Subgroups — C₆₇×#61278 #30740529

Order 17152.

1860 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3354	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3347	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3346	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3340	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3334	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#474×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
15	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2913	C₂	1	2	yes	maximal, complemented
18	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	—	2	2	no	—
21	#556×C₆₇	—	2	1	no	—
22	#556×C₆₇	C₂²	1	2	yes	complemented
23	#555×C₆₇	C₂²	1	2	yes	—
24	#555×C₆₇	C₂²	1	2	yes	complemented
25	#554×C₆₇	C₂²	1	2	yes	complemented
26	#553×C₆₇	—	2	2	no	—
27	#553×C₆₇	C₂²	1	4	yes	—
28	#550×C₆₇	—	2	1	no	—
29	#548×C₆₇	—	2	2	no	—
30	#547×C₆₇	C₂²	1	2	yes	—
31	#547×C₆₇	C₂²	1	2	yes	complemented
32	#542×C₆₇	—	2	2	no	—
33	#538×C₆₇	—	2	2	no	—
34	#537×C₆₇	C₂²	1	2	yes	—
35	#535×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	—	2	1	no	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	—	2	1	no	—
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	#525×C₆₇	—	2	2	no	—
42	#520×C₆₇	C₂²	1	2	yes	—
43	#520×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	#501×C₆₇	C₂²	1	4	yes	complemented
47	#500×C₆₇	C₂²	1	2	yes	complemented
48	#498×C₆₇	C₂²	1	2	yes	complemented
49	#485×C₆₇	C₂²	1	4	yes	complemented
50	#484×C₆₇	C₂²	1	4	yes	complemented
51	#482×C₆₇	C₂²	1	4	yes	—
52	#482×C₆₇	C₂²	1	4	yes	—
53	#482×C₆₇	C₂²	1	4	yes	complemented
54	#481×C₆₇	C₂²	1	4	yes	—
55	#480×C₆₇	C₂²	1	4	yes	—
56	#480×C₆₇	C₂²	1	4	yes	complemented
57	#479×C₆₇	C₂²	1	2	yes	complemented
58	#478×C₆₇	C₂²	1	2	yes	complemented
59	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#474×C₆₇	C₂²	1	2	yes	—
63	#474×C₆₇	C₂²	1	4	yes	—
64	#474×C₆₇	C₂²	1	2	yes	—
65	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#469×C₆₇	C₂²	1	4	yes	—
67	#468×C₆₇	C₂²	1	4	yes	—
68	#466×C₆₇	C₂²	1	4	yes	—
69	#465×C₆₇	C₂²	1	4	yes	—
70	#442×C₆₇	C₂²	1	2	yes	—
71	#440×C₆₇	C₂²	1	2	yes	—
72	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
73	C₄×D₈×C₆₇	C₂²	1	2	yes	—
74	#436×C₆₇	C₂²	1	2	yes	complemented
75	#435×C₆₇	C₂²	1	4	yes	complemented
76	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
77	#428×C₆₇	C₂²	1	2	yes	—
78	#428×C₆₇	C₂²	1	2	yes	—
79	#428×C₆₇	C₂²	1	1	yes	characteristic
80	#428×C₆₇	C₂²	1	4	yes	complemented
81	#428×C₆₇	C₂²	1	4	yes	complemented
82	#427×C₆₇	C₂²	1	2	yes	—
83	#427×C₆₇	C₂²	1	4	yes	complemented
84	C₂×#107×C₆₇	C₂²	1	2	yes	—
85	C₂×#107×C₆₇	C₂²	1	4	yes	complemented
86	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
87	#418×C₆₇	C₂²	1	1	yes	characteristic
88	#417×C₆₇	C₂²	1	1	yes	characteristic
89	#416×C₆₇	C₂²	1	2	yes	—
90	C₂×#102×C₆₇	C₂²	1	2	yes	—
91	#408×C₆₇	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	—	2	2	no	—
95	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×#41×C₆₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₇	—	2	1	no	—
98	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	—	2	1	no	—
100	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
101	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×D₈×C₆₇	C₂³	1	2	yes	—
103	#131×C₆₇	—	2	8	no	—
104	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
108	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₆₇	—	2	1	no	—
110	C₄⋊Q₈×C₆₇	—	2	1	no	—
111	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
116	#127×C₆₇	—	2	2	no	—
117	#127×C₆₇	D₄	1	1	yes	characteristic
118	#126×C₆₇	—	2	4	no	—
119	#126×C₆₇	—	2	4	no	—
120	#125×C₆₇	—	2	2	no	—
121	#125×C₆₇	C₂³	1	2	yes	—
122	#124×C₆₇	—	2	2	no	—
123	#124×C₆₇	—	2	2	no	—
124	#124×C₆₇	—	2	4	no	—
125	#124×C₆₇	—	2	4	no	—
126	#124×C₆₇	D₄	1	2	yes	—
127	#123×C₆₇	—	2	4	no	—
128	#123×C₆₇	—	2	4	no	—
129	#123×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	1	no	—
132	C₂²⋊Q₈×C₆₇	—	2	1	no	—
133	C₂²⋊Q₈×C₆₇	—	2	2	no	—
134	C₂²⋊Q₈×C₆₇	—	2	2	no	—
135	C₂²⋊Q₈×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	—	2	2	no	—
139	#121×C₆₇	—	2	2	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	—	2	4	no	—
142	#121×C₆₇	D₄	1	2	yes	—
143	#121×C₆₇	D₄	1	2	yes	—
144	#121×C₆₇	C₂³	1	4	yes	—
145	#121×C₆₇	C₂³	1	4	yes	—
146	#121×C₆₇	C₂³	1	4	yes	—
147	#120×C₆₇	—	2	4	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₄×D₄×C₆₇	—	2	4	no	—
156	C₄×D₄×C₆₇	—	2	2	no	—
157	C₄×D₄×C₆₇	—	2	4	no	—
158	C₄×D₄×C₆₇	—	2	2	no	—
159	C₄×D₄×C₆₇	—	2	2	no	—
160	C₄×D₄×C₆₇	—	2	1	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	4	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₆₇	C₂³	1	2	yes	—
170	C₄×D₄×C₆₇	C₂³	1	2	yes	—
171	#117×C₆₇	—	2	2	no	—
172	#117×C₆₇	—	2	2	no	—
173	#117×C₆₇	—	2	1	no	—
174	#117×C₆₇	C₂³	1	4	yes	—
175	#117×C₆₇	C₂³	1	4	yes	—
176	#117×C₆₇	C₂³	1	1	yes	characteristic
177	#117×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₄²×C₆₇	—	2	1	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	#107×C₆₇	C₂³	1	4	yes	—
187	#107×C₆₇	C₂³	1	4	yes	—
188	#107×C₆₇	C₂³	1	4	yes	—
189	#107×C₆₇	C₂³	1	2	yes	—
190	#107×C₆₇	C₂³	1	2	yes	—
191	#107×C₆₇	C₂³	1	4	yes	—
192	#107×C₆₇	C₂³	1	2	yes	—
193	#106×C₆₇	C₂³	1	4	yes	—
194	#106×C₆₇	C₂³	1	2	yes	—
195	#106×C₆₇	C₂³	1	2	yes	—
196	#106×C₆₇	C₂³	1	4	yes	—
197	#106×C₆₇	C₂³	1	2	yes	—
198	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
201	#103×C₆₇	C₂³	1	2	yes	—
202	#103×C₆₇	C₂³	1	2	yes	—
203	#103×C₆₇	C₂³	1	2	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	2	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
213	#97×C₆₇	C₂³	1	2	yes	—
214	C₄×C₈×C₆₇	C₂³	1	2	yes	—
215	C₂⁴×C₆₇	—	2	1	no	—
216	#41×C₆₇	—	2	4	no	—
217	#41×C₆₇	—	2	4	no	—
218	#41×C₆₇	—	2	2	no	—
219	#41×C₆₇	—	2	2	no	—
220	#41×C₆₇	—	8	4	no	—
221	#41×C₆₇	—	8	4	no	—
222	C₂×Q₈×C₆₇	—	2	1	no	—
223	C₂×Q₈×C₆₇	—	2	2	no	—
224	C₂×Q₈×C₆₇	—	2	1	no	—
225	C₂×Q₈×C₆₇	—	2	2	no	—
226	C₂×Q₈×C₆₇	—	8	2	no	—
227	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	4	no	—
231	C₂×D₄×C₆₇	—	2	4	no	—
232	C₂×D₄×C₆₇	—	2	4	no	—
233	C₂×D₄×C₆₇	—	2	1	no	—
234	C₂×D₄×C₆₇	—	2	2	no	—
235	C₂×D₄×C₆₇	—	2	2	no	—
236	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
240	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₇	—	2	1	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	1	no	—
247	C₂²×C₄×C₆₇	—	2	1	no	—
248	C₂²×C₄×C₆₇	—	2	1	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	8	2	no	—
252	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	SD₁₆×C₆₇	—	2	4	no	—
257	D₈×C₆₇	—	2	4	no	—
258	M₁₆×C₆₇	—	2	2	no	—
259	M₁₆×C₆₇	—	2	8	no	—
260	M₁₆×C₆₇	#41	1	4	yes	complemented
261	C₂×C₈×C₆₇	—	2	4	no	—
262	C₂×C₈×C₆₇	—	2	8	no	—
263	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
265	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
266	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²⋊C₄×C₆₇	—	2	1	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂²⋊C₄×C₆₇	—	2	1	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
301	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
302	C₄²×C₆₇	—	2	1	no	—
303	C₄²×C₆₇	—	2	1	no	—
304	C₄²×C₆₇	—	2	1	no	—
305	C₄²×C₆₇	—	2	4	no	—
306	C₄²×C₆₇	—	2	4	no	—
307	C₄²×C₆₇	—	2	2	no	—
308	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂³×C₆₇	—	2	1	no	—
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	—	4	2	no	—
315	C₂³×C₆₇	—	8	1	no	—
316	C₂³×C₆₇	—	8	1	no	—
317	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
318	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₆₇	—	2	4	no	—
320	Q₈×C₆₇	—	2	1	no	—
321	Q₈×C₆₇	—	2	1	no	—
322	Q₈×C₆₇	—	4	4	no	—
323	Q₈×C₆₇	—	4	2	no	—
324	Q₈×C₆₇	—	8	1	no	—
325	Q₈×C₆₇	—	8	2	no	—
326	D₄×C₆₇	—	2	8	no	—
327	D₄×C₆₇	—	2	4	no	—
328	D₄×C₆₇	—	2	4	no	—
329	D₄×C₆₇	—	2	1	no	—
330	D₄×C₆₇	—	2	2	no	—
331	D₄×C₆₇	—	2	2	no	—
332	D₄×C₆₇	—	2	1	no	—
333	D₄×C₆₇	—	4	2	no	—
334	D₄×C₆₇	—	4	2	no	—
335	D₄×C₆₇	—	4	2	no	—
336	D₄×C₆₇	—	8	4	no	—
337	D₄×C₆₇	—	8	4	no	—
338	D₄×C₆₇	—	8	4	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	4	no	—
341	C₂×C₄×C₆₇	—	2	4	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	1	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	4	no	—
349	C₂×C₄×C₆₇	—	4	1	no	—
350	C₂×C₄×C₆₇	—	4	2	no	—
351	C₂×C₄×C₆₇	—	4	2	no	—
352	C₂×C₄×C₆₇	—	4	4	no	—
353	C₂×C₄×C₆₇	—	4	2	no	—
354	C₂×C₄×C₆₇	—	8	2	no	—
355	C₂×C₄×C₆₇	—	8	1	no	—
356	C₂×C₄×C₆₇	—	8	2	no	—
357	C₂×C₄×C₆₇	—	8	4	no	—
358	C₂×C₄×C₆₇	—	8	4	no	—
359	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
366	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
367	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
368	C₈×C₆₇	—	2	2	no	—
369	C₈×C₆₇	—	2	2	no	—
370	C₈×C₆₇	—	2	2	no	—
371	C₈×C₆₇	C₂×#41	1	4	yes	—
372	C₂²×C₆₇	—	2	1	no	—
373	C₂²×C₆₇	—	2	1	no	—
374	C₂²×C₆₇	—	2	4	no	—
375	C₂²×C₆₇	—	2	4	no	—
376	C₂²×C₆₇	—	2	4	no	—
377	C₂²×C₆₇	—	4	1	no	—
378	C₂²×C₆₇	—	4	2	no	—
379	C₂²×C₆₇	—	4	1	no	—
380	C₂²×C₆₇	—	4	2	no	—
381	C₂²×C₆₇	—	4	2	no	—
382	C₂²×C₆₇	—	4	1	no	—
383	C₂²×C₆₇	—	8	4	no	—
384	C₂²×C₆₇	#547	1	2	yes	—
385	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
386	C₄×C₆₇	—	2	1	no	—
387	C₄×C₆₇	—	2	1	no	—
388	C₄×C₆₇	—	2	4	no	—
389	C₄×C₆₇	—	2	1	no	—
390	C₄×C₆₇	—	4	1	no	—
391	C₄×C₆₇	—	4	2	no	—
392	C₄×C₆₇	—	4	1	no	—
393	C₄×C₆₇	—	4	2	no	—
394	C₄×C₆₇	—	4	1	no	—
395	C₄×C₆₇	—	4	2	no	—
396	C₄×C₆₇	—	4	4	no	—
397	C₄×C₆₇	#547	1	2	yes	—
398	C₄×C₆₇	#576	1	2	yes	—
399	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
400	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
401	#61278	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂×C₆₇	—	2	2	no	—
403	C₂×C₆₇	—	4	4	no	—
404	C₂×C₆₇	—	8	1	no	—
405	C₂×C₆₇	—	8	2	no	—
406	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
407	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
408	C₂×C₆₇	#3586	1	1	yes	characteristic
409	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
411	#3354	C₂×C₆₇	1	2	yes	complemented
412	#3353	C₂×C₆₇	1	2	yes	complemented
413	#3347	C₂×C₆₇	1	4	yes	complemented
414	#3346	C₂×C₆₇	1	4	yes	complemented
415	#3340	C₂×C₆₇	1	2	yes	complemented
416	#3334	C₂×C₆₇	1	2	yes	complemented
417	#3165	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#3098	C₂×C₆₇	1	2	yes	complemented
419	#3096	C₂×C₆₇	1	2	yes	complemented
420	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
421	C₂×#474	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3062	C₂×C₆₇	1	2	yes	complemented
423	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
424	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
425	#2913	C₂×C₆₇	1	2	yes	complemented
426	C₆₇	#61278	1	1	yes	characteristic, direct product factor, Sylow
427	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
428	C₂×#131	C₂²×C₆₇	1	2	yes	—
429	#559	—	2	2	no	—
430	#556	—	2	1	no	—
431	#556	C₂²×C₆₇	1	2	yes	complemented
432	#555	C₂²×C₆₇	1	2	yes	—
433	#555	C₂²×C₆₇	1	2	yes	complemented
434	#554	C₂²×C₆₇	1	2	yes	complemented
435	#553	—	2	2	no	—
436	#553	C₂²×C₆₇	1	4	yes	—
437	#550	—	2	1	no	—
438	#548	—	2	2	no	—
439	#547	C₂²×C₆₇	1	2	yes	—
440	#547	C₂²×C₆₇	1	2	yes	complemented
441	#542	—	2	2	no	—
442	#538	—	2	2	no	—
443	#537	C₂²×C₆₇	1	2	yes	—
444	#535	C₂²×C₆₇	1	2	yes	—
445	#533	—	2	1	no	—
446	#533	C₂²×C₆₇	1	1	yes	characteristic
447	#532	—	2	1	no	—
448	#532	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
450	#525	—	2	2	no	—
451	#520	C₂²×C₆₇	1	2	yes	—
452	#520	C₂²×C₆₇	1	2	yes	—
453	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
455	#501	C₂²×C₆₇	1	4	yes	complemented
456	#500	C₂²×C₆₇	1	2	yes	complemented
457	#498	C₂²×C₆₇	1	2	yes	complemented
458	#485	C₂²×C₆₇	1	4	yes	complemented
459	#484	C₂²×C₆₇	1	4	yes	complemented
460	#482	C₂²×C₆₇	1	4	yes	—
461	#482	C₂²×C₆₇	1	4	yes	—
462	#482	C₂²×C₆₇	1	4	yes	complemented
463	#481	C₂²×C₆₇	1	4	yes	—
464	#480	C₂²×C₆₇	1	4	yes	—
465	#480	C₂²×C₆₇	1	4	yes	complemented
466	#479	C₂²×C₆₇	1	2	yes	complemented
467	#478	C₂²×C₆₇	1	2	yes	complemented
468	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
469	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
470	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	#474	C₂²×C₆₇	1	2	yes	—
472	#474	C₂²×C₆₇	1	4	yes	—
473	#474	C₂²×C₆₇	1	2	yes	—
474	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
475	#469	C₂²×C₆₇	1	4	yes	—
476	#468	C₂²×C₆₇	1	4	yes	—
477	#466	C₂²×C₆₇	1	4	yes	—
478	#465	C₂²×C₆₇	1	4	yes	—
479	#442	C₂²×C₆₇	1	2	yes	—
480	#440	C₂²×C₆₇	1	2	yes	—
481	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
482	C₄×D₈	C₂²×C₆₇	1	2	yes	—
483	#436	C₂²×C₆₇	1	2	yes	complemented
484	#435	C₂²×C₆₇	1	4	yes	complemented
485	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
486	#428	C₂²×C₆₇	1	2	yes	—
487	#428	C₂²×C₆₇	1	2	yes	—
488	#428	C₂²×C₆₇	1	1	yes	characteristic
489	#428	C₂²×C₆₇	1	4	yes	complemented
490	#428	C₂²×C₆₇	1	4	yes	complemented
491	#427	C₂²×C₆₇	1	2	yes	—
492	#427	C₂²×C₆₇	1	4	yes	complemented
493	C₂×#107	C₂²×C₆₇	1	2	yes	—
494	C₂×#107	C₂²×C₆₇	1	4	yes	complemented
495	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
496	#418	C₂²×C₆₇	1	1	yes	characteristic
497	#417	C₂²×C₆₇	1	1	yes	characteristic
498	#416	C₂²×C₆₇	1	2	yes	—
499	C₂×#102	C₂²×C₆₇	1	2	yes	—
500	#408	C₂²×C₆₇	1	2	yes	—
501	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
505	C₂×#41	C₂³×C₆₇	1	2	yes	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
508	C₂³×C₄	—	2	1	no	—
509	AGL(1,ℤ/8)	—	2	4	no	—
510	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
511	C₂×D₈	C₂³×C₆₇	1	2	yes	—
512	#131	—	2	8	no	—
513	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
514	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
517	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	—	2	1	no	—
520	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
523	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
525	#127	—	2	2	no	—
526	#127	D₄×C₆₇	1	1	yes	characteristic
527	#126	—	2	4	no	—
528	#126	—	2	4	no	—
529	#125	—	2	2	no	—
530	#125	C₂³×C₆₇	1	2	yes	—
531	#124	—	2	2	no	—
532	#124	—	2	2	no	—
533	#124	—	2	4	no	—
534	#124	—	2	4	no	—
535	#124	D₄×C₆₇	1	2	yes	—
536	#123	—	2	4	no	—
537	#123	—	2	4	no	—
538	#123	—	2	4	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	4	no	—
550	#121	—	2	4	no	—
551	#121	D₄×C₆₇	1	2	yes	—
552	#121	D₄×C₆₇	1	2	yes	—
553	#121	C₂³×C₆₇	1	4	yes	—
554	#121	C₂³×C₆₇	1	4	yes	—
555	#121	C₂³×C₆₇	1	4	yes	—
556	#120	—	2	4	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
563	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	4	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	C₂³×C₆₇	1	2	yes	—
575	C₄×D₄	C₂³×C₆₇	1	2	yes	—
576	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₄×D₄	C₂³×C₆₇	1	2	yes	—
579	C₄×D₄	C₂³×C₆₇	1	2	yes	—
580	#117	—	2	2	no	—
581	#117	—	2	2	no	—
582	#117	—	2	1	no	—
583	#117	C₂³×C₆₇	1	1	yes	characteristic
584	#117	C₂³×C₆₇	1	2	yes	—
585	#117	C₂³×C₆₇	1	4	yes	—
586	#117	C₂³×C₆₇	1	4	yes	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₄²	—	2	1	no	—
594	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
595	#107	C₂³×C₆₇	1	4	yes	—
596	#107	C₂³×C₆₇	1	4	yes	—
597	#107	C₂³×C₆₇	1	2	yes	—
598	#107	C₂³×C₆₇	1	2	yes	—
599	#107	C₂³×C₆₇	1	4	yes	—
600	#107	C₂³×C₆₇	1	2	yes	—
601	#107	C₂³×C₆₇	1	4	yes	—
602	#106	C₂³×C₆₇	1	2	yes	—
603	#106	C₂³×C₆₇	1	2	yes	—
604	#106	C₂³×C₆₇	1	2	yes	—
605	#106	C₂³×C₆₇	1	4	yes	—
606	#106	C₂³×C₆₇	1	4	yes	—
607	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
608	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
609	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
610	#103	C₂³×C₆₇	1	2	yes	—
611	#103	C₂³×C₆₇	1	2	yes	—
612	#103	C₂³×C₆₇	1	2	yes	—
613	#102	C₂³×C₆₇	1	4	yes	—
614	#102	C₂³×C₆₇	1	4	yes	—
615	#102	C₂³×C₆₇	1	2	yes	—
616	#102	C₂³×C₆₇	1	2	yes	—
617	#102	C₂³×C₆₇	1	2	yes	—
618	#102	C₂³×C₆₇	1	2	yes	—
619	#102	C₂³×C₆₇	1	2	yes	—
620	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
621	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
622	#97	C₂³×C₆₇	1	2	yes	—
623	C₄×C₈	C₂³×C₆₇	1	2	yes	—
624	C₂⁴	—	2	1	no	—
625	#41	—	2	4	no	—
626	#41	—	2	4	no	—
627	#41	—	2	2	no	—
628	#41	—	2	2	no	—
629	#41	—	8	4	no	—
630	#41	—	8	4	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	8	2	no	—
636	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
637	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
646	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
647	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
648	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
649	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
650	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	8	2	no	—
661	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
664	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
665	SD₁₆	—	2	4	no	—
666	D₈	—	2	4	no	—
667	M₁₆	—	2	2	no	—
668	M₁₆	—	2	8	no	—
669	M₁₆	#41×C₆₇	1	4	yes	complemented
670	C₂×C₈	—	2	4	no	—
671	C₂×C₈	—	2	8	no	—
672	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
673	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
674	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
675	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
690	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
693	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
694	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
710	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	1	no	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	2	no	—
717	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
719	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	8	1	no	—
725	C₂³	—	8	1	no	—
726	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
727	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
728	Q₈	—	2	4	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	4	4	no	—
732	Q₈	—	4	2	no	—
733	Q₈	—	8	2	no	—
734	Q₈	—	8	1	no	—
735	D₄	—	2	8	no	—
736	D₄	—	2	4	no	—
737	D₄	—	2	4	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	1	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	2	no	—
745	D₄	—	8	4	no	—
746	D₄	—	8	4	no	—
747	D₄	—	8	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	—	8	1	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
769	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
774	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
775	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
776	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	C₂×#41×C₆₇	1	4	yes	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	4	no	—
793	C₂²	#547×C₆₇	1	2	yes	—
794	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	4	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	4	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	1	no	—
806	C₄	#547×C₆₇	1	2	yes	—
807	C₄	#576×C₆₇	1	2	yes	—
808	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
809	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
810	C₂	—	2	2	no	—
811	C₂	—	4	4	no	—
812	C₂	—	8	2	no	—
813	C₂	—	8	1	no	—
814	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
815	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
816	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3511	C₂	semidirect
2. C₆₇×#3506	C₂	semidirect
3. C₆₇×#3354	C₂	semidirect
4. C₆₇×#3353	C₂	semidirect
5. C₆₇×#3347	C₂	semidirect
6. C₆₇×#3346	C₂	semidirect
7. C₆₇×#3340	C₂	semidirect
8. C₆₇×#3334	C₂	semidirect
9. C₆₇×#3165	C₂	semidirect
10. C₆₇×#3098	C₂	semidirect
11. C₆₇×#3096	C₂	semidirect
12. C₆₇×#3076	C₂	semidirect
13. C₂×#474×C₆₇	C₂	semidirect
14. C₆₇×#3062	C₂	semidirect
15. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
16. C₆₇×#2935	C₂	semidirect
17. C₆₇×#2913	C₂	semidirect
22. #556×C₆₇	C₂²	semidirect
24. #555×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
31. #547×C₆₇	C₂²	semidirect
46. #501×C₆₇	C₂²	semidirect
47. #500×C₆₇	C₂²	semidirect
48. #498×C₆₇	C₂²	semidirect
49. #485×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
53. #482×C₆₇	C₂²	semidirect
56. #480×C₆₇	C₂²	semidirect
57. #479×C₆₇	C₂²	semidirect
58. #478×C₆₇	C₂²	semidirect
59. #477×C₆₇	C₂²	semidirect
60. #476×C₆₇	C₂²	semidirect
61. #475×C₆₇	C₂²	semidirect
65. #474×C₆₇	C₂²	semidirect
74. #436×C₆₇	C₂²	semidirect
75. #435×C₆₇	C₂²	semidirect
76. C₈×D₄×C₆₇	C₂²	semidirect
80. #428×C₆₇	C₂²	semidirect
81. #428×C₆₇	C₂²	semidirect
83. #427×C₆₇	C₂²	semidirect
85. C₂×#107×C₆₇	C₂²	semidirect
260. M₁₆×C₆₇	#41	semidirect
401. #61278	C₆₇	direct (N × H)
409. #3511	C₂×C₆₇	semidirect
410. #3506	C₂×C₆₇	semidirect
411. #3354	C₂×C₆₇	semidirect
412. #3353	C₂×C₆₇	semidirect
413. #3347	C₂×C₆₇	semidirect
414. #3346	C₂×C₆₇	semidirect
415. #3340	C₂×C₆₇	semidirect
416. #3334	C₂×C₆₇	semidirect
417. #3165	C₂×C₆₇	semidirect
418. #3098	C₂×C₆₇	semidirect
419. #3096	C₂×C₆₇	semidirect
420. #3076	C₂×C₆₇	semidirect
421. C₂×#474	C₂×C₆₇	semidirect
422. #3062	C₂×C₆₇	semidirect
423. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
424. #2935	C₂×C₆₇	semidirect
425. #2913	C₂×C₆₇	semidirect
426. C₆₇	#61278	direct (N × H)
431. #556	C₂²×C₆₇	semidirect
433. #555	C₂²×C₆₇	semidirect
434. #554	C₂²×C₆₇	semidirect
440. #547	C₂²×C₆₇	semidirect
455. #501	C₂²×C₆₇	semidirect
456. #500	C₂²×C₆₇	semidirect
457. #498	C₂²×C₆₇	semidirect
458. #485	C₂²×C₆₇	semidirect
459. #484	C₂²×C₆₇	semidirect
462. #482	C₂²×C₆₇	semidirect
465. #480	C₂²×C₆₇	semidirect
466. #479	C₂²×C₆₇	semidirect
467. #478	C₂²×C₆₇	semidirect
468. #477	C₂²×C₆₇	semidirect
469. #476	C₂²×C₆₇	semidirect
470. #475	C₂²×C₆₇	semidirect
474. #474	C₂²×C₆₇	semidirect
483. #436	C₂²×C₆₇	semidirect
484. #435	C₂²×C₆₇	semidirect
485. C₈×D₄	C₂²×C₆₇	semidirect
489. #428	C₂²×C₆₇	semidirect
490. #428	C₂²×C₆₇	semidirect
492. #427	C₂²×C₆₇	semidirect
494. C₂×#107	C₂²×C₆₇	semidirect
669. M₁₆	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3511	2
C₆₇×#3506	2
C₆₇×#3354	2
C₆₇×#3353	2
C₆₇×#3347	2
C₆₇×#3346	2
C₆₇×#3340	2
C₆₇×#3334	2
C₆₇×#3165	2
C₆₇×#3098	2
C₆₇×#3096	2
C₆₇×#3076	2
C₂×#474×C₆₇	2
C₆₇×#3062	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2935	2
C₆₇×#2913	2
#61278	67

Subgroups — C67×#61278 #30740529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61278 #30740529