Subgroups — C₆₇×#61706 #30740957

Order 17152.

2022 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	C₆₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3345	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3343	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3308	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3306	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3238	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3114	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
13	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#480×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	—	2	1	no	—
17	#553×C₆₇	—	2	2	no	—
18	#553×C₆₇	C₂²	1	2	yes	complemented
19	#552×C₆₇	C₂²	1	2	yes	complemented
20	#551×C₆₇	—	2	2	no	—
21	#548×C₆₇	C₂²	1	2	yes	complemented
22	#547×C₆₇	—	2	2	no	—
23	#547×C₆₇	—	2	2	no	—
24	#547×C₆₇	C₂²	1	4	yes	—
25	#547×C₆₇	C₂²	1	4	yes	complemented
26	#546×C₆₇	C₂²	1	2	yes	complemented
27	#539×C₆₇	—	2	1	no	—
28	#538×C₆₇	—	2	1	no	—
29	#534×C₆₇	—	2	1	no	—
30	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#529×C₆₇	C₂²	1	2	yes	—
32	#525×C₆₇	C₂²	1	2	yes	—
33	C₂×#123×C₆₇	—	2	1	no	—
34	C₂×#123×C₆₇	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#518×C₆₇	—	2	1	no	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#501×C₆₇	C₂²	1	4	yes	complemented
46	#489×C₆₇	C₂²	1	4	yes	complemented
47	#484×C₆₇	C₂²	1	4	yes	complemented
48	#483×C₆₇	C₂²	1	4	yes	complemented
49	#483×C₆₇	C₂²	1	2	yes	complemented
50	#483×C₆₇	C₂²	1	2	yes	complemented
51	#483×C₆₇	C₂²	1	2	yes	complemented
52	#482×C₆₇	C₂²	1	4	yes	complemented
53	#481×C₆₇	C₂²	1	4	yes	complemented
54	#481×C₆₇	C₂²	1	2	yes	complemented
55	#480×C₆₇	C₂²	1	2	yes	—
56	#480×C₆₇	C₂²	1	2	yes	—
57	#480×C₆₇	C₂²	1	2	yes	—
58	#480×C₆₇	C₂²	1	4	yes	complemented
59	#480×C₆₇	C₂²	1	2	yes	complemented
60	#478×C₆₇	C₂²	1	4	yes	complemented
61	#477×C₆₇	C₂²	1	4	yes	complemented
62	#476×C₆₇	C₂²	1	4	yes	complemented
63	#469×C₆₇	C₂²	1	4	yes	complemented
64	#468×C₆₇	C₂²	1	4	yes	complemented
65	#466×C₆₇	C₂²	1	4	yes	complemented
66	#465×C₆₇	C₂²	1	4	yes	complemented
67	#463×C₆₇	C₂²	1	4	yes	complemented
68	#450×C₆₇	C₂²	1	2	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#448×C₆₇	C₂²	1	2	yes	complemented
71	#447×C₆₇	C₂²	1	2	yes	—
72	#447×C₆₇	C₂²	1	2	yes	complemented
73	#442×C₆₇	C₂²	1	4	yes	complemented
74	#440×C₆₇	C₂²	1	4	yes	complemented
75	#435×C₆₇	C₂²	1	4	yes	complemented
76	#435×C₆₇	C₂²	1	4	yes	complemented
77	#432×C₆₇	C₂²	1	2	yes	complemented
78	#428×C₆₇	C₂²	1	4	yes	complemented
79	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
80	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
81	#417×C₆₇	C₂²	1	4	yes	complemented
82	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
83	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
84	#407×C₆₇	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	2	4	no	—
89	C₂×#41×C₆₇	—	4	8	no	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂²×Q₈×C₆₇	—	2	1	no	—
92	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	—	2	1	no	—
94	C₂²×D₄×C₆₇	—	2	1	no	—
95	C₂²×D₄×C₆₇	—	2	1	no	—
96	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	—	2	1	no	—
100	C₂³×C₄×C₆₇	—	2	1	no	—
101	C₂³×C₄×C₆₇	—	2	1	no	—
102	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×D₈×C₆₇	C₂³	1	4	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
111	#126×C₆₇	—	2	2	no	—
112	#126×C₆₇	—	2	2	no	—
113	#126×C₆₇	—	2	2	no	—
114	#125×C₆₇	—	2	2	no	—
115	#125×C₆₇	C₂³	1	2	yes	—
116	#124×C₆₇	—	2	2	no	—
117	#124×C₆₇	C₂³	1	2	yes	—
118	#123×C₆₇	—	2	2	no	—
119	#123×C₆₇	—	2	2	no	—
120	#123×C₆₇	—	2	2	no	—
121	#123×C₆₇	—	2	2	no	—
122	#123×C₆₇	—	2	4	no	—
123	#123×C₆₇	—	2	4	no	—
124	#123×C₆₇	—	2	4	no	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	2	2	no	—
127	C₂²⋊Q₈×C₆₇	—	2	1	no	—
128	C₂²⋊Q₈×C₆₇	—	2	1	no	—
129	C₂²⋊Q₈×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
133	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	1	no	—
138	#121×C₆₇	—	2	1	no	—
139	#121×C₆₇	—	2	1	no	—
140	#121×C₆₇	—	2	1	no	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	2	no	—
143	#121×C₆₇	C₂³	1	2	yes	—
144	#121×C₆₇	C₂³	1	4	yes	—
145	#121×C₆₇	C₂³	1	2	yes	—
146	#121×C₆₇	C₂³	1	2	yes	—
147	#121×C₆₇	C₂³	1	2	yes	—
148	#121×C₆₇	C₂³	1	2	yes	—
149	#120×C₆₇	—	2	2	no	—
150	#120×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₄×D₄×C₆₇	—	2	2	no	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	—	2	2	no	—
156	C₄×D₄×C₆₇	—	2	2	no	—
157	C₄×D₄×C₆₇	—	2	2	no	—
158	C₄×D₄×C₆₇	D₄	1	2	yes	—
159	C₄×D₄×C₆₇	D₄	1	2	yes	—
160	C₄×D₄×C₆₇	C₂³	1	4	yes	—
161	C₄×D₄×C₆₇	C₂³	1	2	yes	—
162	C₄×D₄×C₆₇	C₂³	1	2	yes	—
163	C₄×D₄×C₆₇	C₂³	1	2	yes	—
164	#117×C₆₇	—	2	2	no	—
165	#117×C₆₇	—	2	2	no	—
166	#117×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
168	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
174	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
189	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	#107×C₆₇	C₂³	1	4	yes	—
193	#107×C₆₇	C₂³	1	4	yes	—
194	#107×C₆₇	C₂³	1	4	yes	—
195	#106×C₆₇	C₂³	1	4	yes	—
196	#106×C₆₇	C₂³	1	4	yes	—
197	#106×C₆₇	C₂³	1	4	yes	—
198	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#102×C₆₇	C₂³	1	4	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	#97×C₆₇	C₂³	1	4	yes	—
213	C₂⁴×C₆₇	—	2	1	no	—
214	C₂⁴×C₆₇	—	2	1	no	—
215	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
217	#41×C₆₇	—	4	4	no	—
218	#41×C₆₇	—	4	16	no	—
219	#41×C₆₇	—	4	16	no	—
220	C₂×Q₈×C₆₇	—	2	4	no	—
221	C₂×Q₈×C₆₇	—	2	1	no	—
222	C₂×Q₈×C₆₇	—	4	4	no	—
223	C₂×Q₈×C₆₇	—	4	2	no	—
224	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	2	2	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	2	2	no	—
230	C₂×D₄×C₆₇	—	2	2	no	—
231	C₂×D₄×C₆₇	—	2	2	no	—
232	C₂×D₄×C₆₇	—	2	2	no	—
233	C₂×D₄×C₆₇	—	2	1	no	—
234	C₂×D₄×C₆₇	—	2	1	no	—
235	C₂×D₄×C₆₇	—	4	2	no	—
236	C₂×D₄×C₆₇	—	4	2	no	—
237	C₂×D₄×C₆₇	—	4	4	no	—
238	C₂×D₄×C₆₇	—	4	4	no	—
239	C₂×D₄×C₆₇	—	4	4	no	—
240	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	—	2	1	no	—
245	C₂²×C₄×C₆₇	—	2	1	no	—
246	C₂²×C₄×C₆₇	—	2	1	no	—
247	C₂²×C₄×C₆₇	—	2	1	no	—
248	C₂²×C₄×C₆₇	—	2	4	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	1	no	—
252	C₂²×C₄×C₆₇	—	2	1	no	—
253	C₂²×C₄×C₆₇	—	2	4	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	—	4	4	no	—
259	C₂²×C₄×C₆₇	—	4	4	no	—
260	C₂²×C₄×C₆₇	—	4	4	no	—
261	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	SD₁₆×C₆₇	—	4	4	no	—
273	D₈×C₆₇	—	4	4	no	—
274	M₁₆×C₆₇	—	4	4	no	—
275	C₂×C₈×C₆₇	—	4	2	no	—
276	C₂×C₈×C₆₇	—	4	2	no	—
277	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
278	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
279	C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	1	no	—
289	C₄⋊C₄×C₆₇	—	2	1	no	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	2	no	—
294	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²⋊C₄×C₆₇	—	2	2	no	—
302	C₂²⋊C₄×C₆₇	—	2	2	no	—
303	C₂²⋊C₄×C₆₇	—	2	2	no	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	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	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	2	no	—
315	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
317	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
319	C₄²×C₆₇	—	2	2	no	—
320	C₄²×C₆₇	—	2	2	no	—
321	C₄²×C₆₇	C₂×D₄	1	2	yes	—
322	C₄²×C₆₇	C₂⁴	1	2	yes	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	4	1	no	—
327	C₂³×C₆₇	—	4	1	no	—
328	C₂³×C₆₇	—	4	1	no	—
329	C₂³×C₆₇	—	4	1	no	—
330	C₂³×C₆₇	—	4	2	no	—
331	C₂³×C₆₇	—	4	2	no	—
332	C₂³×C₆₇	—	4	2	no	—
333	C₂³×C₆₇	—	4	2	no	—
334	C₂³×C₆₇	—	8	1	no	—
335	C₂³×C₆₇	—	8	1	no	—
336	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
337	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
338	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₆₇	—	2	4	no	—
342	Q₈×C₆₇	—	4	8	no	—
343	Q₈×C₆₇	—	8	1	no	—
344	D₄×C₆₇	—	2	4	no	—
345	D₄×C₆₇	—	2	4	no	—
346	D₄×C₆₇	—	2	4	no	—
347	D₄×C₆₇	—	2	4	no	—
348	D₄×C₆₇	—	4	2	no	—
349	D₄×C₆₇	—	4	8	no	—
350	D₄×C₆₇	—	4	4	no	—
351	D₄×C₆₇	—	4	4	no	—
352	D₄×C₆₇	—	4	4	no	—
353	D₄×C₆₇	—	4	4	no	—
354	D₄×C₆₇	—	8	1	no	—
355	D₄×C₆₇	—	8	2	no	—
356	D₄×C₆₇	—	8	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	4	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	4	2	no	—
369	C₂×C₄×C₆₇	—	4	1	no	—
370	C₂×C₄×C₆₇	—	4	1	no	—
371	C₂×C₄×C₆₇	—	4	1	no	—
372	C₂×C₄×C₆₇	—	4	1	no	—
373	C₂×C₄×C₆₇	—	4	1	no	—
374	C₂×C₄×C₆₇	—	4	8	no	—
375	C₂×C₄×C₆₇	—	4	8	no	—
376	C₂×C₄×C₆₇	—	4	2	no	—
377	C₂×C₄×C₆₇	—	4	2	no	—
378	C₂×C₄×C₆₇	—	4	2	no	—
379	C₂×C₄×C₆₇	—	4	4	no	—
380	C₂×C₄×C₆₇	—	4	4	no	—
381	C₂×C₄×C₆₇	—	4	2	no	—
382	C₂×C₄×C₆₇	—	8	2	no	—
383	C₂×C₄×C₆₇	—	8	2	no	—
384	C₂×C₄×C₆₇	—	8	1	no	—
385	C₂×C₄×C₆₇	—	8	1	no	—
386	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
393	C₈×C₆₇	—	2	4	no	—
394	C₈×C₆₇	—	2	4	no	—
395	C₂²×C₆₇	—	2	1	no	—
396	C₂²×C₆₇	—	2	1	no	—
397	C₂²×C₆₇	—	2	1	no	—
398	C₂²×C₆₇	—	2	1	no	—
399	C₂²×C₆₇	—	2	1	no	—
400	C₂²×C₆₇	—	2	1	no	—
401	C₂²×C₆₇	—	2	2	no	—
402	C₂²×C₆₇	—	2	2	no	—
403	C₂²×C₆₇	—	2	2	no	—
404	C₂²×C₆₇	—	4	4	no	—
405	C₂²×C₆₇	—	4	4	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	—	4	2	no	—
409	C₂²×C₆₇	—	4	2	no	—
410	C₂²×C₆₇	—	4	2	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	8	4	no	—
413	C₂²×C₆₇	—	16	2	no	—
414	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
415	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
416	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
417	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
418	C₄×C₆₇	—	2	2	no	—
419	C₄×C₆₇	—	2	1	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	1	no	—
422	C₄×C₆₇	—	2	1	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	—	4	2	no	—
428	C₄×C₆₇	—	4	2	no	—
429	C₄×C₆₇	—	4	2	no	—
430	C₄×C₆₇	#585	1	2	yes	—
431	#61706	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂×C₆₇	—	2	2	no	—
433	C₂×C₆₇	—	2	2	no	—
434	C₂×C₆₇	—	2	2	no	—
435	C₂×C₆₇	—	4	2	no	—
436	C₂×C₆₇	—	8	2	no	—
437	C₂×C₆₇	—	8	2	no	—
438	C₂×C₆₇	#3485	1	1	yes	characteristic
439	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂×C₆₇	#3586	1	1	yes	characteristic
441	#3505	C₂×C₆₇	1	1	yes	characteristic, complemented
442	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
443	#3345	C₂×C₆₇	1	4	yes	complemented
444	#3343	C₂×C₆₇	1	4	yes	complemented
445	#3308	C₂×C₆₇	1	4	yes	complemented
446	#3306	C₂×C₆₇	1	4	yes	complemented
447	#3238	C₂×C₆₇	1	2	yes	complemented
448	#3194	C₂×C₆₇	1	2	yes	complemented
449	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#3114	C₂×C₆₇	1	2	yes	complemented
452	#3092	C₂×C₆₇	1	2	yes	complemented
453	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
454	C₂×#480	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
456	C₆₇	#61706	1	1	yes	characteristic, direct product factor, Sylow
457	C₂²×#41	—	2	1	no	—
458	#553	—	2	2	no	—
459	#553	C₂²×C₆₇	1	2	yes	complemented
460	#552	C₂²×C₆₇	1	2	yes	complemented
461	#551	—	2	2	no	—
462	#548	C₂²×C₆₇	1	2	yes	complemented
463	#547	—	2	2	no	—
464	#547	—	2	2	no	—
465	#547	C₂²×C₆₇	1	4	yes	—
466	#547	C₂²×C₆₇	1	4	yes	complemented
467	#546	C₂²×C₆₇	1	2	yes	complemented
468	#539	—	2	1	no	—
469	#538	—	2	1	no	—
470	#534	—	2	1	no	—
471	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
472	#529	C₂²×C₆₇	1	2	yes	—
473	#525	C₂²×C₆₇	1	2	yes	—
474	C₂×#123	—	2	1	no	—
475	C₂×#123	—	2	1	no	—
476	C₂×C₂²⋊Q₈	—	2	1	no	—
477	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
478	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
480	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
481	#518	—	2	1	no	—
482	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
484	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
486	#501	C₂²×C₆₇	1	4	yes	complemented
487	#489	C₂²×C₆₇	1	4	yes	complemented
488	#484	C₂²×C₆₇	1	4	yes	complemented
489	#483	C₂²×C₆₇	1	4	yes	complemented
490	#483	C₂²×C₆₇	1	2	yes	complemented
491	#483	C₂²×C₆₇	1	2	yes	complemented
492	#483	C₂²×C₆₇	1	2	yes	complemented
493	#482	C₂²×C₆₇	1	4	yes	complemented
494	#481	C₂²×C₆₇	1	2	yes	complemented
495	#481	C₂²×C₆₇	1	4	yes	complemented
496	#480	C₂²×C₆₇	1	2	yes	—
497	#480	C₂²×C₆₇	1	2	yes	—
498	#480	C₂²×C₆₇	1	2	yes	—
499	#480	C₂²×C₆₇	1	4	yes	complemented
500	#480	C₂²×C₆₇	1	2	yes	complemented
501	#478	C₂²×C₆₇	1	4	yes	complemented
502	#477	C₂²×C₆₇	1	4	yes	complemented
503	#476	C₂²×C₆₇	1	4	yes	complemented
504	#469	C₂²×C₆₇	1	4	yes	complemented
505	#468	C₂²×C₆₇	1	4	yes	complemented
506	#466	C₂²×C₆₇	1	4	yes	complemented
507	#465	C₂²×C₆₇	1	4	yes	complemented
508	#463	C₂²×C₆₇	1	4	yes	complemented
509	#450	C₂²×C₆₇	1	2	yes	complemented
510	#449	C₂²×C₆₇	1	4	yes	complemented
511	#448	C₂²×C₆₇	1	2	yes	complemented
512	#447	C₂²×C₆₇	1	2	yes	—
513	#447	C₂²×C₆₇	1	2	yes	complemented
514	#442	C₂²×C₆₇	1	4	yes	complemented
515	#440	C₂²×C₆₇	1	4	yes	complemented
516	#435	C₂²×C₆₇	1	4	yes	complemented
517	#435	C₂²×C₆₇	1	4	yes	complemented
518	#432	C₂²×C₆₇	1	2	yes	complemented
519	#428	C₂²×C₆₇	1	4	yes	complemented
520	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
521	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
522	#417	C₂²×C₆₇	1	4	yes	complemented
523	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
524	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
525	#407	C₂²×C₆₇	1	2	yes	complemented
526	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
527	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
528	C₂×#41	—	2	4	no	—
529	C₂×#41	—	2	4	no	—
530	C₂×#41	—	4	8	no	—
531	C₂×#41	C₂³×C₆₇	1	2	yes	—
532	C₂²×Q₈	—	2	1	no	—
533	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂³×C₄	—	2	1	no	—
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
546	C₂×D₈	C₂³×C₆₇	1	4	yes	—
547	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
548	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
549	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	C₂³×C₆₇	1	2	yes	—
557	#124	—	2	2	no	—
558	#124	C₂³×C₆₇	1	2	yes	—
559	#123	—	2	2	no	—
560	#123	—	2	2	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	#123	—	2	4	no	—
566	#123	—	2	4	no	—
567	#123	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
575	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
576	#121	—	2	2	no	—
577	#121	—	2	2	no	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	—	2	2	no	—
583	#121	—	2	2	no	—
584	#121	C₂³×C₆₇	1	2	yes	—
585	#121	C₂³×C₆₇	1	2	yes	—
586	#121	C₂³×C₆₇	1	2	yes	—
587	#121	C₂³×C₆₇	1	2	yes	—
588	#121	C₂³×C₆₇	1	4	yes	—
589	#121	C₂³×C₆₇	1	2	yes	—
590	#120	—	2	2	no	—
591	#120	—	2	2	no	—
592	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	D₄×C₆₇	1	2	yes	—
600	C₄×D₄	D₄×C₆₇	1	2	yes	—
601	C₄×D₄	C₂³×C₆₇	1	4	yes	—
602	C₄×D₄	C₂³×C₆₇	1	2	yes	—
603	C₄×D₄	C₂³×C₆₇	1	2	yes	—
604	C₄×D₄	C₂³×C₆₇	1	2	yes	—
605	#117	—	2	2	no	—
606	#117	—	2	2	no	—
607	#117	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
633	#107	C₂³×C₆₇	1	4	yes	—
634	#107	C₂³×C₆₇	1	4	yes	—
635	#107	C₂³×C₆₇	1	4	yes	—
636	#106	C₂³×C₆₇	1	4	yes	—
637	#106	C₂³×C₆₇	1	4	yes	—
638	#106	C₂³×C₆₇	1	4	yes	—
639	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
640	#103	C₂³×C₆₇	1	4	yes	—
641	#103	C₂³×C₆₇	1	4	yes	—
642	#103	C₂³×C₆₇	1	4	yes	—
643	#102	C₂³×C₆₇	1	4	yes	—
644	#102	C₂³×C₆₇	1	4	yes	—
645	#102	C₂³×C₆₇	1	4	yes	—
646	#102	C₂³×C₆₇	1	4	yes	—
647	#102	C₂³×C₆₇	1	4	yes	—
648	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
649	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
650	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
651	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
652	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
653	#97	C₂³×C₆₇	1	4	yes	—
654	C₂⁴	—	2	1	no	—
655	C₂⁴	—	2	1	no	—
656	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
657	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
658	#41	—	4	4	no	—
659	#41	—	4	16	no	—
660	#41	—	4	16	no	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	4	4	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	4	4	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
682	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
683	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	4	no	—
700	C₂²×C₄	—	4	4	no	—
701	C₂²×C₄	—	4	4	no	—
702	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
713	SD₁₆	—	4	4	no	—
714	D₈	—	4	4	no	—
715	M₁₆	—	4	4	no	—
716	C₂×C₈	—	4	2	no	—
717	C₂×C₈	—	4	2	no	—
718	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
719	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
758	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
759	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	C₂×D₄×C₆₇	1	2	yes	—
763	C₄²	C₂⁴×C₆₇	1	2	yes	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	4	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	8	1	no	—
776	C₂³	—	8	1	no	—
777	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
778	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
779	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
780	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
782	Q₈	—	2	4	no	—
783	Q₈	—	4	8	no	—
784	Q₈	—	8	1	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	4	no	—
788	D₄	—	2	4	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	8	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	4	no	—
795	D₄	—	8	1	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	2	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	—	4	1	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	8	2	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	1	no	—
827	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
833	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
834	C₈	—	2	4	no	—
835	C₈	—	2	4	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	4	4	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	4	no	—
854	C₂²	—	16	2	no	—
855	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
856	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
857	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
858	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	#585×C₆₇	1	2	yes	—
872	C₂	—	2	2	no	—
873	C₂	—	2	2	no	—
874	C₂	—	2	2	no	—
875	C₂	—	4	2	no	—
876	C₂	—	8	2	no	—
877	C₂	—	8	2	no	—
878	C₂	C₆₇×#3485	1	1	yes	characteristic
879	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
880	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3505	C₂	semidirect
2. C₂×#547×C₆₇	C₂	semidirect
3. C₆₇×#3345	C₂	semidirect
4. C₆₇×#3343	C₂	semidirect
5. C₆₇×#3308	C₂	semidirect
6. C₆₇×#3306	C₂	semidirect
7. C₆₇×#3238	C₂	semidirect
8. C₆₇×#3194	C₂	semidirect
9. C₆₇×#3187	C₂	semidirect
10. C₆₇×#3186	C₂	semidirect
11. C₆₇×#3114	C₂	semidirect
12. C₆₇×#3092	C₂	semidirect
13. C₂×#483×C₆₇	C₂	semidirect
14. C₂×#480×C₆₇	C₂	semidirect
15. C₆₇×#2973	C₂	semidirect
18. #553×C₆₇	C₂²	semidirect
19. #552×C₆₇	C₂²	semidirect
21. #548×C₆₇	C₂²	semidirect
25. #547×C₆₇	C₂²	semidirect
26. #546×C₆₇	C₂²	semidirect
30. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
39. C₂×#121×C₆₇	C₂²	semidirect
42. C₂×C₄×D₄×C₆₇	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #484×C₆₇	C₂²	semidirect
48. #483×C₆₇	C₂²	semidirect
49. #483×C₆₇	C₂²	semidirect
50. #483×C₆₇	C₂²	semidirect
51. #483×C₆₇	C₂²	semidirect
52. #482×C₆₇	C₂²	semidirect
53. #481×C₆₇	C₂²	semidirect
54. #481×C₆₇	C₂²	semidirect
58. #480×C₆₇	C₂²	semidirect
59. #480×C₆₇	C₂²	semidirect
60. #478×C₆₇	C₂²	semidirect
61. #477×C₆₇	C₂²	semidirect
62. #476×C₆₇	C₂²	semidirect
63. #469×C₆₇	C₂²	semidirect
64. #468×C₆₇	C₂²	semidirect
65. #466×C₆₇	C₂²	semidirect
66. #465×C₆₇	C₂²	semidirect
67. #463×C₆₇	C₂²	semidirect
68. #450×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
70. #448×C₆₇	C₂²	semidirect
72. #447×C₆₇	C₂²	semidirect
73. #442×C₆₇	C₂²	semidirect
74. #440×C₆₇	C₂²	semidirect
75. #435×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
77. #432×C₆₇	C₂²	semidirect
78. #428×C₆₇	C₂²	semidirect
79. C₂×#107×C₆₇	C₂²	semidirect
80. C₂×#106×C₆₇	C₂²	semidirect
81. #417×C₆₇	C₂²	semidirect
82. C₂×#103×C₆₇	C₂²	semidirect
83. C₂×#102×C₆₇	C₂²	semidirect
84. #407×C₆₇	C₂²	semidirect
431. #61706	C₆₇	direct (N × H)
441. #3505	C₂×C₆₇	semidirect
442. C₂×#547	C₂×C₆₇	semidirect
443. #3345	C₂×C₆₇	semidirect
444. #3343	C₂×C₆₇	semidirect
445. #3308	C₂×C₆₇	semidirect
446. #3306	C₂×C₆₇	semidirect
447. #3238	C₂×C₆₇	semidirect
448. #3194	C₂×C₆₇	semidirect
449. #3187	C₂×C₆₇	semidirect
450. #3186	C₂×C₆₇	semidirect
451. #3114	C₂×C₆₇	semidirect
452. #3092	C₂×C₆₇	semidirect
453. C₂×#483	C₂×C₆₇	semidirect
454. C₂×#480	C₂×C₆₇	semidirect
455. #2973	C₂×C₆₇	semidirect
456. C₆₇	#61706	direct (N × H)
459. #553	C₂²×C₆₇	semidirect
460. #552	C₂²×C₆₇	semidirect
462. #548	C₂²×C₆₇	semidirect
466. #547	C₂²×C₆₇	semidirect
467. #546	C₂²×C₆₇	semidirect
471. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
480. C₂×#121	C₂²×C₆₇	semidirect
483. C₂×C₄×D₄	C₂²×C₆₇	semidirect
485. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
486. #501	C₂²×C₆₇	semidirect
487. #489	C₂²×C₆₇	semidirect
488. #484	C₂²×C₆₇	semidirect
489. #483	C₂²×C₆₇	semidirect
490. #483	C₂²×C₆₇	semidirect
491. #483	C₂²×C₆₇	semidirect
492. #483	C₂²×C₆₇	semidirect
493. #482	C₂²×C₆₇	semidirect
494. #481	C₂²×C₆₇	semidirect
495. #481	C₂²×C₆₇	semidirect
499. #480	C₂²×C₆₇	semidirect
500. #480	C₂²×C₆₇	semidirect
501. #478	C₂²×C₆₇	semidirect
502. #477	C₂²×C₆₇	semidirect
503. #476	C₂²×C₆₇	semidirect
504. #469	C₂²×C₆₇	semidirect
505. #468	C₂²×C₆₇	semidirect
506. #466	C₂²×C₆₇	semidirect
507. #465	C₂²×C₆₇	semidirect
508. #463	C₂²×C₆₇	semidirect
509. #450	C₂²×C₆₇	semidirect
510. #449	C₂²×C₆₇	semidirect
511. #448	C₂²×C₆₇	semidirect
513. #447	C₂²×C₆₇	semidirect
514. #442	C₂²×C₆₇	semidirect
515. #440	C₂²×C₆₇	semidirect
516. #435	C₂²×C₆₇	semidirect
517. #435	C₂²×C₆₇	semidirect
518. #432	C₂²×C₆₇	semidirect
519. #428	C₂²×C₆₇	semidirect
520. C₂×#107	C₂²×C₆₇	semidirect
521. C₂×#106	C₂²×C₆₇	semidirect
522. #417	C₂²×C₆₇	semidirect
523. C₂×#103	C₂²×C₆₇	semidirect
524. C₂×#102	C₂²×C₆₇	semidirect
525. #407	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3505	2
C₂×#547×C₆₇	2
C₆₇×#3345	2
C₆₇×#3343	2
C₆₇×#3308	2
C₆₇×#3306	2
C₆₇×#3238	2
C₆₇×#3194	2
C₆₇×#3187	2
C₆₇×#3186	2
C₆₇×#3114	2
C₆₇×#3092	2
C₂×#483×C₆₇	2
C₂×#480×C₆₇	2
C₆₇×#2973	2
#61706	67

Subgroups — C67×#61706 #30740957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61706 #30740957