Subgroups — #31016745

Order 17152.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#126×D₆₇	C₂	1	1	yes	maximal, characteristic
2	#22563336	C₂	1	1	yes	maximal, characteristic, complemented
3	#22563336	C₂	1	1	yes	maximal, characteristic, complemented
4	#22563332	C₂	1	1	yes	maximal, characteristic, complemented
5	#22563332	C₂	1	1	yes	maximal, characteristic, complemented
6	#22563328	C₂	1	1	yes	maximal, characteristic, complemented
7	#22563328	C₂	1	1	yes	maximal, characteristic, complemented
8	#22563324	C₂	1	1	yes	maximal, characteristic, complemented
9	#22563324	C₂	1	1	yes	maximal, characteristic, complemented
10	#22563085	C₂	1	1	yes	maximal, characteristic, complemented
11	#22563083	C₂	1	1	yes	maximal, characteristic, complemented
12	#22563077	C₂	1	1	yes	maximal, characteristic, complemented
13	#22563075	C₂	1	1	yes	maximal, characteristic, complemented
14	#22563057	C₂	1	1	yes	maximal, characteristic
15	#22563056	C₂	1	1	yes	maximal, characteristic
16	#22563056	C₂	1	1	yes	maximal, characteristic
17	#22563053	C₂	1	1	yes	maximal, characteristic
18	#22562988	C₂	1	1	yes	maximal, characteristic, complemented
19	#22562984	C₂	1	1	yes	maximal, characteristic, complemented
20	#22562980	C₂	1	1	yes	maximal, characteristic, complemented
21	#22562808	C₂	1	1	yes	maximal, characteristic, complemented
22	#22562803	C₂	1	1	yes	maximal, characteristic
23	#22562763	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#14524038	C₂	1	1	yes	maximal, characteristic, complemented
25	#22562759	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×#14524036	C₂	1	1	yes	maximal, characteristic, complemented
27	#22562602	C₂	1	1	yes	maximal, characteristic, complemented
28	#22562563	C₂	1	1	yes	maximal, characteristic, complemented
29	#22562561	C₂	1	1	yes	maximal, characteristic
30	C₄×#14524001	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2334	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14524038	C₂²	1	1	yes	characteristic
33	C₂×#14524038	C₂²	1	1	yes	characteristic
34	C₂×#14524038	C₂²	1	1	yes	characteristic
35	C₂×#14524037	C₂²	1	1	yes	characteristic
36	C₂×#14524036	C₂²	1	1	yes	characteristic
37	C₂×#14524036	C₂²	1	1	yes	characteristic
38	C₂×#14524036	C₂²	1	1	yes	characteristic
39	#126×D₆₇	C₄	1	16	yes	complemented
40	C₂×#14524001	C₂²	1	1	yes	characteristic
41	C₂×#14524001	C₂²	1	1	yes	characteristic
42	C₂×#14524001	C₂²	1	1	yes	characteristic
43	C₂×#14524000	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
47	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
53	#16863295	C₂²	1	1	yes	characteristic, complemented
54	#16863295	C₂²	1	1	yes	characteristic, complemented
55	#16863293	C₂²	1	1	yes	characteristic, complemented
56	#16863293	C₂²	1	1	yes	characteristic, complemented
57	#16863291	C₂²	1	1	yes	characteristic, complemented
58	#16863291	C₂²	1	1	yes	characteristic, complemented
59	#16863290	C₂²	1	1	yes	characteristic
60	#16863290	C₂²	1	1	yes	characteristic
61	#16863290	C₂²	1	1	yes	characteristic
62	#16863289	C₂²	1	1	yes	characteristic
63	#16863289	C₂²	1	1	yes	characteristic
64	#16863289	C₂²	1	1	yes	characteristic
65	#16863288	C₂²	1	1	yes	characteristic
66	#16863288	C₂²	1	1	yes	characteristic
67	#16863288	C₂²	1	1	yes	characteristic
68	#16863288	C₂²	1	1	yes	characteristic
69	#16863288	C₂²	1	1	yes	characteristic
70	#16863287	C₂²	1	1	yes	characteristic
71	#16863286	C₂²	1	1	yes	characteristic
72	#16863286	C₂²	1	1	yes	characteristic
73	#16863286	C₂²	1	1	yes	characteristic
74	#16863286	C₂²	1	1	yes	characteristic
75	#16863286	C₂²	1	1	yes	characteristic
76	#16863285	C₂²	1	1	yes	characteristic
77	#16863284	C₂²	1	1	yes	characteristic
78	#16863284	C₂²	1	1	yes	characteristic
79	#16863284	C₂²	1	1	yes	characteristic
80	#16863283	C₂²	1	1	yes	characteristic, complemented
81	#16863283	C₂²	1	1	yes	characteristic, complemented
82	#16863283	C₂²	1	1	yes	characteristic, complemented
83	#16863283	C₂²	1	1	yes	characteristic, complemented
84	#16863283	C₂²	1	1	yes	characteristic, complemented
85	#16863282	C₂²	1	1	yes	characteristic, complemented
86	#16863282	C₂²	1	1	yes	characteristic, complemented
87	#16863282	C₂²	1	1	yes	characteristic, complemented
88	#16863281	C₂²	1	1	yes	characteristic, complemented
89	#16863281	C₂²	1	1	yes	characteristic, complemented
90	#16863281	C₂²	1	1	yes	characteristic, complemented
91	#16863280	C₂²	1	1	yes	characteristic, complemented
92	#16863279	C₂²	1	1	yes	characteristic, complemented
93	#16863279	C₂²	1	1	yes	characteristic, complemented
94	#16863279	C₂²	1	1	yes	characteristic, complemented
95	#16863278	C₂²	1	1	yes	characteristic, complemented
96	#16863277	C₂²	1	1	yes	characteristic, complemented
97	#16863277	C₂²	1	1	yes	characteristic, complemented
98	#16863277	C₂²	1	1	yes	characteristic, complemented
99	#16863277	C₂²	1	1	yes	characteristic, complemented
100	#16863277	C₂²	1	1	yes	characteristic, complemented
101	#16863271	C₂²	1	1	yes	characteristic
102	#16863271	C₂²	1	1	yes	characteristic
103	#16863270	C₂²	1	1	yes	characteristic
104	#16863270	C₂²	1	1	yes	characteristic
105	#16863267	C₂²	1	1	yes	characteristic
106	#16863267	C₂²	1	1	yes	characteristic
107	#16863263	C₂²	1	1	yes	characteristic, complemented
108	#16863263	C₂²	1	1	yes	characteristic, complemented
109	#16863262	C₂²	1	1	yes	characteristic, complemented
110	#16863258	C₂²	1	1	yes	characteristic
111	#16863258	C₂²	1	1	yes	characteristic
112	#16863258	C₂²	1	1	yes	characteristic
113	#16863258	C₂²	1	1	yes	characteristic
114	#16863255	C₂²	1	1	yes	characteristic
115	#16863255	C₂²	1	1	yes	characteristic
116	#16863253	C₂²	1	1	yes	characteristic
117	#16863253	C₂²	1	1	yes	characteristic
118	#16863253	C₂²	1	1	yes	characteristic
119	#16863253	C₂²	1	1	yes	characteristic
120	#16863251	C₂²	1	1	yes	characteristic
121	#16863251	C₂²	1	1	yes	characteristic
122	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
125	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
126	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
131	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
132	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
133	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
134	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
138	#16863247	C₂²	1	1	yes	characteristic, complemented
139	#16863247	C₂²	1	1	yes	characteristic, complemented
140	#16863247	C₂²	1	1	yes	characteristic, complemented
141	#16863247	C₂²	1	1	yes	characteristic, complemented
142	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
143	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
144	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
145	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
146	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
147	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
148	C₄×(C₂×D₆₇)⋊C₄	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×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
154	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
155	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
156	C₄×C₂²⋊Dic₆₇	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
163	#16863243	C₂²	1	1	yes	characteristic
164	#16863243	C₂²	1	1	yes	characteristic
165	#16863243	C₂²	1	1	yes	characteristic
166	#16863243	C₂²	1	1	yes	characteristic
167	#16863241	C₂²	1	1	yes	characteristic, complemented
168	#16863241	C₂²	1	1	yes	characteristic, complemented
169	#16863241	C₂²	1	1	yes	characteristic, complemented
170	#16863241	C₂²	1	1	yes	characteristic, complemented
171	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
172	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
173	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
174	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
175	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
176	#388×C₆₇	C₂²	1	1	yes	characteristic
177	#388×C₆₇	C₂²	1	1	yes	characteristic
178	#388×C₆₇	C₂²	1	1	yes	characteristic
179	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
181	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
182	#385×C₆₇	C₂²	1	1	yes	characteristic
183	#385×C₆₇	C₂²	1	1	yes	characteristic
184	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
187	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
188	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
189	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
198	#14524038	C₂×C₄	1	8	yes	complemented
199	#14524038	C₂×C₄	1	8	yes	complemented
200	#14524038	C₂×C₄	1	8	yes	complemented
201	#14524037	C₂×C₄	1	8	yes	complemented
202	#14524036	C₂×C₄	1	8	yes	complemented
203	#14524036	C₂×C₄	1	8	yes	complemented
204	#14524036	C₂×C₄	1	8	yes	complemented
205	#14524001	—	2	4	no	—
206	#14524001	—	2	4	no	—
207	#14524001	—	2	4	no	—
208	#14524000	—	2	4	no	—
209	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
219	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
231	C₄⋊C₄×D₆₇	C₂×C₄	1	8	yes	complemented
232	C₄⋊C₄×D₆₇	C₂×C₄	1	8	yes	complemented
233	C₄⋊C₄×D₆₇	C₂×C₄	1	8	yes	complemented
234	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
240	C₂×(C₂×D₆₇)⋊C₄	—	2	4	no	—
241	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×(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	C₂²⋊C₄×D₆₇	—	2	4	no	—
262	C₂²⋊C₄×D₆₇	C₂×C₄	1	8	yes	—
263	C₂²⋊C₄×D₆₇	C₂×C₄	1	8	yes	—
264	C₂²⋊C₄×D₆₇	C₂×C₄	1	8	yes	—
265	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
275	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	C₄²×D₆₇	C₂×C₄	1	8	yes	complemented
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	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	#126×C₆₇	C₂×C₄	1	8	yes	complemented
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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
351	C₂×C₄²×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	#95×C₆₇	C₂³	1	1	yes	characteristic
364	C₂³×D₆₇	—	2	2	no	—
365	C₂³×D₆₇	—	2	2	no	—
366	C₂³×D₆₇	—	4	1	no	—
367	C₂³×D₆₇	—	4	1	no	—
368	C₂³×D₆₇	—	4	1	no	—
369	C₂³×D₆₇	—	4	1	no	—
370	C₂³×D₆₇	C₂²×C₄	1	4	yes	—
371	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
372	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
373	C₂²×Dic₆₇	—	2	2	no	—
374	C₂²×Dic₆₇	—	4	1	no	—
375	C₂²×Dic₆₇	—	4	1	no	—
376	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
378	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×D₆₇	—	2	2	no	—
391	C₂×C₄×D₆₇	—	2	2	no	—
392	C₂×C₄×D₆₇	—	2	2	no	—
393	C₂×C₄×D₆₇	—	2	2	no	—
394	C₂×C₄×D₆₇	—	2	2	no	—
395	C₂×C₄×D₆₇	—	2	2	no	—
396	C₂×C₄×D₆₇	—	4	1	no	—
397	C₂×C₄×D₆₇	—	4	1	no	—
398	C₂×C₄×D₆₇	—	4	1	no	—
399	C₂×C₄×D₆₇	—	4	1	no	—
400	C₂×C₄×D₆₇	—	4	1	no	—
401	C₂×C₄×D₆₇	—	4	1	no	—
402	C₂×C₄×D₆₇	—	4	1	no	—
403	C₂×C₄×D₆₇	—	4	1	no	—
404	C₂×C₄×D₆₇	—	4	1	no	—
405	C₂×C₄×D₆₇	—	4	1	no	—
406	C₂×C₄×D₆₇	—	4	1	no	—
407	C₂×C₄×D₆₇	—	4	1	no	—
408	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
409	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
410	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
411	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
412	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
413	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
414	C₄⋊Dic₆₇	—	2	2	no	—
415	C₄⋊Dic₆₇	—	2	2	no	—
416	C₄⋊Dic₆₇	—	2	2	no	—
417	C₄⋊Dic₆₇	—	4	1	no	—
418	C₄⋊Dic₆₇	—	4	1	no	—
419	C₄⋊Dic₆₇	—	4	1	no	—
420	C₄⋊Dic₆₇	—	4	1	no	—
421	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
422	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
423	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
424	Dic₆₇⋊C₄	—	2	2	no	—
425	Dic₆₇⋊C₄	—	2	2	no	—
426	Dic₆₇⋊C₄	—	4	1	no	—
427	Dic₆₇⋊C₄	—	4	1	no	—
428	Dic₆₇⋊C₄	—	4	1	no	—
429	Dic₆₇⋊C₄	—	4	1	no	—
430	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
431	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
432	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
433	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
434	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
435	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
436	C₂²⋊Dic₆₇	—	2	2	no	—
437	C₂²⋊Dic₆₇	—	4	1	no	—
438	C₂²⋊Dic₆₇	—	4	1	no	—
439	C₂²⋊Dic₆₇	C₂²×C₄	1	4	yes	—
440	C₂²⋊Dic₆₇	C₂²×C₄	1	4	yes	—
441	C₂²⋊Dic₆₇	C₂²×C₄	1	4	yes	—
442	(C₂×D₆₇)⋊C₄	—	2	2	no	—
443	(C₂×D₆₇)⋊C₄	—	2	2	no	—
444	(C₂×D₆₇)⋊C₄	—	2	2	no	—
445	(C₂×D₆₇)⋊C₄	—	2	2	no	—
446	(C₂×D₆₇)⋊C₄	—	2	2	no	—
447	(C₂×D₆₇)⋊C₄	—	2	2	no	—
448	(C₂×D₆₇)⋊C₄	—	2	2	no	—
449	(C₂×D₆₇)⋊C₄	—	2	2	no	—
450	(C₂×D₆₇)⋊C₄	—	4	1	no	—
451	(C₂×D₆₇)⋊C₄	—	4	1	no	—
452	(C₂×D₆₇)⋊C₄	—	4	1	no	—
453	(C₂×D₆₇)⋊C₄	—	4	1	no	—
454	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
455	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
456	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
457	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
458	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
459	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
460	(C₂×D₆₇)⋊C₄	#41	1	4	yes	—
461	(C₂×D₆₇)⋊C₄	#41	1	4	yes	—
462	C₄×Dic₆₇	—	2	2	no	—
463	C₄×Dic₆₇	—	2	2	no	—
464	C₄×Dic₆₇	—	2	2	no	—
465	C₄×Dic₆₇	—	2	2	no	—
466	C₄×Dic₆₇	—	2	2	no	—
467	C₄×Dic₆₇	—	2	2	no	—
468	C₄×Dic₆₇	—	2	2	no	—
469	C₄×Dic₆₇	—	4	1	no	—
470	C₄×Dic₆₇	—	4	1	no	—
471	C₄×Dic₆₇	—	4	1	no	—
472	C₄×Dic₆₇	—	4	1	no	—
473	C₄×Dic₆₇	—	4	1	no	—
474	C₄×Dic₆₇	—	4	1	no	—
475	C₄×Dic₆₇	—	4	1	no	—
476	C₄×Dic₆₇	—	4	1	no	—
477	C₄×Dic₆₇	—	4	1	no	—
478	C₄×Dic₆₇	—	4	1	no	—
479	C₄×Dic₆₇	—	4	1	no	—
480	C₄×Dic₆₇	—	4	1	no	—
481	C₄×Dic₆₇	—	4	1	no	—
482	C₄×Dic₆₇	—	4	1	no	—
483	C₄×Dic₆₇	—	4	1	no	—
484	C₄×Dic₆₇	—	4	1	no	—
485	C₄×Dic₆₇	C₂²×C₄	1	4	yes	—
486	C₄×Dic₆₇	C₂²×C₄	1	4	yes	—
487	C₄×Dic₆₇	C₂²×C₄	1	4	yes	—
488	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₂²×C₄×C₆₇	—	2	2	no	—
490	C₂²×C₄×C₆₇	—	4	1	no	—
491	C₂²×C₄×C₆₇	—	4	1	no	—
492	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
494	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
506	C₄⋊C₄×C₆₇	—	2	2	no	—
507	C₄⋊C₄×C₆₇	—	2	2	no	—
508	C₄⋊C₄×C₆₇	—	2	2	no	—
509	C₄⋊C₄×C₆₇	—	4	1	no	—
510	C₄⋊C₄×C₆₇	—	4	1	no	—
511	C₄⋊C₄×C₆₇	—	4	1	no	—
512	C₄⋊C₄×C₆₇	—	4	1	no	—
513	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
514	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
515	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
516	C₂²⋊C₄×C₆₇	—	2	2	no	—
517	C₂²⋊C₄×C₆₇	—	4	1	no	—
518	C₂²⋊C₄×C₆₇	—	4	1	no	—
519	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
520	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
521	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
522	C₄²×C₆₇	—	2	2	no	—
523	C₄²×C₆₇	—	4	1	no	—
524	C₄²×C₆₇	—	4	1	no	—
525	C₄²×C₆₇	—	4	1	no	—
526	C₄²×C₆₇	—	4	1	no	—
527	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
528	C₂³×C₆₇	—	2	1	no	—
529	C₂³×C₆₇	—	2	1	no	—
530	C₂³×C₆₇	—	2	1	no	—
531	C₂³×C₆₇	—	2	1	no	—
532	C₂³×C₆₇	—	2	1	no	—
533	C₂³×C₆₇	—	2	1	no	—
534	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
535	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
536	C₂²×D₆₇	—	2	1	no	—
537	C₂²×D₆₇	—	2	1	no	—
538	C₂²×D₆₇	—	2	1	no	—
539	C₂²×D₆₇	—	2	1	no	—
540	C₂²×D₆₇	—	2	1	no	—
541	C₂²×D₆₇	—	2	1	no	—
542	C₂²×D₆₇	—	2	1	no	—
543	C₂²×D₆₇	—	2	1	no	—
544	C₂²×D₆₇	—	2	1	no	—
545	C₂²×D₆₇	—	2	1	no	—
546	C₂²×D₆₇	—	2	8	no	—
547	C₂²×D₆₇	—	4	4	no	—
548	C₂²×D₆₇	—	4	4	no	—
549	C₂²×D₆₇	—	8	2	no	—
550	C₂²×D₆₇	—	8	2	no	—
551	C₂²×D₆₇	—	8	2	no	—
552	C₂²×D₆₇	—	8	2	no	—
553	C₂²×D₆₇	C₂³×C₄	1	2	yes	—
554	C₂²×D₆₇	C₂³×C₄	1	2	yes	—
555	C₂²×D₆₇	C₂×#41	1	2	yes	—
556	C₂²×D₆₇	C₂×#41	1	2	yes	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	2	1	no	—
567	C₂×C₄×C₆₇	—	2	1	no	—
568	C₂×C₄×C₆₇	—	2	1	no	—
569	C₂×C₄×C₆₇	—	2	1	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	1	no	—
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	—	8	2	no	—
592	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
593	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
594	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
595	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
596	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
597	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
598	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
599	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
600	C₂×Dic₆₇	—	2	1	no	—
601	C₂×Dic₆₇	—	2	1	no	—
602	C₂×Dic₆₇	—	2	1	no	—
603	C₂×Dic₆₇	—	2	1	no	—
604	C₂×Dic₆₇	—	2	1	no	—
605	C₂×Dic₆₇	—	2	1	no	—
606	C₂×Dic₆₇	—	2	1	no	—
607	C₂×Dic₆₇	—	2	1	no	—
608	C₂×Dic₆₇	—	2	1	no	—
609	C₂×Dic₆₇	—	2	1	no	—
610	C₂×Dic₆₇	—	2	1	no	—
611	C₂×Dic₆₇	—	2	1	no	—
612	C₂×Dic₆₇	—	2	1	no	—
613	C₂×Dic₆₇	—	2	1	no	—
614	C₂×Dic₆₇	—	2	1	no	—
615	C₂×Dic₆₇	—	2	1	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	—	8	2	no	—
635	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
636	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
637	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
638	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
639	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
640	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
641	C₂×Dic₆₇	C₂×#41	1	2	yes	—
642	C₂×Dic₆₇	C₂×#41	1	2	yes	—
643	C₄×D₆₇	—	2	8	no	—
644	C₄×D₆₇	—	2	8	no	—
645	C₄×D₆₇	—	4	4	no	—
646	C₄×D₆₇	—	4	4	no	—
647	C₄×D₆₇	—	4	4	no	—
648	C₄×D₆₇	—	4	4	no	—
649	C₄×D₆₇	—	8	2	no	—
650	C₄×D₆₇	—	8	2	no	—
651	C₂²×C₆₇	—	2	2	no	—
652	C₂²×C₆₇	—	2	2	no	—
653	C₂²×C₆₇	—	2	2	no	—
654	C₂²×C₆₇	—	4	1	no	—
655	C₂²×C₆₇	—	4	1	no	—
656	C₂²×C₆₇	—	4	1	no	—
657	C₂²×C₆₇	—	4	1	no	—
658	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
659	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
660	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
661	C₂²×C₆₇	#585	1	1	yes	characteristic
662	C₂²×C₆₇	#585	1	1	yes	characteristic
663	C₂²×C₆₇	#585	1	1	yes	characteristic
664	C₂²×C₆₇	#585	1	1	yes	characteristic
665	C₂×D₆₇	—	2	2	no	—
666	C₂×D₆₇	—	2	2	no	—
667	C₂×D₆₇	—	2	2	no	—
668	C₂×D₆₇	—	2	2	no	—
669	C₂×D₆₇	—	2	2	no	—
670	C₂×D₆₇	—	2	2	no	—
671	C₂×D₆₇	—	2	2	no	—
672	C₂×D₆₇	—	2	2	no	—
673	C₂×D₆₇	—	2	2	no	—
674	C₂×D₆₇	—	4	1	no	—
675	C₂×D₆₇	—	4	1	no	—
676	C₂×D₆₇	—	4	1	no	—
677	C₂×D₆₇	—	4	1	no	—
678	C₂×D₆₇	—	8	8	no	—
679	C₂×D₆₇	C₄×#41	1	4	yes	—
680	C₄×C₆₇	—	2	2	no	—
681	C₄×C₆₇	—	2	2	no	—
682	C₄×C₆₇	—	2	2	no	—
683	C₄×C₆₇	—	2	2	no	—
684	C₄×C₆₇	—	2	2	no	—
685	C₄×C₆₇	—	2	2	no	—
686	C₄×C₆₇	—	2	2	no	—
687	C₄×C₆₇	—	2	2	no	—
688	C₄×C₆₇	—	4	1	no	—
689	C₄×C₆₇	—	4	1	no	—
690	C₄×C₆₇	—	4	1	no	—
691	C₄×C₆₇	—	4	1	no	—
692	C₄×C₆₇	—	4	1	no	—
693	C₄×C₆₇	—	4	1	no	—
694	Dic₆₇	—	2	2	no	—
695	Dic₆₇	—	2	2	no	—
696	Dic₆₇	—	2	2	no	—
697	Dic₆₇	—	2	2	no	—
698	Dic₆₇	—	2	2	no	—
699	Dic₆₇	—	2	2	no	—
700	Dic₆₇	—	2	2	no	—
701	Dic₆₇	—	2	2	no	—
702	Dic₆₇	—	4	1	no	—
703	Dic₆₇	—	4	1	no	—
704	Dic₆₇	—	4	1	no	—
705	Dic₆₇	—	4	1	no	—
706	Dic₆₇	—	4	1	no	—
707	Dic₆₇	—	4	1	no	—
708	#34247	—	67	1	no	maximal, Sylow
709	C₂×C₆₇	—	4	2	no	—
710	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
711	C₂×C₆₇	#3428	1	1	yes	characteristic
712	C₂×C₆₇	#3428	1	1	yes	characteristic
713	C₂×C₆₇	#3521	1	1	yes	characteristic
714	C₂×C₆₇	#3521	1	1	yes	characteristic
715	C₂×C₆₇	#3521	1	1	yes	characteristic
716	C₂×C₆₇	#3521	1	1	yes	characteristic
717	D₆₇	—	2	4	no	—
718	D₆₇	—	4	2	no	—
719	C₂²×#126	—	67	1	no	—
720	#2373	—	67	1	no	—
721	#2373	—	67	1	no	—
722	#2373	—	67	1	no	—
723	#2373	—	67	1	no	—
724	#2373	—	67	1	no	—
725	#2373	—	67	1	no	—
726	#2373	—	67	1	no	—
727	#2373	—	67	1	no	—
728	#2345	—	67	1	no	—
729	#2345	—	67	1	no	—
730	#2344	—	67	1	no	—
731	#2344	—	67	1	no	—
732	#2342	—	67	1	no	—
733	#2342	—	67	1	no	—
734	#2342	—	67	1	no	—
735	#2342	—	67	1	no	—
736	#2334	—	67	1	no	—
737	#2334	—	67	1	no	—
738	#2334	—	67	1	no	—
739	#2334	D₆₇	1	1	yes	characteristic, complemented
740	#2313	—	67	1	no	—
741	#2312	—	67	1	no	—
742	C₄×#126	—	67	1	no	—
743	C₄×#126	—	67	1	no	—
744	C₄×#126	—	67	1	no	—
745	C₄×#126	—	67	1	no	—
746	#2283	—	67	1	no	—
747	#2274	—	67	1	no	—
748	#2273	—	67	1	no	—
749	C₄×#117	—	67	1	no	—
750	C₆₇	#34247	1	1	yes	characteristic, complemented, Sylow
751	C₂×#126	—	67	16	no	—
752	C₂×#126	—	67	1	no	—
753	C₂×#126	—	67	1	no	—
754	C₂×#126	—	67	1	no	—
755	C₂×#126	—	67	1	no	—
756	C₂×#126	—	67	1	no	—
757	C₂×#126	—	67	1	no	—
758	C₂×#126	—	67	1	no	—
759	C₂×#126	C₂×D₆₇	1	1	yes	characteristic
760	C₂×#117	—	67	1	no	—
761	C₂×#117	—	67	1	no	—
762	C₂×#117	—	67	1	no	—
763	C₂×#117	—	67	1	no	—
764	C₂²×C₄⋊C₄	—	67	1	no	—
765	C₂²×C₄⋊C₄	—	67	1	no	—
766	C₂²×C₄⋊C₄	—	67	1	no	—
767	C₂²×C₂²⋊C₄	—	67	1	no	—
768	C₂²×C₂²⋊C₄	—	67	1	no	—
769	C₂²×C₂²⋊C₄	—	67	1	no	—
770	C₂²×C₂²⋊C₄	—	67	1	no	—
771	C₂²×C₂²⋊C₄	—	67	1	no	—
772	C₂²×C₄²	—	67	1	no	—
773	#389	—	67	1	no	—
774	#389	—	67	1	no	—
775	#389	—	67	1	no	—
776	#389	—	67	1	no	—
777	#389	—	67	1	no	—
778	#389	—	67	1	no	—
779	#389	C₂×D₆₇	1	1	yes	characteristic, complemented
780	#389	C₂×D₆₇	1	1	yes	characteristic, complemented
781	#388	—	67	1	no	—
782	#388	—	67	1	no	—
783	#388	—	67	1	no	—
784	#388	—	67	1	no	—
785	#388	—	67	1	no	—
786	#388	—	67	1	no	—
787	#388	—	67	1	no	—
788	#388	—	67	1	no	—
789	#388	—	67	1	no	—
790	#388	—	67	1	no	—
791	#388	—	67	1	no	—
792	#388	—	67	1	no	—
793	#388	—	67	1	no	—
794	#388	—	67	1	no	—
795	#388	—	67	1	no	—
796	#388	—	67	1	no	—
797	#388	—	67	1	no	—
798	#388	—	67	1	no	—
799	#388	—	67	1	no	—
800	#388	—	67	1	no	—
801	#388	—	67	1	no	—
802	#388	C₂×D₆₇	1	1	yes	characteristic
803	#388	C₂×D₆₇	1	1	yes	characteristic
804	#388	C₂×D₆₇	1	1	yes	characteristic
805	#387	—	67	1	no	—
806	#387	—	67	1	no	—
807	#387	—	67	1	no	—
808	#387	—	67	1	no	—
809	#387	—	67	1	no	—
810	#387	—	67	1	no	—
811	#387	—	67	1	no	—
812	#387	—	67	1	no	—
813	#387	—	67	1	no	—
814	#387	—	67	1	no	—
815	#387	—	67	1	no	—
816	#387	—	67	1	no	—
817	#387	—	67	1	no	—
818	#387	—	67	1	no	—
819	#387	—	67	1	no	—
820	#387	—	67	1	no	—
821	#387	—	67	1	no	—
822	#387	—	67	1	no	—
823	#387	—	67	1	no	—
824	#387	—	67	1	no	—
825	#387	—	67	1	no	—
826	#387	C₂×D₆₇	1	1	yes	characteristic, complemented
827	#387	C₂×D₆₇	1	1	yes	characteristic, complemented
828	#387	C₂×D₆₇	1	1	yes	characteristic, complemented
829	#385	—	67	1	no	—
830	#385	—	67	1	no	—
831	#385	—	67	1	no	—
832	#385	—	67	1	no	—
833	#385	—	67	1	no	—
834	#385	—	67	1	no	—
835	#385	C₂×D₆₇	1	1	yes	characteristic
836	#385	C₂×D₆₇	1	1	yes	characteristic
837	#383	—	67	1	no	—
838	#383	—	67	1	no	—
839	#382	—	67	1	no	—
840	#382	C₂×D₆₇	1	1	yes	characteristic, complemented
841	#381	—	67	1	no	—
842	#381	—	67	1	no	—
843	#381	—	67	1	no	—
844	#381	—	67	1	no	—
845	#380	—	67	1	no	—
846	#380	—	67	1	no	—
847	#380	—	67	1	no	—
848	#380	—	67	1	no	—
849	#380	—	67	1	no	—
850	#380	—	67	1	no	—
851	#379	—	67	1	no	—
852	#379	—	67	1	no	—
853	C₄×C₄⋊C₄	—	67	1	no	—
854	C₄×C₄⋊C₄	—	67	1	no	—
855	C₄×C₄⋊C₄	—	67	1	no	—
856	C₄×C₄⋊C₄	—	67	1	no	—
857	C₄×C₄⋊C₄	—	67	1	no	—
858	C₄×C₄⋊C₄	—	67	1	no	—
859	C₄×C₄⋊C₄	—	67	1	no	—
860	C₄×C₄⋊C₄	—	67	1	no	—
861	C₄×C₄⋊C₄	—	67	1	no	—
862	C₄×C₄⋊C₄	—	67	1	no	—
863	C₄×C₄⋊C₄	—	67	1	no	—
864	C₄×C₄⋊C₄	—	67	1	no	—
865	C₄×C₄⋊C₄	—	67	1	no	—
866	C₄×C₄⋊C₄	—	67	1	no	—
867	C₄×C₄⋊C₄	—	67	1	no	—
868	C₄×C₄⋊C₄	—	67	1	no	—
869	C₄×C₄⋊C₄	—	67	1	no	—
870	C₄×C₄⋊C₄	—	67	1	no	—
871	C₄×C₄⋊C₄	—	67	1	no	—
872	C₄×C₄⋊C₄	—	67	1	no	—
873	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
874	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
875	C₄×C₂²⋊C₄	—	67	1	no	—
876	C₄×C₂²⋊C₄	—	67	1	no	—
877	C₄×C₂²⋊C₄	—	67	1	no	—
878	C₄×C₂²⋊C₄	—	67	1	no	—
879	C₄×C₂²⋊C₄	—	67	1	no	—
880	C₄×C₂²⋊C₄	—	67	1	no	—
881	C₄×C₂²⋊C₄	—	67	1	no	—
882	C₄×C₂²⋊C₄	—	67	1	no	—
883	C₄×C₂²⋊C₄	—	67	1	no	—
884	C₄×C₂²⋊C₄	—	67	1	no	—
885	C₄×C₂²⋊C₄	—	67	1	no	—
886	C₄×C₂²⋊C₄	—	67	1	no	—
887	C₄×C₂²⋊C₄	—	67	1	no	—
888	C₄×C₂²⋊C₄	—	67	1	no	—
889	C₄×C₂²⋊C₄	—	67	1	no	—
890	C₄×C₂²⋊C₄	—	67	1	no	—
891	C₄×C₂²⋊C₄	—	67	1	no	—
892	C₄×C₂²⋊C₄	—	67	1	no	—
893	C₄×C₂²⋊C₄	—	67	1	no	—
894	C₄×C₂²⋊C₄	—	67	1	no	—
895	C₄×C₂²⋊C₄	—	67	1	no	—
896	C₄×C₂²⋊C₄	—	67	1	no	—
897	C₄×C₂²⋊C₄	—	67	1	no	—
898	C₄×C₂²⋊C₄	—	67	1	no	—
899	C₄×C₂²⋊C₄	—	67	1	no	—
900	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
901	#376	—	67	1	no	—
902	#376	—	67	1	no	—
903	#376	—	67	1	no	—
904	#376	—	67	1	no	—
905	C₄³	—	67	1	no	—
906	C₄³	—	67	1	no	—
907	C₂⁵	—	67	1	no	—
908	C₂³×C₄	—	67	1	no	—
909	C₂³×C₄	—	67	1	no	—
910	C₂³×C₄	—	67	1	no	—
911	C₂³×C₄	—	67	1	no	—
912	C₂³×C₄	—	67	1	no	—
913	C₂³×C₄	—	67	1	no	—
914	C₂³×C₄	—	67	1	no	—
915	C₂³×C₄	—	67	1	no	—
916	C₂³×C₄	—	67	1	no	—
917	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
918	#126	—	67	8	no	—
919	#126	—	67	8	no	—
920	#126	—	67	8	no	—
921	#126	—	67	8	no	—
922	#126	—	67	8	no	—
923	#126	—	67	8	no	—
924	#126	—	67	8	no	—
925	#126	C₄×D₆₇	1	8	yes	complemented
926	#117	—	134	4	no	—
927	#117	—	134	4	no	—
928	#117	—	134	4	no	—
929	#117	—	134	4	no	—
930	C₂×C₄⋊C₄	—	67	1	no	—
931	C₂×C₄⋊C₄	—	67	1	no	—
932	C₂×C₄⋊C₄	—	67	1	no	—
933	C₂×C₄⋊C₄	—	67	1	no	—
934	C₂×C₄⋊C₄	—	67	1	no	—
935	C₂×C₄⋊C₄	—	67	1	no	—
936	C₂×C₄⋊C₄	—	67	1	no	—
937	C₂×C₄⋊C₄	—	67	1	no	—
938	C₂×C₄⋊C₄	—	67	1	no	—
939	C₂×C₄⋊C₄	—	67	1	no	—
940	C₂×C₄⋊C₄	—	67	1	no	—
941	C₂×C₄⋊C₄	—	67	1	no	—
942	C₂×C₄⋊C₄	—	67	1	no	—
943	C₂×C₄⋊C₄	—	67	1	no	—
944	C₂×C₄⋊C₄	—	67	1	no	—
945	C₂×C₄⋊C₄	—	67	1	no	—
946	C₂×C₄⋊C₄	—	67	1	no	—
947	C₂×C₄⋊C₄	—	67	8	no	—
948	C₂×C₄⋊C₄	—	67	8	no	—
949	C₂×C₄⋊C₄	—	67	8	no	—
950	C₂×C₄⋊C₄	—	67	1	no	—
951	C₂×C₄⋊C₄	—	67	1	no	—
952	C₂×C₄⋊C₄	—	67	1	no	—
953	C₂×C₄⋊C₄	—	67	1	no	—
954	C₂×C₄⋊C₄	—	67	1	no	—
955	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	—	67	1	no	—
966	C₂×C₂²⋊C₄	—	67	1	no	—
967	C₂×C₂²⋊C₄	—	67	1	no	—
968	C₂×C₂²⋊C₄	—	67	1	no	—
969	C₂×C₂²⋊C₄	—	67	1	no	—
970	C₂×C₂²⋊C₄	—	67	1	no	—
971	C₂×C₂²⋊C₄	—	67	1	no	—
972	C₂×C₂²⋊C₄	—	67	1	no	—
973	C₂×C₂²⋊C₄	—	67	1	no	—
974	C₂×C₂²⋊C₄	—	67	1	no	—
975	C₂×C₂²⋊C₄	—	67	1	no	—
976	C₂×C₂²⋊C₄	—	67	1	no	—
977	C₂×C₂²⋊C₄	—	67	1	no	—
978	C₂×C₂²⋊C₄	—	67	1	no	—
979	C₂×C₂²⋊C₄	—	67	1	no	—
980	C₂×C₂²⋊C₄	—	67	1	no	—
981	C₂×C₂²⋊C₄	—	67	1	no	—
982	C₂×C₂²⋊C₄	—	67	8	no	—
983	C₂×C₂²⋊C₄	—	67	8	no	—
984	C₂×C₂²⋊C₄	—	67	8	no	—
985	C₂×C₂²⋊C₄	—	67	1	no	—
986	C₂×C₂²⋊C₄	—	67	1	no	—
987	C₂×C₂²⋊C₄	—	67	1	no	—
988	C₂×C₂²⋊C₄	—	67	1	no	—
989	C₂×C₂²⋊C₄	—	67	1	no	—
990	C₂×C₂²⋊C₄	—	67	1	no	—
991	C₂×C₂²⋊C₄	—	67	1	no	—
992	C₂×C₂²⋊C₄	—	67	1	no	—
993	C₂×C₂²⋊C₄	—	67	1	no	—
994	C₂×C₂²⋊C₄	—	134	4	no	—
995	C₂×C₂²⋊C₄	—	134	4	no	—
996	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1002	C₂×C₄²	—	67	1	no	—
1003	C₂×C₄²	—	67	1	no	—
1004	C₂×C₄²	—	67	1	no	—
1005	C₂×C₄²	—	67	1	no	—
1006	C₂×C₄²	—	67	1	no	—
1007	C₂×C₄²	—	67	1	no	—
1008	C₂×C₄²	—	67	1	no	—
1009	C₂×C₄²	—	67	1	no	—
1010	C₂×C₄²	—	67	1	no	—
1011	C₂×C₄²	—	67	1	no	—
1012	C₂×C₄²	—	67	1	no	—
1013	C₂×C₄²	—	67	1	no	—
1014	C₂×C₄²	—	67	1	no	—
1015	C₂×C₄²	—	67	1	no	—
1016	C₂×C₄²	—	67	1	no	—
1017	C₂×C₄²	—	67	1	no	—
1018	C₂×C₄²	—	67	1	no	—
1019	C₂×C₄²	—	67	1	no	—
1020	C₂×C₄²	—	67	1	no	—
1021	C₂×C₄²	—	67	8	no	—
1022	C₂×C₄²	—	67	1	no	—
1023	C₂×C₄²	—	67	1	no	—
1024	C₂×C₄²	—	67	1	no	—
1025	C₂×C₄²	—	67	1	no	—
1026	C₂×C₄²	—	67	1	no	—
1027	C₂×C₄²	—	67	1	no	—
1028	C₂×C₄²	—	67	1	no	—
1029	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1030	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1031	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1032	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1033	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1034	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1035	#95	—	67	1	no	—
1036	#95	—	67	1	no	—
1037	#95	—	67	1	no	—
1038	#95	—	67	1	no	—
1039	#95	—	67	1	no	—
1040	#95	—	67	1	no	—
1041	#95	—	67	1	no	—
1042	#95	—	67	1	no	—
1043	#95	—	67	1	no	—
1044	#95	—	67	1	no	—
1045	#95	—	67	1	no	—
1046	#95	—	67	1	no	—
1047	#95	—	67	1	no	—
1048	#95	—	67	1	no	—
1049	#95	—	67	1	no	—
1050	#95	—	67	1	no	—
1051	#95	—	67	1	no	—
1052	#95	—	67	1	no	—
1053	#95	—	67	1	no	—
1054	#95	—	67	1	no	—
1055	#95	—	67	1	no	—
1056	#95	—	67	1	no	—
1057	#95	—	67	1	no	—
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	C₂²×D₆₇	1	1	yes	characteristic
1072	#95	C₂²×D₆₇	1	1	yes	characteristic
1073	#95	C₂²×D₆₇	1	1	yes	characteristic
1074	#95	C₂²×D₆₇	1	1	yes	characteristic
1075	#95	C₂²×D₆₇	1	1	yes	characteristic
1076	#95	C₂²×D₆₇	1	1	yes	characteristic
1077	#95	C₂²×D₆₇	1	1	yes	characteristic
1078	#95	C₂²×D₆₇	1	1	yes	characteristic
1079	#95	C₂²×D₆₇	1	1	yes	characteristic
1080	#95	C₂²×D₆₇	1	1	yes	characteristic
1081	#95	C₂²×D₆₇	1	1	yes	characteristic
1082	#95	C₂²×D₆₇	1	1	yes	characteristic
1083	C₂⁴	—	268	1	no	—
1084	C₂⁴	—	268	1	no	—
1085	C₂⁴	—	268	1	no	—
1086	C₂⁴	—	268	1	no	—
1087	C₂⁴	—	67	4	no	—
1088	C₂⁴	—	67	1	no	—
1089	C₂⁴	—	67	1	no	—
1090	C₂⁴	—	134	2	no	—
1091	C₂⁴	—	134	2	no	—
1092	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1093	C₂²×C₄	—	2	2	no	—
1094	C₂²×C₄	—	4	1	no	—
1095	C₂²×C₄	—	4	1	no	—
1096	C₂²×C₄	—	268	1	no	—
1097	C₂²×C₄	—	268	1	no	—
1098	C₂²×C₄	—	268	1	no	—
1099	C₂²×C₄	—	268	1	no	—
1100	C₂²×C₄	—	268	1	no	—
1101	C₂²×C₄	—	268	1	no	—
1102	C₂²×C₄	—	268	1	no	—
1103	C₂²×C₄	—	268	1	no	—
1104	C₂²×C₄	—	268	1	no	—
1105	C₂²×C₄	—	268	1	no	—
1106	C₂²×C₄	—	268	1	no	—
1107	C₂²×C₄	—	268	1	no	—
1108	C₂²×C₄	—	268	1	no	—
1109	C₂²×C₄	—	268	1	no	—
1110	C₂²×C₄	—	67	4	no	—
1111	C₂²×C₄	—	67	4	no	—
1112	C₂²×C₄	—	67	4	no	—
1113	C₂²×C₄	—	67	4	no	—
1114	C₂²×C₄	—	67	1	no	—
1115	C₂²×C₄	—	67	1	no	—
1116	C₂²×C₄	—	67	1	no	—
1117	C₂²×C₄	—	67	1	no	—
1118	C₂²×C₄	—	67	1	no	—
1119	C₂²×C₄	—	67	1	no	—
1120	C₂²×C₄	—	67	1	no	—
1121	C₂²×C₄	—	67	1	no	—
1122	C₂²×C₄	—	67	4	no	—
1123	C₂²×C₄	—	67	4	no	—
1124	C₂²×C₄	—	67	1	no	—
1125	C₂²×C₄	—	67	1	no	—
1126	C₂²×C₄	—	67	1	no	—
1127	C₂²×C₄	—	67	1	no	—
1128	C₂²×C₄	—	67	1	no	—
1129	C₂²×C₄	—	67	1	no	—
1130	C₂²×C₄	—	134	2	no	—
1131	C₂²×C₄	—	134	2	no	—
1132	C₂²×C₄	—	134	2	no	—
1133	C₂²×C₄	—	134	2	no	—
1134	C₂²×C₄	—	134	2	no	—
1135	C₂²×C₄	—	134	2	no	—
1136	C₂²×C₄	—	134	2	no	—
1137	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1138	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1139	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1140	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1141	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1142	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1143	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1144	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1145	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1147	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1148	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1151	C₄⋊C₄	—	2	2	no	—
1152	C₄⋊C₄	—	2	2	no	—
1153	C₄⋊C₄	—	2	2	no	—
1154	C₄⋊C₄	—	4	1	no	—
1155	C₄⋊C₄	—	4	1	no	—
1156	C₄⋊C₄	—	4	1	no	—
1157	C₄⋊C₄	—	4	1	no	—
1158	C₄⋊C₄	—	268	1	no	—
1159	C₄⋊C₄	—	268	1	no	—
1160	C₄⋊C₄	—	268	1	no	—
1161	C₄⋊C₄	—	268	1	no	—
1162	C₄⋊C₄	—	268	1	no	—
1163	C₄⋊C₄	—	268	1	no	—
1164	C₄⋊C₄	—	268	1	no	—
1165	C₄⋊C₄	—	268	1	no	—
1166	C₄⋊C₄	—	67	4	no	—
1167	C₄⋊C₄	—	67	4	no	—
1168	C₄⋊C₄	—	67	4	no	—
1169	C₄⋊C₄	—	67	4	no	—
1170	C₄⋊C₄	—	67	4	no	—
1171	C₄⋊C₄	—	67	4	no	—
1172	C₄⋊C₄	—	67	4	no	—
1173	C₄⋊C₄	—	67	4	no	—
1174	C₄⋊C₄	—	67	4	no	—
1175	C₄⋊C₄	—	134	2	no	—
1176	C₄⋊C₄	—	134	2	no	—
1177	C₄⋊C₄	—	134	2	no	—
1178	C₄⋊C₄	—	134	2	no	—
1179	C₄⋊C₄	—	134	2	no	—
1180	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1181	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1182	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1183	C₂²⋊C₄	—	2	2	no	—
1184	C₂²⋊C₄	—	4	1	no	—
1185	C₂²⋊C₄	—	4	1	no	—
1186	C₂²⋊C₄	—	268	1	no	—
1187	C₂²⋊C₄	—	268	1	no	—
1188	C₂²⋊C₄	—	268	1	no	—
1189	C₂²⋊C₄	—	268	1	no	—
1190	C₂²⋊C₄	—	268	1	no	—
1191	C₂²⋊C₄	—	268	1	no	—
1192	C₂²⋊C₄	—	67	4	no	—
1193	C₂²⋊C₄	—	67	4	no	—
1194	C₂²⋊C₄	—	67	4	no	—
1195	C₂²⋊C₄	—	67	4	no	—
1196	C₂²⋊C₄	—	67	4	no	—
1197	C₂²⋊C₄	—	67	4	no	—
1198	C₂²⋊C₄	—	67	4	no	—
1199	C₂²⋊C₄	—	67	4	no	—
1200	C₂²⋊C₄	—	67	4	no	—
1201	C₂²⋊C₄	—	67	4	no	—
1202	C₂²⋊C₄	—	67	4	no	—
1203	C₂²⋊C₄	—	134	2	no	—
1204	C₂²⋊C₄	—	134	2	no	—
1205	C₂²⋊C₄	—	134	2	no	—
1206	C₂²⋊C₄	—	134	2	no	—
1207	C₂²⋊C₄	—	134	2	no	—
1208	C₂²⋊C₄	—	134	2	no	—
1209	C₂²⋊C₄	—	134	2	no	—
1210	C₂²⋊C₄	—	134	2	no	—
1211	C₂²⋊C₄	—	134	2	no	—
1212	C₂²⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1213	C₂²⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1214	C₂²⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1215	C₄²	—	2	2	no	—
1216	C₄²	—	4	1	no	—
1217	C₄²	—	4	1	no	—
1218	C₄²	—	4	1	no	—
1219	C₄²	—	4	1	no	—
1220	C₄²	—	268	1	no	—
1221	C₄²	—	268	1	no	—
1222	C₄²	—	268	1	no	—
1223	C₄²	—	268	1	no	—
1224	C₄²	—	268	1	no	—
1225	C₄²	—	268	1	no	—
1226	C₄²	—	268	1	no	—
1227	C₄²	—	268	1	no	—
1228	C₄²	—	268	1	no	—
1229	C₄²	—	268	1	no	—
1230	C₄²	—	268	1	no	—
1231	C₄²	—	268	1	no	—
1232	C₄²	—	268	1	no	—
1233	C₄²	—	268	1	no	—
1234	C₄²	—	268	1	no	—
1235	C₄²	—	268	1	no	—
1236	C₄²	—	67	4	no	—
1237	C₄²	—	67	4	no	—
1238	C₄²	—	67	4	no	—
1239	C₄²	—	134	2	no	—
1240	C₄²	—	134	2	no	—
1241	C₄²	—	134	2	no	—
1242	C₄²	—	134	2	no	—
1243	C₄²	—	134	2	no	—
1244	C₄²	—	134	2	no	—
1245	C₄²	—	134	2	no	—
1246	C₄²	C₂×C₄×D₆₇	1	4	yes	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	2	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	268	4	no	—
1254	C₂³	—	268	4	no	—
1255	C₂³	—	536	2	no	—
1256	C₂³	—	536	2	no	—
1257	C₂³	—	536	2	no	—
1258	C₂³	—	536	2	no	—
1259	C₂³	—	67	2	no	—
1260	C₂³	—	67	2	no	—
1261	C₂³	—	67	2	no	—
1262	C₂³	—	67	2	no	—
1263	C₂³	—	134	8	no	—
1264	C₂³	—	134	1	no	—
1265	C₂³	—	134	1	no	—
1266	C₂³	—	134	1	no	—
1267	C₂³	—	134	1	no	—
1268	C₂³	—	134	1	no	—
1269	C₂³	—	134	1	no	—
1270	C₂³	—	134	1	no	—
1271	C₂³	—	134	1	no	—
1272	C₂³	—	134	1	no	—
1273	C₂³	—	134	1	no	—
1274	C₂³	C₂²×C₄×D₆₇	1	2	yes	—
1275	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	8	2	no	—
1311	C₂×C₄	—	268	4	no	—
1312	C₂×C₄	—	268	4	no	—
1313	C₂×C₄	—	268	4	no	—
1314	C₂×C₄	—	268	4	no	—
1315	C₂×C₄	—	536	2	no	—
1316	C₂×C₄	—	536	2	no	—
1317	C₂×C₄	—	536	2	no	—
1318	C₂×C₄	—	67	2	no	—
1319	C₂×C₄	—	67	2	no	—
1320	C₂×C₄	—	67	2	no	—
1321	C₂×C₄	—	67	2	no	—
1322	C₂×C₄	—	67	2	no	—
1323	C₂×C₄	—	67	2	no	—
1324	C₂×C₄	—	67	2	no	—
1325	C₂×C₄	—	67	2	no	—
1326	C₂×C₄	—	134	8	no	—
1327	C₂×C₄	—	134	8	no	—
1328	C₂×C₄	—	134	1	no	—
1329	C₂×C₄	—	134	1	no	—
1330	C₂×C₄	—	134	1	no	—
1331	C₂×C₄	—	134	1	no	—
1332	C₂×C₄	—	134	1	no	—
1333	C₂×C₄	—	134	1	no	—
1334	C₂×C₄	—	134	1	no	—
1335	C₂×C₄	—	134	1	no	—
1336	C₂×C₄	—	134	1	no	—
1337	C₂×C₄	—	134	1	no	—
1338	C₂×C₄	—	134	1	no	—
1339	C₂×C₄	—	134	1	no	—
1340	C₂×C₄	—	134	1	no	—
1341	C₂×C₄	—	134	1	no	—
1342	C₂×C₄	—	134	1	no	—
1343	C₂×C₄	—	134	1	no	—
1344	C₂×C₄	—	134	1	no	—
1345	C₂×C₄	—	134	1	no	—
1346	C₂×C₄	—	134	1	no	—
1347	C₂×C₄	—	134	1	no	—
1348	C₂×C₄	—	134	1	no	—
1349	C₂×C₄	—	134	1	no	—
1350	C₂×C₄	—	134	1	no	—
1351	C₂×C₄	—	134	1	no	—
1352	C₂×C₄	—	134	1	no	—
1353	C₂×C₄	—	134	1	no	—
1354	C₂×C₄	—	134	1	no	—
1355	C₂×C₄	—	134	1	no	—
1356	C₂×C₄	—	134	1	no	—
1357	C₂×C₄	—	134	1	no	—
1358	C₂×C₄	—	134	1	no	—
1359	C₂×C₄	—	134	1	no	—
1360	C₂×C₄	—	134	1	no	—
1361	C₂×C₄	—	134	1	no	—
1362	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1363	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1364	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1365	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1366	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1367	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1368	C₂×C₄	#41×D₆₇	1	2	yes	—
1369	C₂×C₄	#41×D₆₇	1	2	yes	—
1370	C₂²	—	2	2	no	—
1371	C₂²	—	2	2	no	—
1372	C₂²	—	2	2	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	268	1	no	—
1378	C₂²	—	268	1	no	—
1379	C₂²	—	268	1	no	—
1380	C₂²	—	268	1	no	—
1381	C₂²	—	536	8	no	—
1382	C₂²	—	67	4	no	—
1383	C₂²	—	134	2	no	—
1384	C₂²	—	134	2	no	—
1385	C₂²	—	134	2	no	—
1386	C₂²	—	134	2	no	—
1387	C₂²	—	134	2	no	—
1388	C₂²	—	134	2	no	—
1389	C₂²	—	134	2	no	—
1390	C₂²	—	134	2	no	—
1391	C₂²	—	134	2	no	—
1392	C₂²	C₂³×C₄×D₆₇	1	1	yes	characteristic
1393	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1394	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
1395	C₂²	#16864231	1	1	yes	characteristic
1396	C₂²	#16864231	1	1	yes	characteristic
1397	C₂²	#16864233	1	1	yes	characteristic
1398	C₂²	#16864233	1	1	yes	characteristic
1399	C₄	—	2	2	no	—
1400	C₄	—	2	2	no	—
1401	C₄	—	2	2	no	—
1402	C₄	—	2	2	no	—
1403	C₄	—	2	2	no	—
1404	C₄	—	2	2	no	—
1405	C₄	—	2	2	no	—
1406	C₄	—	2	2	no	—
1407	C₄	—	4	1	no	—
1408	C₄	—	4	1	no	—
1409	C₄	—	4	1	no	—
1410	C₄	—	4	1	no	—
1411	C₄	—	4	1	no	—
1412	C₄	—	4	1	no	—
1413	C₄	—	268	1	no	—
1414	C₄	—	268	1	no	—
1415	C₄	—	268	1	no	—
1416	C₄	—	268	1	no	—
1417	C₄	—	268	1	no	—
1418	C₄	—	268	1	no	—
1419	C₄	—	134	2	no	—
1420	C₄	—	134	2	no	—
1421	C₄	—	134	2	no	—
1422	C₄	—	134	2	no	—
1423	C₄	—	134	2	no	—
1424	C₄	—	134	2	no	—
1425	C₄	—	134	2	no	—
1426	C₄	—	134	2	no	—
1427	C₂	—	4	2	no	—
1428	C₂	—	268	2	no	—
1429	C₂	—	134	4	no	—
1430	C₂	C₄×#41×D₆₇	1	1	yes	characteristic
1431	C₂	#22573409	1	1	yes	characteristic
1432	C₂	#22573409	1	1	yes	characteristic
1433	C₂	#22574267	1	1	yes	characteristic
1434	C₂	#22574273	1	1	yes	characteristic
1435	C₂	#22574275	1	1	yes	characteristic
1436	C₂	#22574283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₆₇×#2334	C₂
socle, cosocle	C₂³×C₆₇	C₂⁵
prime radical	C₂⁴×D₆₇	C₂³
hypercenter	#2334	D₆₇
hypocenter	C₆₇	#34247
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2334

Complements

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

N	H ≅ G/N	type
2. #22563336	C₂	semidirect
3. #22563336	C₂	semidirect
4. #22563332	C₂	semidirect
5. #22563332	C₂	semidirect
6. #22563328	C₂	semidirect
7. #22563328	C₂	semidirect
8. #22563324	C₂	semidirect
9. #22563324	C₂	semidirect
10. #22563085	C₂	semidirect
11. #22563083	C₂	semidirect
12. #22563077	C₂	semidirect
13. #22563075	C₂	semidirect
18. #22562988	C₂	semidirect
19. #22562984	C₂	semidirect
20. #22562980	C₂	semidirect
21. #22562808	C₂	semidirect
23. #22562763	C₂	semidirect
24. C₄×#14524038	C₂	semidirect
25. #22562759	C₂	semidirect
26. C₄×#14524036	C₂	semidirect
27. #22562602	C₂	semidirect
28. #22562563	C₂	semidirect
30. C₄×#14524001	C₂	semidirect
31. C₆₇×#2334	C₂	semidirect
39. #126×D₆₇	C₄	semidirect
53. #16863295	C₂²	semidirect
54. #16863295	C₂²	semidirect
55. #16863293	C₂²	semidirect
56. #16863293	C₂²	semidirect
57. #16863291	C₂²	semidirect
58. #16863291	C₂²	semidirect
80. #16863283	C₂²	semidirect
81. #16863283	C₂²	semidirect
82. #16863283	C₂²	semidirect
83. #16863283	C₂²	semidirect
84. #16863283	C₂²	semidirect
85. #16863282	C₂²	semidirect
86. #16863282	C₂²	semidirect
87. #16863282	C₂²	semidirect
88. #16863281	C₂²	semidirect
89. #16863281	C₂²	semidirect
90. #16863281	C₂²	semidirect
91. #16863280	C₂²	semidirect
92. #16863279	C₂²	semidirect
93. #16863279	C₂²	semidirect
94. #16863279	C₂²	semidirect
95. #16863278	C₂²	semidirect
96. #16863277	C₂²	semidirect
97. #16863277	C₂²	semidirect
98. #16863277	C₂²	semidirect
99. #16863277	C₂²	semidirect
100. #16863277	C₂²	semidirect
107. #16863263	C₂²	semidirect
108. #16863263	C₂²	semidirect
109. #16863262	C₂²	semidirect
122. C₄⋊C₄×Dic₆₇	C₂²	semidirect
123. C₄⋊C₄×Dic₆₇	C₂²	semidirect
124. C₄⋊C₄×Dic₆₇	C₂²	semidirect
125. C₄⋊C₄×Dic₆₇	C₂²	semidirect
126. C₄⋊C₄×Dic₆₇	C₂²	semidirect
127. C₄⋊C₄×Dic₆₇	C₂²	semidirect
128. C₄⋊C₄×Dic₆₇	C₂²	semidirect
129. C₄⋊C₄×Dic₆₇	C₂²	semidirect
130. C₄×Dic₆₇⋊C₄	C₂²	semidirect
131. C₄×Dic₆₇⋊C₄	C₂²	semidirect
132. C₄×Dic₆₇⋊C₄	C₂²	semidirect
133. C₄×Dic₆₇⋊C₄	C₂²	semidirect
134. C₄×C₄⋊Dic₆₇	C₂²	semidirect
135. C₄×C₄⋊Dic₆₇	C₂²	semidirect
136. C₄×C₄⋊Dic₆₇	C₂²	semidirect
137. C₄×C₄⋊Dic₆₇	C₂²	semidirect
138. #16863247	C₂²	semidirect
139. #16863247	C₂²	semidirect
140. #16863247	C₂²	semidirect
141. #16863247	C₂²	semidirect
167. #16863241	C₂²	semidirect
168. #16863241	C₂²	semidirect
169. #16863241	C₂²	semidirect
170. #16863241	C₂²	semidirect
171. C₄²×Dic₆₇	C₂²	semidirect
172. C₄²×Dic₆₇	C₂²	semidirect
174. #389×C₆₇	C₂²	semidirect
175. #389×C₆₇	C₂²	semidirect
179. #387×C₆₇	C₂²	semidirect
180. #387×C₆₇	C₂²	semidirect
181. #387×C₆₇	C₂²	semidirect
184. #382×C₆₇	C₂²	semidirect
185. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
186. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
198. #14524038	C₂×C₄	semidirect
199. #14524038	C₂×C₄	semidirect
200. #14524038	C₂×C₄	semidirect
201. #14524037	C₂×C₄	semidirect
202. #14524036	C₂×C₄	semidirect
203. #14524036	C₂×C₄	semidirect
204. #14524036	C₂×C₄	semidirect
231. C₄⋊C₄×D₆₇	C₂×C₄	semidirect
232. C₄⋊C₄×D₆₇	C₂×C₄	semidirect
233. C₄⋊C₄×D₆₇	C₂×C₄	semidirect
291. C₄²×D₆₇	C₂×C₄	semidirect
329. #126×C₆₇	C₂×C₄	semidirect
739. #2334	D₆₇	semidirect
750. C₆₇	#34247	semidirect
779. #389	C₂×D₆₇	semidirect
780. #389	C₂×D₆₇	semidirect
826. #387	C₂×D₆₇	semidirect
827. #387	C₂×D₆₇	semidirect
828. #387	C₂×D₆₇	semidirect
840. #382	C₂×D₆₇	semidirect
873. C₄×C₄⋊C₄	C₂×D₆₇	semidirect
874. C₄×C₄⋊C₄	C₂×D₆₇	semidirect
925. #126	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#126×D₆₇	2
#22563336	2
#22563332	2
#22563328	2
#22563324	2
#22563085	2
#22563083	2
#22563077	2
#22563075	2
#22563057	2
#22563056	2
#22563053	2
#22562988	2
#22562984	2
#22562980	2
#22562808	2
#22562803	2
#22562763	2
C₄×#14524038	2
#22562759	2
C₄×#14524036	2
#22562602	2
#22562563	2
#22562561	2
C₄×#14524001	2
C₆₇×#2334	2
#34247	67