Subgroups — C₆₇×#22414 #30701665

Order 17152.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 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×C₈×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1958	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
20	#546×C₆₇	—	2	4	no	—
21	#546×C₆₇	C₄	1	8	yes	complemented
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#123×C₆₇	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₇	—	2	1	no	—
26	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#120×C₆₇	—	2	1	no	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
33	C₈×D₄×C₆₇	—	2	4	no	—
34	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#416×C₆₇	—	2	4	no	—
36	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#102×C₆₇	—	2	4	no	—
41	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#388×C₆₇	—	2	1	no	—
53	#387×C₆₇	—	2	1	no	—
54	#386×C₆₇	—	2	1	no	—
55	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#380×C₆₇	C₂²	1	1	yes	characteristic
57	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
60	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#340×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂⁵×C₆₇	—	2	1	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	—	4	1	no	—
69	C₂×#41×C₆₇	—	4	1	no	—
70	C₂×#41×C₆₇	C₂×C₄	1	4	yes	complemented
71	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₇	—	2	2	no	—
73	C₂²×D₄×C₆₇	—	2	2	no	—
74	C₂²×D₄×C₆₇	—	2	1	no	—
75	C₂²×D₄×C₆₇	—	2	1	no	—
76	C₂²×D₄×C₆₇	—	2	1	no	—
77	C₂²×D₄×C₆₇	—	2	2	no	—
78	C₂²×D₄×C₆₇	—	4	1	no	—
79	C₂²×D₄×C₆₇	—	4	1	no	—
80	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
81	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₆₇	—	2	1	no	—
85	C₂³×C₄×C₆₇	—	2	1	no	—
86	C₂³×C₄×C₆₇	—	2	1	no	—
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	—	2	2	no	—
90	C₂²×C₈×C₆₇	—	2	2	no	—
91	C₂²×C₈×C₆₇	—	2	2	no	—
92	C₂²×C₈×C₆₇	—	2	2	no	—
93	C₂²×C₈×C₆₇	—	4	1	no	—
94	C₂²×C₈×C₆₇	—	4	1	no	—
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	#124×C₆₇	—	2	2	no	—
100	#124×C₆₇	C₂×C₄	1	4	yes	complemented
101	#123×C₆₇	—	2	8	no	—
102	C₂²⋊Q₈×C₆₇	—	2	2	no	—
103	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
104	#121×C₆₇	—	2	2	no	—
105	#121×C₆₇	—	2	8	no	—
106	#121×C₆₇	C₂×C₄	1	4	yes	complemented
107	#120×C₆₇	—	2	8	no	—
108	C₄×D₄×C₆₇	—	2	2	no	—
109	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
110	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	complemented
111	C₄×D₄×C₆₇	D₄	1	4	yes	—
112	#117×C₆₇	—	2	2	no	—
113	#117×C₆₇	—	4	1	no	—
114	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
115	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
116	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
117	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
118	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
130	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	—	2	1	no	—
136	C₂×C₄²×C₆₇	—	2	1	no	—
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₆₇	—	2	2	no	—
139	#103×C₆₇	—	2	2	no	—
140	#103×C₆₇	—	2	2	no	—
141	#103×C₆₇	—	4	1	no	—
142	#103×C₆₇	—	4	1	no	—
143	#102×C₆₇	—	2	2	no	—
144	#102×C₆₇	—	2	2	no	—
145	#102×C₆₇	—	2	2	no	—
146	#102×C₆₇	—	2	2	no	—
147	#102×C₆₇	—	2	2	no	—
148	#102×C₆₇	—	4	1	no	—
149	#102×C₆₇	—	4	1	no	—
150	#102×C₆₇	D₄	1	4	yes	complemented
151	C₂²⋊C₈×C₆₇	—	2	2	no	—
152	C₂²⋊C₈×C₆₇	—	2	2	no	—
153	C₄×C₈×C₆₇	—	2	2	no	—
154	#95×C₆₇	—	2	1	no	—
155	#95×C₆₇	—	2	1	no	—
156	#95×C₆₇	—	2	1	no	—
157	#95×C₆₇	—	2	1	no	—
158	#95×C₆₇	—	2	1	no	—
159	C₂⁴×C₆₇	—	2	1	no	—
160	C₂⁴×C₆₇	—	2	1	no	—
161	C₂⁴×C₆₇	—	2	4	no	—
162	C₂⁴×C₆₇	—	4	2	no	—
163	C₂⁴×C₆₇	—	4	2	no	—
164	C₂⁴×C₆₇	—	4	2	no	—
165	C₂⁴×C₆₇	—	4	2	no	—
166	C₂⁴×C₆₇	—	8	1	no	—
167	C₂⁴×C₆₇	—	8	1	no	—
168	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
170	#41×C₆₇	—	2	8	no	—
171	#41×C₆₇	—	4	4	no	—
172	#41×C₆₇	—	4	4	no	—
173	#41×C₆₇	—	4	4	no	—
174	C₂×Q₈×C₆₇	—	2	1	no	—
175	C₂×Q₈×C₆₇	—	2	1	no	—
176	C₂×Q₈×C₆₇	—	2	1	no	—
177	C₂×Q₈×C₆₇	—	2	1	no	—
178	C₂×Q₈×C₆₇	—	2	1	no	—
179	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
180	C₂×D₄×C₆₇	—	2	2	no	—
181	C₂×D₄×C₆₇	—	2	2	no	—
182	C₂×D₄×C₆₇	—	2	8	no	—
183	C₂×D₄×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	1	no	—
187	C₂×D₄×C₆₇	—	2	1	no	—
188	C₂×D₄×C₆₇	—	2	1	no	—
189	C₂×D₄×C₆₇	—	2	1	no	—
190	C₂×D₄×C₆₇	—	2	1	no	—
191	C₂×D₄×C₆₇	—	2	1	no	—
192	C₂×D₄×C₆₇	—	2	1	no	—
193	C₂×D₄×C₆₇	—	2	1	no	—
194	C₂×D₄×C₆₇	—	4	4	no	—
195	C₂×D₄×C₆₇	—	4	4	no	—
196	C₂×D₄×C₆₇	—	4	4	no	—
197	C₂×D₄×C₆₇	—	4	2	no	—
198	C₂×D₄×C₆₇	—	4	2	no	—
199	C₂×D₄×C₆₇	—	4	2	no	—
200	C₂×D₄×C₆₇	—	4	2	no	—
201	C₂×D₄×C₆₇	—	8	1	no	—
202	C₂×D₄×C₆₇	—	8	1	no	—
203	C₂×D₄×C₆₇	C₂²⋊C₄	1	4	yes	—
204	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
205	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
206	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₆₇	#41	1	2	yes	—
208	C₂²×C₄×C₆₇	—	2	1	no	—
209	C₂²×C₄×C₆₇	—	2	1	no	—
210	C₂²×C₄×C₆₇	—	2	1	no	—
211	C₂²×C₄×C₆₇	—	2	1	no	—
212	C₂²×C₄×C₆₇	—	2	1	no	—
213	C₂²×C₄×C₆₇	—	2	1	no	—
214	C₂²×C₄×C₆₇	—	2	1	no	—
215	C₂²×C₄×C₆₇	—	2	1	no	—
216	C₂²×C₄×C₆₇	—	2	1	no	—
217	C₂²×C₄×C₆₇	—	2	1	no	—
218	C₂²×C₄×C₆₇	—	2	1	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	1	no	—
222	C₂²×C₄×C₆₇	—	2	1	no	—
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	4	2	no	—
225	C₂²×C₄×C₆₇	—	4	2	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	2	no	—
228	C₂²×C₄×C₆₇	—	8	1	no	—
229	C₂²×C₄×C₆₇	—	8	1	no	—
230	C₂²×C₄×C₆₇	—	8	1	no	—
231	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₆₇	—	2	1	no	—
241	C₂×C₈×C₆₇	—	2	1	no	—
242	C₂×C₈×C₆₇	—	2	1	no	—
243	C₂×C₈×C₆₇	—	2	1	no	—
244	C₂×C₈×C₆₇	—	2	1	no	—
245	C₂×C₈×C₆₇	—	2	1	no	—
246	C₂×C₈×C₆₇	—	2	1	no	—
247	C₂×C₈×C₆₇	—	2	1	no	—
248	C₂×C₈×C₆₇	—	2	1	no	—
249	C₂×C₈×C₆₇	—	2	1	no	—
250	C₂×C₈×C₆₇	—	2	1	no	—
251	C₂×C₈×C₆₇	—	4	4	no	—
252	C₂×C₈×C₆₇	—	4	4	no	—
253	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	1	no	—
256	C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₄⋊C₄×C₆₇	—	4	2	no	—
264	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
265	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
266	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	4	2	no	—
273	C₂²⋊C₄×C₆₇	—	4	2	no	—
274	C₂²⋊C₄×C₆₇	—	8	1	no	—
275	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
276	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
277	C₄²×C₆₇	—	4	2	no	—
278	C₄²×C₆₇	—	8	1	no	—
279	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
280	C₄²×C₆₇	C₂×D₄	1	2	yes	—
281	C₂³×C₆₇	—	2	1	no	—
282	C₂³×C₆₇	—	2	1	no	—
283	C₂³×C₆₇	—	2	1	no	—
284	C₂³×C₆₇	—	2	1	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	1	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	1	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	1	no	—
291	C₂³×C₆₇	—	2	1	no	—
292	C₂³×C₆₇	—	2	1	no	—
293	C₂³×C₆₇	—	2	1	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	4	8	no	—
296	C₂³×C₆₇	—	4	1	no	—
297	C₂³×C₆₇	—	4	1	no	—
298	C₂³×C₆₇	—	4	1	no	—
299	C₂³×C₆₇	—	4	1	no	—
300	C₂³×C₆₇	—	4	1	no	—
301	C₂³×C₆₇	—	4	1	no	—
302	C₂³×C₆₇	—	4	1	no	—
303	C₂³×C₆₇	—	4	1	no	—
304	C₂³×C₆₇	—	4	1	no	—
305	C₂³×C₆₇	—	4	1	no	—
306	C₂³×C₆₇	—	4	8	no	—
307	C₂³×C₆₇	—	8	4	no	—
308	C₂³×C₆₇	—	8	4	no	—
309	C₂³×C₆₇	—	8	4	no	—
310	C₂³×C₆₇	—	8	4	no	—
311	C₂³×C₆₇	—	8	4	no	—
312	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
313	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
314	C₂³×C₆₇	#135	1	2	yes	—
315	C₂³×C₆₇	#135	1	2	yes	—
316	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₆₇	—	2	2	no	—
318	Q₈×C₆₇	—	2	2	no	—
319	Q₈×C₆₇	—	4	1	no	—
320	Q₈×C₆₇	—	4	1	no	—
321	D₄×C₆₇	—	2	8	no	—
322	D₄×C₆₇	—	2	2	no	—
323	D₄×C₆₇	—	2	2	no	—
324	D₄×C₆₇	—	2	2	no	—
325	D₄×C₆₇	—	2	2	no	—
326	D₄×C₆₇	—	2	2	no	—
327	D₄×C₆₇	—	4	8	no	—
328	D₄×C₆₇	—	4	8	no	—
329	D₄×C₆₇	—	4	1	no	—
330	D₄×C₆₇	—	4	1	no	—
331	D₄×C₆₇	—	8	4	no	—
332	D₄×C₆₇	C₄×D₄	1	4	yes	—
333	C₂×C₄×C₆₇	—	2	1	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	1	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	1	no	—
339	C₂×C₄×C₆₇	—	2	1	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	4	8	no	—
353	C₂×C₄×C₆₇	—	4	1	no	—
354	C₂×C₄×C₆₇	—	4	1	no	—
355	C₂×C₄×C₆₇	—	4	1	no	—
356	C₂×C₄×C₆₇	—	4	1	no	—
357	C₂×C₄×C₆₇	—	4	1	no	—
358	C₂×C₄×C₆₇	—	4	1	no	—
359	C₂×C₄×C₆₇	—	4	1	no	—
360	C₂×C₄×C₆₇	—	4	1	no	—
361	C₂×C₄×C₆₇	—	4	1	no	—
362	C₂×C₄×C₆₇	—	4	1	no	—
363	C₂×C₄×C₆₇	—	4	1	no	—
364	C₂×C₄×C₆₇	—	4	1	no	—
365	C₂×C₄×C₆₇	—	4	1	no	—
366	C₂×C₄×C₆₇	—	4	1	no	—
367	C₂×C₄×C₆₇	—	4	1	no	—
368	C₂×C₄×C₆₇	—	8	4	no	—
369	C₂×C₄×C₆₇	—	8	4	no	—
370	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
371	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
372	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
373	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
374	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
375	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
380	C₈×C₆₇	—	2	2	no	—
381	C₈×C₆₇	—	4	1	no	—
382	C₈×C₆₇	—	4	1	no	—
383	C₈×C₆₇	—	4	1	no	—
384	C₂²×C₆₇	—	2	2	no	—
385	C₂²×C₆₇	—	2	2	no	—
386	C₂²×C₆₇	—	2	2	no	—
387	C₂²×C₆₇	—	2	2	no	—
388	C₂²×C₆₇	—	2	2	no	—
389	C₂²×C₆₇	—	2	2	no	—
390	C₂²×C₆₇	—	2	2	no	—
391	C₂²×C₆₇	—	2	4	no	—
392	C₂²×C₆₇	—	2	2	no	—
393	C₂²×C₆₇	—	2	2	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	1	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	1	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	4	1	no	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	1	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	8	16	no	—
408	C₂²×C₆₇	—	8	1	no	—
409	C₂²×C₆₇	—	8	1	no	—
410	C₂²×C₆₇	—	8	1	no	—
411	C₂²×C₆₇	—	8	1	no	—
412	C₂²×C₆₇	#416	1	4	yes	complemented
413	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
414	C₂²×C₆₇	D₄²	1	1	yes	characteristic
415	C₂²×C₆₇	#546	1	1	yes	characteristic
416	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
417	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
418	C₂²×C₆₇	#576	1	1	yes	characteristic
419	C₂²×C₆₇	#577	1	1	yes	characteristic
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	2	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	2	no	—
427	C₄×C₆₇	—	8	1	no	—
428	C₄×C₆₇	—	8	1	no	—
429	C₄×C₆₇	—	8	1	no	—
430	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
431	C₄×C₆₇	#518	1	1	yes	characteristic
432	C₄×C₆₇	D₄²	1	1	yes	characteristic
433	C₄×C₆₇	#546	1	1	yes	characteristic
434	#22414	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
435	C₂×C₆₇	—	2	4	no	—
436	C₂×C₆₇	—	4	2	no	—
437	C₂×C₆₇	—	4	4	no	—
438	C₂×C₆₇	—	8	2	no	—
439	C₂×C₆₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
440	C₂×C₆₇	C₂×#416	1	1	yes	characteristic
441	C₂×C₆₇	#2897	1	1	yes	characteristic
442	C₂×C₆₇	#3280	1	1	yes	characteristic
443	C₂×C₆₇	#3282	1	1	yes	characteristic
444	C₂×C₆₇	#3296	1	1	yes	characteristic
445	C₂×C₆₇	#3297	1	1	yes	characteristic
446	C₂×#546	C₂×C₆₇	1	1	yes	characteristic
447	C₂×C₈×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
448	C₂×#416	C₂×C₆₇	1	1	yes	characteristic, complemented
449	C₂²×#102	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#1983	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#1958	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#1893	C₂×C₆₇	1	1	yes	characteristic, complemented
454	#1892	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#1875	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#1872	C₂×C₆₇	1	1	yes	characteristic, complemented
457	#1804	C₂×C₆₇	1	1	yes	characteristic, complemented
458	#1788	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#1786	C₂×C₆₇	1	1	yes	characteristic, complemented
460	C₄×#102	C₂×C₆₇	1	1	yes	characteristic, complemented
461	C₆₇	#22414	1	1	yes	characteristic, direct product factor, Sylow
462	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
463	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
464	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
465	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
466	#546	—	2	4	no	—
467	#546	C₄×C₆₇	1	8	yes	complemented
468	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×#123	—	2	1	no	—
470	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#121	—	2	1	no	—
472	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#120	—	2	1	no	—
474	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
477	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
478	C₂²×C₂²⋊C₄	—	2	1	no	—
479	C₈×D₄	—	2	4	no	—
480	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
481	#416	—	2	4	no	—
482	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
483	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
484	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
486	C₂×#102	—	2	4	no	—
487	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
494	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
495	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
496	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
498	#388	—	2	1	no	—
499	#387	—	2	1	no	—
500	#386	—	2	1	no	—
501	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
502	#380	C₂²×C₆₇	1	1	yes	characteristic
503	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
504	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	C₄×C₂²⋊C₄	—	2	1	no	—
506	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
507	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
508	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
509	#340	C₂²×C₆₇	1	1	yes	characteristic, complemented
510	C₂⁵	—	2	1	no	—
511	C₂×#41	—	2	2	no	—
512	C₂×#41	—	2	2	no	—
513	C₂×#41	—	2	2	no	—
514	C₂×#41	—	4	1	no	—
515	C₂×#41	—	4	1	no	—
516	C₂×#41	C₂×C₄×C₆₇	1	4	yes	complemented
517	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₂²×D₄	—	2	2	no	—
519	C₂²×D₄	—	2	2	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	2	no	—
524	C₂²×D₄	—	4	1	no	—
525	C₂²×D₄	—	4	1	no	—
526	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
527	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
535	C₂²×C₈	—	2	2	no	—
536	C₂²×C₈	—	2	2	no	—
537	C₂²×C₈	—	2	2	no	—
538	C₂²×C₈	—	2	2	no	—
539	C₂²×C₈	—	4	1	no	—
540	C₂²×C₈	—	4	1	no	—
541	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
542	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
544	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
545	#124	—	2	2	no	—
546	#124	C₂×C₄×C₆₇	1	4	yes	complemented
547	#123	—	2	8	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
550	#121	—	2	2	no	—
551	#121	—	2	8	no	—
552	#121	C₂×C₄×C₆₇	1	4	yes	complemented
553	#120	—	2	8	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
556	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	complemented
557	C₄×D₄	D₄×C₆₇	1	4	yes	—
558	#117	—	2	2	no	—
559	#117	—	4	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	4	1	no	—
564	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	8	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	—	2	1	no	—
583	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
584	C₄⋊C₈	—	2	2	no	—
585	#103	—	2	2	no	—
586	#103	—	2	2	no	—
587	#103	—	4	1	no	—
588	#103	—	4	1	no	—
589	#102	—	2	2	no	—
590	#102	—	2	2	no	—
591	#102	—	2	2	no	—
592	#102	—	2	2	no	—
593	#102	—	2	2	no	—
594	#102	—	4	1	no	—
595	#102	—	4	1	no	—
596	#102	D₄×C₆₇	1	4	yes	complemented
597	C₂²⋊C₈	—	2	2	no	—
598	C₂²⋊C₈	—	2	2	no	—
599	C₄×C₈	—	2	2	no	—
600	#95	—	2	1	no	—
601	#95	—	2	1	no	—
602	#95	—	2	1	no	—
603	#95	—	2	1	no	—
604	#95	—	2	1	no	—
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	1	no	—
607	C₂⁴	—	2	4	no	—
608	C₂⁴	—	4	2	no	—
609	C₂⁴	—	4	2	no	—
610	C₂⁴	—	4	2	no	—
611	C₂⁴	—	4	2	no	—
612	C₂⁴	—	8	1	no	—
613	C₂⁴	—	8	1	no	—
614	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
615	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
616	#41	—	2	8	no	—
617	#41	—	4	4	no	—
618	#41	—	4	4	no	—
619	#41	—	4	4	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	4	4	no	—
641	C₂×D₄	—	4	4	no	—
642	C₂×D₄	—	4	4	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	—	8	1	no	—
648	C₂×D₄	—	8	1	no	—
649	C₂×D₄	C₂²⋊C₄×C₆₇	1	4	yes	—
650	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
651	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
652	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
653	C₂×D₄	#41×C₆₇	1	2	yes	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	8	1	no	—
675	C₂²×C₄	—	8	1	no	—
676	C₂²×C₄	—	8	1	no	—
677	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
678	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	4	4	no	—
698	C₂×C₈	—	4	4	no	—
699	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
711	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	8	1	no	—
721	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
722	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
723	C₄²	—	4	2	no	—
724	C₄²	—	8	1	no	—
725	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
726	C₄²	C₂×D₄×C₆₇	1	2	yes	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	4	8	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	8	no	—
753	C₂³	—	8	4	no	—
754	C₂³	—	8	4	no	—
755	C₂³	—	8	4	no	—
756	C₂³	—	8	4	no	—
757	C₂³	—	8	4	no	—
758	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
759	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
760	C₂³	#135×C₆₇	1	2	yes	—
761	C₂³	#135×C₆₇	1	2	yes	—
762	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	4	1	no	—
766	Q₈	—	4	1	no	—
767	D₄	—	2	8	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	2	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	1	no	—
776	D₄	—	4	1	no	—
777	D₄	—	8	4	no	—
778	D₄	C₄×D₄×C₆₇	1	4	yes	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	8	4	no	—
815	C₂×C₄	—	8	4	no	—
816	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
817	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
818	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
819	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
820	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
823	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
824	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
825	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
826	C₈	—	2	2	no	—
827	C₈	—	4	1	no	—
828	C₈	—	4	1	no	—
829	C₈	—	4	1	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	8	16	no	—
854	C₂²	—	8	1	no	—
855	C₂²	—	8	1	no	—
856	C₂²	—	8	1	no	—
857	C₂²	—	8	1	no	—
858	C₂²	#416×C₆₇	1	4	yes	complemented
859	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
860	C₂²	D₄²×C₆₇	1	1	yes	characteristic
861	C₂²	#546×C₆₇	1	1	yes	characteristic
862	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
863	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
864	C₂²	#576×C₆₇	1	1	yes	characteristic
865	C₂²	#577×C₆₇	1	1	yes	characteristic
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	8	1	no	—
874	C₄	—	8	1	no	—
875	C₄	—	8	1	no	—
876	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
877	C₄	#518×C₆₇	1	1	yes	characteristic
878	C₄	D₄²×C₆₇	1	1	yes	characteristic
879	C₄	#546×C₆₇	1	1	yes	characteristic
880	C₂	—	2	4	no	—
881	C₂	—	4	2	no	—
882	C₂	—	4	4	no	—
883	C₂	—	8	2	no	—
884	C₂	D₄×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
885	C₂	C₂×#416×C₆₇	1	1	yes	characteristic
886	C₂	C₆₇×#2897	1	1	yes	characteristic
887	C₂	C₆₇×#3280	1	1	yes	characteristic
888	C₂	C₆₇×#3282	1	1	yes	characteristic
889	C₂	C₆₇×#3296	1	1	yes	characteristic
890	C₂	C₆₇×#3297	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#546×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₄×C₆₇	C₂	semidirect
3. C₂×#416×C₆₇	C₂	semidirect
4. C₂²×#102×C₆₇	C₂	semidirect
5. C₆₇×#2352	C₂	semidirect
6. C₆₇×#1983	C₂	semidirect
7. C₆₇×#1958	C₂	semidirect
8. C₆₇×#1893	C₂	semidirect
9. C₆₇×#1892	C₂	semidirect
10. C₆₇×#1875	C₂	semidirect
11. C₆₇×#1872	C₂	semidirect
12. C₆₇×#1804	C₂	semidirect
13. C₆₇×#1788	C₂	semidirect
14. C₆₇×#1786	C₂	semidirect
15. C₄×#102×C₆₇	C₂	semidirect
19. C₂³×C₈×C₆₇	C₂²	semidirect
21. #546×C₆₇	C₄	semidirect
30. C₂×#117×C₆₇	C₂²	semidirect
34. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
36. C₂×#103×C₆₇	C₂²	semidirect
37. C₂×#103×C₆₇	C₂²	semidirect
38. C₂×#103×C₆₇	C₂²	semidirect
39. C₂×#103×C₆₇	C₂²	semidirect
50. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
51. C₂×C₄×C₈×C₆₇	C₂²	semidirect
55. #382×C₆₇	C₂²	semidirect
57. #380×C₆₇	C₂²	semidirect
58. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
60. #340×C₆₇	C₂²	semidirect
61. #340×C₆₇	C₂²	semidirect
62. #340×C₆₇	C₂²	semidirect
63. #340×C₆₇	C₂²	semidirect
70. C₂×#41×C₆₇	C₂×C₄	semidirect
100. #124×C₆₇	C₂×C₄	semidirect
106. #121×C₆₇	C₂×C₄	semidirect
110. C₄×D₄×C₆₇	C₂×C₄	semidirect
150. #102×C₆₇	D₄	semidirect
412. C₂²×C₆₇	#416	semidirect
434. #22414	C₆₇	direct (N × H)
447. C₂×C₈×D₄	C₂×C₆₇	semidirect
448. C₂×#416	C₂×C₆₇	semidirect
449. C₂²×#102	C₂×C₆₇	semidirect
450. #2352	C₂×C₆₇	semidirect
451. #1983	C₂×C₆₇	semidirect
452. #1958	C₂×C₆₇	semidirect
453. #1893	C₂×C₆₇	semidirect
454. #1892	C₂×C₆₇	semidirect
455. #1875	C₂×C₆₇	semidirect
456. #1872	C₂×C₆₇	semidirect
457. #1804	C₂×C₆₇	semidirect
458. #1788	C₂×C₆₇	semidirect
459. #1786	C₂×C₆₇	semidirect
460. C₄×#102	C₂×C₆₇	semidirect
461. C₆₇	#22414	direct (N × H)
465. C₂³×C₈	C₂²×C₆₇	semidirect
467. #546	C₄×C₆₇	semidirect
476. C₂×#117	C₂²×C₆₇	semidirect
480. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
482. C₂×#103	C₂²×C₆₇	semidirect
483. C₂×#103	C₂²×C₆₇	semidirect
484. C₂×#103	C₂²×C₆₇	semidirect
485. C₂×#103	C₂²×C₆₇	semidirect
496. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
497. C₂×C₄×C₈	C₂²×C₆₇	semidirect
501. #382	C₂²×C₆₇	semidirect
503. #380	C₂²×C₆₇	semidirect
504. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
506. #340	C₂²×C₆₇	semidirect
507. #340	C₂²×C₆₇	semidirect
508. #340	C₂²×C₆₇	semidirect
509. #340	C₂²×C₆₇	semidirect
516. C₂×#41	C₂×C₄×C₆₇	semidirect
546. #124	C₂×C₄×C₆₇	semidirect
552. #121	C₂×C₄×C₆₇	semidirect
556. C₄×D₄	C₂×C₄×C₆₇	semidirect
596. #102	D₄×C₆₇	semidirect
858. C₂²	#416×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×C₈×D₄×C₆₇	2
C₂×#416×C₆₇	2
C₂²×#102×C₆₇	2
C₆₇×#2352	2
C₆₇×#1983	2
C₆₇×#1958	2
C₆₇×#1893	2
C₆₇×#1892	2
C₆₇×#1875	2
C₆₇×#1872	2
C₆₇×#1804	2
C₆₇×#1788	2
C₆₇×#1786	2
C₄×#102×C₆₇	2
#22414	67

Subgroups — C67×#22414 #30701665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22414 #30701665