Subgroups — C₆₇×#22422 #30701673

Order 17152.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1961	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	#550×C₆₇	—	2	4	no	—
21	#550×C₆₇	C₄	1	8	yes	complemented
22	C₂×#127×C₆₇	—	2	1	no	—
23	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#121×C₆₇	—	2	1	no	—
25	C₂×#121×C₆₇	—	2	1	no	—
26	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	—	2	1	no	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	#435×C₆₇	—	2	4	no	—
34	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
35	#417×C₆₇	—	2	4	no	—
36	#416×C₆₇	—	2	4	no	—
37	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
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
51	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
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
56	#380×C₆₇	C₂²	1	1	yes	characteristic
57	#380×C₆₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
60	#340×C₆₇	C₂²	1	1	yes	characteristic
61	#340×C₆₇	C₂²	1	1	yes	characteristic
62	#340×C₆₇	C₂²	1	1	yes	characteristic
63	#340×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#41×C₆₇	—	2	2	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	—	2	2	no	—
69	C₂×#41×C₆₇	—	2	2	no	—
70	C₂×#41×C₆₇	—	4	1	no	—
71	C₂×#41×C₆₇	—	4	1	no	—
72	C₂×#41×C₆₇	—	4	1	no	—
73	C₂×#41×C₆₇	—	4	1	no	—
74	C₂×#41×C₆₇	C₂×C₄	1	4	yes	—
75	C₂×#41×C₆₇	C₂×C₄	1	4	yes	complemented
76	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₆₇	—	2	1	no	—
78	C₂²×D₄×C₆₇	—	2	1	no	—
79	C₂²×D₄×C₆₇	—	2	1	no	—
80	C₂²×D₄×C₆₇	—	2	1	no	—
81	C₂²×D₄×C₆₇	—	2	1	no	—
82	C₂²×D₄×C₆₇	—	2	1	no	—
83	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₆₇	—	2	1	no	—
87	C₂³×C₄×C₆₇	—	2	1	no	—
88	C₂³×C₄×C₆₇	—	2	1	no	—
89	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₆₇	—	2	2	no	—
92	C₂×M₁₆×C₆₇	—	2	2	no	—
93	C₂×M₁₆×C₆₇	—	4	1	no	—
94	C₂²×C₈×C₆₇	—	2	2	no	—
95	C₂²×C₈×C₆₇	—	2	2	no	—
96	C₂²×C₈×C₆₇	—	4	1	no	—
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
101	#127×C₆₇	—	2	8	no	—
102	#127×C₆₇	—	2	2	no	—
103	#127×C₆₇	C₂×C₄	1	4	yes	complemented
104	#121×C₆₇	—	2	2	no	—
105	#121×C₆₇	—	2	2	no	—
106	#121×C₆₇	—	2	8	no	—
107	#121×C₆₇	—	2	8	no	—
108	#121×C₆₇	C₂×C₄	1	4	yes	—
109	#121×C₆₇	C₂×C₄	1	4	yes	complemented
110	C₄×Q₈×C₆₇	—	2	2	no	—
111	C₄×Q₈×C₆₇	C₂×C₄	1	4	yes	complemented
112	C₄×D₄×C₆₇	—	2	8	no	—
113	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
114	C₄×D₄×C₆₇	D₄	1	4	yes	—
115	#117×C₆₇	—	2	2	no	—
116	#117×C₆₇	—	4	1	no	—
117	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
118	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
120	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
121	C₂×C₄⋊C₄×C₆₇	D₄	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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₆₇	—	2	1	no	—
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	—	2	2	no	—
142	#103×C₆₇	D₄	1	4	yes	complemented
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	—	4	1	no	—
148	#102×C₆₇	—	4	1	no	—
149	#102×C₆₇	—	4	1	no	—
150	#102×C₆₇	—	4	1	no	—
151	C₂²⋊C₈×C₆₇	—	2	2	no	—
152	C₂²⋊C₈×C₆₇	—	2	2	no	—
153	#97×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	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
163	#41×C₆₇	—	2	8	no	—
164	#41×C₆₇	—	2	8	no	—
165	#41×C₆₇	—	4	4	no	—
166	#41×C₆₇	—	4	4	no	—
167	#41×C₆₇	—	4	4	no	—
168	#41×C₆₇	—	4	4	no	—
169	#41×C₆₇	—	4	4	no	—
170	#41×C₆₇	—	4	4	no	—
171	C₂×Q₈×C₆₇	—	2	1	no	—
172	C₂×Q₈×C₆₇	—	2	1	no	—
173	C₂×Q₈×C₆₇	—	2	1	no	—
174	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
175	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
176	C₂×Q₈×C₆₇	#41	1	2	yes	—
177	C₂×D₄×C₆₇	—	2	4	no	—
178	C₂×D₄×C₆₇	—	2	4	no	—
179	C₂×D₄×C₆₇	—	2	4	no	—
180	C₂×D₄×C₆₇	—	2	4	no	—
181	C₂×D₄×C₆₇	—	2	4	no	—
182	C₂×D₄×C₆₇	—	2	4	no	—
183	C₂×D₄×C₆₇	—	2	1	no	—
184	C₂×D₄×C₆₇	—	2	1	no	—
185	C₂×D₄×C₆₇	—	2	1	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	—	4	1	no	—
194	C₂×D₄×C₆₇	—	4	1	no	—
195	C₂×D₄×C₆₇	—	4	2	no	—
196	C₂×D₄×C₆₇	—	4	2	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	—	8	1	no	—
204	C₂×D₄×C₆₇	—	8	1	no	—
205	C₂×D₄×C₆₇	—	8	1	no	—
206	C₂×D₄×C₆₇	—	8	1	no	—
207	C₂×D₄×C₆₇	C₂²⋊C₄	1	4	yes	—
208	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
209	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
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	1	no	—
220	C₂²×C₄×C₆₇	—	2	1	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	2	1	no	—
225	C₂²×C₄×C₆₇	—	2	1	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	2	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	—	4	2	no	—
230	C₂²×C₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	4	2	no	—
232	C₂²×C₄×C₆₇	—	8	1	no	—
233	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
234	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	M₁₆×C₆₇	—	4	4	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	—	2	1	no	—
252	C₂×C₈×C₆₇	—	2	1	no	—
253	C₂×C₈×C₆₇	—	2	1	no	—
254	C₂×C₈×C₆₇	—	4	4	no	—
255	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₇	—	2	4	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	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	1	no	—
265	C₄⋊C₄×C₆₇	—	4	2	no	—
266	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
267	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	4	2	no	—
272	C₂²⋊C₄×C₆₇	—	4	2	no	—
273	C₂²⋊C₄×C₆₇	—	8	1	no	—
274	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
275	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
276	C₄²×C₆₇	—	2	4	no	—
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	1	no	—
286	C₂³×C₆₇	—	2	1	no	—
287	C₂³×C₆₇	—	2	1	no	—
288	C₂³×C₆₇	—	2	1	no	—
289	C₂³×C₆₇	—	2	1	no	—
290	C₂³×C₆₇	—	2	1	no	—
291	C₂³×C₆₇	—	2	1	no	—
292	C₂³×C₆₇	—	2	1	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	4	1	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	1	no	—
307	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₆₇	—	2	2	no	—
311	Q₈×C₆₇	—	2	2	no	—
312	Q₈×C₆₇	—	2	2	no	—
313	Q₈×C₆₇	C₄×D₄	1	4	yes	—
314	D₄×C₆₇	—	2	2	no	—
315	D₄×C₆₇	—	2	2	no	—
316	D₄×C₆₇	—	2	2	no	—
317	D₄×C₆₇	—	2	2	no	—
318	D₄×C₆₇	—	4	4	no	—
319	D₄×C₆₇	—	4	8	no	—
320	D₄×C₆₇	—	4	8	no	—
321	D₄×C₆₇	—	4	8	no	—
322	D₄×C₆₇	—	4	1	no	—
323	D₄×C₆₇	—	4	1	no	—
324	D₄×C₆₇	—	4	1	no	—
325	D₄×C₆₇	—	4	1	no	—
326	D₄×C₆₇	—	8	4	no	—
327	D₄×C₆₇	—	8	4	no	—
328	D₄×C₆₇	—	8	4	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	1	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	1	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	2	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	2	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	—	4	8	no	—
351	C₂×C₄×C₆₇	—	4	8	no	—
352	C₂×C₄×C₆₇	—	4	1	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	—	8	4	no	—
366	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
367	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
368	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
369	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
370	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
376	C₈×C₆₇	—	2	2	no	—
377	C₈×C₆₇	—	4	1	no	—
378	C₈×C₆₇	—	4	1	no	—
379	C₈×C₆₇	—	4	1	no	—
380	C₂²×C₆₇	—	2	2	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	2	2	no	—
383	C₂²×C₆₇	—	2	2	no	—
384	C₂²×C₆₇	—	2	2	no	—
385	C₂²×C₆₇	—	2	2	no	—
386	C₂²×C₆₇	—	4	1	no	—
387	C₂²×C₆₇	—	4	1	no	—
388	C₂²×C₆₇	—	4	1	no	—
389	C₂²×C₆₇	—	4	1	no	—
390	C₂²×C₆₇	—	4	1	no	—
391	C₂²×C₆₇	—	4	1	no	—
392	C₂²×C₆₇	—	4	1	no	—
393	C₂²×C₆₇	—	4	1	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	2	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	8	1	no	—
401	C₂²×C₆₇	—	8	1	no	—
402	C₂²×C₆₇	—	8	1	no	—
403	C₂²×C₆₇	—	8	1	no	—
404	C₂²×C₆₇	—	8	1	no	—
405	C₂²×C₆₇	—	8	1	no	—
406	C₂²×C₆₇	—	8	1	no	—
407	C₂²×C₆₇	—	8	1	no	—
408	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₂²×C₆₇	D₄²	1	1	yes	characteristic
410	C₂²×C₆₇	#546	1	1	yes	characteristic
411	C₂²×C₆₇	#575	1	1	yes	characteristic
412	C₂²×C₆₇	#575	1	1	yes	characteristic
413	C₂²×C₆₇	#576	1	1	yes	characteristic
414	C₂²×C₆₇	#577	1	1	yes	characteristic
415	C₄×C₆₇	—	2	2	no	—
416	C₄×C₆₇	—	2	2	no	—
417	C₄×C₆₇	—	2	4	no	—
418	C₄×C₆₇	—	2	2	no	—
419	C₄×C₆₇	—	2	2	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	2	no	—
422	C₄×C₆₇	—	8	1	no	—
423	C₄×C₆₇	—	8	1	no	—
424	C₄×C₆₇	—	8	1	no	—
425	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
426	C₄×C₆₇	#518	1	1	yes	characteristic
427	C₄×C₆₇	D₄²	1	1	yes	characteristic
428	C₄×C₆₇	#546	1	1	yes	characteristic
429	#22422	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₂×C₆₇	—	4	2	no	—
431	C₂×C₆₇	—	4	2	no	—
432	C₂×C₆₇	—	8	2	no	—
433	C₂×C₆₇	—	8	2	no	—
434	C₂×C₆₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
435	C₂×C₆₇	#2896	1	1	yes	characteristic
436	C₂×C₆₇	#2897	1	1	yes	characteristic
437	C₂×C₆₇	#3268	1	1	yes	characteristic
438	C₂×C₆₇	#3271	1	1	yes	characteristic
439	C₂×C₆₇	#3309	1	1	yes	characteristic
440	C₂×C₆₇	#3317	1	1	yes	characteristic
441	C₂×#550	C₂×C₆₇	1	1	yes	characteristic
442	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
443	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
444	C₂×#416	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#1982	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#1961	C₂×C₆₇	1	1	yes	characteristic, complemented
448	#1895	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#1893	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#1875	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#1874	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#1805	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#1788	C₂×C₆₇	1	1	yes	characteristic, complemented
454	#1788	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#1763	C₂×C₆₇	1	1	yes	characteristic, complemented
456	C₆₇	#22422	1	1	yes	characteristic, direct product factor, Sylow
457	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
458	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
459	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
460	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
461	#550	—	2	4	no	—
462	#550	C₄×C₆₇	1	8	yes	complemented
463	C₂×#127	—	2	1	no	—
464	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×#121	—	2	1	no	—
466	C₂×#121	—	2	1	no	—
467	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×C₄×D₄	—	2	1	no	—
471	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
473	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
474	#435	—	2	4	no	—
475	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
476	#417	—	2	4	no	—
477	#416	—	2	4	no	—
478	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
480	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
482	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
484	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
485	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
486	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
493	#388	—	2	1	no	—
494	#387	—	2	1	no	—
495	#386	—	2	1	no	—
496	#382	C₂²×C₆₇	1	1	yes	characteristic
497	#380	C₂²×C₆₇	1	1	yes	characteristic
498	#380	C₂²×C₆₇	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	—	2	1	no	—
501	#340	C₂²×C₆₇	1	1	yes	characteristic
502	#340	C₂²×C₆₇	1	1	yes	characteristic
503	#340	C₂²×C₆₇	1	1	yes	characteristic
504	#340	C₂²×C₆₇	1	1	yes	characteristic
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	2	2	no	—
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	4	1	no	—
512	C₂×#41	—	4	1	no	—
513	C₂×#41	—	4	1	no	—
514	C₂×#41	—	4	1	no	—
515	C₂×#41	C₂×C₄×C₆₇	1	4	yes	—
516	C₂×#41	C₂×C₄×C₆₇	1	4	yes	complemented
517	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
527	C₂³×C₄	—	2	1	no	—
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
532	C₂×M₁₆	—	2	2	no	—
533	C₂×M₁₆	—	2	2	no	—
534	C₂×M₁₆	—	4	1	no	—
535	C₂²×C₈	—	2	2	no	—
536	C₂²×C₈	—	2	2	no	—
537	C₂²×C₈	—	4	1	no	—
538	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
540	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
542	#127	—	2	8	no	—
543	#127	—	2	2	no	—
544	#127	C₂×C₄×C₆₇	1	4	yes	complemented
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	8	no	—
548	#121	—	2	8	no	—
549	#121	C₂×C₄×C₆₇	1	4	yes	—
550	#121	C₂×C₄×C₆₇	1	4	yes	complemented
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	C₂×C₄×C₆₇	1	4	yes	complemented
553	C₄×D₄	—	2	8	no	—
554	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
555	C₄×D₄	D₄×C₆₇	1	4	yes	—
556	#117	—	2	2	no	—
557	#117	—	4	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	4	1	no	—
562	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×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×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₆₇	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	—	2	1	no	—
577	C₂×C₄²	—	2	1	no	—
578	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
579	C₄⋊C₈	—	2	2	no	—
580	#103	—	2	2	no	—
581	#103	—	2	2	no	—
582	#103	—	2	2	no	—
583	#103	D₄×C₆₇	1	4	yes	complemented
584	#102	—	2	2	no	—
585	#102	—	2	2	no	—
586	#102	—	2	2	no	—
587	#102	—	2	2	no	—
588	#102	—	4	1	no	—
589	#102	—	4	1	no	—
590	#102	—	4	1	no	—
591	#102	—	4	1	no	—
592	C₂²⋊C₈	—	2	2	no	—
593	C₂²⋊C₈	—	2	2	no	—
594	#97	—	2	2	no	—
595	#95	—	2	1	no	—
596	#95	—	2	1	no	—
597	#95	—	2	1	no	—
598	#95	—	2	1	no	—
599	#95	—	2	1	no	—
600	C₂⁴	—	2	1	no	—
601	C₂⁴	—	2	1	no	—
602	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
604	#41	—	2	8	no	—
605	#41	—	2	8	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
616	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
617	C₂×Q₈	#41×C₆₇	1	2	yes	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	8	1	no	—
643	C₂×D₄	—	8	1	no	—
644	C₂×D₄	—	8	1	no	—
645	C₂×D₄	—	8	1	no	—
646	C₂×D₄	—	8	1	no	—
647	C₂×D₄	—	8	1	no	—
648	C₂×D₄	C₂²⋊C₄×C₆₇	1	4	yes	—
649	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
650	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
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	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	8	1	no	—
674	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
675	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
676	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
683	M₁₆	—	4	4	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
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	—	4	4	no	—
696	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	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	—	4	2	no	—
707	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
708	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
709	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	8	1	no	—
715	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
716	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
717	C₄²	—	2	4	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	8	1	no	—
720	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
721	C₄²	C₂×D₄×C₆₇	1	2	yes	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	4	1	no	—
737	C₂³	—	4	1	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	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	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
749	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
750	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	C₄×D₄×C₆₇	1	4	yes	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	4	4	no	—
760	D₄	—	4	8	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	4	no	—
769	D₄	—	8	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	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	—	4	8	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	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	—	8	4	no	—
807	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
808	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
809	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
810	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
811	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
814	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
815	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
816	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
817	C₈	—	2	2	no	—
818	C₈	—	4	1	no	—
819	C₈	—	4	1	no	—
820	C₈	—	4	1	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	8	1	no	—
842	C₂²	—	8	1	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	1	no	—
848	C₂²	—	8	1	no	—
849	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
850	C₂²	D₄²×C₆₇	1	1	yes	characteristic
851	C₂²	#546×C₆₇	1	1	yes	characteristic
852	C₂²	#575×C₆₇	1	1	yes	characteristic
853	C₂²	#575×C₆₇	1	1	yes	characteristic
854	C₂²	#576×C₆₇	1	1	yes	characteristic
855	C₂²	#577×C₆₇	1	1	yes	characteristic
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	4	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	8	1	no	—
864	C₄	—	8	1	no	—
865	C₄	—	8	1	no	—
866	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
867	C₄	#518×C₆₇	1	1	yes	characteristic
868	C₄	D₄²×C₆₇	1	1	yes	characteristic
869	C₄	#546×C₆₇	1	1	yes	characteristic
870	C₂	—	4	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	2	no	—
874	C₂	D₄×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
875	C₂	C₆₇×#2896	1	1	yes	characteristic
876	C₂	C₆₇×#2897	1	1	yes	characteristic
877	C₂	C₆₇×#3268	1	1	yes	characteristic
878	C₂	C₆₇×#3271	1	1	yes	characteristic
879	C₂	C₆₇×#3309	1	1	yes	characteristic
880	C₂	C₆₇×#3317	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×#550×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×#435×C₆₇	C₂	semidirect
3. C₂×#417×C₆₇	C₂	semidirect
4. C₂×#416×C₆₇	C₂	semidirect
5. C₆₇×#2352	C₂	semidirect
6. C₆₇×#1982	C₂	semidirect
7. C₆₇×#1961	C₂	semidirect
8. C₆₇×#1895	C₂	semidirect
9. C₆₇×#1893	C₂	semidirect
10. C₆₇×#1875	C₂	semidirect
11. C₆₇×#1874	C₂	semidirect
12. C₆₇×#1805	C₂	semidirect
13. C₆₇×#1788	C₂	semidirect
14. C₆₇×#1788	C₂	semidirect
15. C₆₇×#1763	C₂	semidirect
21. #550×C₆₇	C₄	semidirect
75. C₂×#41×C₆₇	C₂×C₄	semidirect
103. #127×C₆₇	C₂×C₄	semidirect
109. #121×C₆₇	C₂×C₄	semidirect
111. C₄×Q₈×C₆₇	C₂×C₄	semidirect
142. #103×C₆₇	D₄	semidirect
429. #22422	C₆₇	direct (N × H)
442. C₂×#435	C₂×C₆₇	semidirect
443. C₂×#417	C₂×C₆₇	semidirect
444. C₂×#416	C₂×C₆₇	semidirect
445. #2352	C₂×C₆₇	semidirect
446. #1982	C₂×C₆₇	semidirect
447. #1961	C₂×C₆₇	semidirect
448. #1895	C₂×C₆₇	semidirect
449. #1893	C₂×C₆₇	semidirect
450. #1875	C₂×C₆₇	semidirect
451. #1874	C₂×C₆₇	semidirect
452. #1805	C₂×C₆₇	semidirect
453. #1788	C₂×C₆₇	semidirect
454. #1788	C₂×C₆₇	semidirect
455. #1763	C₂×C₆₇	semidirect
456. C₆₇	#22422	direct (N × H)
462. #550	C₄×C₆₇	semidirect
516. C₂×#41	C₂×C₄×C₆₇	semidirect
544. #127	C₂×C₄×C₆₇	semidirect
550. #121	C₂×C₄×C₆₇	semidirect
552. C₄×Q₈	C₂×C₄×C₆₇	semidirect
583. #103	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×#550×C₆₇	2
C₂×#435×C₆₇	2
C₂×#417×C₆₇	2
C₂×#416×C₆₇	2
C₆₇×#2352	2
C₆₇×#1982	2
C₆₇×#1961	2
C₆₇×#1895	2
C₆₇×#1893	2
C₆₇×#1875	2
C₆₇×#1874	2
C₆₇×#1805	2
C₆₇×#1788	2
C₆₇×#1763	2
#22422	67

Subgroups — C67×#22422 #30701673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22422 #30701673