Subgroups — C₆₇×#34292 #30713543

Order 17152.

3296 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2325	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
19	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#388×C₆₇	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	#546×C₆₇	C₄	1	16	yes	complemented
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#123×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	2	yes	—
32	C₂×#120×C₆₇	C₂²	1	2	yes	—
33	#518×C₆₇	—	2	8	no	—
34	C₄×#41×C₆₇	—	2	8	no	—
35	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
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×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
50	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
55	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
56	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
57	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
58	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
59	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
60	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#390×C₆₇	C₂²	1	2	yes	—
65	#390×C₆₇	C₂²	1	1	yes	characteristic
66	#390×C₆₇	C₂²	1	2	yes	complemented
67	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#389×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	1	yes	characteristic
71	#388×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	1	yes	characteristic
75	#388×C₆₇	C₂²	1	2	yes	—
76	#388×C₆₇	C₂²	1	2	yes	—
77	#388×C₆₇	C₂²	1	2	yes	complemented
78	#388×C₆₇	C₂²	1	2	yes	complemented
79	#388×C₆₇	C₂²	1	2	yes	complemented
80	#388×C₆₇	C₂²	1	2	yes	complemented
81	#388×C₆₇	C₂²	1	2	yes	complemented
82	#388×C₆₇	C₂²	1	2	yes	complemented
83	#388×C₆₇	C₂²	1	2	yes	complemented
84	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#387×C₆₇	C₂²	1	2	yes	complemented
87	#387×C₆₇	C₂²	1	2	yes	complemented
88	#386×C₆₇	C₂²	1	1	yes	characteristic
89	#386×C₆₇	C₂²	1	1	yes	characteristic
90	#386×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	2	yes	—
92	#386×C₆₇	C₂²	1	2	yes	complemented
93	#386×C₆₇	C₂²	1	2	yes	complemented
94	#386×C₆₇	C₂²	1	2	yes	complemented
95	#386×C₆₇	C₂²	1	2	yes	complemented
96	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#385×C₆₇	C₂²	1	2	yes	complemented
99	#385×C₆₇	C₂²	1	2	yes	complemented
100	#385×C₆₇	C₂²	1	2	yes	complemented
101	#385×C₆₇	C₂²	1	2	yes	complemented
102	#385×C₆₇	C₂²	1	2	yes	complemented
103	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#381×C₆₇	C₂²	1	2	yes	complemented
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#380×C₆₇	C₂²	1	2	yes	complemented
108	#379×C₆₇	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
123	#376×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
125	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
126	C₂⁵×C₆₇	C₂³	1	2	yes	—
127	C₂×#41×C₆₇	—	2	4	no	—
128	C₂×#41×C₆₇	—	2	4	no	—
129	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₆₇	—	2	4	no	—
132	C₂²×D₄×C₆₇	—	2	4	no	—
133	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
134	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
135	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
149	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
152	#124×C₆₇	C₂×C₄	1	8	yes	complemented
153	#123×C₆₇	C₂×C₄	1	16	yes	complemented
154	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
155	#121×C₆₇	C₂×C₄	1	8	yes	complemented
156	#121×C₆₇	C₂×C₄	1	16	yes	complemented
157	#120×C₆₇	C₂×C₄	1	16	yes	complemented
158	C₄×Q₈×C₆₇	—	2	4	no	—
159	C₄×Q₈×C₆₇	—	2	4	no	—
160	C₄×D₄×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	4	no	—
162	C₄×D₄×C₆₇	—	2	4	no	—
163	C₄×D₄×C₆₇	—	2	8	no	—
164	C₄×D₄×C₆₇	—	2	8	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	8	no	—
167	C₄×D₄×C₆₇	—	2	8	no	—
168	C₄×D₄×C₆₇	—	2	4	no	—
169	C₄×D₄×C₆₇	—	4	4	no	—
170	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
171	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
172	C₄×D₄×C₆₇	D₄	1	8	yes	complemented
173	#117×C₆₇	—	2	4	no	—
174	#117×C₆₇	—	2	4	no	—
175	#117×C₆₇	—	2	8	no	—
176	#117×C₆₇	—	2	4	no	—
177	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
196	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
197	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
198	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₄²×C₆₇	—	2	8	no	—
227	C₂×C₄²×C₆₇	—	2	4	no	—
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
236	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
238	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
239	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
240	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
242	#95×C₆₇	C₂³	1	1	yes	characteristic
243	#95×C₆₇	C₂³	1	1	yes	characteristic
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	#95×C₆₇	C₂³	1	1	yes	characteristic
251	#95×C₆₇	C₂³	1	1	yes	characteristic
252	#95×C₆₇	C₂³	1	1	yes	characteristic
253	#95×C₆₇	C₂³	1	1	yes	characteristic
254	#95×C₆₇	C₂³	1	1	yes	characteristic
255	#95×C₆₇	C₂³	1	1	yes	characteristic
256	#95×C₆₇	C₂³	1	1	yes	characteristic
257	#95×C₆₇	C₂³	1	2	yes	—
258	#95×C₆₇	C₂³	1	2	yes	—
259	#95×C₆₇	C₂³	1	2	yes	—
260	#95×C₆₇	C₂³	1	2	yes	—
261	#95×C₆₇	C₂³	1	2	yes	—
262	#95×C₆₇	C₂³	1	1	yes	characteristic
263	C₂⁴×C₆₇	—	2	4	no	—
264	C₂⁴×C₆₇	—	2	4	no	—
265	C₂⁴×C₆₇	—	4	2	no	—
266	C₂⁴×C₆₇	—	4	2	no	—
267	C₂⁴×C₆₇	—	4	2	no	—
268	C₂⁴×C₆₇	—	4	2	no	—
269	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
270	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
272	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
274	#41×C₆₇	—	2	32	no	—
275	C₂×Q₈×C₆₇	—	2	2	no	—
276	C₂×Q₈×C₆₇	—	2	2	no	—
277	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
278	C₂×D₄×C₆₇	—	2	4	no	—
279	C₂×D₄×C₆₇	—	2	4	no	—
280	C₂×D₄×C₆₇	—	2	4	no	—
281	C₂×D₄×C₆₇	—	2	4	no	—
282	C₂×D₄×C₆₇	—	2	32	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	4	2	no	—
286	C₂×D₄×C₆₇	—	4	1	no	—
287	C₂×D₄×C₆₇	—	4	2	no	—
288	C₂×D₄×C₆₇	—	4	1	no	—
289	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
290	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
291	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
292	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
293	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
294	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
295	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
296	C₂×D₄×C₆₇	#41	1	4	yes	—
297	C₂²×C₄×C₆₇	—	2	4	no	—
298	C₂²×C₄×C₆₇	—	2	4	no	—
299	C₂²×C₄×C₆₇	—	2	2	no	—
300	C₂²×C₄×C₆₇	—	2	2	no	—
301	C₂²×C₄×C₆₇	—	2	2	no	—
302	C₂²×C₄×C₆₇	—	2	2	no	—
303	C₂²×C₄×C₆₇	—	2	4	no	—
304	C₂²×C₄×C₆₇	—	2	4	no	—
305	C₂²×C₄×C₆₇	—	2	4	no	—
306	C₂²×C₄×C₆₇	—	2	2	no	—
307	C₂²×C₄×C₆₇	—	2	2	no	—
308	C₂²×C₄×C₆₇	—	2	4	no	—
309	C₂²×C₄×C₆₇	—	2	2	no	—
310	C₂²×C₄×C₆₇	—	2	4	no	—
311	C₂²×C₄×C₆₇	—	2	4	no	—
312	C₂²×C₄×C₆₇	—	4	2	no	—
313	C₂²×C₄×C₆₇	—	4	2	no	—
314	C₂²×C₄×C₆₇	—	4	2	no	—
315	C₂²×C₄×C₆₇	—	4	2	no	—
316	C₂²×C₄×C₆₇	—	4	1	no	—
317	C₂²×C₄×C₆₇	—	4	1	no	—
318	C₂²×C₄×C₆₇	—	4	2	no	—
319	C₂²×C₄×C₆₇	—	4	1	no	—
320	C₂²×C₄×C₆₇	—	4	2	no	—
321	C₂²×C₄×C₆₇	—	4	2	no	—
322	C₂²×C₄×C₆₇	—	4	2	no	—
323	C₂²×C₄×C₆₇	—	4	2	no	—
324	C₂²×C₄×C₆₇	—	4	2	no	—
325	C₂²×C₄×C₆₇	—	4	2	no	—
326	C₂²×C₄×C₆₇	—	4	2	no	—
327	C₂²×C₄×C₆₇	—	4	2	no	—
328	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
329	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
330	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
331	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
332	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
333	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₄⋊C₄×C₆₇	—	2	2	no	—
353	C₄⋊C₄×C₆₇	—	2	2	no	—
354	C₄⋊C₄×C₆₇	—	2	2	no	—
355	C₄⋊C₄×C₆₇	—	2	4	no	—
356	C₄⋊C₄×C₆₇	—	2	4	no	—
357	C₄⋊C₄×C₆₇	—	2	2	no	—
358	C₄⋊C₄×C₆₇	—	2	2	no	—
359	C₄⋊C₄×C₆₇	—	2	2	no	—
360	C₄⋊C₄×C₆₇	—	2	4	no	—
361	C₄⋊C₄×C₆₇	—	4	2	no	—
362	C₄⋊C₄×C₆₇	—	4	2	no	—
363	C₄⋊C₄×C₆₇	—	4	2	no	—
364	C₄⋊C₄×C₆₇	—	4	1	no	—
365	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
366	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
367	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
368	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
369	C₂²⋊C₄×C₆₇	—	2	4	no	—
370	C₂²⋊C₄×C₆₇	—	2	4	no	—
371	C₂²⋊C₄×C₆₇	—	2	4	no	—
372	C₂²⋊C₄×C₆₇	—	2	2	no	—
373	C₂²⋊C₄×C₆₇	—	2	4	no	—
374	C₂²⋊C₄×C₆₇	—	2	2	no	—
375	C₂²⋊C₄×C₆₇	—	2	4	no	—
376	C₂²⋊C₄×C₆₇	—	2	4	no	—
377	C₂²⋊C₄×C₆₇	—	2	4	no	—
378	C₂²⋊C₄×C₆₇	—	2	2	no	—
379	C₂²⋊C₄×C₆₇	—	2	4	no	—
380	C₂²⋊C₄×C₆₇	—	4	2	no	—
381	C₂²⋊C₄×C₆₇	—	4	2	no	—
382	C₂²⋊C₄×C₆₇	—	4	1	no	—
383	C₂²⋊C₄×C₆₇	—	4	2	no	—
384	C₂²⋊C₄×C₆₇	—	4	2	no	—
385	C₂²⋊C₄×C₆₇	—	4	1	no	—
386	C₂²⋊C₄×C₆₇	—	4	1	no	—
387	C₂²⋊C₄×C₆₇	—	4	2	no	—
388	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
389	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
390	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
391	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
392	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
393	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
394	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
395	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
396	C₄²×C₆₇	—	2	2	no	—
397	C₄²×C₆₇	—	2	4	no	—
398	C₄²×C₆₇	—	2	2	no	—
399	C₄²×C₆₇	—	2	4	no	—
400	C₄²×C₆₇	—	2	2	no	—
401	C₄²×C₆₇	—	2	4	no	—
402	C₄²×C₆₇	—	2	4	no	—
403	C₄²×C₆₇	—	2	2	no	—
404	C₄²×C₆₇	—	2	2	no	—
405	C₄²×C₆₇	—	4	2	no	—
406	C₄²×C₆₇	—	4	2	no	—
407	C₄²×C₆₇	—	4	2	no	—
408	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
409	C₄²×C₆₇	C₂×D₄	1	4	yes	—
410	C₂³×C₆₇	—	2	2	no	—
411	C₂³×C₆₇	—	2	2	no	—
412	C₂³×C₆₇	—	2	2	no	—
413	C₂³×C₆₇	—	2	2	no	—
414	C₂³×C₆₇	—	2	1	no	—
415	C₂³×C₆₇	—	2	1	no	—
416	C₂³×C₆₇	—	2	2	no	—
417	C₂³×C₆₇	—	2	1	no	—
418	C₂³×C₆₇	—	2	1	no	—
419	C₂³×C₆₇	—	2	2	no	—
420	C₂³×C₆₇	—	2	1	no	—
421	C₂³×C₆₇	—	2	2	no	—
422	C₂³×C₆₇	—	2	1	no	—
423	C₂³×C₆₇	—	2	1	no	—
424	C₂³×C₆₇	—	2	1	no	—
425	C₂³×C₆₇	—	2	2	no	—
426	C₂³×C₆₇	—	2	2	no	—
427	C₂³×C₆₇	—	2	1	no	—
428	C₂³×C₆₇	—	2	1	no	—
429	C₂³×C₆₇	—	2	2	no	—
430	C₂³×C₆₇	—	2	1	no	—
431	C₂³×C₆₇	—	2	1	no	—
432	C₂³×C₆₇	—	2	16	no	—
433	C₂³×C₆₇	—	4	8	no	—
434	C₂³×C₆₇	—	4	8	no	—
435	C₂³×C₆₇	—	8	4	no	—
436	C₂³×C₆₇	—	8	4	no	—
437	C₂³×C₆₇	—	8	4	no	—
438	C₂³×C₆₇	—	8	4	no	—
439	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
440	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
441	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
442	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
443	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
444	C₂³×C₆₇	C₂×#41	1	4	yes	—
445	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
446	Q₈×C₆₇	—	2	8	no	—
447	D₄×C₆₇	—	2	16	no	—
448	D₄×C₆₇	—	2	16	no	—
449	D₄×C₆₇	—	2	8	no	—
450	D₄×C₆₇	—	4	4	no	—
451	D₄×C₆₇	—	4	8	no	—
452	D₄×C₆₇	C₄×D₄	1	16	yes	complemented
453	C₂×C₄×C₆₇	—	2	16	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	1	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	8	no	—
475	C₂×C₄×C₆₇	—	2	8	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	4	8	no	—
501	C₂×C₄×C₆₇	—	4	8	no	—
502	C₂×C₄×C₆₇	—	4	4	no	—
503	C₂×C₄×C₆₇	—	4	8	no	—
504	C₂×C₄×C₆₇	—	4	4	no	—
505	C₂×C₄×C₆₇	—	8	4	no	—
506	C₂×C₄×C₆₇	—	8	4	no	—
507	C₂×C₄×C₆₇	—	8	4	no	—
508	C₂×C₄×C₆₇	—	8	4	no	—
509	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
510	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
511	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
512	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
513	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
514	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
515	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
516	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
518	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
521	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
522	C₂²×C₆₇	—	2	4	no	—
523	C₂²×C₆₇	—	2	4	no	—
524	C₂²×C₆₇	—	2	4	no	—
525	C₂²×C₆₇	—	2	4	no	—
526	C₂²×C₆₇	—	2	4	no	—
527	C₂²×C₆₇	—	2	4	no	—
528	C₂²×C₆₇	—	2	2	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	4	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	2	no	—
533	C₂²×C₆₇	—	2	4	no	—
534	C₂²×C₆₇	—	2	2	no	—
535	C₂²×C₆₇	—	2	4	no	—
536	C₂²×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	4	1	no	—
538	C₂²×C₆₇	—	4	2	no	—
539	C₂²×C₆₇	—	4	1	no	—
540	C₂²×C₆₇	—	4	1	no	—
541	C₂²×C₆₇	—	4	2	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	1	no	—
544	C₂²×C₆₇	—	4	2	no	—
545	C₂²×C₆₇	—	4	1	no	—
546	C₂²×C₆₇	—	4	1	no	—
547	C₂²×C₆₇	—	4	2	no	—
548	C₂²×C₆₇	—	4	1	no	—
549	C₂²×C₆₇	—	8	16	no	—
550	C₂²×C₆₇	C₂×C₄×D₄	1	8	yes	—
551	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
552	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
553	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
554	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
555	C₂²×C₆₇	#585	1	1	yes	characteristic
556	C₂²×C₆₇	#585	1	1	yes	characteristic
557	C₂²×C₆₇	#585	1	1	yes	characteristic
558	C₄×C₆₇	—	2	2	no	—
559	C₄×C₆₇	—	2	2	no	—
560	C₄×C₆₇	—	2	4	no	—
561	C₄×C₆₇	—	2	2	no	—
562	C₄×C₆₇	—	2	2	no	—
563	C₄×C₆₇	—	2	4	no	—
564	C₄×C₆₇	—	2	2	no	—
565	C₄×C₆₇	—	2	4	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	2	no	—
568	C₄×C₆₇	—	4	1	no	—
569	C₄×C₆₇	—	4	1	no	—
570	C₄×C₆₇	—	4	2	no	—
571	C₄×C₆₇	—	4	2	no	—
572	C₄×C₆₇	—	4	1	no	—
573	C₄×C₆₇	—	4	2	no	—
574	C₄×C₆₇	—	4	1	no	—
575	C₄×C₆₇	—	4	1	no	—
576	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
577	#34292	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
578	C₂×C₆₇	—	2	8	no	—
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	4	4	no	—
581	C₂×C₆₇	—	4	2	no	—
582	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
583	C₂×C₆₇	#3428	1	1	yes	characteristic
584	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂×C₆₇	#3485	1	1	yes	characteristic
586	C₂×C₆₇	#3488	1	1	yes	characteristic
587	C₂×C₆₇	#3514	1	1	yes	characteristic
588	C₂×C₆₇	#3521	1	1	yes	characteristic
589	C₂×#546	C₂×C₆₇	1	1	yes	characteristic
590	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
591	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#2363	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#2362	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#2361	C₂×C₆₇	1	2	yes	complemented
596	#2359	C₂×C₆₇	1	2	yes	complemented
597	#2358	C₂×C₆₇	1	2	yes	complemented
598	#2354	C₂×C₆₇	1	1	yes	characteristic, complemented
599	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#2342	C₂×C₆₇	1	2	yes	complemented
601	#2339	C₂×C₆₇	1	1	yes	characteristic, complemented
602	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#2326	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#2325	C₂×C₆₇	1	2	yes	complemented
605	#2323	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2321	C₂×C₆₇	1	2	yes	complemented
607	C₄×#123	C₂×C₆₇	1	2	yes	complemented
608	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
610	C₂×#388	C₂×C₆₇	1	2	yes	complemented
611	#2275	C₂×C₆₇	1	1	yes	characteristic, complemented
612	C₆₇	#34292	1	1	yes	characteristic, direct product factor, Sylow
613	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
614	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
615	#546	C₄×C₆₇	1	16	yes	complemented
616	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
617	C₂×#123	C₂²×C₆₇	1	2	yes	—
618	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
619	C₂×#121	C₂²×C₆₇	1	2	yes	—
620	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
621	C₂×#120	C₂²×C₆₇	1	2	yes	—
622	#518	—	2	8	no	—
623	C₄×#41	—	2	8	no	—
624	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
627	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
628	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
629	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
630	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
631	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
632	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
633	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
634	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
635	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
637	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
638	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
639	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
640	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
641	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
642	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
644	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
645	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
646	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
647	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
648	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
649	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#390	C₂²×C₆₇	1	2	yes	—
653	#390	C₂²×C₆₇	1	1	yes	characteristic
654	#390	C₂²×C₆₇	1	1	yes	characteristic
655	#390	C₂²×C₆₇	1	2	yes	complemented
656	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#389	C₂²×C₆₇	1	2	yes	complemented
658	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
659	#388	C₂²×C₆₇	1	2	yes	—
660	#388	C₂²×C₆₇	1	2	yes	—
661	#388	C₂²×C₆₇	1	2	yes	—
662	#388	C₂²×C₆₇	1	1	yes	characteristic
663	#388	C₂²×C₆₇	1	2	yes	—
664	#388	C₂²×C₆₇	1	2	yes	—
665	#388	C₂²×C₆₇	1	1	yes	characteristic
666	#388	C₂²×C₆₇	1	2	yes	complemented
667	#388	C₂²×C₆₇	1	2	yes	complemented
668	#388	C₂²×C₆₇	1	2	yes	complemented
669	#388	C₂²×C₆₇	1	2	yes	complemented
670	#388	C₂²×C₆₇	1	2	yes	complemented
671	#388	C₂²×C₆₇	1	2	yes	complemented
672	#388	C₂²×C₆₇	1	2	yes	complemented
673	#387	C₂²×C₆₇	1	2	yes	complemented
674	#387	C₂²×C₆₇	1	2	yes	complemented
675	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	#386	C₂²×C₆₇	1	1	yes	characteristic
678	#386	C₂²×C₆₇	1	2	yes	—
679	#386	C₂²×C₆₇	1	2	yes	—
680	#386	C₂²×C₆₇	1	1	yes	characteristic
681	#386	C₂²×C₆₇	1	2	yes	complemented
682	#386	C₂²×C₆₇	1	2	yes	complemented
683	#386	C₂²×C₆₇	1	2	yes	complemented
684	#386	C₂²×C₆₇	1	2	yes	complemented
685	#385	C₂²×C₆₇	1	2	yes	complemented
686	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#385	C₂²×C₆₇	1	2	yes	complemented
688	#385	C₂²×C₆₇	1	2	yes	complemented
689	#385	C₂²×C₆₇	1	2	yes	complemented
690	#385	C₂²×C₆₇	1	2	yes	complemented
691	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#381	C₂²×C₆₇	1	2	yes	complemented
694	#380	C₂²×C₆₇	1	1	yes	characteristic
695	#380	C₂²×C₆₇	1	2	yes	complemented
696	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#379	C₂²×C₆₇	1	2	yes	—
698	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
700	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
701	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
703	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
705	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
706	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
708	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
709	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
710	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
711	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
712	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
714	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
715	C₂⁵	C₂³×C₆₇	1	2	yes	—
716	C₂×#41	—	2	4	no	—
717	C₂×#41	—	2	4	no	—
718	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
719	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₂²×D₄	—	2	4	no	—
721	C₂²×D₄	—	2	4	no	—
722	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
723	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
724	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
725	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
726	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
728	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
729	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
730	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
731	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
732	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
735	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
736	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
737	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
738	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
740	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
741	#124	C₂×C₄×C₆₇	1	8	yes	complemented
742	#123	C₂×C₄×C₆₇	1	16	yes	complemented
743	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
744	#121	C₂×C₄×C₆₇	1	8	yes	complemented
745	#121	C₂×C₄×C₆₇	1	16	yes	complemented
746	#120	C₂×C₄×C₆₇	1	16	yes	complemented
747	C₄×Q₈	—	2	4	no	—
748	C₄×Q₈	—	2	4	no	—
749	C₄×D₄	—	2	4	no	—
750	C₄×D₄	—	2	4	no	—
751	C₄×D₄	—	2	4	no	—
752	C₄×D₄	—	2	8	no	—
753	C₄×D₄	—	2	8	no	—
754	C₄×D₄	—	2	4	no	—
755	C₄×D₄	—	2	8	no	—
756	C₄×D₄	—	2	8	no	—
757	C₄×D₄	—	2	4	no	—
758	C₄×D₄	—	4	4	no	—
759	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
760	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
761	C₄×D₄	D₄×C₆₇	1	8	yes	complemented
762	#117	—	2	4	no	—
763	#117	—	2	4	no	—
764	#117	—	2	8	no	—
765	#117	—	2	4	no	—
766	C₂×C₄⋊C₄	—	4	4	no	—
767	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
768	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
777	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
778	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
780	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
781	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	—	2	8	no	—
785	C₂×C₂²⋊C₄	—	2	8	no	—
786	C₂×C₂²⋊C₄	—	4	4	no	—
787	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
788	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
792	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
808	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
813	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
815	C₂×C₄²	—	2	8	no	—
816	C₂×C₄²	—	2	4	no	—
817	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
819	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
821	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
822	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
823	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
824	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
825	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
826	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
827	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
828	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
829	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
830	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
831	#95	C₂³×C₆₇	1	1	yes	characteristic
832	#95	C₂³×C₆₇	1	1	yes	characteristic
833	#95	C₂³×C₆₇	1	2	yes	—
834	#95	C₂³×C₆₇	1	2	yes	—
835	#95	C₂³×C₆₇	1	2	yes	—
836	#95	C₂³×C₆₇	1	2	yes	—
837	#95	C₂³×C₆₇	1	2	yes	—
838	#95	C₂³×C₆₇	1	2	yes	—
839	#95	C₂³×C₆₇	1	1	yes	characteristic
840	#95	C₂³×C₆₇	1	1	yes	characteristic
841	#95	C₂³×C₆₇	1	1	yes	characteristic
842	#95	C₂³×C₆₇	1	1	yes	characteristic
843	#95	C₂³×C₆₇	1	1	yes	characteristic
844	#95	C₂³×C₆₇	1	1	yes	characteristic
845	#95	C₂³×C₆₇	1	1	yes	characteristic
846	#95	C₂³×C₆₇	1	2	yes	—
847	#95	C₂³×C₆₇	1	2	yes	—
848	#95	C₂³×C₆₇	1	2	yes	—
849	#95	C₂³×C₆₇	1	2	yes	—
850	#95	C₂³×C₆₇	1	2	yes	—
851	#95	C₂³×C₆₇	1	1	yes	characteristic
852	C₂⁴	—	2	4	no	—
853	C₂⁴	—	2	4	no	—
854	C₂⁴	—	4	2	no	—
855	C₂⁴	—	4	2	no	—
856	C₂⁴	—	4	2	no	—
857	C₂⁴	—	4	2	no	—
858	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
859	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
860	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
861	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
862	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
863	#41	—	2	32	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
867	C₂×D₄	—	2	4	no	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	32	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	4	2	no	—
875	C₂×D₄	—	4	1	no	—
876	C₂×D₄	—	4	2	no	—
877	C₂×D₄	—	4	1	no	—
878	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
879	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
880	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
881	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
882	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
883	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
884	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
885	C₂×D₄	#41×C₆₇	1	4	yes	—
886	C₂²×C₄	—	2	4	no	—
887	C₂²×C₄	—	2	4	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	4	no	—
893	C₂²×C₄	—	2	4	no	—
894	C₂²×C₄	—	2	4	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	4	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	4	no	—
900	C₂²×C₄	—	2	4	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	2	no	—
903	C₂²×C₄	—	4	2	no	—
904	C₂²×C₄	—	4	2	no	—
905	C₂²×C₄	—	4	1	no	—
906	C₂²×C₄	—	4	1	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	1	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	4	2	no	—
913	C₂²×C₄	—	4	2	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
918	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
919	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
920	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
921	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
922	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
934	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	4	no	—
945	C₄⋊C₄	—	2	4	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	4	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	4	2	no	—
953	C₄⋊C₄	—	4	1	no	—
954	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
955	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
956	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
957	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	—	2	4	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	4	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	4	no	—
965	C₂²⋊C₄	—	2	4	no	—
966	C₂²⋊C₄	—	2	4	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	4	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	4	1	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	1	no	—
976	C₂²⋊C₄	—	4	1	no	—
977	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
978	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
979	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
980	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
981	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
982	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
983	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
984	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	4	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	4	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	4	no	—
991	C₄²	—	2	4	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	4	2	no	—
995	C₄²	—	4	2	no	—
996	C₄²	—	4	2	no	—
997	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
998	C₄²	C₂×D₄×C₆₇	1	4	yes	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	16	no	—
1022	C₂³	—	4	8	no	—
1023	C₂³	—	4	8	no	—
1024	C₂³	—	8	4	no	—
1025	C₂³	—	8	4	no	—
1026	C₂³	—	8	4	no	—
1027	C₂³	—	8	4	no	—
1028	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1029	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
1030	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1031	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
1032	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
1033	C₂³	C₂×#41×C₆₇	1	4	yes	—
1034	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1035	Q₈	—	2	8	no	—
1036	D₄	—	2	16	no	—
1037	D₄	—	2	16	no	—
1038	D₄	—	2	8	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	8	no	—
1041	D₄	C₄×D₄×C₆₇	1	16	yes	complemented
1042	C₂×C₄	—	2	16	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	8	no	—
1064	C₂×C₄	—	2	8	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	8	no	—
1090	C₂×C₄	—	4	8	no	—
1091	C₂×C₄	—	4	4	no	—
1092	C₂×C₄	—	4	8	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	8	4	no	—
1095	C₂×C₄	—	8	4	no	—
1096	C₂×C₄	—	8	4	no	—
1097	C₂×C₄	—	8	4	no	—
1098	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1099	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1100	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1101	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1102	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1103	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1104	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1107	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1109	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1110	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1111	C₂²	—	2	4	no	—
1112	C₂²	—	2	4	no	—
1113	C₂²	—	2	4	no	—
1114	C₂²	—	2	4	no	—
1115	C₂²	—	2	4	no	—
1116	C₂²	—	2	4	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	4	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	4	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	4	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	8	16	no	—
1139	C₂²	C₂×C₄×D₄×C₆₇	1	8	yes	—
1140	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1141	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1142	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1143	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1144	C₂²	#585×C₆₇	1	1	yes	characteristic
1145	C₂²	#585×C₆₇	1	1	yes	characteristic
1146	C₂²	#585×C₆₇	1	1	yes	characteristic
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	4	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	4	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	4	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	2	no	—
1165	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
1166	C₂	—	2	8	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	4	4	no	—
1169	C₂	—	4	2	no	—
1170	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
1171	C₂	C₆₇×#3428	1	1	yes	characteristic
1172	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1173	C₂	C₆₇×#3485	1	1	yes	characteristic
1174	C₂	C₆₇×#3488	1	1	yes	characteristic
1175	C₂	C₆₇×#3514	1	1	yes	characteristic
1176	C₂	C₆₇×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#546×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₆₇	C₂	semidirect
3. C₂×C₄×#41×C₆₇	C₂	semidirect
4. C₆₇×#2367	C₂	semidirect
5. C₆₇×#2363	C₂	semidirect
6. C₆₇×#2362	C₂	semidirect
7. C₆₇×#2361	C₂	semidirect
8. C₆₇×#2359	C₂	semidirect
9. C₆₇×#2358	C₂	semidirect
10. C₆₇×#2354	C₂	semidirect
11. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
12. C₆₇×#2342	C₂	semidirect
13. C₆₇×#2339	C₂	semidirect
14. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
15. C₆₇×#2326	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₆₇×#2323	C₂	semidirect
18. C₆₇×#2321	C₂	semidirect
19. C₄×#123×C₆₇	C₂	semidirect
20. C₄×#121×C₆₇	C₂	semidirect
21. C₆₇×#2290	C₂	semidirect
22. C₂×#388×C₆₇	C₂	semidirect
23. C₆₇×#2275	C₂	semidirect
26. #546×C₆₇	C₄	semidirect
35. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
36. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
47. C₂×C₄×D₄×C₆₇	C₂²	semidirect
48. C₂×C₄×D₄×C₆₇	C₂²	semidirect
49. C₂×C₄×D₄×C₆₇	C₂²	semidirect
52. C₂×#117×C₆₇	C₂²	semidirect
53. C₂×#117×C₆₇	C₂²	semidirect
54. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
59. C₂²×C₄²×C₆₇	C₂²	semidirect
60. C₂²×C₄²×C₆₇	C₂²	semidirect
61. #391×C₆₇	C₂²	semidirect
62. #391×C₆₇	C₂²	semidirect
66. #390×C₆₇	C₂²	semidirect
67. #389×C₆₇	C₂²	semidirect
68. #389×C₆₇	C₂²	semidirect
69. #389×C₆₇	C₂²	semidirect
77. #388×C₆₇	C₂²	semidirect
78. #388×C₆₇	C₂²	semidirect
79. #388×C₆₇	C₂²	semidirect
80. #388×C₆₇	C₂²	semidirect
81. #388×C₆₇	C₂²	semidirect
82. #388×C₆₇	C₂²	semidirect
83. #388×C₆₇	C₂²	semidirect
84. #387×C₆₇	C₂²	semidirect
85. #387×C₆₇	C₂²	semidirect
86. #387×C₆₇	C₂²	semidirect
87. #387×C₆₇	C₂²	semidirect
92. #386×C₆₇	C₂²	semidirect
93. #386×C₆₇	C₂²	semidirect
94. #386×C₆₇	C₂²	semidirect
95. #386×C₆₇	C₂²	semidirect
96. #385×C₆₇	C₂²	semidirect
97. #385×C₆₇	C₂²	semidirect
98. #385×C₆₇	C₂²	semidirect
99. #385×C₆₇	C₂²	semidirect
100. #385×C₆₇	C₂²	semidirect
101. #385×C₆₇	C₂²	semidirect
102. #385×C₆₇	C₂²	semidirect
103. #384×C₆₇	C₂²	semidirect
104. #381×C₆₇	C₂²	semidirect
106. #380×C₆₇	C₂²	semidirect
107. #380×C₆₇	C₂²	semidirect
109. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
110. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
111. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
112. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
113. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
114. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
116. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
123. #376×C₆₇	C₂²	semidirect
124. C₂×#95×C₆₇	C₂²	semidirect
125. C₂×#95×C₆₇	C₂²	semidirect
129. C₂×#41×C₆₇	C₂×C₄	semidirect
133. C₂²×D₄×C₆₇	C₂×C₄	semidirect
152. #124×C₆₇	C₂×C₄	semidirect
153. #123×C₆₇	C₂×C₄	semidirect
154. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
155. #121×C₆₇	C₂×C₄	semidirect
156. #121×C₆₇	C₂×C₄	semidirect
157. #120×C₆₇	C₂×C₄	semidirect
170. C₄×D₄×C₆₇	C₂×C₄	semidirect
171. C₄×D₄×C₆₇	C₂×C₄	semidirect
172. C₄×D₄×C₆₇	D₄	semidirect
198. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
452. D₄×C₆₇	C₄×D₄	semidirect
577. #34292	C₆₇	direct (N × H)
590. C₂×#518	C₂×C₆₇	semidirect
591. C₂×C₄×#41	C₂×C₆₇	semidirect
592. #2367	C₂×C₆₇	semidirect
593. #2363	C₂×C₆₇	semidirect
594. #2362	C₂×C₆₇	semidirect
595. #2361	C₂×C₆₇	semidirect
596. #2359	C₂×C₆₇	semidirect
597. #2358	C₂×C₆₇	semidirect
598. #2354	C₂×C₆₇	semidirect
599. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
600. #2342	C₂×C₆₇	semidirect
601. #2339	C₂×C₆₇	semidirect
602. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
603. #2326	C₂×C₆₇	semidirect
604. #2325	C₂×C₆₇	semidirect
605. #2323	C₂×C₆₇	semidirect
606. #2321	C₂×C₆₇	semidirect
607. C₄×#123	C₂×C₆₇	semidirect
608. C₄×#121	C₂×C₆₇	semidirect
609. #2290	C₂×C₆₇	semidirect
610. C₂×#388	C₂×C₆₇	semidirect
611. #2275	C₂×C₆₇	semidirect
612. C₆₇	#34292	direct (N × H)
615. #546	C₄×C₆₇	semidirect
624. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
625. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
636. C₂×C₄×D₄	C₂²×C₆₇	semidirect
637. C₂×C₄×D₄	C₂²×C₆₇	semidirect
638. C₂×C₄×D₄	C₂²×C₆₇	semidirect
641. C₂×#117	C₂²×C₆₇	semidirect
642. C₂×#117	C₂²×C₆₇	semidirect
643. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
648. C₂²×C₄²	C₂²×C₆₇	semidirect
649. C₂²×C₄²	C₂²×C₆₇	semidirect
650. #391	C₂²×C₆₇	semidirect
651. #391	C₂²×C₆₇	semidirect
655. #390	C₂²×C₆₇	semidirect
656. #389	C₂²×C₆₇	semidirect
657. #389	C₂²×C₆₇	semidirect
658. #389	C₂²×C₆₇	semidirect
666. #388	C₂²×C₆₇	semidirect
667. #388	C₂²×C₆₇	semidirect
668. #388	C₂²×C₆₇	semidirect
669. #388	C₂²×C₆₇	semidirect
670. #388	C₂²×C₆₇	semidirect
671. #388	C₂²×C₆₇	semidirect
672. #388	C₂²×C₆₇	semidirect
673. #387	C₂²×C₆₇	semidirect
674. #387	C₂²×C₆₇	semidirect
675. #387	C₂²×C₆₇	semidirect
676. #387	C₂²×C₆₇	semidirect
681. #386	C₂²×C₆₇	semidirect
682. #386	C₂²×C₆₇	semidirect
683. #386	C₂²×C₆₇	semidirect
684. #386	C₂²×C₆₇	semidirect
685. #385	C₂²×C₆₇	semidirect
686. #385	C₂²×C₆₇	semidirect
687. #385	C₂²×C₆₇	semidirect
688. #385	C₂²×C₆₇	semidirect
689. #385	C₂²×C₆₇	semidirect
690. #385	C₂²×C₆₇	semidirect
691. #385	C₂²×C₆₇	semidirect
692. #384	C₂²×C₆₇	semidirect
693. #381	C₂²×C₆₇	semidirect
695. #380	C₂²×C₆₇	semidirect
696. #380	C₂²×C₆₇	semidirect
698. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
699. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
700. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
701. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
702. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
703. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
705. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
706. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
707. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
708. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
709. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
710. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
711. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
712. #376	C₂²×C₆₇	semidirect
713. C₂×#95	C₂²×C₆₇	semidirect
714. C₂×#95	C₂²×C₆₇	semidirect
718. C₂×#41	C₂×C₄×C₆₇	semidirect
722. C₂²×D₄	C₂×C₄×C₆₇	semidirect
741. #124	C₂×C₄×C₆₇	semidirect
742. #123	C₂×C₄×C₆₇	semidirect
743. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
744. #121	C₂×C₄×C₆₇	semidirect
745. #121	C₂×C₄×C₆₇	semidirect
746. #120	C₂×C₄×C₆₇	semidirect
759. C₄×D₄	C₂×C₄×C₆₇	semidirect
760. C₄×D₄	C₂×C₄×C₆₇	semidirect
761. C₄×D₄	D₄×C₆₇	semidirect
787. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
1041. D₄	C₄×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₆₇	2
C₂×#518×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#2367	2
C₆₇×#2363	2
C₆₇×#2362	2
C₆₇×#2361	2
C₆₇×#2359	2
C₆₇×#2358	2
C₆₇×#2354	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2342	2
C₆₇×#2339	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2326	2
C₆₇×#2325	2
C₆₇×#2323	2
C₆₇×#2321	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2290	2
C₂×#388×C₆₇	2
C₆₇×#2275	2
#34292	67

Subgroups — C67×#34292 #30713543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34292 #30713543