Subgroups — C₆₇×#61551 #30740802

Order 17152.

1886 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3351	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3310	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3307	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3303	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3174	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3123	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
26	#557×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	#555×C₆₇	C₂²	1	1	yes	characteristic
28	#554×C₆₇	C₂²	1	1	yes	characteristic
29	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#553×C₆₇	—	2	1	no	—
32	#553×C₆₇	—	2	1	no	—
33	#553×C₆₇	C₂²	1	2	yes	—
34	#552×C₆₇	—	2	2	no	—
35	#552×C₆₇	—	2	1	no	—
36	#552×C₆₇	C₂²	1	2	yes	complemented
37	#550×C₆₇	C₂²	1	1	yes	characteristic
38	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#547×C₆₇	C₂²	1	2	yes	complemented
40	#546×C₆₇	—	2	1	no	—
41	#546×C₆₇	—	2	2	no	—
42	D₄²×C₆₇	C₂²	1	1	yes	characteristic
43	D₄²×C₆₇	C₂²	1	2	yes	—
44	#541×C₆₇	C₂²	1	2	yes	complemented
45	#540×C₆₇	C₂²	1	2	yes	—
46	#539×C₆₇	—	2	2	no	—
47	#538×C₆₇	—	2	2	no	—
48	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#532×C₆₇	C₂²	1	1	yes	characteristic
50	#529×C₆₇	—	2	1	no	—
51	#529×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×#125×C₆₇	—	2	1	no	—
53	#525×C₆₇	—	2	1	no	—
54	C₂×#121×C₆₇	—	2	1	no	—
55	#520×C₆₇	C₂²	1	2	yes	complemented
56	#518×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
59	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#499×C₆₇	C₂²	1	2	yes	complemented
61	#492×C₆₇	C₂²	1	2	yes	complemented
62	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#491×C₆₇	C₂²	1	2	yes	complemented
64	#490×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#485×C₆₇	C₂²	1	2	yes	complemented
69	#483×C₆₇	C₂²	1	2	yes	complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#481×C₆₇	C₂²	1	2	yes	complemented
72	#480×C₆₇	C₂²	1	2	yes	complemented
73	#479×C₆₇	C₂²	1	2	yes	complemented
74	#478×C₆₇	C₂²	1	2	yes	—
75	#478×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	2	yes	complemented
77	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#476×C₆₇	C₂²	1	1	yes	characteristic
79	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#468×C₆₇	C₂²	1	2	yes	complemented
82	#468×C₆₇	C₂²	1	2	yes	complemented
83	#468×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#465×C₆₇	C₂²	1	2	yes	complemented
87	#461×C₆₇	C₂²	1	1	yes	characteristic
88	#461×C₆₇	C₂²	1	2	yes	—
89	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#461×C₆₇	C₂²	1	2	yes	complemented
91	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#460×C₆₇	C₂²	1	2	yes	complemented
93	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#459×C₆₇	C₂²	1	2	yes	complemented
95	#450×C₆₇	C₂²	1	2	yes	—
96	#450×C₆₇	C₂²	1	2	yes	—
97	#450×C₆₇	C₂²	1	2	yes	—
98	#449×C₆₇	C₂²	1	2	yes	complemented
99	#449×C₆₇	C₂²	1	2	yes	complemented
100	#449×C₆₇	C₂²	1	2	yes	complemented
101	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#442×C₆₇	C₂²	1	1	yes	characteristic
104	#442×C₆₇	C₂²	1	2	yes	complemented
105	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#440×C₆₇	C₂²	1	2	yes	—
107	#440×C₆₇	C₂²	1	1	yes	characteristic
108	#440×C₆₇	C₂²	1	2	yes	complemented
109	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#440×C₆₇	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
117	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₆₇	C₂²	1	2	yes	—
119	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	2	yes	complemented
122	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#433×C₆₇	C₂²	1	2	yes	complemented
126	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#428×C₆₇	C₂²	1	2	yes	complemented
129	#418×C₆₇	C₂²	1	1	yes	characteristic
130	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#416×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	2	yes	—
133	#405×C₆₇	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	—	2	1	no	—
140	C₂²×D₄×C₆₇	—	2	2	no	—
141	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	—	2	1	no	—
144	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
145	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
146	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	#127×C₆₇	C₂³	1	1	yes	characteristic
165	#127×C₆₇	C₂³	1	2	yes	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	D₄	1	2	yes	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	1	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	2	no	—
176	#125×C₆₇	—	2	2	no	—
177	#125×C₆₇	—	2	1	no	—
178	#125×C₆₇	D₄	1	1	yes	characteristic
179	#125×C₆₇	C₂³	1	2	yes	—
180	#125×C₆₇	C₂³	1	2	yes	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	—	2	1	no	—
183	#124×C₆₇	D₄	1	1	yes	characteristic
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	D₄	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	2	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	—	2	1	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	D₄	1	1	yes	characteristic
214	#121×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#120×C₆₇	—	2	2	no	—
218	#120×C₆₇	—	2	2	no	—
219	#120×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	—	2	1	no	—
221	C₄×Q₈×C₆₇	—	2	1	no	—
222	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	1	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	—	2	1	no	—
236	C₄×D₄×C₆₇	—	2	1	no	—
237	C₄×D₄×C₆₇	—	2	1	no	—
238	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₇	C₂³	1	2	yes	—
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	2	yes	—
248	C₄×D₄×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
250	#117×C₆₇	—	2	1	no	—
251	#117×C₆₇	—	2	2	no	—
252	#117×C₆₇	—	2	1	no	—
253	#117×C₆₇	—	2	2	no	—
254	#117×C₆₇	—	2	1	no	—
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	2	yes	—
257	#117×C₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#107×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	2	yes	—
273	#107×C₆₇	C₂³	1	2	yes	—
274	#107×C₆₇	C₂³	1	1	yes	characteristic
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	1	yes	characteristic
279	#106×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	2	yes	—
291	#102×C₆₇	C₂³	1	2	yes	—
292	#102×C₆₇	C₂³	1	1	yes	characteristic
293	#102×C₆₇	C₂³	1	2	yes	—
294	#102×C₆₇	C₂³	1	1	yes	characteristic
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	1	yes	characteristic
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₂⁴×C₆₇	—	2	1	no	—
315	C₂⁴×C₆₇	—	2	2	no	—
316	#41×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	2	4	no	—
318	#41×C₆₇	—	4	2	no	—
319	#41×C₆₇	—	4	1	no	—
320	#41×C₆₇	—	8	2	no	—
321	#41×C₆₇	—	8	2	no	—
322	C₂×Q₈×C₆₇	—	2	1	no	—
323	C₂×Q₈×C₆₇	—	2	1	no	—
324	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
327	C₂×D₄×C₆₇	—	2	2	no	—
328	C₂×D₄×C₆₇	—	2	4	no	—
329	C₂×D₄×C₆₇	—	2	2	no	—
330	C₂×D₄×C₆₇	—	2	1	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	1	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	1	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	4	2	no	—
341	C₂×D₄×C₆₇	—	4	1	no	—
342	C₂×D₄×C₆₇	—	8	2	no	—
343	C₂×D₄×C₆₇	—	8	4	no	—
344	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
348	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₆₇	—	2	1	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	1	no	—
353	C₂²×C₄×C₆₇	—	2	1	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	1	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	1	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	—	2	2	no	—
361	C₂²×C₄×C₆₇	—	2	2	no	—
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	8	2	no	—
365	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
369	SD₁₆×C₆₇	—	2	2	no	—
370	SD₁₆×C₆₇	—	2	4	no	—
371	SD₁₆×C₆₇	—	2	4	no	—
372	SD₁₆×C₆₇	—	2	2	no	—
373	SD₁₆×C₆₇	—	4	2	no	—
374	SD₁₆×C₆₇	—	4	2	no	—
375	SD₁₆×C₆₇	—	4	2	no	—
376	D₈×C₆₇	—	2	2	no	—
377	D₈×C₆₇	—	2	4	no	—
378	D₈×C₆₇	#41	1	4	yes	complemented
379	M₁₆×C₆₇	—	2	2	no	—
380	M₁₆×C₆₇	—	2	4	no	—
381	M₁₆×C₆₇	—	4	1	no	—
382	C₂×C₈×C₆₇	—	4	2	no	—
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
387	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	1	no	—
391	C₄⋊C₄×C₆₇	—	2	1	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	—	2	1	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	1	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	1	no	—
432	C₂²⋊C₄×C₆₇	—	2	1	no	—
433	C₂²⋊C₄×C₆₇	—	2	1	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	1	no	—
445	C₄²×C₆₇	—	2	1	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄²×C₆₇	C₂⁴	1	2	yes	—
453	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂³×C₆₇	—	2	1	no	—
455	C₂³×C₆₇	—	2	1	no	—
456	C₂³×C₆₇	—	2	2	no	—
457	C₂³×C₆₇	—	2	1	no	—
458	C₂³×C₆₇	—	4	2	no	—
459	C₂³×C₆₇	—	4	4	no	—
460	C₂³×C₆₇	—	4	2	no	—
461	C₂³×C₆₇	—	8	1	no	—
462	C₂³×C₆₇	—	8	2	no	—
463	C₂³×C₆₇	—	8	2	no	—
464	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
465	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₆₇	—	2	2	no	—
467	Q₈×C₆₇	—	2	1	no	—
468	Q₈×C₆₇	—	2	2	no	—
469	Q₈×C₆₇	—	2	1	no	—
470	Q₈×C₆₇	—	2	2	no	—
471	Q₈×C₆₇	—	8	1	no	—
472	Q₈×C₆₇	—	8	1	no	—
473	D₄×C₆₇	—	2	2	no	—
474	D₄×C₆₇	—	2	1	no	—
475	D₄×C₆₇	—	2	2	no	—
476	D₄×C₆₇	—	2	1	no	—
477	D₄×C₆₇	—	2	1	no	—
478	D₄×C₆₇	—	2	1	no	—
479	D₄×C₆₇	—	2	2	no	—
480	D₄×C₆₇	—	4	2	no	—
481	D₄×C₆₇	—	4	4	no	—
482	D₄×C₆₇	—	4	2	no	—
483	D₄×C₆₇	—	4	2	no	—
484	D₄×C₆₇	—	4	4	no	—
485	D₄×C₆₇	—	4	4	no	—
486	D₄×C₆₇	—	4	2	no	—
487	D₄×C₆₇	—	8	2	no	—
488	D₄×C₆₇	—	8	1	no	—
489	D₄×C₆₇	—	8	2	no	—
490	D₄×C₆₇	—	8	2	no	—
491	D₄×C₆₇	—	8	2	no	—
492	D₄×C₆₇	C₂×#41	1	2	yes	—
493	D₄×C₆₇	C₂×#41	1	2	yes	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	4	1	no	—
508	C₂×C₄×C₆₇	—	4	2	no	—
509	C₂×C₄×C₆₇	—	4	4	no	—
510	C₂×C₄×C₆₇	—	4	2	no	—
511	C₂×C₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	8	1	no	—
514	C₂×C₄×C₆₇	—	8	2	no	—
515	C₂×C₄×C₆₇	—	8	1	no	—
516	C₂×C₄×C₆₇	—	8	1	no	—
517	C₂×C₄×C₆₇	—	8	2	no	—
518	C₂×C₄×C₆₇	—	8	2	no	—
519	C₂×C₄×C₆₇	—	8	2	no	—
520	C₂×C₄×C₆₇	—	8	2	no	—
521	C₂×C₄×C₆₇	—	8	1	no	—
522	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
531	C₈×C₆₇	—	2	2	no	—
532	C₈×C₆₇	—	2	1	no	—
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	—	2	2	no	—
535	C₈×C₆₇	—	2	1	no	—
536	C₈×C₆₇	C₂×#41	1	2	yes	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	2	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	2	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	2	no	—
545	C₂²×C₆₇	—	4	1	no	—
546	C₂²×C₆₇	—	4	1	no	—
547	C₂²×C₆₇	—	4	1	no	—
548	C₂²×C₆₇	—	4	1	no	—
549	C₂²×C₆₇	—	4	2	no	—
550	C₂²×C₆₇	—	4	1	no	—
551	C₂²×C₆₇	—	4	1	no	—
552	C₂²×C₆₇	—	4	2	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	8	4	no	—
556	C₂²×C₆₇	—	16	4	no	—
557	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₆₇	—	2	1	no	—
559	C₄×C₆₇	—	2	1	no	—
560	C₄×C₆₇	—	2	2	no	—
561	C₄×C₆₇	—	2	2	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	1	no	—
564	C₄×C₆₇	—	2	2	no	—
565	C₄×C₆₇	—	4	1	no	—
566	C₄×C₆₇	—	4	2	no	—
567	C₄×C₆₇	—	4	2	no	—
568	C₄×C₆₇	—	4	1	no	—
569	C₄×C₆₇	—	4	2	no	—
570	C₄×C₆₇	—	4	1	no	—
571	C₄×C₆₇	—	4	1	no	—
572	C₄×C₆₇	—	4	1	no	—
573	C₄×C₆₇	#577	1	2	yes	—
574	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
575	C₄×C₆₇	#585	1	1	yes	characteristic
576	#61551	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
577	C₂×C₆₇	—	4	1	no	—
578	C₂×C₆₇	—	4	2	no	—
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	4	2	no	—
581	C₂×C₆₇	—	8	1	no	—
582	C₂×C₆₇	—	8	2	no	—
583	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
584	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
585	C₂×C₆₇	#3585	1	1	yes	characteristic
586	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3515	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3392	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3380	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3372	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3366	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#3357	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#3351	C₂×C₆₇	1	2	yes	complemented
594	#3310	C₂×C₆₇	1	2	yes	complemented
595	#3307	C₂×C₆₇	1	2	yes	complemented
596	#3303	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#3295	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#3272	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3272	C₂×C₆₇	1	2	yes	complemented
600	#3182	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3174	C₂×C₆₇	1	2	yes	complemented
602	#3123	C₂×C₆₇	1	2	yes	complemented
603	#3119	C₂×C₆₇	1	2	yes	complemented
604	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3101	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2946	C₂×C₆₇	1	2	yes	complemented
608	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
609	C₆₇	#61551	1	1	yes	characteristic, direct product factor, Sylow
610	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
611	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
612	#557	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	#555	C₂²×C₆₇	1	1	yes	characteristic
614	#554	C₂²×C₆₇	1	1	yes	characteristic
615	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
616	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
617	#553	—	2	1	no	—
618	#553	—	2	1	no	—
619	#553	C₂²×C₆₇	1	2	yes	—
620	#552	—	2	2	no	—
621	#552	—	2	1	no	—
622	#552	C₂²×C₆₇	1	2	yes	complemented
623	#550	C₂²×C₆₇	1	1	yes	characteristic
624	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#547	C₂²×C₆₇	1	2	yes	complemented
626	#546	—	2	1	no	—
627	#546	—	2	2	no	—
628	D₄²	C₂²×C₆₇	1	1	yes	characteristic
629	D₄²	C₂²×C₆₇	1	2	yes	—
630	#541	C₂²×C₆₇	1	2	yes	complemented
631	#540	C₂²×C₆₇	1	2	yes	—
632	#539	—	2	2	no	—
633	#538	—	2	2	no	—
634	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	#532	C₂²×C₆₇	1	1	yes	characteristic
636	#529	—	2	1	no	—
637	#529	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×#125	—	2	1	no	—
639	#525	—	2	1	no	—
640	C₂×#121	—	2	1	no	—
641	#520	C₂²×C₆₇	1	2	yes	complemented
642	#518	C₂²×C₆₇	1	2	yes	—
643	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
645	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#499	C₂²×C₆₇	1	2	yes	complemented
647	#492	C₂²×C₆₇	1	2	yes	complemented
648	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	#491	C₂²×C₆₇	1	2	yes	complemented
650	#490	C₂²×C₆₇	1	2	yes	complemented
651	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#485	C₂²×C₆₇	1	2	yes	complemented
654	#485	C₂²×C₆₇	1	2	yes	complemented
655	#483	C₂²×C₆₇	1	2	yes	complemented
656	#482	C₂²×C₆₇	1	2	yes	complemented
657	#481	C₂²×C₆₇	1	2	yes	complemented
658	#480	C₂²×C₆₇	1	2	yes	complemented
659	#479	C₂²×C₆₇	1	2	yes	complemented
660	#478	C₂²×C₆₇	1	2	yes	—
661	#478	C₂²×C₆₇	1	2	yes	complemented
662	#478	C₂²×C₆₇	1	2	yes	complemented
663	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#476	C₂²×C₆₇	1	1	yes	characteristic
665	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#468	C₂²×C₆₇	1	2	yes	complemented
668	#468	C₂²×C₆₇	1	2	yes	complemented
669	#468	C₂²×C₆₇	1	2	yes	complemented
670	#468	C₂²×C₆₇	1	2	yes	complemented
671	#465	C₂²×C₆₇	1	2	yes	complemented
672	#465	C₂²×C₆₇	1	2	yes	complemented
673	#461	C₂²×C₆₇	1	1	yes	characteristic
674	#461	C₂²×C₆₇	1	2	yes	—
675	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#461	C₂²×C₆₇	1	2	yes	complemented
677	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#460	C₂²×C₆₇	1	2	yes	complemented
679	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#459	C₂²×C₆₇	1	2	yes	complemented
681	#450	C₂²×C₆₇	1	2	yes	—
682	#450	C₂²×C₆₇	1	2	yes	—
683	#450	C₂²×C₆₇	1	2	yes	—
684	#449	C₂²×C₆₇	1	2	yes	complemented
685	#449	C₂²×C₆₇	1	2	yes	complemented
686	#449	C₂²×C₆₇	1	2	yes	complemented
687	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#442	C₂²×C₆₇	1	1	yes	characteristic
690	#442	C₂²×C₆₇	1	2	yes	complemented
691	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#440	C₂²×C₆₇	1	2	yes	—
693	#440	C₂²×C₆₇	1	1	yes	characteristic
694	#440	C₂²×C₆₇	1	2	yes	complemented
695	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	#440	C₂²×C₆₇	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
698	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
703	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
704	C₄×D₈	C₂²×C₆₇	1	2	yes	—
705	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
706	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#436	C₂²×C₆₇	1	2	yes	complemented
708	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#435	C₂²×C₆₇	1	2	yes	complemented
710	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#433	C₂²×C₆₇	1	2	yes	complemented
712	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#428	C₂²×C₆₇	1	2	yes	complemented
715	#418	C₂²×C₆₇	1	1	yes	characteristic
716	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
717	#416	C₂²×C₆₇	1	2	yes	complemented
718	C₂×#102	C₂²×C₆₇	1	2	yes	—
719	#405	C₂²×C₆₇	1	2	yes	complemented
720	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
724	C₂×#41	C₂³×C₆₇	1	2	yes	—
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
729	C₂³×C₄	—	2	1	no	—
730	AGL(1,ℤ/8)	—	2	4	no	—
731	AGL(1,ℤ/8)	—	2	8	no	—
732	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
739	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₆₇	1	2	yes	—
741	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
744	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
746	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
748	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
750	#127	C₂³×C₆₇	1	1	yes	characteristic
751	#127	C₂³×C₆₇	1	2	yes	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	D₄×C₆₇	1	2	yes	—
757	#125	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	—	2	1	no	—
760	#125	—	2	1	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	D₄×C₆₇	1	1	yes	characteristic
765	#125	C₂³×C₆₇	1	2	yes	—
766	#125	C₂³×C₆₇	1	2	yes	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	D₄×C₆₇	1	1	yes	characteristic
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	D₄×C₆₇	1	2	yes	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
788	#121	—	2	2	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	D₄×C₆₇	1	1	yes	characteristic
800	#121	C₂³×C₆₇	1	2	yes	—
801	#121	C₂³×C₆₇	1	2	yes	—
802	#121	C₂³×C₆₇	1	2	yes	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
811	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
812	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₆₇	1	2	yes	—
831	C₄×D₄	C₂³×C₆₇	1	2	yes	—
832	C₄×D₄	C₂³×C₆₇	1	2	yes	—
833	C₄×D₄	C₂³×C₆₇	1	2	yes	—
834	C₄×D₄	C₂³×C₆₇	1	2	yes	—
835	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	—	2	1	no	—
841	#117	C₂³×C₆₇	1	1	yes	characteristic
842	#117	C₂³×C₆₇	1	2	yes	—
843	#117	C₂³×C₆₇	1	2	yes	—
844	C₂×C₄⋊C₄	—	2	2	no	—
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	2	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
851	C₂×C₂²⋊C₄	—	2	1	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
856	#107	C₂³×C₆₇	1	1	yes	characteristic
857	#107	C₂³×C₆₇	1	2	yes	—
858	#107	C₂³×C₆₇	1	2	yes	—
859	#107	C₂³×C₆₇	1	1	yes	characteristic
860	#107	C₂³×C₆₇	1	2	yes	—
861	#106	C₂³×C₆₇	1	1	yes	characteristic
862	#106	C₂³×C₆₇	1	2	yes	—
863	#106	C₂³×C₆₇	1	1	yes	characteristic
864	#106	C₂³×C₆₇	1	2	yes	—
865	#106	C₂³×C₆₇	1	2	yes	—
866	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
870	#103	C₂³×C₆₇	1	2	yes	—
871	#103	C₂³×C₆₇	1	2	yes	—
872	#103	C₂³×C₆₇	1	1	yes	characteristic
873	#103	C₂³×C₆₇	1	1	yes	characteristic
874	#103	C₂³×C₆₇	1	2	yes	—
875	#103	C₂³×C₆₇	1	2	yes	—
876	#103	C₂³×C₆₇	1	2	yes	—
877	#102	C₂³×C₆₇	1	1	yes	characteristic
878	#102	C₂³×C₆₇	1	2	yes	—
879	#102	C₂³×C₆₇	1	2	yes	—
880	#102	C₂³×C₆₇	1	2	yes	—
881	#102	C₂³×C₆₇	1	1	yes	characteristic
882	#102	C₂³×C₆₇	1	2	yes	—
883	#102	C₂³×C₆₇	1	1	yes	characteristic
884	#102	C₂³×C₆₇	1	1	yes	characteristic
885	#102	C₂³×C₆₇	1	1	yes	characteristic
886	#102	C₂³×C₆₇	1	1	yes	characteristic
887	#102	C₂³×C₆₇	1	2	yes	—
888	#102	C₂³×C₆₇	1	2	yes	—
889	#102	C₂³×C₆₇	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
893	#97	C₂³×C₆₇	1	1	yes	characteristic
894	#97	C₂³×C₆₇	1	1	yes	characteristic
895	#97	C₂³×C₆₇	1	2	yes	—
896	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₆₇	1	2	yes	—
899	C₄×C₈	C₂³×C₆₇	1	2	yes	—
900	C₂⁴	—	2	1	no	—
901	C₂⁴	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	2	4	no	—
904	#41	—	4	2	no	—
905	#41	—	4	1	no	—
906	#41	—	8	2	no	—
907	#41	—	8	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	4	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	1	no	—
928	C₂×D₄	—	8	2	no	—
929	C₂×D₄	—	8	4	no	—
930	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
931	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
932	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
933	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	8	2	no	—
951	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	4	no	—
957	SD₁₆	—	2	2	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	D₈	—	2	2	no	—
963	D₈	—	2	4	no	—
964	D₈	#41×C₆₇	1	4	yes	complemented
965	M₁₆	—	2	2	no	—
966	M₁₆	—	2	4	no	—
967	M₁₆	—	4	1	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
970	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
974	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
995	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₆₇	1	2	yes	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	8	1	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1051	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	8	1	no	—
1058	Q₈	—	8	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	C₂×#41×C₆₇	1	2	yes	—
1079	D₄	C₂×#41×C₆₇	1	2	yes	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	8	1	no	—
1100	C₂×C₄	—	8	1	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1116	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1117	C₈	—	2	1	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	C₂×#41×C₆₇	1	2	yes	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	8	4	no	—
1142	C₂²	—	16	4	no	—
1143	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	#577×C₆₇	1	2	yes	—
1160	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1161	C₄	#585×C₆₇	1	1	yes	characteristic
1162	C₂	—	4	1	no	—
1163	C₂	—	4	2	no	—
1164	C₂	—	4	2	no	—
1165	C₂	—	4	2	no	—
1166	C₂	—	8	1	no	—
1167	C₂	—	8	2	no	—
1168	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1169	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1170	C₂	C₆₇×#3585	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3519	C₂	semidirect
2. C₆₇×#3515	C₂	semidirect
3. C₆₇×#3392	C₂	semidirect
4. C₆₇×#3380	C₂	semidirect
5. C₆₇×#3372	C₂	semidirect
6. C₆₇×#3366	C₂	semidirect
7. C₆₇×#3357	C₂	semidirect
8. C₆₇×#3351	C₂	semidirect
9. C₆₇×#3310	C₂	semidirect
10. C₆₇×#3307	C₂	semidirect
11. C₆₇×#3303	C₂	semidirect
12. C₆₇×#3295	C₂	semidirect
13. C₆₇×#3272	C₂	semidirect
14. C₆₇×#3272	C₂	semidirect
15. C₆₇×#3182	C₂	semidirect
16. C₆₇×#3174	C₂	semidirect
17. C₆₇×#3123	C₂	semidirect
18. C₆₇×#3119	C₂	semidirect
19. C₆₇×#3106	C₂	semidirect
20. C₆₇×#3101	C₂	semidirect
21. C₆₇×#2969	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
26. #557×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
30. #554×C₆₇	C₂²	semidirect
36. #552×C₆₇	C₂²	semidirect
38. #547×C₆₇	C₂²	semidirect
39. #547×C₆₇	C₂²	semidirect
44. #541×C₆₇	C₂²	semidirect
48. #533×C₆₇	C₂²	semidirect
55. #520×C₆₇	C₂²	semidirect
57. C₄×#41×C₆₇	C₂²	semidirect
59. #500×C₆₇	C₂²	semidirect
60. #499×C₆₇	C₂²	semidirect
61. #492×C₆₇	C₂²	semidirect
62. #492×C₆₇	C₂²	semidirect
63. #491×C₆₇	C₂²	semidirect
64. #490×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #483×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #481×C₆₇	C₂²	semidirect
72. #480×C₆₇	C₂²	semidirect
73. #479×C₆₇	C₂²	semidirect
75. #478×C₆₇	C₂²	semidirect
76. #478×C₆₇	C₂²	semidirect
77. #477×C₆₇	C₂²	semidirect
79. #476×C₆₇	C₂²	semidirect
80. #476×C₆₇	C₂²	semidirect
81. #468×C₆₇	C₂²	semidirect
82. #468×C₆₇	C₂²	semidirect
83. #468×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
86. #465×C₆₇	C₂²	semidirect
89. #461×C₆₇	C₂²	semidirect
90. #461×C₆₇	C₂²	semidirect
91. #460×C₆₇	C₂²	semidirect
92. #460×C₆₇	C₂²	semidirect
93. #459×C₆₇	C₂²	semidirect
94. #459×C₆₇	C₂²	semidirect
98. #449×C₆₇	C₂²	semidirect
99. #449×C₆₇	C₂²	semidirect
100. #449×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. C₈×Q₈×C₆₇	C₂²	semidirect
104. #442×C₆₇	C₂²	semidirect
105. #442×C₆₇	C₂²	semidirect
108. #440×C₆₇	C₂²	semidirect
109. #440×C₆₇	C₂²	semidirect
110. #440×C₆₇	C₂²	semidirect
113. C₄×SD₁₆×C₆₇	C₂²	semidirect
114. C₄×SD₁₆×C₆₇	C₂²	semidirect
115. C₄×SD₁₆×C₆₇	C₂²	semidirect
116. C₄×SD₁₆×C₆₇	C₂²	semidirect
119. C₄×D₈×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. #433×C₆₇	C₂²	semidirect
126. #431×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
133. #405×C₆₇	C₂²	semidirect
134. C₄×M₁₆×C₆₇	C₂²	semidirect
378. D₈×C₆₇	#41	semidirect
576. #61551	C₆₇	direct (N × H)
586. #3519	C₂×C₆₇	semidirect
587. #3515	C₂×C₆₇	semidirect
588. #3392	C₂×C₆₇	semidirect
589. #3380	C₂×C₆₇	semidirect
590. #3372	C₂×C₆₇	semidirect
591. #3366	C₂×C₆₇	semidirect
592. #3357	C₂×C₆₇	semidirect
593. #3351	C₂×C₆₇	semidirect
594. #3310	C₂×C₆₇	semidirect
595. #3307	C₂×C₆₇	semidirect
596. #3303	C₂×C₆₇	semidirect
597. #3295	C₂×C₆₇	semidirect
598. #3272	C₂×C₆₇	semidirect
599. #3272	C₂×C₆₇	semidirect
600. #3182	C₂×C₆₇	semidirect
601. #3174	C₂×C₆₇	semidirect
602. #3123	C₂×C₆₇	semidirect
603. #3119	C₂×C₆₇	semidirect
604. #3106	C₂×C₆₇	semidirect
605. #3101	C₂×C₆₇	semidirect
606. #2969	C₂×C₆₇	semidirect
607. #2946	C₂×C₆₇	semidirect
608. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
609. C₆₇	#61551	direct (N × H)
612. #557	C₂²×C₆₇	semidirect
615. #554	C₂²×C₆₇	semidirect
616. #554	C₂²×C₆₇	semidirect
622. #552	C₂²×C₆₇	semidirect
624. #547	C₂²×C₆₇	semidirect
625. #547	C₂²×C₆₇	semidirect
630. #541	C₂²×C₆₇	semidirect
634. #533	C₂²×C₆₇	semidirect
641. #520	C₂²×C₆₇	semidirect
643. C₄×#41	C₂²×C₆₇	semidirect
645. #500	C₂²×C₆₇	semidirect
646. #499	C₂²×C₆₇	semidirect
647. #492	C₂²×C₆₇	semidirect
648. #492	C₂²×C₆₇	semidirect
649. #491	C₂²×C₆₇	semidirect
650. #490	C₂²×C₆₇	semidirect
651. #487	C₂²×C₆₇	semidirect
652. #486	C₂²×C₆₇	semidirect
653. #485	C₂²×C₆₇	semidirect
654. #485	C₂²×C₆₇	semidirect
655. #483	C₂²×C₆₇	semidirect
656. #482	C₂²×C₆₇	semidirect
657. #481	C₂²×C₆₇	semidirect
658. #480	C₂²×C₆₇	semidirect
659. #479	C₂²×C₆₇	semidirect
661. #478	C₂²×C₆₇	semidirect
662. #478	C₂²×C₆₇	semidirect
663. #477	C₂²×C₆₇	semidirect
665. #476	C₂²×C₆₇	semidirect
666. #476	C₂²×C₆₇	semidirect
667. #468	C₂²×C₆₇	semidirect
668. #468	C₂²×C₆₇	semidirect
669. #468	C₂²×C₆₇	semidirect
670. #468	C₂²×C₆₇	semidirect
671. #465	C₂²×C₆₇	semidirect
672. #465	C₂²×C₆₇	semidirect
675. #461	C₂²×C₆₇	semidirect
676. #461	C₂²×C₆₇	semidirect
677. #460	C₂²×C₆₇	semidirect
678. #460	C₂²×C₆₇	semidirect
679. #459	C₂²×C₆₇	semidirect
680. #459	C₂²×C₆₇	semidirect
684. #449	C₂²×C₆₇	semidirect
685. #449	C₂²×C₆₇	semidirect
686. #449	C₂²×C₆₇	semidirect
687. #446	C₂²×C₆₇	semidirect
688. C₈×Q₈	C₂²×C₆₇	semidirect
690. #442	C₂²×C₆₇	semidirect
691. #442	C₂²×C₆₇	semidirect
694. #440	C₂²×C₆₇	semidirect
695. #440	C₂²×C₆₇	semidirect
696. #440	C₂²×C₆₇	semidirect
699. C₄×SD₁₆	C₂²×C₆₇	semidirect
700. C₄×SD₁₆	C₂²×C₆₇	semidirect
701. C₄×SD₁₆	C₂²×C₆₇	semidirect
702. C₄×SD₁₆	C₂²×C₆₇	semidirect
705. C₄×D₈	C₂²×C₆₇	semidirect
706. C₄×D₈	C₂²×C₆₇	semidirect
707. #436	C₂²×C₆₇	semidirect
708. #436	C₂²×C₆₇	semidirect
709. #435	C₂²×C₆₇	semidirect
710. C₈×D₄	C₂²×C₆₇	semidirect
711. #433	C₂²×C₆₇	semidirect
712. #431	C₂²×C₆₇	semidirect
713. #428	C₂²×C₆₇	semidirect
714. #428	C₂²×C₆₇	semidirect
716. #417	C₂²×C₆₇	semidirect
717. #416	C₂²×C₆₇	semidirect
719. #405	C₂²×C₆₇	semidirect
720. C₄×M₁₆	C₂²×C₆₇	semidirect
964. D₈	#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×#3519	2
C₆₇×#3515	2
C₆₇×#3392	2
C₆₇×#3380	2
C₆₇×#3372	2
C₆₇×#3366	2
C₆₇×#3357	2
C₆₇×#3351	2
C₆₇×#3310	2
C₆₇×#3307	2
C₆₇×#3303	2
C₆₇×#3295	2
C₆₇×#3272	2
C₆₇×#3182	2
C₆₇×#3174	2
C₆₇×#3123	2
C₆₇×#3119	2
C₆₇×#3106	2
C₆₇×#3101	2
C₆₇×#2969	2
C₆₇×#2946	2
C₄×AGL(1,ℤ/8)×C₆₇	2
#61551	67

Subgroups — C67×#61551 #30740802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61551 #30740802