Subgroups — C₆₇×#34960 #30714211

Order 17152.

1976 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2596	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2594	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2590	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2588	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2577	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2575	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2560	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2558	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2493	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2481	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2473	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2443	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2425	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2419	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2402	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2401	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2396	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2395	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
29	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
53	#401×C₆₇	C₂²	1	1	yes	characteristic
54	#400×C₆₇	C₂²	1	1	yes	characteristic
55	#400×C₆₇	C₂²	1	1	yes	characteristic
56	#400×C₆₇	C₂²	1	1	yes	characteristic
57	#400×C₆₇	C₂²	1	1	yes	characteristic
58	#400×C₆₇	C₂²	1	1	yes	characteristic
59	#400×C₆₇	C₂²	1	1	yes	characteristic
60	#400×C₆₇	C₂²	1	1	yes	characteristic
61	#400×C₆₇	C₂²	1	1	yes	characteristic
62	#400×C₆₇	C₂²	1	1	yes	characteristic
63	#399×C₆₇	C₂²	1	1	yes	characteristic
64	#399×C₆₇	C₂²	1	1	yes	characteristic
65	#398×C₆₇	C₂²	1	1	yes	characteristic
66	#398×C₆₇	C₂²	1	1	yes	characteristic
67	#398×C₆₇	C₂²	1	1	yes	characteristic
68	#398×C₆₇	C₂²	1	1	yes	characteristic
69	#398×C₆₇	C₂²	1	1	yes	characteristic
70	#398×C₆₇	C₂²	1	1	yes	characteristic
71	#398×C₆₇	C₂²	1	1	yes	characteristic
72	#397×C₆₇	C₂²	1	1	yes	characteristic
73	#397×C₆₇	C₂²	1	1	yes	characteristic
74	#397×C₆₇	C₂²	1	1	yes	characteristic
75	#397×C₆₇	C₂²	1	1	yes	characteristic
76	#397×C₆₇	C₂²	1	1	yes	characteristic
77	#397×C₆₇	C₂²	1	1	yes	characteristic
78	#396×C₆₇	C₂²	1	1	yes	characteristic
79	#396×C₆₇	C₂²	1	1	yes	characteristic
80	#396×C₆₇	C₂²	1	1	yes	characteristic
81	#395×C₆₇	C₂²	1	1	yes	characteristic
82	#394×C₆₇	C₂²	1	1	yes	characteristic
83	#394×C₆₇	C₂²	1	1	yes	characteristic
84	#393×C₆₇	C₂²	1	1	yes	characteristic
85	#391×C₆₇	C₂²	1	1	yes	characteristic
86	#391×C₆₇	C₂²	1	1	yes	characteristic
87	#390×C₆₇	C₂²	1	1	yes	characteristic
88	#389×C₆₇	C₂²	1	1	yes	characteristic
89	#389×C₆₇	C₂²	1	1	yes	characteristic
90	#389×C₆₇	C₂²	1	1	yes	characteristic
91	#389×C₆₇	C₂²	1	1	yes	characteristic
92	#389×C₆₇	C₂²	1	1	yes	characteristic
93	#388×C₆₇	C₂²	1	1	yes	characteristic
94	#388×C₆₇	C₂²	1	1	yes	characteristic
95	#388×C₆₇	C₂²	1	1	yes	characteristic
96	#388×C₆₇	C₂²	1	1	yes	characteristic
97	#388×C₆₇	C₂²	1	1	yes	characteristic
98	#388×C₆₇	C₂²	1	1	yes	characteristic
99	#388×C₆₇	C₂²	1	1	yes	characteristic
100	#388×C₆₇	C₂²	1	1	yes	characteristic
101	#388×C₆₇	C₂²	1	1	yes	characteristic
102	#388×C₆₇	C₂²	1	1	yes	characteristic
103	#388×C₆₇	C₂²	1	1	yes	characteristic
104	#388×C₆₇	C₂²	1	1	yes	characteristic
105	#388×C₆₇	C₂²	1	1	yes	characteristic
106	#387×C₆₇	C₂²	1	1	yes	characteristic
107	#387×C₆₇	C₂²	1	1	yes	characteristic
108	#387×C₆₇	C₂²	1	1	yes	characteristic
109	#387×C₆₇	C₂²	1	1	yes	characteristic
110	#387×C₆₇	C₂²	1	1	yes	characteristic
111	#387×C₆₇	C₂²	1	1	yes	characteristic
112	#387×C₆₇	C₂²	1	1	yes	characteristic
113	#387×C₆₇	C₂²	1	1	yes	characteristic
114	#387×C₆₇	C₂²	1	1	yes	characteristic
115	#387×C₆₇	C₂²	1	1	yes	characteristic
116	#387×C₆₇	C₂²	1	1	yes	characteristic
117	#387×C₆₇	C₂²	1	1	yes	characteristic
118	#387×C₆₇	C₂²	1	1	yes	characteristic
119	#387×C₆₇	C₂²	1	1	yes	characteristic
120	#387×C₆₇	C₂²	1	1	yes	characteristic
121	#387×C₆₇	C₂²	1	1	yes	characteristic
122	#387×C₆₇	C₂²	1	1	yes	characteristic
123	#387×C₆₇	C₂²	1	1	yes	characteristic
124	#387×C₆₇	C₂²	1	1	yes	characteristic
125	#386×C₆₇	C₂²	1	1	yes	characteristic
126	#386×C₆₇	C₂²	1	1	yes	characteristic
127	#386×C₆₇	C₂²	1	1	yes	characteristic
128	#386×C₆₇	C₂²	1	1	yes	characteristic
129	#386×C₆₇	C₂²	1	1	yes	characteristic
130	#386×C₆₇	C₂²	1	1	yes	characteristic
131	#386×C₆₇	C₂²	1	1	yes	characteristic
132	#385×C₆₇	C₂²	1	1	yes	characteristic
133	#385×C₆₇	C₂²	1	1	yes	characteristic
134	#385×C₆₇	C₂²	1	1	yes	characteristic
135	#385×C₆₇	C₂²	1	1	yes	characteristic
136	#385×C₆₇	C₂²	1	1	yes	characteristic
137	#385×C₆₇	C₂²	1	1	yes	characteristic
138	#385×C₆₇	C₂²	1	1	yes	characteristic
139	#385×C₆₇	C₂²	1	1	yes	characteristic
140	#385×C₆₇	C₂²	1	1	yes	characteristic
141	#383×C₆₇	C₂²	1	1	yes	characteristic
142	#382×C₆₇	C₂²	1	1	yes	characteristic
143	#381×C₆₇	C₂²	1	1	yes	characteristic
144	#381×C₆₇	C₂²	1	1	yes	characteristic
145	#381×C₆₇	C₂²	1	1	yes	characteristic
146	#380×C₆₇	C₂²	1	1	yes	characteristic
147	#380×C₆₇	C₂²	1	1	yes	characteristic
148	#380×C₆₇	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
156	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
157	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
158	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
159	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
169	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
170	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
171	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
183	#376×C₆₇	C₂²	1	1	yes	characteristic
184	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
185	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
186	C₄³×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
188	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
202	#126×C₆₇	—	2	4	no	—
203	#125×C₆₇	—	2	4	no	—
204	#123×C₆₇	—	2	4	no	—
205	#123×C₆₇	—	2	4	no	—
206	#123×C₆₇	—	2	4	no	—
207	C₂²⋊Q₈×C₆₇	—	2	4	no	—
208	C₂²⋊Q₈×C₆₇	—	2	4	no	—
209	#121×C₆₇	—	2	4	no	—
210	C₄×Q₈×C₆₇	—	4	2	no	—
211	C₄×D₄×C₆₇	—	2	4	no	—
212	C₄×D₄×C₆₇	—	2	4	no	—
213	C₄×D₄×C₆₇	—	2	4	no	—
214	C₄×D₄×C₆₇	—	2	4	no	—
215	C₄×D₄×C₆₇	—	4	2	no	—
216	#117×C₆₇	—	4	2	no	—
217	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
219	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₆₇	—	2	4	no	—
284	C₂×C₄²×C₆₇	—	4	2	no	—
285	C₂×C₄²×C₆₇	—	4	2	no	—
286	C₂×C₄²×C₆₇	—	4	2	no	—
287	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
288	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
311	#95×C₆₇	C₂³	1	1	yes	characteristic
312	#95×C₆₇	C₂³	1	1	yes	characteristic
313	#95×C₆₇	C₂³	1	1	yes	characteristic
314	#95×C₆₇	C₂³	1	1	yes	characteristic
315	#95×C₆₇	C₂³	1	1	yes	characteristic
316	#95×C₆₇	C₂³	1	1	yes	characteristic
317	#95×C₆₇	C₂³	1	1	yes	characteristic
318	#95×C₆₇	C₂³	1	1	yes	characteristic
319	#95×C₆₇	C₂³	1	1	yes	characteristic
320	#95×C₆₇	C₂³	1	1	yes	characteristic
321	#95×C₆₇	C₂³	1	1	yes	characteristic
322	#95×C₆₇	C₂³	1	1	yes	characteristic
323	#95×C₆₇	C₂³	1	1	yes	characteristic
324	#95×C₆₇	C₂³	1	1	yes	characteristic
325	#95×C₆₇	C₂³	1	1	yes	characteristic
326	#95×C₆₇	C₂³	1	1	yes	characteristic
327	#95×C₆₇	C₂³	1	1	yes	characteristic
328	#95×C₆₇	C₂³	1	1	yes	characteristic
329	#95×C₆₇	C₂³	1	1	yes	characteristic
330	#95×C₆₇	C₂³	1	1	yes	characteristic
331	#95×C₆₇	C₂³	1	1	yes	characteristic
332	#95×C₆₇	C₂³	1	1	yes	characteristic
333	#95×C₆₇	C₂³	1	1	yes	characteristic
334	#95×C₆₇	C₂³	1	1	yes	characteristic
335	#95×C₆₇	C₂³	1	1	yes	characteristic
336	#95×C₆₇	C₂³	1	1	yes	characteristic
337	#95×C₆₇	C₂³	1	1	yes	characteristic
338	#95×C₆₇	C₂³	1	1	yes	characteristic
339	#95×C₆₇	C₂³	1	1	yes	characteristic
340	#95×C₆₇	C₂³	1	1	yes	characteristic
341	#95×C₆₇	C₂³	1	1	yes	characteristic
342	#95×C₆₇	C₂³	1	1	yes	characteristic
343	#95×C₆₇	C₂³	1	1	yes	characteristic
344	#95×C₆₇	C₂³	1	1	yes	characteristic
345	#95×C₆₇	C₂³	1	1	yes	characteristic
346	#95×C₆₇	C₂³	1	1	yes	characteristic
347	#95×C₆₇	C₂³	1	1	yes	characteristic
348	#95×C₆₇	C₂³	1	1	yes	characteristic
349	#95×C₆₇	C₂³	1	1	yes	characteristic
350	#95×C₆₇	C₂³	1	1	yes	characteristic
351	#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	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×Q₈×C₆₇	—	2	2	no	—
367	C₂×Q₈×C₆₇	—	2	2	no	—
368	C₂×Q₈×C₆₇	—	4	1	no	—
369	C₂×D₄×C₆₇	—	2	2	no	—
370	C₂×D₄×C₆₇	—	2	2	no	—
371	C₂×D₄×C₆₇	—	2	2	no	—
372	C₂×D₄×C₆₇	—	2	2	no	—
373	C₂×D₄×C₆₇	—	2	2	no	—
374	C₂×D₄×C₆₇	—	2	2	no	—
375	C₂×D₄×C₆₇	—	2	2	no	—
376	C₂×D₄×C₆₇	—	4	1	no	—
377	C₂×D₄×C₆₇	#41	1	4	yes	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	2	no	—
380	C₂²×C₄×C₆₇	—	2	2	no	—
381	C₂²×C₄×C₆₇	—	2	2	no	—
382	C₂²×C₄×C₆₇	—	2	2	no	—
383	C₂²×C₄×C₆₇	—	2	2	no	—
384	C₂²×C₄×C₆₇	—	2	2	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	—	2	2	no	—
387	C₂²×C₄×C₆₇	—	2	2	no	—
388	C₂²×C₄×C₆₇	—	2	2	no	—
389	C₂²×C₄×C₆₇	—	2	2	no	—
390	C₂²×C₄×C₆₇	—	2	2	no	—
391	C₂²×C₄×C₆₇	—	2	2	no	—
392	C₂²×C₄×C₆₇	—	2	2	no	—
393	C₂²×C₄×C₆₇	—	2	2	no	—
394	C₂²×C₄×C₆₇	—	2	2	no	—
395	C₂²×C₄×C₆₇	—	2	2	no	—
396	C₂²×C₄×C₆₇	—	2	2	no	—
397	C₂²×C₄×C₆₇	—	2	2	no	—
398	C₂²×C₄×C₆₇	—	2	2	no	—
399	C₂²×C₄×C₆₇	—	2	2	no	—
400	C₂²×C₄×C₆₇	—	2	2	no	—
401	C₂²×C₄×C₆₇	—	2	2	no	—
402	C₂²×C₄×C₆₇	—	2	2	no	—
403	C₂²×C₄×C₆₇	—	2	2	no	—
404	C₂²×C₄×C₆₇	—	4	1	no	—
405	C₂²×C₄×C₆₇	—	4	1	no	—
406	C₂²×C₄×C₆₇	—	4	1	no	—
407	C₂²×C₄×C₆₇	—	4	1	no	—
408	C₂²×C₄×C₆₇	—	4	1	no	—
409	C₂²×C₄×C₆₇	—	4	1	no	—
410	C₂²×C₄×C₆₇	#41	1	4	yes	—
411	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	—	2	2	no	—
440	C₄⋊C₄×C₆₇	—	2	2	no	—
441	C₄⋊C₄×C₆₇	—	2	2	no	—
442	C₄⋊C₄×C₆₇	—	2	2	no	—
443	C₄⋊C₄×C₆₇	—	2	2	no	—
444	C₄⋊C₄×C₆₇	—	2	2	no	—
445	C₄⋊C₄×C₆₇	—	2	2	no	—
446	C₄⋊C₄×C₆₇	—	2	2	no	—
447	C₄⋊C₄×C₆₇	—	2	2	no	—
448	C₄⋊C₄×C₆₇	—	2	2	no	—
449	C₄⋊C₄×C₆₇	—	2	2	no	—
450	C₄⋊C₄×C₆₇	—	2	2	no	—
451	C₄⋊C₄×C₆₇	—	2	2	no	—
452	C₄⋊C₄×C₆₇	—	2	2	no	—
453	C₄⋊C₄×C₆₇	—	2	2	no	—
454	C₄⋊C₄×C₆₇	—	2	2	no	—
455	C₄⋊C₄×C₆₇	—	2	2	no	—
456	C₄⋊C₄×C₆₇	—	2	2	no	—
457	C₄⋊C₄×C₆₇	—	2	2	no	—
458	C₄⋊C₄×C₆₇	—	2	2	no	—
459	C₄⋊C₄×C₆₇	—	2	2	no	—
460	C₄⋊C₄×C₆₇	—	2	2	no	—
461	C₄⋊C₄×C₆₇	—	2	2	no	—
462	C₄⋊C₄×C₆₇	—	2	2	no	—
463	C₄⋊C₄×C₆₇	—	2	2	no	—
464	C₄⋊C₄×C₆₇	—	2	2	no	—
465	C₄⋊C₄×C₆₇	—	2	2	no	—
466	C₄⋊C₄×C₆₇	—	2	2	no	—
467	C₄⋊C₄×C₆₇	—	4	1	no	—
468	C₄⋊C₄×C₆₇	—	4	1	no	—
469	C₄⋊C₄×C₆₇	—	4	1	no	—
470	C₄⋊C₄×C₆₇	—	4	1	no	—
471	C₄⋊C₄×C₆₇	—	4	1	no	—
472	C₄⋊C₄×C₆₇	—	4	1	no	—
473	C₄⋊C₄×C₆₇	#41	1	4	yes	—
474	C₄⋊C₄×C₆₇	#41	1	4	yes	—
475	C₂²⋊C₄×C₆₇	—	2	2	no	—
476	C₂²⋊C₄×C₆₇	—	2	2	no	—
477	C₂²⋊C₄×C₆₇	—	2	2	no	—
478	C₂²⋊C₄×C₆₇	—	2	2	no	—
479	C₂²⋊C₄×C₆₇	—	2	2	no	—
480	C₂²⋊C₄×C₆₇	—	2	2	no	—
481	C₂²⋊C₄×C₆₇	—	2	2	no	—
482	C₂²⋊C₄×C₆₇	—	2	2	no	—
483	C₂²⋊C₄×C₆₇	—	2	2	no	—
484	C₂²⋊C₄×C₆₇	—	2	2	no	—
485	C₂²⋊C₄×C₆₇	—	2	2	no	—
486	C₂²⋊C₄×C₆₇	—	2	2	no	—
487	C₂²⋊C₄×C₆₇	—	2	2	no	—
488	C₂²⋊C₄×C₆₇	—	2	2	no	—
489	C₂²⋊C₄×C₆₇	—	2	2	no	—
490	C₂²⋊C₄×C₆₇	—	2	2	no	—
491	C₂²⋊C₄×C₆₇	—	2	2	no	—
492	C₂²⋊C₄×C₆₇	—	2	2	no	—
493	C₂²⋊C₄×C₆₇	—	2	2	no	—
494	C₂²⋊C₄×C₆₇	—	2	2	no	—
495	C₂²⋊C₄×C₆₇	—	2	2	no	—
496	C₂²⋊C₄×C₆₇	—	2	2	no	—
497	C₂²⋊C₄×C₆₇	—	2	2	no	—
498	C₂²⋊C₄×C₆₇	—	4	1	no	—
499	C₂²⋊C₄×C₆₇	—	4	1	no	—
500	C₂²⋊C₄×C₆₇	—	4	1	no	—
501	C₂²⋊C₄×C₆₇	—	4	1	no	—
502	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
503	C₄²×C₆₇	—	2	2	no	—
504	C₄²×C₆₇	—	2	2	no	—
505	C₄²×C₆₇	—	2	2	no	—
506	C₄²×C₆₇	—	2	2	no	—
507	C₄²×C₆₇	—	2	2	no	—
508	C₄²×C₆₇	—	2	2	no	—
509	C₄²×C₆₇	—	2	2	no	—
510	C₄²×C₆₇	—	2	2	no	—
511	C₄²×C₆₇	—	2	2	no	—
512	C₄²×C₆₇	—	2	2	no	—
513	C₄²×C₆₇	—	2	2	no	—
514	C₄²×C₆₇	—	2	2	no	—
515	C₄²×C₆₇	—	2	2	no	—
516	C₄²×C₆₇	—	2	2	no	—
517	C₄²×C₆₇	—	2	2	no	—
518	C₄²×C₆₇	—	2	2	no	—
519	C₄²×C₆₇	—	2	2	no	—
520	C₄²×C₆₇	—	2	2	no	—
521	C₄²×C₆₇	—	4	1	no	—
522	C₄²×C₆₇	—	4	1	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	C₂³×C₆₇	—	2	1	no	—
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	—	2	1	no	—
535	C₂³×C₆₇	—	2	1	no	—
536	C₂³×C₆₇	—	2	1	no	—
537	C₂³×C₆₇	—	2	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	C₂×#41	1	2	yes	—
546	C₂³×C₆₇	C₂×#41	1	2	yes	—
547	C₂³×C₆₇	C₂×#41	1	2	yes	—
548	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
549	Q₈×C₆₇	—	4	4	no	—
550	D₄×C₆₇	—	2	8	no	—
551	D₄×C₆₇	—	4	4	no	—
552	D₄×C₆₇	—	4	4	no	—
553	C₂×C₄×C₆₇	—	2	8	no	—
554	C₂×C₄×C₆₇	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	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	8	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	—	2	1	no	—
613	C₂×C₄×C₆₇	—	2	1	no	—
614	C₂×C₄×C₆₇	—	2	1	no	—
615	C₂×C₄×C₆₇	—	2	1	no	—
616	C₂×C₄×C₆₇	—	2	1	no	—
617	C₂×C₄×C₆₇	—	2	1	no	—
618	C₂×C₄×C₆₇	—	2	1	no	—
619	C₂×C₄×C₆₇	—	2	1	no	—
620	C₂×C₄×C₆₇	—	2	1	no	—
621	C₂×C₄×C₆₇	—	2	1	no	—
622	C₂×C₄×C₆₇	—	2	1	no	—
623	C₂×C₄×C₆₇	—	2	1	no	—
624	C₂×C₄×C₆₇	—	2	1	no	—
625	C₂×C₄×C₆₇	—	2	1	no	—
626	C₂×C₄×C₆₇	—	4	4	no	—
627	C₂×C₄×C₆₇	—	4	4	no	—
628	C₂×C₄×C₆₇	—	4	4	no	—
629	C₂×C₄×C₆₇	—	4	4	no	—
630	C₂×C₄×C₆₇	—	4	4	no	—
631	C₂×C₄×C₆₇	—	4	4	no	—
632	C₂×C₄×C₆₇	—	4	4	no	—
633	C₂×C₄×C₆₇	—	4	4	no	—
634	C₂×C₄×C₆₇	—	4	4	no	—
635	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
636	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
637	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
638	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
639	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
640	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
641	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
642	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
643	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
644	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
645	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
646	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
647	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
648	C₂²×C₆₇	—	2	2	no	—
649	C₂²×C₆₇	—	2	2	no	—
650	C₂²×C₆₇	—	2	2	no	—
651	C₂²×C₆₇	—	2	2	no	—
652	C₂²×C₆₇	—	2	2	no	—
653	C₂²×C₆₇	—	2	2	no	—
654	C₂²×C₆₇	—	2	2	no	—
655	C₂²×C₆₇	—	2	2	no	—
656	C₂²×C₆₇	—	2	2	no	—
657	C₂²×C₆₇	—	4	1	no	—
658	C₂²×C₆₇	—	4	1	no	—
659	C₂²×C₆₇	—	4	1	no	—
660	C₂²×C₆₇	—	4	1	no	—
661	C₂²×C₆₇	—	4	1	no	—
662	C₂²×C₆₇	—	4	1	no	—
663	C₂²×C₆₇	—	4	1	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	4	1	no	—
666	C₂²×C₆₇	—	4	1	no	—
667	C₂²×C₆₇	—	4	1	no	—
668	C₂²×C₆₇	#529	1	4	yes	—
669	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
670	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
671	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
672	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
673	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
674	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
676	C₄×C₆₇	—	2	2	no	—
677	C₄×C₆₇	—	2	2	no	—
678	C₄×C₆₇	—	2	2	no	—
679	C₄×C₆₇	—	2	2	no	—
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	—	4	1	no	—
687	C₄×C₆₇	—	4	1	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	C₄×C₆₇	—	4	1	no	—
695	C₄×C₆₇	—	4	1	no	—
696	C₄×C₆₇	—	4	1	no	—
697	C₄×C₆₇	—	4	1	no	—
698	C₄×C₆₇	—	4	1	no	—
699	C₄×C₆₇	—	4	1	no	—
700	C₄×C₆₇	—	4	1	no	—
701	C₄×C₆₇	—	4	1	no	—
702	C₄×C₆₇	—	4	1	no	—
703	C₄×C₆₇	#539	1	4	yes	—
704	#34960	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
705	C₂×C₆₇	—	2	4	no	—
706	C₂×C₆₇	—	4	2	no	—
707	C₂×C₆₇	—	8	1	no	—
708	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
709	C₂×C₆₇	#3444	1	1	yes	characteristic
710	C₂×C₆₇	C₂×#539	1	1	yes	characteristic
711	C₂×C₆₇	#3481	1	1	yes	characteristic
712	C₂×C₆₇	#3481	1	1	yes	characteristic
713	C₂×C₆₇	#3482	1	1	yes	characteristic
714	C₂×C₆₇	#3482	1	1	yes	characteristic
715	#2596	C₂×C₆₇	1	1	yes	characteristic, complemented
716	#2594	C₂×C₆₇	1	1	yes	characteristic, complemented
717	#2590	C₂×C₆₇	1	1	yes	characteristic, complemented
718	#2588	C₂×C₆₇	1	1	yes	characteristic, complemented
719	#2577	C₂×C₆₇	1	1	yes	characteristic, complemented
720	#2575	C₂×C₆₇	1	1	yes	characteristic, complemented
721	#2560	C₂×C₆₇	1	1	yes	characteristic, complemented
722	#2558	C₂×C₆₇	1	1	yes	characteristic, complemented
723	#2493	C₂×C₆₇	1	1	yes	characteristic, complemented
724	#2488	C₂×C₆₇	1	1	yes	characteristic, complemented
725	#2481	C₂×C₆₇	1	1	yes	characteristic, complemented
726	#2473	C₂×C₆₇	1	1	yes	characteristic, complemented
727	#2449	C₂×C₆₇	1	1	yes	characteristic, complemented
728	#2443	C₂×C₆₇	1	1	yes	characteristic
729	#2425	C₂×C₆₇	1	1	yes	characteristic
730	#2419	C₂×C₆₇	1	1	yes	characteristic, complemented
731	#2402	C₂×C₆₇	1	1	yes	characteristic, complemented
732	#2401	C₂×C₆₇	1	1	yes	characteristic, complemented
733	#2396	C₂×C₆₇	1	1	yes	characteristic, complemented
734	#2395	C₂×C₆₇	1	1	yes	characteristic, complemented
735	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
736	C₄×#126	C₂×C₆₇	1	1	yes	characteristic, complemented
737	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
738	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
739	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
740	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
741	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
742	C₄×#121	C₂×C₆₇	1	1	yes	characteristic
743	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
744	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
745	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
746	C₆₇	#34960	1	1	yes	characteristic, direct product factor, Sylow
747	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
748	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
749	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
750	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
751	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
752	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
753	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
754	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
755	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
756	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
757	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
758	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
759	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
760	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
761	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
762	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
763	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
764	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
765	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
766	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
767	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
768	#401	C₂²×C₆₇	1	1	yes	characteristic
769	#400	C₂²×C₆₇	1	1	yes	characteristic
770	#400	C₂²×C₆₇	1	1	yes	characteristic
771	#400	C₂²×C₆₇	1	1	yes	characteristic
772	#400	C₂²×C₆₇	1	1	yes	characteristic
773	#400	C₂²×C₆₇	1	1	yes	characteristic
774	#400	C₂²×C₆₇	1	1	yes	characteristic
775	#400	C₂²×C₆₇	1	1	yes	characteristic
776	#400	C₂²×C₆₇	1	1	yes	characteristic
777	#400	C₂²×C₆₇	1	1	yes	characteristic
778	#399	C₂²×C₆₇	1	1	yes	characteristic
779	#399	C₂²×C₆₇	1	1	yes	characteristic
780	#398	C₂²×C₆₇	1	1	yes	characteristic
781	#398	C₂²×C₆₇	1	1	yes	characteristic
782	#398	C₂²×C₆₇	1	1	yes	characteristic
783	#398	C₂²×C₆₇	1	1	yes	characteristic
784	#398	C₂²×C₆₇	1	1	yes	characteristic
785	#398	C₂²×C₆₇	1	1	yes	characteristic
786	#398	C₂²×C₆₇	1	1	yes	characteristic
787	#397	C₂²×C₆₇	1	1	yes	characteristic
788	#397	C₂²×C₆₇	1	1	yes	characteristic
789	#397	C₂²×C₆₇	1	1	yes	characteristic
790	#397	C₂²×C₆₇	1	1	yes	characteristic
791	#397	C₂²×C₆₇	1	1	yes	characteristic
792	#397	C₂²×C₆₇	1	1	yes	characteristic
793	#396	C₂²×C₆₇	1	1	yes	characteristic
794	#396	C₂²×C₆₇	1	1	yes	characteristic
795	#396	C₂²×C₆₇	1	1	yes	characteristic
796	#395	C₂²×C₆₇	1	1	yes	characteristic
797	#394	C₂²×C₆₇	1	1	yes	characteristic
798	#394	C₂²×C₆₇	1	1	yes	characteristic
799	#393	C₂²×C₆₇	1	1	yes	characteristic
800	#391	C₂²×C₆₇	1	1	yes	characteristic
801	#391	C₂²×C₆₇	1	1	yes	characteristic
802	#390	C₂²×C₆₇	1	1	yes	characteristic
803	#389	C₂²×C₆₇	1	1	yes	characteristic
804	#389	C₂²×C₆₇	1	1	yes	characteristic
805	#389	C₂²×C₆₇	1	1	yes	characteristic
806	#389	C₂²×C₆₇	1	1	yes	characteristic
807	#389	C₂²×C₆₇	1	1	yes	characteristic
808	#388	C₂²×C₆₇	1	1	yes	characteristic
809	#388	C₂²×C₆₇	1	1	yes	characteristic
810	#388	C₂²×C₆₇	1	1	yes	characteristic
811	#388	C₂²×C₆₇	1	1	yes	characteristic
812	#388	C₂²×C₆₇	1	1	yes	characteristic
813	#388	C₂²×C₆₇	1	1	yes	characteristic
814	#388	C₂²×C₆₇	1	1	yes	characteristic
815	#388	C₂²×C₆₇	1	1	yes	characteristic
816	#388	C₂²×C₆₇	1	1	yes	characteristic
817	#388	C₂²×C₆₇	1	1	yes	characteristic
818	#388	C₂²×C₆₇	1	1	yes	characteristic
819	#388	C₂²×C₆₇	1	1	yes	characteristic
820	#388	C₂²×C₆₇	1	1	yes	characteristic
821	#387	C₂²×C₆₇	1	1	yes	characteristic
822	#387	C₂²×C₆₇	1	1	yes	characteristic
823	#387	C₂²×C₆₇	1	1	yes	characteristic
824	#387	C₂²×C₆₇	1	1	yes	characteristic
825	#387	C₂²×C₆₇	1	1	yes	characteristic
826	#387	C₂²×C₆₇	1	1	yes	characteristic
827	#387	C₂²×C₆₇	1	1	yes	characteristic
828	#387	C₂²×C₆₇	1	1	yes	characteristic
829	#387	C₂²×C₆₇	1	1	yes	characteristic
830	#387	C₂²×C₆₇	1	1	yes	characteristic
831	#387	C₂²×C₆₇	1	1	yes	characteristic
832	#387	C₂²×C₆₇	1	1	yes	characteristic
833	#387	C₂²×C₆₇	1	1	yes	characteristic
834	#387	C₂²×C₆₇	1	1	yes	characteristic
835	#387	C₂²×C₆₇	1	1	yes	characteristic
836	#387	C₂²×C₆₇	1	1	yes	characteristic
837	#387	C₂²×C₆₇	1	1	yes	characteristic
838	#387	C₂²×C₆₇	1	1	yes	characteristic
839	#387	C₂²×C₆₇	1	1	yes	characteristic
840	#386	C₂²×C₆₇	1	1	yes	characteristic
841	#386	C₂²×C₆₇	1	1	yes	characteristic
842	#386	C₂²×C₆₇	1	1	yes	characteristic
843	#386	C₂²×C₆₇	1	1	yes	characteristic
844	#386	C₂²×C₆₇	1	1	yes	characteristic
845	#386	C₂²×C₆₇	1	1	yes	characteristic
846	#386	C₂²×C₆₇	1	1	yes	characteristic
847	#385	C₂²×C₆₇	1	1	yes	characteristic
848	#385	C₂²×C₆₇	1	1	yes	characteristic
849	#385	C₂²×C₆₇	1	1	yes	characteristic
850	#385	C₂²×C₆₇	1	1	yes	characteristic
851	#385	C₂²×C₆₇	1	1	yes	characteristic
852	#385	C₂²×C₆₇	1	1	yes	characteristic
853	#385	C₂²×C₆₇	1	1	yes	characteristic
854	#385	C₂²×C₆₇	1	1	yes	characteristic
855	#385	C₂²×C₆₇	1	1	yes	characteristic
856	#383	C₂²×C₆₇	1	1	yes	characteristic
857	#382	C₂²×C₆₇	1	1	yes	characteristic
858	#381	C₂²×C₆₇	1	1	yes	characteristic
859	#381	C₂²×C₆₇	1	1	yes	characteristic
860	#381	C₂²×C₆₇	1	1	yes	characteristic
861	#380	C₂²×C₆₇	1	1	yes	characteristic
862	#380	C₂²×C₆₇	1	1	yes	characteristic
863	#380	C₂²×C₆₇	1	1	yes	characteristic
864	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
865	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
866	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
867	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
868	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
869	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
870	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
871	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
872	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
873	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
874	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
875	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
876	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
877	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
878	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
879	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
880	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
881	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
882	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
883	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
884	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
885	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
886	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
887	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
888	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
889	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
890	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
891	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
892	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
893	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
894	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
895	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
896	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
897	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
898	#376	C₂²×C₆₇	1	1	yes	characteristic
899	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
900	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
901	C₄³	C₂²×C₆₇	1	1	yes	characteristic
902	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
903	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
904	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
905	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
906	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
907	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
908	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
909	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
910	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
912	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
913	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
914	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
915	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
917	#126	—	2	4	no	—
918	#125	—	2	4	no	—
919	#123	—	2	4	no	—
920	#123	—	2	4	no	—
921	#123	—	2	4	no	—
922	C₂²⋊Q₈	—	2	4	no	—
923	C₂²⋊Q₈	—	2	4	no	—
924	#121	—	2	4	no	—
925	C₄×Q₈	—	4	2	no	—
926	C₄×D₄	—	2	4	no	—
927	C₄×D₄	—	2	4	no	—
928	C₄×D₄	—	2	4	no	—
929	C₄×D₄	—	2	4	no	—
930	C₄×D₄	—	4	2	no	—
931	#117	—	4	2	no	—
932	C₂×C₄⋊C₄	—	2	4	no	—
933	C₂×C₄⋊C₄	—	2	4	no	—
934	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
936	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
937	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
953	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
972	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
973	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
974	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
975	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
976	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
978	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
979	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
980	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
981	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
982	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
983	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
984	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
985	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
986	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
987	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
988	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
991	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
992	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
998	C₂×C₄²	—	2	4	no	—
999	C₂×C₄²	—	4	2	no	—
1000	C₂×C₄²	—	4	2	no	—
1001	C₂×C₄²	—	4	2	no	—
1002	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1003	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1004	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1005	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1006	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1007	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1008	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1009	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1010	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1011	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1012	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1013	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1014	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1015	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1016	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1017	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1018	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1019	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1020	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1021	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1022	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1023	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1024	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1025	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1026	#95	C₂³×C₆₇	1	1	yes	characteristic
1027	#95	C₂³×C₆₇	1	1	yes	characteristic
1028	#95	C₂³×C₆₇	1	1	yes	characteristic
1029	#95	C₂³×C₆₇	1	1	yes	characteristic
1030	#95	C₂³×C₆₇	1	1	yes	characteristic
1031	#95	C₂³×C₆₇	1	1	yes	characteristic
1032	#95	C₂³×C₆₇	1	1	yes	characteristic
1033	#95	C₂³×C₆₇	1	1	yes	characteristic
1034	#95	C₂³×C₆₇	1	1	yes	characteristic
1035	#95	C₂³×C₆₇	1	1	yes	characteristic
1036	#95	C₂³×C₆₇	1	1	yes	characteristic
1037	#95	C₂³×C₆₇	1	1	yes	characteristic
1038	#95	C₂³×C₆₇	1	1	yes	characteristic
1039	#95	C₂³×C₆₇	1	1	yes	characteristic
1040	#95	C₂³×C₆₇	1	1	yes	characteristic
1041	#95	C₂³×C₆₇	1	1	yes	characteristic
1042	#95	C₂³×C₆₇	1	1	yes	characteristic
1043	#95	C₂³×C₆₇	1	1	yes	characteristic
1044	#95	C₂³×C₆₇	1	1	yes	characteristic
1045	#95	C₂³×C₆₇	1	1	yes	characteristic
1046	#95	C₂³×C₆₇	1	1	yes	characteristic
1047	#95	C₂³×C₆₇	1	1	yes	characteristic
1048	#95	C₂³×C₆₇	1	1	yes	characteristic
1049	#95	C₂³×C₆₇	1	1	yes	characteristic
1050	#95	C₂³×C₆₇	1	1	yes	characteristic
1051	#95	C₂³×C₆₇	1	1	yes	characteristic
1052	#95	C₂³×C₆₇	1	1	yes	characteristic
1053	#95	C₂³×C₆₇	1	1	yes	characteristic
1054	#95	C₂³×C₆₇	1	1	yes	characteristic
1055	#95	C₂³×C₆₇	1	1	yes	characteristic
1056	#95	C₂³×C₆₇	1	1	yes	characteristic
1057	#95	C₂³×C₆₇	1	1	yes	characteristic
1058	#95	C₂³×C₆₇	1	1	yes	characteristic
1059	#95	C₂³×C₆₇	1	1	yes	characteristic
1060	#95	C₂³×C₆₇	1	1	yes	characteristic
1061	#95	C₂³×C₆₇	1	1	yes	characteristic
1062	#95	C₂³×C₆₇	1	1	yes	characteristic
1063	#95	C₂³×C₆₇	1	1	yes	characteristic
1064	#95	C₂³×C₆₇	1	1	yes	characteristic
1065	#95	C₂³×C₆₇	1	1	yes	characteristic
1066	#95	C₂³×C₆₇	1	1	yes	characteristic
1067	#95	C₂³×C₆₇	1	1	yes	characteristic
1068	#95	C₂³×C₆₇	1	1	yes	characteristic
1069	#95	C₂³×C₆₇	1	1	yes	characteristic
1070	#95	C₂³×C₆₇	1	1	yes	characteristic
1071	#95	C₂³×C₆₇	1	1	yes	characteristic
1072	#95	C₂³×C₆₇	1	1	yes	characteristic
1073	#95	C₂³×C₆₇	1	1	yes	characteristic
1074	#95	C₂³×C₆₇	1	1	yes	characteristic
1075	#95	C₂³×C₆₇	1	1	yes	characteristic
1076	#95	C₂³×C₆₇	1	1	yes	characteristic
1077	#95	C₂³×C₆₇	1	1	yes	characteristic
1078	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1079	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1080	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1081	C₂×Q₈	—	2	2	no	—
1082	C₂×Q₈	—	2	2	no	—
1083	C₂×Q₈	—	4	1	no	—
1084	C₂×D₄	—	2	2	no	—
1085	C₂×D₄	—	2	2	no	—
1086	C₂×D₄	—	2	2	no	—
1087	C₂×D₄	—	2	2	no	—
1088	C₂×D₄	—	2	2	no	—
1089	C₂×D₄	—	2	2	no	—
1090	C₂×D₄	—	2	2	no	—
1091	C₂×D₄	—	4	1	no	—
1092	C₂×D₄	#41×C₆₇	1	4	yes	—
1093	C₂²×C₄	—	2	2	no	—
1094	C₂²×C₄	—	2	2	no	—
1095	C₂²×C₄	—	2	2	no	—
1096	C₂²×C₄	—	2	2	no	—
1097	C₂²×C₄	—	2	2	no	—
1098	C₂²×C₄	—	2	2	no	—
1099	C₂²×C₄	—	2	2	no	—
1100	C₂²×C₄	—	2	2	no	—
1101	C₂²×C₄	—	2	2	no	—
1102	C₂²×C₄	—	2	2	no	—
1103	C₂²×C₄	—	2	2	no	—
1104	C₂²×C₄	—	2	2	no	—
1105	C₂²×C₄	—	2	2	no	—
1106	C₂²×C₄	—	2	2	no	—
1107	C₂²×C₄	—	2	2	no	—
1108	C₂²×C₄	—	2	2	no	—
1109	C₂²×C₄	—	2	2	no	—
1110	C₂²×C₄	—	2	2	no	—
1111	C₂²×C₄	—	2	2	no	—
1112	C₂²×C₄	—	2	2	no	—
1113	C₂²×C₄	—	2	2	no	—
1114	C₂²×C₄	—	2	2	no	—
1115	C₂²×C₄	—	2	2	no	—
1116	C₂²×C₄	—	2	2	no	—
1117	C₂²×C₄	—	2	2	no	—
1118	C₂²×C₄	—	2	2	no	—
1119	C₂²×C₄	—	4	1	no	—
1120	C₂²×C₄	—	4	1	no	—
1121	C₂²×C₄	—	4	1	no	—
1122	C₂²×C₄	—	4	1	no	—
1123	C₂²×C₄	—	4	1	no	—
1124	C₂²×C₄	—	4	1	no	—
1125	C₂²×C₄	#41×C₆₇	1	4	yes	—
1126	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1127	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1128	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1129	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1130	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1131	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1132	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1133	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1134	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1135	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1136	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1137	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1138	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1139	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1140	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1141	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1142	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1143	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1144	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1145	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1146	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1147	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1148	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1149	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1150	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1151	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1152	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1153	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1154	C₄⋊C₄	—	2	2	no	—
1155	C₄⋊C₄	—	2	2	no	—
1156	C₄⋊C₄	—	2	2	no	—
1157	C₄⋊C₄	—	2	2	no	—
1158	C₄⋊C₄	—	2	2	no	—
1159	C₄⋊C₄	—	2	2	no	—
1160	C₄⋊C₄	—	2	2	no	—
1161	C₄⋊C₄	—	2	2	no	—
1162	C₄⋊C₄	—	2	2	no	—
1163	C₄⋊C₄	—	2	2	no	—
1164	C₄⋊C₄	—	2	2	no	—
1165	C₄⋊C₄	—	2	2	no	—
1166	C₄⋊C₄	—	2	2	no	—
1167	C₄⋊C₄	—	2	2	no	—
1168	C₄⋊C₄	—	2	2	no	—
1169	C₄⋊C₄	—	2	2	no	—
1170	C₄⋊C₄	—	2	2	no	—
1171	C₄⋊C₄	—	2	2	no	—
1172	C₄⋊C₄	—	2	2	no	—
1173	C₄⋊C₄	—	2	2	no	—
1174	C₄⋊C₄	—	2	2	no	—
1175	C₄⋊C₄	—	2	2	no	—
1176	C₄⋊C₄	—	2	2	no	—
1177	C₄⋊C₄	—	2	2	no	—
1178	C₄⋊C₄	—	2	2	no	—
1179	C₄⋊C₄	—	2	2	no	—
1180	C₄⋊C₄	—	2	2	no	—
1181	C₄⋊C₄	—	2	2	no	—
1182	C₄⋊C₄	—	4	1	no	—
1183	C₄⋊C₄	—	4	1	no	—
1184	C₄⋊C₄	—	4	1	no	—
1185	C₄⋊C₄	—	4	1	no	—
1186	C₄⋊C₄	—	4	1	no	—
1187	C₄⋊C₄	—	4	1	no	—
1188	C₄⋊C₄	#41×C₆₇	1	4	yes	—
1189	C₄⋊C₄	#41×C₆₇	1	4	yes	—
1190	C₂²⋊C₄	—	2	2	no	—
1191	C₂²⋊C₄	—	2	2	no	—
1192	C₂²⋊C₄	—	2	2	no	—
1193	C₂²⋊C₄	—	2	2	no	—
1194	C₂²⋊C₄	—	2	2	no	—
1195	C₂²⋊C₄	—	2	2	no	—
1196	C₂²⋊C₄	—	2	2	no	—
1197	C₂²⋊C₄	—	2	2	no	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	2	2	no	—
1201	C₂²⋊C₄	—	2	2	no	—
1202	C₂²⋊C₄	—	2	2	no	—
1203	C₂²⋊C₄	—	2	2	no	—
1204	C₂²⋊C₄	—	2	2	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	2	2	no	—
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	2	no	—
1213	C₂²⋊C₄	—	4	1	no	—
1214	C₂²⋊C₄	—	4	1	no	—
1215	C₂²⋊C₄	—	4	1	no	—
1216	C₂²⋊C₄	—	4	1	no	—
1217	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
1218	C₄²	—	2	2	no	—
1219	C₄²	—	2	2	no	—
1220	C₄²	—	2	2	no	—
1221	C₄²	—	2	2	no	—
1222	C₄²	—	2	2	no	—
1223	C₄²	—	2	2	no	—
1224	C₄²	—	2	2	no	—
1225	C₄²	—	2	2	no	—
1226	C₄²	—	2	2	no	—
1227	C₄²	—	2	2	no	—
1228	C₄²	—	2	2	no	—
1229	C₄²	—	2	2	no	—
1230	C₄²	—	2	2	no	—
1231	C₄²	—	2	2	no	—
1232	C₄²	—	2	2	no	—
1233	C₄²	—	2	2	no	—
1234	C₄²	—	2	2	no	—
1235	C₄²	—	2	2	no	—
1236	C₄²	—	4	1	no	—
1237	C₄²	—	4	1	no	—
1238	C₄²	—	4	1	no	—
1239	C₄²	—	4	1	no	—
1240	C₄²	—	4	1	no	—
1241	C₄²	—	4	1	no	—
1242	C₂³	—	2	1	no	—
1243	C₂³	—	2	1	no	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	1	no	—
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	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	1	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	1	no	—
1259	C₂³	C₂×#41×C₆₇	1	2	yes	—
1260	C₂³	C₂×#41×C₆₇	1	2	yes	—
1261	C₂³	C₂×#41×C₆₇	1	2	yes	—
1262	C₂³	C₂×#41×C₆₇	1	2	yes	—
1263	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1264	Q₈	—	4	4	no	—
1265	D₄	—	2	8	no	—
1266	D₄	—	4	4	no	—
1267	D₄	—	4	4	no	—
1268	C₂×C₄	—	2	8	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
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	8	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	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	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	—	4	4	no	—
1342	C₂×C₄	—	4	4	no	—
1343	C₂×C₄	—	4	4	no	—
1344	C₂×C₄	—	4	4	no	—
1345	C₂×C₄	—	4	4	no	—
1346	C₂×C₄	—	4	4	no	—
1347	C₂×C₄	—	4	4	no	—
1348	C₂×C₄	—	4	4	no	—
1349	C₂×C₄	—	4	4	no	—
1350	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1351	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1352	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1353	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1354	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1355	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1356	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1357	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1358	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1359	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1360	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1361	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1362	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1363	C₂²	—	2	2	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	2	2	no	—
1366	C₂²	—	2	2	no	—
1367	C₂²	—	2	2	no	—
1368	C₂²	—	2	2	no	—
1369	C₂²	—	2	2	no	—
1370	C₂²	—	2	2	no	—
1371	C₂²	—	2	2	no	—
1372	C₂²	—	4	1	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	4	1	no	—
1378	C₂²	—	4	1	no	—
1379	C₂²	—	4	1	no	—
1380	C₂²	—	4	1	no	—
1381	C₂²	—	4	1	no	—
1382	C₂²	—	4	1	no	—
1383	C₂²	#529×C₆₇	1	4	yes	—
1384	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1385	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1386	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1387	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1388	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1389	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1390	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1391	C₄	—	2	2	no	—
1392	C₄	—	2	2	no	—
1393	C₄	—	2	2	no	—
1394	C₄	—	2	2	no	—
1395	C₄	—	2	2	no	—
1396	C₄	—	2	2	no	—
1397	C₄	—	2	2	no	—
1398	C₄	—	2	2	no	—
1399	C₄	—	2	2	no	—
1400	C₄	—	2	2	no	—
1401	C₄	—	4	1	no	—
1402	C₄	—	4	1	no	—
1403	C₄	—	4	1	no	—
1404	C₄	—	4	1	no	—
1405	C₄	—	4	1	no	—
1406	C₄	—	4	1	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	—	4	1	no	—
1414	C₄	—	4	1	no	—
1415	C₄	—	4	1	no	—
1416	C₄	—	4	1	no	—
1417	C₄	—	4	1	no	—
1418	C₄	#539×C₆₇	1	4	yes	—
1419	C₂	—	2	4	no	—
1420	C₂	—	4	2	no	—
1421	C₂	—	8	1	no	—
1422	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
1423	C₂	C₆₇×#3444	1	1	yes	characteristic
1424	C₂	C₂×#539×C₆₇	1	1	yes	characteristic
1425	C₂	C₆₇×#3481	1	1	yes	characteristic
1426	C₂	C₆₇×#3481	1	1	yes	characteristic
1427	C₂	C₆₇×#3482	1	1	yes	characteristic
1428	C₂	C₆₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#121×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2596	C₂	semidirect
2. C₆₇×#2594	C₂	semidirect
3. C₆₇×#2590	C₂	semidirect
4. C₆₇×#2588	C₂	semidirect
5. C₆₇×#2577	C₂	semidirect
6. C₆₇×#2575	C₂	semidirect
7. C₆₇×#2560	C₂	semidirect
8. C₆₇×#2558	C₂	semidirect
9. C₆₇×#2493	C₂	semidirect
10. C₆₇×#2488	C₂	semidirect
11. C₆₇×#2481	C₂	semidirect
12. C₆₇×#2473	C₂	semidirect
13. C₆₇×#2449	C₂	semidirect
16. C₆₇×#2419	C₂	semidirect
17. C₆₇×#2402	C₂	semidirect
18. C₆₇×#2401	C₂	semidirect
19. C₆₇×#2396	C₂	semidirect
20. C₆₇×#2395	C₂	semidirect
21. C₄×#125×C₆₇	C₂	semidirect
22. C₄×#126×C₆₇	C₂	semidirect
23. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
24. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
25. C₄×#123×C₆₇	C₂	semidirect
26. C₄×#123×C₆₇	C₂	semidirect
27. C₄×#123×C₆₇	C₂	semidirect
29. C₆₇×#2290	C₂	semidirect
30. C₄²×D₄×C₆₇	C₂	semidirect
31. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
704. #34960	C₆₇	direct (N × H)
715. #2596	C₂×C₆₇	semidirect
716. #2594	C₂×C₆₇	semidirect
717. #2590	C₂×C₆₇	semidirect
718. #2588	C₂×C₆₇	semidirect
719. #2577	C₂×C₆₇	semidirect
720. #2575	C₂×C₆₇	semidirect
721. #2560	C₂×C₆₇	semidirect
722. #2558	C₂×C₆₇	semidirect
723. #2493	C₂×C₆₇	semidirect
724. #2488	C₂×C₆₇	semidirect
725. #2481	C₂×C₆₇	semidirect
726. #2473	C₂×C₆₇	semidirect
727. #2449	C₂×C₆₇	semidirect
730. #2419	C₂×C₆₇	semidirect
731. #2402	C₂×C₆₇	semidirect
732. #2401	C₂×C₆₇	semidirect
733. #2396	C₂×C₆₇	semidirect
734. #2395	C₂×C₆₇	semidirect
735. C₄×#125	C₂×C₆₇	semidirect
736. C₄×#126	C₂×C₆₇	semidirect
737. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
738. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
739. C₄×#123	C₂×C₆₇	semidirect
740. C₄×#123	C₂×C₆₇	semidirect
741. C₄×#123	C₂×C₆₇	semidirect
743. #2290	C₂×C₆₇	semidirect
744. C₄²×D₄	C₂×C₆₇	semidirect
745. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
746. C₆₇	#34960	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2596	2
C₆₇×#2594	2
C₆₇×#2590	2
C₆₇×#2588	2
C₆₇×#2577	2
C₆₇×#2575	2
C₆₇×#2560	2
C₆₇×#2558	2
C₆₇×#2493	2
C₆₇×#2488	2
C₆₇×#2481	2
C₆₇×#2473	2
C₆₇×#2449	2
C₆₇×#2443	2
C₆₇×#2425	2
C₆₇×#2419	2
C₆₇×#2402	2
C₆₇×#2401	2
C₆₇×#2396	2
C₆₇×#2395	2
C₄×#125×C₆₇	2
C₄×#126×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2290	2
C₄²×D₄×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
#34960	67

Subgroups — C67×#34960 #30714211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34960 #30714211