes	characteristic
78	#16863308	C₂²	1	1	yes	characteristic
79	#16863301	C₂²	1	1	yes	characteristic, complemented
80	#16863300	C₂²	1	1	yes	characteristic, complemented
81	#16863297	C₂²	1	1	yes	characteristic
82	#16863296	C₂²	1	1	yes	characteristic
83	#16863296	C₂²	1	1	yes	characteristic
84	#16863293	C₂²	1	1	yes	characteristic, complemented
85	#16863293	C₂²	1	1	yes	characteristic, complemented
86	#16863291	C₂²	1	1	yes	characteristic, complemented
87	#16863290	C₂²	1	1	yes	characteristic
88	#16863289	C₂²	1	1	yes	characteristic
89	#16863289	C₂²	1	1	yes	characteristic
90	#16863288	C₂²	1	1	yes	characteristic, complemented
91	#16863287	C₂²	1	1	yes	characteristic, complemented
92	#16863287	C₂²	1	1	yes	characteristic, complemented
93	#16863287	C₂²	1	1	yes	characteristic, complemented
94	#16863285	C₂²	1	1	yes	characteristic
95	#16863285	C₂²	1	1	yes	characteristic
96	#16863285	C₂²	1	1	yes	characteristic
97	#16863285	C₂²	1	1	yes	characteristic
98	#16863285	C₂²	1	1	yes	characteristic
99	#16863285	C₂²	1	1	yes	characteristic, complemented
100	#16863285	C₂²	1	1	yes	characteristic, complemented
101	#16863285	C₂²	1	1	yes	characteristic, complemented
102	#16863285	C₂²	1	1	yes	characteristic, complemented
103	#16863284	C₂²	1	1	yes	characteristic
104	#16863283	C₂²	1	1	yes	characteristic, complemented
105	#16863282	C₂²	1	1	yes	characteristic, complemented
106	#16863280	C₂²	1	1	yes	characteristic, complemented
107	#16863280	C₂²	1	1	yes	characteristic, complemented
108	#16863278	C₂²	1	1	yes	characteristic, complemented
109	#16863278	C₂²	1	1	yes	characteristic, complemented
110	#16863278	C₂²	1	1	yes	characteristic, complemented
111	#16863278	C₂²	1	1	yes	characteristic, complemented
112	#16863277	C₂²	1	1	yes	characteristic, complemented
113	#16863277	C₂²	1	1	yes	characteristic, complemented
114	#16863275	C₂²	1	1	yes	characteristic
115	#16863274	C₂²	1	1	yes	characteristic
116	#16863274	C₂²	1	1	yes	characteristic
117	#16863274	C₂²	1	1	yes	characteristic
118	#16863274	C₂²	1	1	yes	characteristic
119	#16863274	C₂²	1	1	yes	characteristic
120	#16863270	C₂²	1	1	yes	characteristic
121	#16863270	C₂²	1	1	yes	characteristic
122	#16863270	C₂²	1	1	yes	characteristic
123	#16863267	C₂²	1	1	yes	characteristic
124	#16863267	C₂²	1	1	yes	characteristic
125	#16863267	C₂²	1	1	yes	characteristic
126	#16863267	C₂²	1	1	yes	characteristic
127	#16863259	C₂²	1	1	yes	characteristic
128	#16863258	C₂²	1	1	yes	characteristic
129	#16863255	C₂²	1	1	yes	characteristic
130	#16863255	C₂²	1	1	yes	characteristic
131	#16863255	C₂²	1	1	yes	characteristic
132	#16863255	C₂²	1	1	yes	characteristic
133	#16863255	C₂²	1	1	yes	characteristic
134	#16863251	C₂²	1	1	yes	characteristic
135	#16863251	C₂²	1	1	yes	characteristic
136	#16863251	C₂²	1	1	yes	characteristic
137	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
140	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
141	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
142	#16863247	C₂²	1	1	yes	characteristic, complemented
143	#16863247	C₂²	1	1	yes	characteristic, complemented
144	#16863247	C₂²	1	1	yes	characteristic, complemented
145	#16863247	C₂²	1	1	yes	characteristic, complemented
146	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
147	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
148	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
149	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
150	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
151	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
152	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
153	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
154	#16863243	C₂²	1	1	yes	characteristic
155	#16863243	C₂²	1	1	yes	characteristic
156	#16863243	C₂²	1	1	yes	characteristic
157	#16863243	C₂²	1	1	yes	characteristic
158	#16863243	C₂²	1	1	yes	characteristic
159	#16863243	C₂²	1	1	yes	characteristic
160	#16863243	C₂²	1	1	yes	characteristic
161	#16863243	C₂²	1	1	yes	characteristic
162	#16863243	C₂²	1	1	yes	characteristic, complemented
163	#16863243	C₂²	1	1	yes	characteristic, complemented
164	#16863243	C₂²	1	1	yes	characteristic, complemented
165	#16863241	C₂²	1	1	yes	characteristic, complemented
166	#16863241	C₂²	1	1	yes	characteristic, complemented
167	#16863241	C₂²	1	1	yes	characteristic, complemented
168	#95×D₆₇	C₂²	1	1	yes	characteristic
169	#95×D₆₇	C₂²	1	1	yes	characteristic
170	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
171	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
172	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
173	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
174	#397×C₆₇	C₂²	1	1	yes	characteristic
175	#396×C₆₇	C₂²	1	1	yes	characteristic
176	#388×C₆₇	C₂²	1	1	yes	characteristic
177	#388×C₆₇	C₂²	1	1	yes	characteristic
178	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
179	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
181	#385×C₆₇	C₂²	1	1	yes	characteristic
182	#383×C₆₇	C₂²	1	1	yes	characteristic, complemented
183	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
184	#381×C₆₇	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
187	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
189	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
190	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
191	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
192	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₆₇	—	2	4	no	—
194	C₂²×C₄×D₆₇	—	2	4	no	—
195	C₂²×C₄×D₆₇	—	4	2	no	—
196	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
202	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
205	#14524037	—	2	4	no	—
206	#14524031	—	2	4	no	—
207	#14524028	—	2	4	no	—
208	#14524021	—	2	4	no	—
209	#14524013	—	2	4	no	—
210	#14524008	—	4	2	no	—
211	#14524005	—	2	4	no	—
212	#14524005	—	4	2	no	—
213	(C₂²⋊D₆₇)⋊C₄	—	2	4	no	—
214	#14524001	—	2	4	no	—
215	#14524001	—	2	4	no	—
216	#14524001	—	4	2	no	—
217	#14523999	—	2	4	no	—
218	#14523999	—	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×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
244	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×(C₂×D₆₇)⋊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	C₂²⋊C₄×D₆₇	—	2	4	no	—
274	C₂²⋊C₄×D₆₇	—	2	4	no	—
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	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
294	C₄²×D₆₇	—	2	4	no	—
295	C₄²×D₆₇	—	4	2	no	—
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	C₆₇⋊#95	C₂³	1	1	yes	characteristic
327	C₆₇⋊#95	C₂³	1	1	yes	characteristic
328	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
347	#95×C₆₇	C₂³	1	1	yes	characteristic
348	#95×C₆₇	C₂³	1	1	yes	characteristic
349	#95×C₆₇	C₂³	1	1	yes	characteristic
350	#95×C₆₇	C₂³	1	1	yes	characteristic
351	#95×C₆₇	C₂³	1	1	yes	characteristic
352	#95×C₆₇	C₂³	1	1	yes	characteristic
353	#95×C₆₇	C₂³	1	1	yes	characteristic
354	#95×C₆₇	C₂³	1	1	yes	characteristic
355	#95×C₆₇	C₂³	1	1	yes	characteristic
356	#95×C₆₇	C₂³	1	1	yes	characteristic
357	#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	—	2	2	no	—
364	C₂³×D₆₇	—	2	2	no	—
365	C₂³×D₆₇	—	2	2	no	—
366	C₂³×D₆₇	—	2	2	no	—
367	C₂³×D₆₇	—	2	2	no	—
368	C₂³×D₆₇	—	4	1	no	—
369	C₂³×D₆₇	—	4	1	no	—
370	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
371	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
372	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×Dic₁₃₄	—	2	2	no	—
374	C₂×Dic₁₃₄	—	2	2	no	—
375	C₂×Dic₁₃₄	—	4	1	no	—
376	C₂×D₂₆₈	—	2	2	no	—
377	C₂×D₂₆₈	—	2	2	no	—
378	C₂×D₂₆₈	—	2	2	no	—
379	C₂×D₂₆₈	—	2	2	no	—
380	C₂×D₂₆₈	—	2	2	no	—
381	C₂×D₂₆₈	—	4	1	no	—
382	C₂×C₂²⋊D₆₇	—	2	2	no	—
383	C₂×C₂²⋊D₆₇	—	2	2	no	—
384	C₂×C₂²⋊D₆₇	—	4	1	no	—
385	C₂²×Dic₆₇	—	2	2	no	—
386	C₂²×Dic₆₇	—	2	2	no	—
387	C₂²×Dic₆₇	#41	1	4	yes	—
388	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×D₆₇	—	2	2	no	—
402	C₂×C₄×D₆₇	—	2	2	no	—
403	C₂×C₄×D₆₇	—	2	2	no	—
404	C₂×C₄×D₆₇	—	2	2	no	—
405	C₂×C₄×D₆₇	—	2	2	no	—
406	C₂×C₄×D₆₇	—	2	2	no	—
407	C₂×C₄×D₆₇	—	2	2	no	—
408	C₂×C₄×D₆₇	—	2	2	no	—
409	C₂×C₄×D₆₇	—	2	2	no	—
410	C₂×C₄×D₆₇	—	2	2	no	—
411	C₂×C₄×D₆₇	—	2	2	no	—
412	C₂×C₄×D₆₇	—	2	2	no	—
413	C₂×C₄×D₆₇	—	2	2	no	—
414	C₂×C₄×D₆₇	—	2	2	no	—
415	C₂×C₄×D₆₇	—	2	2	no	—
416	C₂×C₄×D₆₇	—	2	2	no	—
417	C₂×C₄×D₆₇	—	2	2	no	—
418	C₂×C₄×D₆₇	—	2	2	no	—
419	C₂×C₄×D₆₇	—	2	2	no	—
420	C₂×C₄×D₆₇	—	4	16	no	—
421	C₂×C₄×D₆₇	—	4	1	no	—
422	C₂×C₄×D₆₇	—	4	1	no	—
423	C₂×C₄×D₆₇	—	4	1	no	—
424	C₂×C₄×D₆₇	—	4	1	no	—
425	C₂×C₄×D₆₇	—	4	1	no	—
426	C₂×C₄×D₆₇	—	4	1	no	—
427	C₂×C₄×D₆₇	#41	1	4	yes	—
428	C₂×C₄×D₆₇	#41	1	4	yes	—
429	C₄⋊Dic₆₇	—	2	2	no	—
430	C₄⋊Dic₆₇	—	2	2	no	—
431	C₄⋊Dic₆₇	—	4	1	no	—
432	C₄⋊Dic₆₇	—	4	1	no	—
433	C₄⋊Dic₆₇	—	4	1	no	—
434	Dic₆₇⋊C₄	—	2	2	no	—
435	Dic₆₇⋊C₄	—	2	2	no	—
436	Dic₆₇⋊C₄	—	2	2	no	—
437	Dic₆₇⋊C₄	—	2	2	no	—
438	Dic₆₇⋊C₄	—	2	2	no	—
439	Dic₆₇⋊C₄	—	2	2	no	—
440	Dic₆₇⋊C₄	—	2	2	no	—
441	Dic₆₇⋊C₄	—	2	2	no	—
442	Dic₆₇⋊C₄	—	2	2	no	—
443	Dic₆₇⋊C₄	—	4	1	no	—
444	Dic₆₇⋊C₄	—	4	1	no	—
445	Dic₆₇⋊C₄	—	4	1	no	—
446	Dic₆₇⋊C₄	—	4	1	no	—
447	Dic₆₇⋊C₄	—	4	1	no	—
448	Dic₆₇⋊C₄	—	4	1	no	—
449	C₂²⋊Dic₆₇	—	2	2	no	—
450	C₂²⋊Dic₆₇	—	2	2	no	—
451	C₂²⋊Dic₆₇	—	2	2	no	—
452	C₂²⋊Dic₆₇	—	4	1	no	—
453	C₂²⋊Dic₆₇	—	4	1	no	—
454	(C₂×D₆₇)⋊C₄	—	2	2	no	—
455	(C₂×D₆₇)⋊C₄	—	2	2	no	—
456	(C₂×D₆₇)⋊C₄	—	2	2	no	—
457	(C₂×D₆₇)⋊C₄	—	2	2	no	—
458	(C₂×D₆₇)⋊C₄	—	2	2	no	—
459	(C₂×D₆₇)⋊C₄	—	2	2	no	—
460	(C₂×D₆₇)⋊C₄	—	2	2	no	—
461	(C₂×D₆₇)⋊C₄	—	2	2	no	—
462	(C₂×D₆₇)⋊C₄	—	2	2	no	—
463	(C₂×D₆₇)⋊C₄	—	2	2	no	—
464	(C₂×D₆₇)⋊C₄	—	2	2	no	—
465	(C₂×D₆₇)⋊C₄	—	2	2	no	—
466	(C₂×D₆₇)⋊C₄	—	2	2	no	—
467	(C₂×D₆₇)⋊C₄	—	2	2	no	—
468	(C₂×D₆₇)⋊C₄	—	2	2	no	—
469	(C₂×D₆₇)⋊C₄	—	2	2	no	—
470	(C₂×D₆₇)⋊C₄	—	2	2	no	—
471	(C₂×D₆₇)⋊C₄	—	2	2	no	—
472	(C₂×D₆₇)⋊C₄	—	2	2	no	—
473	(C₂×D₆₇)⋊C₄	—	4	1	no	—
474	(C₂×D₆₇)⋊C₄	—	4	1	no	—
475	(C₂×D₆₇)⋊C₄	—	4	1	no	—
476	(C₂×D₆₇)⋊C₄	—	4	1	no	—
477	(C₂×D₆₇)⋊C₄	—	4	1	no	—
478	(C₂×D₆₇)⋊C₄	—	4	1	no	—
479	(C₂×D₆₇)⋊C₄	—	4	1	no	—
480	(C₂×D₆₇)⋊C₄	—	4	1	no	—
481	(C₂×D₆₇)⋊C₄	#41	1	4	yes	—
482	(C₂×D₆₇)⋊C₄	#41	1	4	yes	—
483	C₄×Dic₆₇	—	2	2	no	—
484	C₄×Dic₆₇	—	2	2	no	—
485	C₄×Dic₆₇	—	2	2	no	—
486	C₄×Dic₆₇	—	2	2	no	—
487	C₄×Dic₆₇	—	2	2	no	—
488	C₄×Dic₆₇	—	2	2	no	—
489	C₄×Dic₆₇	—	2	2	no	—
490	C₄×Dic₆₇	—	2	2	no	—
491	C₄×Dic₆₇	—	2	2	no	—
492	C₄×Dic₆₇	—	2	2	no	—
493	C₄×Dic₆₇	—	2	2	no	—
494	C₄×Dic₆₇	—	2	2	no	—
495	C₄×Dic₆₇	—	2	2	no	—
496	C₄×Dic₆₇	—	2	2	no	—
497	C₄×Dic₆₇	—	2	2	no	—
498	C₄×Dic₆₇	—	2	2	no	—
499	C₄×Dic₆₇	—	4	1	no	—
500	C₄×Dic₆₇	—	4	1	no	—
501	C₄×Dic₆₇	—	4	1	no	—
502	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₆₇	—	2	2	no	—
504	C₂²×C₄×C₆₇	—	2	2	no	—
505	C₂²×C₄×C₆₇	—	4	1	no	—
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	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
520	C₄⋊C₄×C₆₇	—	2	2	no	—
521	C₄⋊C₄×C₆₇	—	2	2	no	—
522	C₄⋊C₄×C₆₇	—	2	2	no	—
523	C₄⋊C₄×C₆₇	—	2	2	no	—
524	C₄⋊C₄×C₆₇	—	2	2	no	—
525	C₄⋊C₄×C₆₇	—	4	1	no	—
526	C₄⋊C₄×C₆₇	—	4	1	no	—
527	C₄⋊C₄×C₆₇	—	4	1	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	—	2	2	no	—
533	C₂²⋊C₄×C₆₇	—	4	1	no	—
534	C₄²×C₆₇	—	2	2	no	—
535	C₄²×C₆₇	—	2	2	no	—
536	C₄²×C₆₇	—	2	2	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	1	no	—
543	C₂³×C₆₇	—	2	1	no	—
544	C₂³×C₆₇	C₂×#41	1	2	yes	—
545	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
546	C₂²×D₆₇	—	2	1	no	—
547	C₂²×D₆₇	—	2	1	no	—
548	C₂²×D₆₇	—	2	1	no	—
549	C₂²×D₆₇	—	2	1	no	—
550	C₂²×D₆₇	—	2	8	no	—
551	C₂²×D₆₇	—	2	1	no	—
552	C₂²×D₆₇	—	2	1	no	—
553	C₂²×D₆₇	—	2	1	no	—
554	C₂²×D₆₇	—	2	1	no	—
555	C₂²×D₆₇	—	2	1	no	—
556	C₂²×D₆₇	—	2	1	no	—
557	C₂²×D₆₇	—	2	1	no	—
558	C₂²×D₆₇	—	2	1	no	—
559	C₂²×D₆₇	—	2	1	no	—
560	C₂²×D₆₇	—	2	1	no	—
561	C₂²×D₆₇	—	2	1	no	—
562	C₂²×D₆₇	—	2	1	no	—
563	C₂²×D₆₇	—	2	1	no	—
564	C₂²×D₆₇	—	4	4	no	—
565	C₂²×D₆₇	—	4	4	no	—
566	C₂²×D₆₇	—	4	4	no	—
567	C₂²×D₆₇	—	4	4	no	—
568	C₂²×D₆₇	—	4	4	no	—
569	C₂²×D₆₇	—	4	4	no	—
570	C₂²×D₆₇	C₂×#41	1	2	yes	—
571	C₂²×D₆₇	C₂×#41	1	2	yes	—
572	C₂²×D₆₇	C₂×#41	1	2	yes	—
573	C₂²×D₆₇	C₂×#41	1	2	yes	—
574	C₂×C₄×C₆₇	—	2	1	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	2	1	no	—
577	C₂×C₄×C₆₇	—	2	1	no	—
578	C₂×C₄×C₆₇	—	2	1	no	—
579	C₂×C₄×C₆₇	—	2	1	no	—
580	C₂×C₄×C₆₇	—	2	1	no	—
581	C₂×C₄×C₆₇	—	2	1	no	—
582	C₂×C₄×C₆₇	—	2	1	no	—
583	C₂×C₄×C₆₇	—	2	1	no	—
584	C₂×C₄×C₆₇	—	2	1	no	—
585	C₂×C₄×C₆₇	—	2	1	no	—
586	C₂×C₄×C₆₇	—	2	1	no	—
587	C₂×C₄×C₆₇	—	2	1	no	—
588	C₂×C₄×C₆₇	—	2	1	no	—
589	C₂×C₄×C₆₇	—	2	1	no	—
590	C₂×C₄×C₆₇	—	2	1	no	—
591	C₂×C₄×C₆₇	—	2	1	no	—
592	C₂×C₄×C₆₇	—	2	1	no	—
593	C₂×C₄×C₆₇	—	2	1	no	—
594	C₂×C₄×C₆₇	—	2	1	no	—
595	C₂×C₄×C₆₇	—	2	1	no	—
596	C₂×C₄×C₆₇	—	2	1	no	—
597	C₂×C₄×C₆₇	—	2	1	no	—
598	C₂×C₄×C₆₇	—	2	1	no	—
599	C₂×C₄×C₆₇	—	2	1	no	—
600	C₂×C₄×C₆₇	—	2	1	no	—
601	C₂×C₄×C₆₇	—	2	1	no	—
602	C₂×C₄×C₆₇	—	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	—	2	1	no	—
610	C₂×C₄×C₆₇	—	2	1	no	—
611	C₂×C₄×C₆₇	—	2	1	no	—
612	C₂×C₄×C₆₇	—	4	4	no	—
613	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
614	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
615	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
616	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
617	C₂²⋊D₆₇	—	4	4	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	8	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	C₂×#41	1	2	yes	—
652	C₂×Dic₆₇	C₂×#41	1	2	yes	—
653	C₂×Dic₆₇	C₂×#41	1	2	yes	—
654	C₂×Dic₆₇	C₂×#41	1	2	yes	—
655	C₂×Dic₆₇	C₂×#41	1	2	yes	—
656	C₂×Dic₆₇	C₂×#41	1	2	yes	—
657	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
658	D₂₆₈	—	4	4	no	—
659	D₂₆₈	—	4	4	no	—
660	C₄×D₆₇	—	2	8	no	—
661	C₄×D₆₇	—	2	8	no	—
662	C₄×D₆₇	—	4	4	no	—
663	C₄×D₆₇	—	4	4	no	—
664	C₄×D₆₇	—	4	4	no	—
665	C₄×D₆₇	—	4	4	no	—
666	C₄×D₆₇	—	4	4	no	—
667	C₄×D₆₇	—	4	4	no	—
668	C₄×D₆₇	—	4	4	no	—
669	Dic₁₃₄	—	4	4	no	—
670	C₂²×C₆₇	—	2	2	no	—
671	C₂²×C₆₇	—	2	2	no	—
672	C₂²×C₆₇	—	2	2	no	—
673	C₂²×C₆₇	—	4	1	no	—
674	C₂²×C₆₇	—	4	1	no	—
675	C₂²×C₆₇	—	4	1	no	—
676	C₂²×C₆₇	—	4	1	no	—
677	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
678	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
679	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
680	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
681	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
682	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂²×C₆₇	#585	1	1	yes	characteristic
684	C₂×D₆₇	—	2	2	no	—
685	C₂×D₆₇	—	2	2	no	—
686	C₂×D₆₇	—	2	2	no	—
687	C₂×D₆₇	—	2	2	no	—
688	C₂×D₆₇	—	2	2	no	—
689	C₂×D₆₇	—	2	2	no	—
690	C₂×D₆₇	—	2	2	no	—
691	C₂×D₆₇	—	2	2	no	—
692	C₂×D₆₇	—	2	2	no	—
693	C₂×D₆₇	—	4	16	no	—
694	C₂×D₆₇	—	4	1	no	—
695	C₂×D₆₇	—	4	1	no	—
696	C₂×D₆₇	—	4	1	no	—
697	C₂×D₆₇	—	4	1	no	—
698	C₂×D₆₇	—	4	1	no	—
699	C₂×D₆₇	—	4	1	no	—
700	C₂×D₆₇	—	4	1	no	—
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	#529	1	4	yes	—
706	C₄×C₆₇	—	2	2	no	—
707	C₄×C₆₇	—	2	2	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	—	2	2	no	—
722	Dic₆₇	—	2	2	no	—
723	Dic₆₇	—	2	2	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	#551	1	4	yes	—
733	#34806	—	67	1	no	maximal, Sylow
734	C₂×C₆₇	—	4	2	no	—
735	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
736	C₂×C₆₇	#3444	1	1	yes	characteristic
737	C₂×C₆₇	#3460	1	1	yes	characteristic
738	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
739	C₂×C₆₇	#3475	1	1	yes	characteristic
740	C₂×C₆₇	#3475	1	1	yes	characteristic
741	C₂×C₆₇	#3481	1	1	yes	characteristic
742	D₆₇	—	2	4	no	—
743	D₆₇	—	4	2	no	—
744	D₆₇	—	8	1	no	—
745	#2531	—	67	1	no	—
746	#2530	—	67	1	no	—
747	#2527	—	67	1	no	—
748	#2526	—	67	1	no	—
749	#2522	—	67	1	no	—
750	#2521	—	67	1	no	—
751	#2516	—	67	1	no	—
752	#2515	D₆₇	1	1	yes	characteristic, complemented
753	#2510	—	67	1	no	—
754	#2505	—	67	1	no	—
755	#2498	—	67	1	no	—
756	#2482	—	67	1	no	—
757	#2480	—	67	1	no	—
758	#2472	—	67	1	no	—
759	#2438	—	67	1	no	—
760	#2411	—	67	1	no	—
761	#2401	—	67	1	no	—
762	#2396	—	67	1	no	—
763	#2395	—	67	1	no	—
764	#2395	—	67	1	no	—
765	C₄×#126	—	67	1	no	—
766	C₄×#124	—	67	1	no	—
767	C₄×C₂²⋊Q₈	—	67	1	no	—
768	C₄×#123	—	67	1	no	—
769	C₄×#120	—	67	1	no	—
770	#2298	—	67	1	no	—
771	#2293	—	67	1	no	—
772	#2290	—	67	1	no	—
773	#2280	—	67	1	no	—
774	C₄×#117	—	67	1	no	—
775	C₂×C₄×C₂²⋊C₄	—	67	1	no	—
776	C₆₇	#34806	1	1	yes	characteristic, complemented, Sylow
777	C₂⁴×C₄	—	67	1	no	—
778	C₂×#126	—	67	1	no	—
779	C₂×#124	—	67	1	no	—
780	C₂×#123	—	67	1	no	—
781	C₂×C₂²⋊Q₈	—	67	1	no	—
782	C₂×#120	—	67	1	no	—
783	C₂×C₄×Q₈	—	67	1	no	—
784	C₂×C₄×D₄	—	67	1	no	—
785	C₂×C₄×D₄	—	67	1	no	—
786	C₂×C₄×D₄	—	67	1	no	—
787	C₂×#117	—	67	1	no	—
788	C₂×#117	—	67	1	no	—
789	C₂×#117	—	67	1	no	—
790	C₂×#117	—	67	1	no	—
791	C₂×#117	—	67	1	no	—
792	C₂²×C₂²⋊C₄	—	67	1	no	—
793	C₂²×C₂²⋊C₄	—	67	1	no	—
794	C₂²×C₄²	—	67	1	no	—
795	C₂²×C₄²	—	67	1	no	—
796	#401	—	67	1	no	—
797	#400	—	67	1	no	—
798	#400	—	67	1	no	—
799	#400	—	67	1	no	—
800	#400	—	67	1	no	—
801	#400	—	67	1	no	—
802	#400	C₂×D₆₇	1	1	yes	characteristic, complemented
803	#399	—	67	1	no	—
804	#399	—	67	1	no	—
805	#399	—	67	1	no	—
806	#398	—	67	1	no	—
807	#398	—	67	1	no	—
808	#398	—	67	1	no	—
809	#398	C₂×D₆₇	1	1	yes	characteristic, complemented
810	#397	—	67	1	no	—
811	#397	—	67	1	no	—
812	#397	—	67	1	no	—
813	#397	—	67	1	no	—
814	#397	—	67	1	no	—
815	#397	—	67	1	no	—
816	#397	—	67	1	no	—
817	#397	—	67	1	no	—
818	#397	C₂×D₆₇	1	1	yes	characteristic
819	#396	—	67	1	no	—
820	#396	—	67	1	no	—
821	#396	C₂×D₆₇	1	1	yes	characteristic
822	#395	—	67	1	no	—
823	#394	—	67	1	no	—
824	#394	—	67	1	no	—
825	#394	—	67	1	no	—
826	#394	—	67	1	no	—
827	#393	—	67	1	no	—
828	#391	—	67	1	no	—
829	#391	—	67	1	no	—
830	#390	—	67	1	no	—
831	#390	—	67	1	no	—
832	#390	—	67	1	no	—
833	#389	—	67	1	no	—
834	#389	—	67	1	no	—
835	#389	—	67	1	no	—
836	#388	—	67	1	no	—
837	#388	—	67	1	no	—
838	#388	—	67	1	no	—
839	#388	—	67	1	no	—
840	#388	—	67	1	no	—
841	#388	—	67	1	no	—
842	#388	—	67	1	no	—
843	#388	—	67	1	no	—
844	#388	—	67	1	no	—
845	#388	—	67	1	no	—
846	#388	—	67	1	no	—
847	#388	—	67	1	no	—
848	#388	—	67	1	no	—
849	#388	—	67	1	no	—
850	#388	—	67	1	no	—
851	#388	—	67	1	no	—
852	#388	—	67	1	no	—
853	#388	C₂×D₆₇	1	1	yes	characteristic
854	#388	C₂×D₆₇	1	1	yes	characteristic
855	#387	—	67	1	no	—
856	#387	—	67	1	no	—
857	#387	—	67	1	no	—
858	#387	—	67	1	no	—
859	#387	—	67	1	no	—
860	#387	—	67	1	no	—
861	#387	—	67	1	no	—
862	#387	—	67	1	no	—
863	#387	—	67	1	no	—
864	#387	—	67	1	no	—
865	#387	C₂×D₆₇	1	1	yes	characteristic, complemented
866	#387	C₂×D₆₇	1	1	yes	characteristic, complemented
867	#387	C₂×D₆₇	1	1	yes	characteristic, complemented
868	#386	—	67	1	no	—
869	#386	—	67	1	no	—
870	#386	—	67	1	no	—
871	#386	—	67	1	no	—
872	#386	—	67	1	no	—
873	#386	—	67	1	no	—
874	#385	—	67	1	no	—
875	#385	—	67	1	no	—
876	#385	—	67	1	no	—
877	#385	—	67	1	no	—
878	#385	—	67	1	no	—
879	#385	—	67	1	no	—
880	#385	—	67	1	no	—
881	#385	C₂×D₆₇	1	1	yes	characteristic
882	#383	C₂×D₆₇	1	1	yes	characteristic, complemented
883	#382	C₂×D₆₇	1	1	yes	characteristic, complemented
884	#381	—	67	1	no	—
885	#381	—	67	1	no	—
886	#381	C₂×D₆₇	1	1	yes	characteristic
887	#380	—	67	1	no	—
888	#380	—	67	1	no	—
889	#380	—	67	1	no	—
890	#380	—	67	1	no	—
891	#380	—	67	1	no	—
892	#379	—	67	1	no	—
893	#379	—	67	1	no	—
894	#379	—	67	1	no	—
895	C₄×C₄⋊C₄	—	67	1	no	—
896	C₄×C₄⋊C₄	—	67	1	no	—
897	C₄×C₄⋊C₄	—	67	1	no	—
898	C₄×C₄⋊C₄	—	67	1	no	—
899	C₄×C₄⋊C₄	—	67	1	no	—
900	C₄×C₄⋊C₄	—	67	1	no	—
901	C₄×C₄⋊C₄	—	67	1	no	—
902	C₄×C₄⋊C₄	—	67	1	no	—
903	C₄×C₄⋊C₄	—	67	1	no	—
904	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
905	C₄×C₂²⋊C₄	—	67	1	no	—
906	C₄×C₂²⋊C₄	—	67	1	no	—
907	C₄×C₂²⋊C₄	—	67	1	no	—
908	C₄×C₂²⋊C₄	—	67	1	no	—
909	C₄×C₂²⋊C₄	—	67	1	no	—
910	C₄×C₂²⋊C₄	—	67	1	no	—
911	C₄×C₂²⋊C₄	—	67	1	no	—
912	C₄×C₂²⋊C₄	—	67	1	no	—
913	C₄×C₂²⋊C₄	—	67	1	no	—
914	C₄×C₂²⋊C₄	—	67	1	no	—
915	C₄×C₂²⋊C₄	—	67	1	no	—
916	C₄×C₂²⋊C₄	—	67	1	no	—
917	C₄×C₂²⋊C₄	—	67	1	no	—
918	C₄×C₂²⋊C₄	—	67	1	no	—
919	C₄×C₂²⋊C₄	—	67	1	no	—
920	C₄×C₂²⋊C₄	—	67	1	no	—
921	C₄×C₂²⋊C₄	—	67	1	no	—
922	C₄×C₂²⋊C₄	—	67	1	no	—
923	C₄×C₂²⋊C₄	—	67	1	no	—
924	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
925	#376	—	67	1	no	—
926	#376	—	67	1	no	—
927	#376	—	67	1	no	—
928	C₂×#95	—	67	1	no	—
929	C₂×#95	—	67	1	no	—
930	C₄³	—	67	1	no	—
931	C₄³	—	67	1	no	—
932	C₂⁵	—	67	1	no	—
933	C₂²×Q₈	—	67	1	no	—
934	C₂²×D₄	—	67	1	no	—
935	C₂²×D₄	—	67	1	no	—
936	C₂²×D₄	—	67	1	no	—
937	C₂³×C₄	—	268	2	no	—
938	C₂³×C₄	—	67	1	no	—
939	C₂³×C₄	—	67	1	no	—
940	C₂³×C₄	—	67	1	no	—
941	C₂³×C₄	—	67	1	no	—
942	C₂³×C₄	—	67	1	no	—
943	C₂³×C₄	—	67	1	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	—	134	4	no	—
949	C₂³×C₄	—	134	4	no	—
950	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
951	#126	—	134	4	no	—
952	#124	—	134	4	no	—
953	#123	—	134	4	no	—
954	C₂²⋊Q₈	—	134	4	no	—
955	#120	—	134	4	no	—
956	C₄×Q₈	—	268	2	no	—
957	C₄×D₄	—	268	2	no	—
958	C₄×D₄	—	134	4	no	—
959	C₄×D₄	—	134	4	no	—
960	#117	—	268	2	no	—
961	#117	—	268	2	no	—
962	#117	—	134	4	no	—
963	#117	—	134	4	no	—
964	#117	—	134	4	no	—
965	C₂×C₄⋊C₄	—	67	1	no	—
966	C₂×C₄⋊C₄	—	67	1	no	—
967	C₂×C₄⋊C₄	—	67	1	no	—
968	C₂×C₄⋊C₄	—	67	1	no	—
969	C₂×C₄⋊C₄	—	67	1	no	—
970	C₂×C₄⋊C₄	—	67	1	no	—
971	C₂×C₄⋊C₄	—	67	1	no	—
972	C₂×C₄⋊C₄	—	67	1	no	—
973	C₂×C₄⋊C₄	—	67	1	no	—
974	C₂×C₄⋊C₄	—	67	1	no	—
975	C₂×C₄⋊C₄	—	67	1	no	—
976	C₂×C₄⋊C₄	—	67	1	no	—
977	C₂×C₄⋊C₄	—	67	1	no	—
978	C₂×C₄⋊C₄	—	67	1	no	—
979	C₂×C₄⋊C₄	—	67	1	no	—
980	C₂×C₄⋊C₄	—	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	C₂²×D₆₇	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	—	67	1	no	—
994	C₂×C₂²⋊C₄	—	67	1	no	—
995	C₂×C₂²⋊C₄	—	67	1	no	—
996	C₂×C₂²⋊C₄	—	67	1	no	—
997	C₂×C₂²⋊C₄	—	67	1	no	—
998	C₂×C₂²⋊C₄	—	67	1	no	—
999	C₂×C₂²⋊C₄	—	67	1	no	—
1000	C₂×C₂²⋊C₄	—	67	1	no	—
1001	C₂×C₂²⋊C₄	—	67	1	no	—
1002	C₂×C₂²⋊C₄	—	67	1	no	—
1003	C₂×C₂²⋊C₄	—	67	1	no	—
1004	C₂×C₂²⋊C₄	—	67	1	no	—
1005	C₂×C₂²⋊C₄	—	67	1	no	—
1006	C₂×C₂²⋊C₄	—	67	1	no	—
1007	C₂×C₂²⋊C₄	—	67	1	no	—
1008	C₂×C₂²⋊C₄	—	67	1	no	—
1009	C₂×C₂²⋊C₄	—	67	1	no	—
1010	C₂×C₂²⋊C₄	—	67	1	no	—
1011	C₂×C₂²⋊C₄	—	67	1	no	—
1012	C₂×C₂²⋊C₄	—	67	1	no	—
1013	C₂×C₂²⋊C₄	—	67	1	no	—
1014	C₂×C₂²⋊C₄	—	67	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	—	134	4	no	—
1028	C₂×C₂²⋊C₄	—	134	4	no	—
1029	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1035	C₂×C₄²	—	268	2	no	—
1036	C₂×C₄²	—	67	1	no	—
1037	C₂×C₄²	—	67	1	no	—
1038	C₂×C₄²	—	67	1	no	—
1039	C₂×C₄²	—	67	1	no	—
1040	C₂×C₄²	—	67	1	no	—
1041	C₂×C₄²	—	67	1	no	—
1042	C₂×C₄²	—	67	1	no	—
1043	C₂×C₄²	—	67	1	no	—
1044	C₂×C₄²	—	67	1	no	—
1045	C₂×C₄²	—	67	1	no	—
1046	C₂×C₄²	—	67	1	no	—
1047	C₂×C₄²	—	67	1	no	—
1048	C₂×C₄²	—	67	1	no	—
1049	C₂×C₄²	—	67	1	no	—
1050	C₂×C₄²	—	67	1	no	—
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	—	134	4	no	—
1056	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1057	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1058	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1059	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
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	C₂²×D₆₇	1	1	yes	characteristic
1093	#95	C₂²×D₆₇	1	1	yes	characteristic
1094	#95	C₂²×D₆₇	1	1	yes	characteristic
1095	#95	C₂²×D₆₇	1	1	yes	characteristic
1096	#95	C₂²×D₆₇	1	1	yes	characteristic
1097	#95	C₂²×D₆₇	1	1	yes	characteristic
1098	#95	C₂²×D₆₇	1	1	yes	characteristic
1099	#95	C₂²×D₆₇	1	1	yes	characteristic
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	C₂⁴	—	268	1	no	—
1109	C₂⁴	—	268	1	no	—
1110	C₂⁴	—	67	1	no	—
1111	C₂⁴	—	67	1	no	—
1112	C₂⁴	—	67	1	no	—
1113	C₂⁴	—	134	2	no	—
1114	C₂⁴	—	134	2	no	—
1115	C₂⁴	—	134	2	no	—
1116	C₂⁴	—	134	2	no	—
1117	C₂⁴	—	134	2	no	—
1118	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1119	C₂×Q₈	—	268	1	no	—
1120	C₂×Q₈	—	134	2	no	—
1121	C₂×Q₈	—	134	2	no	—
1122	C₂×D₄	—	268	1	no	—
1123	C₂×D₄	—	268	1	no	—
1124	C₂×D₄	—	134	2	no	—
1125	C₂×D₄	—	134	2	no	—
1126	C₂×D₄	—	134	2	no	—
1127	C₂×D₄	—	134	2	no	—
1128	C₂×D₄	—	134	2	no	—
1129	C₂×D₄	—	134	2	no	—
1130	C₂×D₄	—	134	2	no	—
1131	C₂²×C₄	—	2	2	no	—
1132	C₂²×C₄	—	2	2	no	—
1133	C₂²×C₄	—	4	1	no	—
1134	C₂²×C₄	—	268	1	no	—
1135	C₂²×C₄	—	268	1	no	—
1136	C₂²×C₄	—	268	1	no	—
1137	C₂²×C₄	—	268	1	no	—
1138	C₂²×C₄	—	268	1	no	—
1139	C₂²×C₄	—	268	1	no	—
1140	C₂²×C₄	—	268	16	no	—
1141	C₂²×C₄	—	67	1	no	—
1142	C₂²×C₄	—	67	4	no	—
1143	C₂²×C₄	—	67	1	no	—
1144	C₂²×C₄	—	67	1	no	—
1145	C₂²×C₄	—	67	1	no	—
1146	C₂²×C₄	—	67	1	no	—
1147	C₂²×C₄	—	67	4	no	—
1148	C₂²×C₄	—	67	4	no	—
1149	C₂²×C₄	—	67	1	no	—
1150	C₂²×C₄	—	67	1	no	—
1151	C₂²×C₄	—	67	1	no	—
1152	C₂²×C₄	—	67	1	no	—
1153	C₂²×C₄	—	67	1	no	—
1154	C₂²×C₄	—	67	1	no	—
1155	C₂²×C₄	—	67	1	no	—
1156	C₂²×C₄	—	67	1	no	—
1157	C₂²×C₄	—	134	2	no	—
1158	C₂²×C₄	—	134	2	no	—
1159	C₂²×C₄	—	134	2	no	—
1160	C₂²×C₄	—	134	2	no	—
1161	C₂²×C₄	—	134	2	no	—
1162	C₂²×C₄	—	134	2	no	—
1163	C₂²×C₄	—	134	2	no	—
1164	C₂²×C₄	—	134	2	no	—
1165	C₂²×C₄	—	134	2	no	—
1166	C₂²×C₄	—	134	2	no	—
1167	C₂²×C₄	—	134	2	no	—
1168	C₂²×C₄	—	134	2	no	—
1169	C₂²×C₄	—	134	2	no	—
1170	C₂²×C₄	—	134	2	no	—
1171	C₂²×C₄	—	134	2	no	—
1172	C₂²×C₄	—	134	2	no	—
1173	C₂²×C₄	—	134	2	no	—
1174	C₂²×C₄	—	134	2	no	—
1175	C₂²×C₄	—	134	2	no	—
1176	C₂²×C₄	—	134	2	no	—
1177	C₂²×C₄	—	134	2	no	—
1178	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1179	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1180	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1183	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1184	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1185	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1186	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1187	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
1193	C₄⋊C₄	—	2	2	no	—
1194	C₄⋊C₄	—	2	2	no	—
1195	C₄⋊C₄	—	2	2	no	—
1196	C₄⋊C₄	—	2	2	no	—
1197	C₄⋊C₄	—	4	1	no	—
1198	C₄⋊C₄	—	4	1	no	—
1199	C₄⋊C₄	—	4	1	no	—
1200	C₄⋊C₄	—	268	1	no	—
1201	C₄⋊C₄	—	268	1	no	—
1202	C₄⋊C₄	—	268	1	no	—
1203	C₄⋊C₄	—	268	1	no	—
1204	C₄⋊C₄	—	268	1	no	—
1205	C₄⋊C₄	—	268	1	no	—
1206	C₄⋊C₄	—	268	1	no	—
1207	C₄⋊C₄	—	268	1	no	—
1208	C₄⋊C₄	—	268	1	no	—
1209	C₄⋊C₄	—	134	2	no	—
1210	C₄⋊C₄	—	134	2	no	—
1211	C₄⋊C₄	—	134	2	no	—
1212	C₄⋊C₄	—	134	2	no	—
1213	C₄⋊C₄	—	134	2	no	—
1214	C₄⋊C₄	—	134	2	no	—
1215	C₄⋊C₄	—	134	2	no	—
1216	C₄⋊C₄	—	134	2	no	—
1217	C₄⋊C₄	—	134	2	no	—
1218	C₄⋊C₄	—	134	2	no	—
1219	C₄⋊C₄	—	134	2	no	—
1220	C₂²⋊C₄	—	2	2	no	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	2	2	no	—
1225	C₂²⋊C₄	—	4	1	no	—
1226	C₂²⋊C₄	—	268	1	no	—
1227	C₂²⋊C₄	—	268	1	no	—
1228	C₂²⋊C₄	—	268	1	no	—
1229	C₂²⋊C₄	—	268	1	no	—
1230	C₂²⋊C₄	—	268	1	no	—
1231	C₂²⋊C₄	—	268	1	no	—
1232	C₂²⋊C₄	—	268	1	no	—
1233	C₂²⋊C₄	—	268	1	no	—
1234	C₂²⋊C₄	—	268	1	no	—
1235	C₂²⋊C₄	—	268	1	no	—
1236	C₂²⋊C₄	—	67	4	no	—
1237	C₂²⋊C₄	—	67	4	no	—
1238	C₂²⋊C₄	—	134	2	no	—
1239	C₂²⋊C₄	—	134	2	no	—
1240	C₂²⋊C₄	—	134	2	no	—
1241	C₂²⋊C₄	—	134	2	no	—
1242	C₂²⋊C₄	—	134	2	no	—
1243	C₂²⋊C₄	—	134	2	no	—
1244	C₂²⋊C₄	—	134	2	no	—
1245	C₂²⋊C₄	—	134	2	no	—
1246	C₂²⋊C₄	—	134	2	no	—
1247	C₂²⋊C₄	—	134	2	no	—
1248	C₂²⋊C₄	—	134	2	no	—
1249	C₂²⋊C₄	—	134	2	no	—
1250	C₂²⋊C₄	—	134	2	no	—
1251	C₂²⋊C₄	—	134	2	no	—
1252	C₂²⋊C₄	—	134	2	no	—
1253	C₂²⋊C₄	—	134	2	no	—
1254	C₂²⋊C₄	—	134	2	no	—
1255	C₂²⋊C₄	—	134	2	no	—
1256	C₂²⋊C₄	—	134	2	no	—
1257	C₂²⋊C₄	—	134	2	no	—
1258	C₂²⋊C₄	—	134	2	no	—
1259	C₂²⋊C₄	—	134	2	no	—
1260	C₄²	—	2	2	no	—
1261	C₄²	—	2	2	no	—
1262	C₄²	—	2	2	no	—
1263	C₄²	—	4	1	no	—
1264	C₄²	—	268	1	no	—
1265	C₄²	—	268	1	no	—
1266	C₄²	—	268	1	no	—
1267	C₄²	—	134	2	no	—
1268	C₄²	—	134	2	no	—
1269	C₄²	—	134	2	no	—
1270	C₄²	—	134	2	no	—
1271	C₄²	—	134	2	no	—
1272	C₄²	—	134	2	no	—
1273	C₄²	—	134	2	no	—
1274	C₄²	—	134	2	no	—
1275	C₄²	—	134	2	no	—
1276	C₄²	—	134	2	no	—
1277	C₄²	—	134	2	no	—
1278	C₄²	—	134	2	no	—
1279	C₄²	—	134	2	no	—
1280	C₄²	—	134	2	no	—
1281	C₄²	—	134	2	no	—
1282	C₄²	—	134	2	no	—
1283	C₂³	—	2	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	268	4	no	—
1290	C₂³	—	268	4	no	—
1291	C₂³	—	268	4	no	—
1292	C₂³	—	268	4	no	—
1293	C₂³	—	268	4	no	—
1294	C₂³	—	268	4	no	—
1295	C₂³	—	67	2	no	—
1296	C₂³	—	67	2	no	—
1297	C₂³	—	67	2	no	—
1298	C₂³	—	67	2	no	—
1299	C₂³	—	134	8	no	—
1300	C₂³	—	134	1	no	—
1301	C₂³	—	134	1	no	—
1302	C₂³	—	134	1	no	—
1303	C₂³	—	134	1	no	—
1304	C₂³	—	134	1	no	—
1305	C₂³	—	134	1	no	—
1306	C₂³	—	134	1	no	—
1307	C₂³	—	134	1	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	—	134	1	no	—
1316	C₂³	—	134	1	no	—
1317	C₂³	#41×D₆₇	1	2	yes	—
1318	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1319	Q₈	—	268	4	no	—
1320	D₄	—	268	4	no	—
1321	D₄	—	268	4	no	—
1322	D₄	—	268	4	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	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	—	268	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	—	67	2	no	—
1370	C₂×C₄	—	67	2	no	—
1371	C₂×C₄	—	67	2	no	—
1372	C₂×C₄	—	67	2	no	—
1373	C₂×C₄	—	67	2	no	—
1374	C₂×C₄	—	67	2	no	—
1375	C₂×C₄	—	67	2	no	—
1376	C₂×C₄	—	134	8	no	—
1377	C₂×C₄	—	134	8	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	8	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	#41×D₆₇	1	2	yes	—
1412	C₂×C₄	#41×D₆₇	1	2	yes	—
1413	C₂×C₄	#41×D₆₇	1	2	yes	—
1414	C₂×C₄	#41×D₆₇	1	2	yes	—
1415	C₂²	—	2	2	no	—
1416	C₂²	—	2	2	no	—
1417	C₂²	—	2	2	no	—
1418	C₂²	—	4	1	no	—
1419	C₂²	—	4	1	no	—
1420	C₂²	—	4	1	no	—
1421	C₂²	—	4	1	no	—
1422	C₂²	—	268	16	no	—
1423	C₂²	—	268	1	no	—
1424	C₂²	—	268	1	no	—
1425	C₂²	—	268	1	no	—
1426	C₂²	—	268	1	no	—
1427	C₂²	—	268	1	no	—
1428	C₂²	—	268	1	no	—
1429	C₂²	—	268	1	no	—
1430	C₂²	—	268	1	no	—
1431	C₂²	—	268	1	no	—
1432	C₂²	—	268	1	no	—
1433	C₂²	—	268	1	no	—
1434	C₂²	—	67	4	no	—
1435	C₂²	—	134	2	no	—
1436	C₂²	—	134	2	no	—
1437	C₂²	—	134	2	no	—
1438	C₂²	—	134	2	no	—
1439	C₂²	—	134	2	no	—
1440	C₂²	—	134	2	no	—
1441	C₂²	—	134	2	no	—
1442	C₂²	—	134	2	no	—
1443	C₂²	—	134	2	no	—
1444	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1445	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1446	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1447	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1448	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1449	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1450	C₂²	#16864233	1	1	yes	characteristic
1451	C₄	—	2	2	no	—
1452	C₄	—	2	2	no	—
1453	C₄	—	2	2	no	—
1454	C₄	—	2	2	no	—
1455	C₄	—	4	1	no	—
1456	C₄	—	4	1	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	—	268	1	no	—
1466	C₄	—	268	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	—	67	4	no	—
1474	C₄	—	134	2	no	—
1475	C₄	—	134	2	no	—
1476	C₄	—	134	2	no	—
1477	C₄	—	134	2	no	—
1478	C₂	—	4	2	no	—
1479	C₂	—	268	2	no	—
1480	C₂	—	536	1	no	—
1481	C₂	—	134	4	no	—
1482	C₂	#529×D₆₇	1	1	yes	characteristic
1483	C₂	#22573503	1	1	yes	characteristic
1484	C₂	#22573629	1	1	yes	characteristic
1485	C₂	#551×D₆₇	1	1	yes	characteristic
1486	C₂	#22573762	1	1	yes	characteristic
1487	C₂	#22573774	1	1	yes	characteristic
1488	C₂	#22573816	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2515	C₂
prime radical	C₂×#14524013	C₂²
hypercenter	#2515	D₆₇
hypocenter	C₆₇	#34806
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2515

Complements

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

N	H ≅ G/N	type
1. #22565062	C₂	semidirect
2. #22565039	C₂	semidirect
3. #22565000	C₂	semidirect
4. #22564977	C₂	semidirect
5. #22564929	C₂	semidirect
6. #22564906	C₂	semidirect
7. #22564843	C₂	semidirect
8. #22564776	C₂	semidirect
9. #22564709	C₂	semidirect
10. #22564648	C₂	semidirect
11. #22564478	C₂	semidirect
12. #22564459	C₂	semidirect
14. #22563880	C₂	semidirect
16. #22563508	C₂	semidirect
17. #22563484	C₂	semidirect
18. #22563473	C₂	semidirect
19. #22563467	C₂	semidirect
20. #22562757	C₂	semidirect
21. #22562748	C₂	semidirect
22. #22562743	C₂	semidirect
23. #22562730	C₂	semidirect
25. #22562703	C₂	semidirect
26. #22562669	C₂	semidirect
27. #22562647	C₂	semidirect
28. #22562589	C₂	semidirect
29. C₄×#14524001	C₂	semidirect
30. C₄×C₂²⋊C₄×D₆₇	C₂	semidirect
31. C₆₇×#2515	C₂	semidirect
38. C₂×#14524008	C₂²	semidirect
44. C₂×#14524001	C₂²	semidirect
51. C₆₇⋊#401	C₂²	semidirect
52. #16863338	C₂²	semidirect
53. #16863337	C₂²	semidirect
54. #16863337	C₂²	semidirect
55. #16863336	C₂²	semidirect
56. #16863335	C₂²	semidirect
59. #16863331	C₂²	semidirect
60. #16863330	C₂²	semidirect
61. #16863329	C₂²	semidirect
62. #16863326	C₂²	semidirect
64. #16863325	C₂²	semidirect
67. #16863323	C₂²	semidirect
68. #16863323	C₂²	semidirect
73. #16863316	C₂²	semidirect
79. #16863301	C₂²	semidirect
80. #16863300	C₂²	semidirect
84. #16863293	C₂²	semidirect
85. #16863293	C₂²	semidirect
86. #16863291	C₂²	semidirect
90. #16863288	C₂²	semidirect
91. #16863287	C₂²	semidirect
92. #16863287	C₂²	semidirect
93. #16863287	C₂²	semidirect
99. #16863285	C₂²	semidirect
100. #16863285	C₂²	semidirect
101. #16863285	C₂²	semidirect
102. #16863285	C₂²	semidirect
104. #16863283	C₂²	semidirect
105. #16863282	C₂²	semidirect
106. #16863280	C₂²	semidirect
107. #16863280	C₂²	semidirect
108. #16863278	C₂²	semidirect
109. #16863278	C₂²	semidirect
110. #16863278	C₂²	semidirect
111. #16863278	C₂²	semidirect
112. #16863277	C₂²	semidirect
113. #16863277	C₂²	semidirect
137. C₄⋊C₄×Dic₆₇	C₂²	semidirect
138. C₄⋊C₄×Dic₆₇	C₂²	semidirect
139. C₄⋊C₄×Dic₆₇	C₂²	semidirect
140. C₄⋊C₄×Dic₆₇	C₂²	semidirect
141. C₄×C₄⋊Dic₆₇	C₂²	semidirect
142. #16863247	C₂²	semidirect
143. #16863247	C₂²	semidirect
144. #16863247	C₂²	semidirect
145. #16863247	C₂²	semidirect
162. #16863243	C₂²	semidirect
163. #16863243	C₂²	semidirect
164. #16863243	C₂²	semidirect
165. #16863241	C₂²	semidirect
166. #16863241	C₂²	semidirect
167. #16863241	C₂²	semidirect
170. C₄²×Dic₆₇	C₂²	semidirect
171. C₄²×Dic₆₇	C₂²	semidirect
172. #400×C₆₇	C₂²	semidirect
173. #398×C₆₇	C₂²	semidirect
178. #387×C₆₇	C₂²	semidirect
179. #387×C₆₇	C₂²	semidirect
180. #387×C₆₇	C₂²	semidirect
182. #383×C₆₇	C₂²	semidirect
183. #382×C₆₇	C₂²	semidirect
185. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
752. #2515	D₆₇	semidirect
776. C₆₇	#34806	semidirect
802. #400	C₂×D₆₇	semidirect
809. #398	C₂×D₆₇	semidirect
865. #387	C₂×D₆₇	semidirect
866. #387	C₂×D₆₇	semidirect
867. #387	C₂×D₆₇	semidirect
882. #383	C₂×D₆₇	semidirect
883. #382	C₂×D₆₇	semidirect
904. C₄×C₄⋊C₄	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22565062	2
#22565039	2
#22565000	2
#22564977	2
#22564929	2
#22564906	2
#22564843	2
#22564776	2
#22564709	2
#22564648	2
#22564478	2
#22564459	2
#22564339	2
#22563880	2
#22563589	2
#22563508	2
#22563484	2
#22563473	2
#22563467	2
#22562757	2
#22562748	2
#22562743	2
#22562730	2
#22562710	2
#22562703	2
#22562669	2
#22562647	2
#22562589	2
C₄×#14524001	2
C₄×C₂²⋊C₄×D₆₇	2
C₆₇×#2515	2
#34806	67