Subgroups — C₆₇×#60598 #30739849

Order 17152.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3126	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3108	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3102	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	#553×C₆₇	—	2	2	no	—
30	#553×C₆₇	—	2	2	no	—
31	#553×C₆₇	—	2	1	no	—
32	#553×C₆₇	—	2	1	no	—
33	#552×C₆₇	—	2	1	no	—
34	#552×C₆₇	—	2	1	no	—
35	#541×C₆₇	C₂²	1	2	yes	—
36	#540×C₆₇	C₂²	1	2	yes	—
37	#537×C₆₇	C₂²	1	1	yes	characteristic
38	#537×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#529×C₆₇	C₂²	1	2	yes	—
41	#529×C₆₇	C₂²	1	2	yes	—
42	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
43	#520×C₆₇	—	2	2	no	—
44	#520×C₆₇	—	2	1	no	—
45	#520×C₆₇	C₂²	1	2	yes	—
46	#520×C₆₇	C₂²	1	1	yes	characteristic
47	#520×C₆₇	C₂²	1	1	yes	characteristic
48	#520×C₆₇	C₂²	1	1	yes	characteristic
49	#520×C₆₇	C₂²	1	1	yes	characteristic
50	#519×C₆₇	—	2	1	no	—
51	#519×C₆₇	C₂²	1	2	yes	—
52	#519×C₆₇	C₂²	1	1	yes	characteristic
53	C₄×#41×C₆₇	—	2	2	no	—
54	C₄×#41×C₆₇	—	2	1	no	—
55	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
56	C₄×#41×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
59	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
61	#485×C₆₇	C₂²	1	2	yes	—
62	#485×C₆₇	C₂²	1	2	yes	—
63	#484×C₆₇	C₂²	1	2	yes	—
64	#483×C₆₇	C₂²	1	2	yes	—
65	#482×C₆₇	C₂²	1	2	yes	—
66	#482×C₆₇	C₂²	1	2	yes	—
67	#481×C₆₇	C₂²	1	2	yes	—
68	#480×C₆₇	C₂²	1	2	yes	—
69	#479×C₆₇	C₂²	1	2	yes	—
70	#479×C₆₇	C₂²	1	2	yes	—
71	#479×C₆₇	C₂²	1	2	yes	—
72	#479×C₆₇	C₂²	1	2	yes	—
73	#479×C₆₇	C₂²	1	2	yes	—
74	#479×C₆₇	C₂²	1	2	yes	—
75	#478×C₆₇	C₂²	1	2	yes	—
76	#478×C₆₇	C₂²	1	2	yes	—
77	#464×C₆₇	C₂²	1	1	yes	characteristic
78	#464×C₆₇	C₂²	1	1	yes	characteristic
79	#464×C₆₇	C₂²	1	2	yes	—
80	#464×C₆₇	C₂²	1	2	yes	—
81	#463×C₆₇	C₂²	1	1	yes	characteristic
82	#463×C₆₇	C₂²	1	1	yes	characteristic
83	#462×C₆₇	C₂²	1	1	yes	characteristic
84	#462×C₆₇	C₂²	1	2	yes	—
85	#461×C₆₇	C₂²	1	1	yes	characteristic
86	#460×C₆₇	C₂²	1	1	yes	characteristic
87	#460×C₆₇	C₂²	1	2	yes	—
88	#459×C₆₇	C₂²	1	1	yes	characteristic
89	#452×C₆₇	C₂²	1	2	yes	—
90	#452×C₆₇	C₂²	1	2	yes	—
91	#451×C₆₇	C₂²	1	2	yes	—
92	#451×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	—
95	#448×C₆₇	C₂²	1	2	yes	—
96	#448×C₆₇	C₂²	1	2	yes	—
97	#442×C₆₇	C₂²	1	2	yes	—
98	#441×C₆₇	C₂²	1	2	yes	—
99	#441×C₆₇	C₂²	1	2	yes	—
100	#441×C₆₇	C₂²	1	2	yes	—
101	#440×C₆₇	C₂²	1	2	yes	—
102	#440×C₆₇	C₂²	1	2	yes	—
103	#440×C₆₇	C₂²	1	2	yes	—
104	#440×C₆₇	C₂²	1	2	yes	—
105	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
106	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
107	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
109	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
110	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
112	C₄×D₈×C₆₇	C₂²	1	2	yes	—
113	#433×C₆₇	C₂²	1	2	yes	—
114	#433×C₆₇	C₂²	1	2	yes	—
115	#432×C₆₇	C₂²	1	2	yes	—
116	#431×C₆₇	C₂²	1	2	yes	—
117	#428×C₆₇	C₂²	1	1	yes	characteristic
118	#428×C₆₇	C₂²	1	1	yes	characteristic
119	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
120	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
121	#423×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
123	#417×C₆₇	C₂²	1	1	yes	characteristic
124	#417×C₆₇	C₂²	1	1	yes	characteristic
125	#417×C₆₇	C₂²	1	1	yes	characteristic
126	#417×C₆₇	C₂²	1	1	yes	characteristic
127	#416×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
131	#408×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	#405×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	2	4	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	2	no	—
139	C₂×#41×C₆₇	C₂³	1	2	yes	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₇	—	2	1	no	—
145	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
147	#137×C₆₇	—	2	4	no	—
148	#137×C₆₇	—	2	4	no	—
149	#135×C₆₇	—	2	4	no	—
150	#135×C₆₇	—	2	4	no	—
151	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
168	#127×C₆₇	C₂³	1	1	yes	characteristic
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	2	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	C₂³	1	2	yes	—
178	#125×C₆₇	C₂³	1	2	yes	—
179	#124×C₆₇	C₂³	1	1	yes	characteristic
180	#124×C₆₇	C₂³	1	1	yes	characteristic
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	1	no	—
187	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
189	#121×C₆₇	—	2	1	no	—
190	#121×C₆₇	—	2	1	no	—
191	#121×C₆₇	—	2	2	no	—
192	#121×C₆₇	—	2	2	no	—
193	#121×C₆₇	—	2	1	no	—
194	#121×C₆₇	—	2	1	no	—
195	#121×C₆₇	—	2	2	no	—
196	#121×C₆₇	—	2	2	no	—
197	#121×C₆₇	C₂³	1	2	yes	—
198	#121×C₆₇	C₂³	1	2	yes	—
199	C₄×Q₈×C₆₇	—	2	1	no	—
200	C₄×Q₈×C₆₇	—	2	1	no	—
201	C₄×Q₈×C₆₇	—	2	2	no	—
202	C₄×Q₈×C₆₇	—	2	1	no	—
203	C₄×Q₈×C₆₇	—	2	2	no	—
204	C₄×Q₈×C₆₇	—	2	2	no	—
205	C₄×Q₈×C₆₇	—	2	1	no	—
206	C₄×Q₈×C₆₇	—	2	2	no	—
207	C₄×Q₈×C₆₇	—	2	1	no	—
208	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
209	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
210	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
211	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
214	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
215	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
217	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
219	C₄×D₄×C₆₇	—	2	2	no	—
220	C₄×D₄×C₆₇	—	2	1	no	—
221	C₄×D₄×C₆₇	—	2	1	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	1	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	D₄	1	2	yes	—
235	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
236	C₄×D₄×C₆₇	D₄	1	2	yes	—
237	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
238	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	#117×C₆₇	—	2	1	no	—
244	#117×C₆₇	—	2	2	no	—
245	#117×C₆₇	—	2	1	no	—
246	#117×C₆₇	—	2	1	no	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	—	2	2	no	—
250	#117×C₆₇	—	2	2	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	—	2	2	no	—
254	#117×C₆₇	C₂³	1	2	yes	—
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	1	yes	characteristic
257	#117×C₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
264	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
265	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
266	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₆₇	—	2	1	no	—
271	C₂×C₄²×C₆₇	—	2	2	no	—
272	C₂×C₄²×C₆₇	—	2	2	no	—
273	C₂×C₄²×C₆₇	—	2	1	no	—
274	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	2	yes	—
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	2	yes	—
280	#106×C₆₇	C₂³	1	2	yes	—
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	2	yes	—
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	1	yes	characteristic
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	1	yes	characteristic
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	#102×C₆₇	C₂³	1	2	yes	—
309	#102×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	#97×C₆₇	C₂³	1	2	yes	—
315	#97×C₆₇	C₂³	1	2	yes	—
316	C₄×C₈×C₆₇	C₂³	1	2	yes	—
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	#41×C₆₇	—	2	16	no	—
319	#41×C₆₇	—	2	8	no	—
320	#41×C₆₇	—	2	4	no	—
321	#41×C₆₇	—	2	4	no	—
322	#41×C₆₇	—	2	2	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	#41	1	4	yes	—
330	C₂×Q₈×C₆₇	—	2	8	no	—
331	C₂×Q₈×C₆₇	—	2	4	no	—
332	C₂×Q₈×C₆₇	—	2	4	no	—
333	C₂×Q₈×C₆₇	—	2	2	no	—
334	C₂×Q₈×C₆₇	—	2	1	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₂×Q₈×C₆₇	#41	1	4	yes	—
338	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
342	C₂×D₄×C₆₇	—	2	2	no	—
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	1	no	—
346	C₂×D₄×C₆₇	—	2	2	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	—	2	1	no	—
349	C₂×D₄×C₆₇	—	2	1	no	—
350	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	2	no	—
358	C₂²×C₄×C₆₇	—	2	1	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	1	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	2	no	—
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	Q₁₆×C₆₇	—	2	2	no	—
377	Q₁₆×C₆₇	—	2	2	no	—
378	Q₁₆×C₆₇	—	2	4	no	—
379	Q₁₆×C₆₇	—	2	4	no	—
380	SD₁₆×C₆₇	—	2	2	no	—
381	SD₁₆×C₆₇	—	2	2	no	—
382	SD₁₆×C₆₇	—	2	4	no	—
383	SD₁₆×C₆₇	—	2	4	no	—
384	SD₁₆×C₆₇	—	2	2	no	—
385	SD₁₆×C₆₇	—	2	2	no	—
386	D₈×C₆₇	—	2	2	no	—
387	D₈×C₆₇	—	2	2	no	—
388	M₁₆×C₆₇	—	2	2	no	—
389	M₁₆×C₆₇	—	2	2	no	—
390	C₂×C₈×C₆₇	—	2	2	no	—
391	C₂×C₈×C₆₇	—	2	2	no	—
392	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
393	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
394	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	1	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	1	no	—
435	C₂²⋊C₄×C₆₇	—	2	1	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₂²⋊C₄×C₆₇	—	2	1	no	—
443	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	—	2	1	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	2	no	—
452	C₄²×C₆₇	—	2	2	no	—
453	C₄²×C₆₇	—	2	2	no	—
454	C₄²×C₆₇	—	2	1	no	—
455	C₄²×C₆₇	—	2	2	no	—
456	C₄²×C₆₇	—	2	2	no	—
457	C₄²×C₆₇	C₂×D₄	1	2	yes	—
458	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₆₇	C₂×D₄	1	2	yes	—
460	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
461	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
462	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₄²×C₆₇	C₂⁴	1	2	yes	—
464	C₂³×C₆₇	—	2	1	no	—
465	C₂³×C₆₇	—	2	1	no	—
466	C₂³×C₆₇	—	2	1	no	—
467	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
468	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
469	Q₈×C₆₇	—	2	8	no	—
470	Q₈×C₆₇	—	2	2	no	—
471	Q₈×C₆₇	—	2	4	no	—
472	Q₈×C₆₇	—	2	1	no	—
473	Q₈×C₆₇	—	2	2	no	—
474	Q₈×C₆₇	—	2	1	no	—
475	Q₈×C₆₇	—	2	1	no	—
476	Q₈×C₆₇	—	2	1	no	—
477	Q₈×C₆₇	—	2	1	no	—
478	Q₈×C₆₇	C₂×#41	1	2	yes	—
479	Q₈×C₆₇	C₂×#41	1	4	yes	—
480	D₄×C₆₇	—	2	8	no	—
481	D₄×C₆₇	—	2	4	no	—
482	D₄×C₆₇	—	2	4	no	—
483	D₄×C₆₇	—	2	2	no	—
484	D₄×C₆₇	—	2	1	no	—
485	D₄×C₆₇	—	2	1	no	—
486	D₄×C₆₇	—	2	1	no	—
487	D₄×C₆₇	—	2	1	no	—
488	D₄×C₆₇	—	2	1	no	—
489	D₄×C₆₇	—	4	2	no	—
490	D₄×C₆₇	—	4	2	no	—
491	D₄×C₆₇	—	8	1	no	—
492	D₄×C₆₇	—	8	1	no	—
493	D₄×C₆₇	—	8	2	no	—
494	D₄×C₆₇	—	8	2	no	—
495	D₄×C₆₇	C₂×#41	1	2	yes	—
496	C₂×C₄×C₆₇	—	2	8	no	—
497	C₂×C₄×C₆₇	—	2	8	no	—
498	C₂×C₄×C₆₇	—	2	4	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	4	no	—
502	C₂×C₄×C₆₇	—	2	2	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	2	no	—
511	C₂×C₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	—	4	1	no	—
513	C₂×C₄×C₆₇	—	4	2	no	—
514	C₂×C₄×C₆₇	—	4	1	no	—
515	C₂×C₄×C₆₇	—	4	2	no	—
516	C₂×C₄×C₆₇	—	4	2	no	—
517	C₂×C₄×C₆₇	—	4	2	no	—
518	C₂×C₄×C₆₇	—	8	2	no	—
519	C₂×C₄×C₆₇	—	8	2	no	—
520	C₂×C₄×C₆₇	—	8	1	no	—
521	C₂×C₄×C₆₇	—	8	2	no	—
522	C₂×C₄×C₆₇	—	8	1	no	—
523	C₂×C₄×C₆₇	—	8	2	no	—
524	C₂×C₄×C₆₇	—	8	1	no	—
525	C₂×C₄×C₆₇	—	8	1	no	—
526	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
535	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
536	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
537	C₈×C₆₇	—	2	1	no	—
538	C₈×C₆₇	—	2	1	no	—
539	C₈×C₆₇	—	2	1	no	—
540	C₈×C₆₇	—	2	1	no	—
541	C₈×C₆₇	—	2	2	no	—
542	C₈×C₆₇	—	2	2	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	1	no	—
545	C₂²×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	2	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	4	1	no	—
550	C₂²×C₆₇	—	4	1	no	—
551	C₂²×C₆₇	—	4	1	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	1	no	—
555	C₂²×C₆₇	—	4	1	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	#525	1	2	yes	—
558	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₆₇	—	2	1	no	—
560	C₄×C₆₇	—	2	2	no	—
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	2	no	—
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	4	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	2	no	—
568	C₄×C₆₇	—	4	2	no	—
569	C₄×C₆₇	—	4	1	no	—
570	C₄×C₆₇	—	4	2	no	—
571	C₄×C₆₇	—	4	1	no	—
572	C₄×C₆₇	—	4	2	no	—
573	C₄×C₆₇	—	4	1	no	—
574	C₄×C₆₇	—	4	1	no	—
575	C₄×C₆₇	#525	1	2	yes	—
576	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
577	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
578	#60598	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
579	C₂×C₆₇	—	2	2	no	—
580	C₂×C₆₇	—	4	2	no	—
581	C₂×C₆₇	—	4	2	no	—
582	C₂×C₆₇	—	8	1	no	—
583	C₂×C₆₇	—	8	1	no	—
584	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
585	C₂×C₆₇	#3584	1	1	yes	characteristic
586	C₂×C₆₇	#3586	1	1	yes	characteristic
587	#3512	C₂×C₆₇	1	1	yes	characteristic, complemented
588	C₄×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3127	C₂×C₆₇	1	2	yes	complemented
590	#3126	C₂×C₆₇	1	2	yes	complemented
591	#3120	C₂×C₆₇	1	2	yes	complemented
592	#3119	C₂×C₆₇	1	2	yes	complemented
593	#3117	C₂×C₆₇	1	2	yes	complemented
594	#3111	C₂×C₆₇	1	2	yes	complemented
595	#3108	C₂×C₆₇	1	2	yes	complemented
596	#3102	C₂×C₆₇	1	2	yes	complemented
597	#3099	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3080	C₂×C₆₇	1	1	yes	characteristic, complemented
600	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#2952	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2951	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
610	C₆₇	#60598	1	1	yes	characteristic, direct product factor, Sylow
611	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
612	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
613	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
614	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
615	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
616	#553	—	2	2	no	—
617	#553	—	2	2	no	—
618	#553	—	2	1	no	—
619	#553	—	2	1	no	—
620	#552	—	2	1	no	—
621	#552	—	2	1	no	—
622	#541	C₂²×C₆₇	1	2	yes	—
623	#540	C₂²×C₆₇	1	2	yes	—
624	#537	C₂²×C₆₇	1	1	yes	characteristic
625	#537	C₂²×C₆₇	1	1	yes	characteristic
626	#532	C₂²×C₆₇	1	1	yes	characteristic
627	#529	C₂²×C₆₇	1	2	yes	—
628	#529	C₂²×C₆₇	1	2	yes	—
629	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
630	#520	—	2	2	no	—
631	#520	—	2	1	no	—
632	#520	C₂²×C₆₇	1	2	yes	—
633	#520	C₂²×C₆₇	1	1	yes	characteristic
634	#520	C₂²×C₆₇	1	1	yes	characteristic
635	#520	C₂²×C₆₇	1	1	yes	characteristic
636	#520	C₂²×C₆₇	1	1	yes	characteristic
637	#519	—	2	1	no	—
638	#519	C₂²×C₆₇	1	2	yes	—
639	#519	C₂²×C₆₇	1	1	yes	characteristic
640	C₄×#41	—	2	2	no	—
641	C₄×#41	—	2	1	no	—
642	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
643	C₄×#41	C₂²×C₆₇	1	2	yes	—
644	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
645	C₂×C₄×Q₈	—	2	1	no	—
646	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
647	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
648	#485	C₂²×C₆₇	1	2	yes	—
649	#485	C₂²×C₆₇	1	2	yes	—
650	#484	C₂²×C₆₇	1	2	yes	—
651	#483	C₂²×C₆₇	1	2	yes	—
652	#482	C₂²×C₆₇	1	2	yes	—
653	#482	C₂²×C₆₇	1	2	yes	—
654	#481	C₂²×C₆₇	1	2	yes	—
655	#480	C₂²×C₆₇	1	2	yes	—
656	#479	C₂²×C₆₇	1	2	yes	—
657	#479	C₂²×C₆₇	1	2	yes	—
658	#479	C₂²×C₆₇	1	2	yes	—
659	#479	C₂²×C₆₇	1	2	yes	—
660	#479	C₂²×C₆₇	1	2	yes	—
661	#479	C₂²×C₆₇	1	2	yes	—
662	#478	C₂²×C₆₇	1	2	yes	—
663	#478	C₂²×C₆₇	1	2	yes	—
664	#464	C₂²×C₆₇	1	2	yes	—
665	#464	C₂²×C₆₇	1	1	yes	characteristic
666	#464	C₂²×C₆₇	1	2	yes	—
667	#464	C₂²×C₆₇	1	1	yes	characteristic
668	#463	C₂²×C₆₇	1	1	yes	characteristic
669	#463	C₂²×C₆₇	1	1	yes	characteristic
670	#462	C₂²×C₆₇	1	2	yes	—
671	#462	C₂²×C₆₇	1	1	yes	characteristic
672	#461	C₂²×C₆₇	1	1	yes	characteristic
673	#460	C₂²×C₆₇	1	2	yes	—
674	#460	C₂²×C₆₇	1	1	yes	characteristic
675	#459	C₂²×C₆₇	1	1	yes	characteristic
676	#452	C₂²×C₆₇	1	2	yes	—
677	#452	C₂²×C₆₇	1	2	yes	—
678	#451	C₂²×C₆₇	1	2	yes	—
679	#451	C₂²×C₆₇	1	2	yes	—
680	#449	C₂²×C₆₇	1	2	yes	—
681	#449	C₂²×C₆₇	1	2	yes	—
682	#448	C₂²×C₆₇	1	2	yes	—
683	#448	C₂²×C₆₇	1	2	yes	—
684	#442	C₂²×C₆₇	1	2	yes	—
685	#441	C₂²×C₆₇	1	2	yes	—
686	#441	C₂²×C₆₇	1	2	yes	—
687	#441	C₂²×C₆₇	1	2	yes	—
688	#440	C₂²×C₆₇	1	2	yes	—
689	#440	C₂²×C₆₇	1	2	yes	—
690	#440	C₂²×C₆₇	1	2	yes	—
691	#440	C₂²×C₆₇	1	2	yes	—
692	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
693	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
694	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
695	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
696	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
697	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
698	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
699	C₄×D₈	C₂²×C₆₇	1	2	yes	—
700	#433	C₂²×C₆₇	1	2	yes	—
701	#433	C₂²×C₆₇	1	2	yes	—
702	#432	C₂²×C₆₇	1	2	yes	—
703	#431	C₂²×C₆₇	1	2	yes	—
704	#428	C₂²×C₆₇	1	1	yes	characteristic
705	#428	C₂²×C₆₇	1	1	yes	characteristic
706	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
708	#423	C₂²×C₆₇	1	1	yes	characteristic
709	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
710	#417	C₂²×C₆₇	1	1	yes	characteristic
711	#417	C₂²×C₆₇	1	1	yes	characteristic
712	#417	C₂²×C₆₇	1	1	yes	characteristic
713	#417	C₂²×C₆₇	1	1	yes	characteristic
714	#416	C₂²×C₆₇	1	1	yes	characteristic
715	#416	C₂²×C₆₇	1	1	yes	characteristic
716	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
717	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
718	#408	C₂²×C₆₇	1	1	yes	characteristic
719	#408	C₂²×C₆₇	1	1	yes	characteristic
720	#405	C₂²×C₆₇	1	1	yes	characteristic
721	#405	C₂²×C₆₇	1	1	yes	characteristic
722	2₋¹⁺⁴	—	2	4	no	—
723	2₋¹⁺⁴	—	2	4	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	2	no	—
726	C₂×#41	C₂³×C₆₇	1	2	yes	—
727	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
731	C₂²×Q₈	—	2	1	no	—
732	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
733	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
734	#137	—	2	4	no	—
735	#137	—	2	4	no	—
736	#135	—	2	4	no	—
737	#135	—	2	4	no	—
738	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
741	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
748	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
749	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
753	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
754	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
755	#127	C₂³×C₆₇	1	1	yes	characteristic
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	2	no	—
762	#125	—	2	1	no	—
763	#125	—	2	1	no	—
764	#125	C₂³×C₆₇	1	2	yes	—
765	#125	C₂³×C₆₇	1	2	yes	—
766	#124	C₂³×C₆₇	1	1	yes	characteristic
767	#124	C₂³×C₆₇	1	1	yes	characteristic
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	C₂³×C₆₇	1	2	yes	—
785	#121	C₂³×C₆₇	1	2	yes	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	2	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
796	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
798	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
800	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
801	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
805	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	D₄×C₆₇	1	2	yes	—
822	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
823	C₄×D₄	D₄×C₆₇	1	2	yes	—
824	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₆₇	1	2	yes	—
827	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₆₇	1	2	yes	—
829	C₄×D₄	C₂³×C₆₇	1	2	yes	—
830	#117	—	2	1	no	—
831	#117	—	2	2	no	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	—	2	2	no	—
841	#117	C₂³×C₆₇	1	1	yes	characteristic
842	#117	C₂³×C₆₇	1	2	yes	—
843	#117	C₂³×C₆₇	1	1	yes	characteristic
844	#117	C₂³×C₆₇	1	2	yes	—
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	2	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	2	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
855	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
857	C₂×C₄²	—	2	1	no	—
858	C₂×C₄²	—	2	2	no	—
859	C₂×C₄²	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
862	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
863	#107	C₂³×C₆₇	1	2	yes	—
864	#107	C₂³×C₆₇	1	2	yes	—
865	#107	C₂³×C₆₇	1	2	yes	—
866	#107	C₂³×C₆₇	1	2	yes	—
867	#106	C₂³×C₆₇	1	2	yes	—
868	#106	C₂³×C₆₇	1	2	yes	—
869	#106	C₂³×C₆₇	1	2	yes	—
870	#106	C₂³×C₆₇	1	2	yes	—
871	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
876	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
877	#103	C₂³×C₆₇	1	2	yes	—
878	#103	C₂³×C₆₇	1	2	yes	—
879	#103	C₂³×C₆₇	1	2	yes	—
880	#103	C₂³×C₆₇	1	2	yes	—
881	#103	C₂³×C₆₇	1	1	yes	characteristic
882	#103	C₂³×C₆₇	1	1	yes	characteristic
883	#103	C₂³×C₆₇	1	1	yes	characteristic
884	#103	C₂³×C₆₇	1	1	yes	characteristic
885	#103	C₂³×C₆₇	1	2	yes	—
886	#103	C₂³×C₆₇	1	2	yes	—
887	#103	C₂³×C₆₇	1	2	yes	—
888	#103	C₂³×C₆₇	1	2	yes	—
889	#102	C₂³×C₆₇	1	1	yes	characteristic
890	#102	C₂³×C₆₇	1	1	yes	characteristic
891	#102	C₂³×C₆₇	1	1	yes	characteristic
892	#102	C₂³×C₆₇	1	1	yes	characteristic
893	#102	C₂³×C₆₇	1	2	yes	—
894	#102	C₂³×C₆₇	1	2	yes	—
895	#102	C₂³×C₆₇	1	2	yes	—
896	#102	C₂³×C₆₇	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
901	#97	C₂³×C₆₇	1	2	yes	—
902	#97	C₂³×C₆₇	1	2	yes	—
903	C₄×C₈	C₂³×C₆₇	1	2	yes	—
904	C₄×C₈	C₂³×C₆₇	1	2	yes	—
905	#41	—	2	16	no	—
906	#41	—	2	8	no	—
907	#41	—	2	4	no	—
908	#41	—	2	4	no	—
909	#41	—	2	2	no	—
910	#41	—	2	2	no	—
911	#41	—	2	2	no	—
912	#41	—	2	2	no	—
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	#41×C₆₇	1	4	yes	—
917	C₂×Q₈	—	2	8	no	—
918	C₂×Q₈	—	2	4	no	—
919	C₂×Q₈	—	2	4	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
924	C₂×Q₈	#41×C₆₇	1	4	yes	—
925	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
938	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
939	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
959	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
960	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
963	Q₁₆	—	2	2	no	—
964	Q₁₆	—	2	2	no	—
965	Q₁₆	—	2	4	no	—
966	Q₁₆	—	2	4	no	—
967	SD₁₆	—	2	2	no	—
968	SD₁₆	—	2	2	no	—
969	SD₁₆	—	2	4	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	2	2	no	—
973	D₈	—	2	2	no	—
974	D₈	—	2	2	no	—
975	M₁₆	—	2	2	no	—
976	M₁₆	—	2	2	no	—
977	C₂×C₈	—	2	2	no	—
978	C₂×C₈	—	2	2	no	—
979	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
982	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
983	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1009	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1010	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1011	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	2	no	—
1044	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1045	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1046	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1047	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1048	C₄²	C₂⁴×C₆₇	1	2	yes	—
1049	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1055	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1056	Q₈	—	2	8	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	4	no	—
1059	Q₈	—	2	1	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	C₂×#41×C₆₇	1	2	yes	—
1066	Q₈	C₂×#41×C₆₇	1	4	yes	—
1067	D₄	—	2	8	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	4	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	C₂×#41×C₆₇	1	2	yes	—
1083	C₂×C₄	—	2	8	no	—
1084	C₂×C₄	—	2	8	no	—
1085	C₂×C₄	—	2	4	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	4	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	1	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	1	no	—
1112	C₂×C₄	—	8	1	no	—
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	C₂²×D₄×C₆₇	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1121	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1122	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1123	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	2	no	—
1129	C₈	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	#525×C₆₇	1	2	yes	—
1145	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	4	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	#525×C₆₇	1	2	yes	—
1163	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1164	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1165	C₂	—	2	2	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	1	no	—
1170	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1171	C₂	C₆₇×#3584	1	1	yes	characteristic
1172	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 ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3512	C₂	semidirect
2. C₄×2₋¹⁺⁴×C₆₇	C₂	semidirect
3. C₆₇×#3127	C₂	semidirect
4. C₆₇×#3126	C₂	semidirect
5. C₆₇×#3120	C₂	semidirect
6. C₆₇×#3119	C₂	semidirect
7. C₆₇×#3117	C₂	semidirect
8. C₆₇×#3111	C₂	semidirect
9. C₆₇×#3108	C₂	semidirect
10. C₆₇×#3102	C₂	semidirect
11. C₆₇×#3099	C₂	semidirect
12. C₆₇×#3098	C₂	semidirect
13. C₆₇×#3080	C₂	semidirect
14. C₂×#479×C₆₇	C₂	semidirect
15. C₆₇×#3037	C₂	semidirect
16. C₆₇×#3035	C₂	semidirect
17. C₆₇×#3013	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#2952	C₂	semidirect
20. C₆₇×#2951	C₂	semidirect
21. C₆₇×#2947	C₂	semidirect
22. C₆₇×#2947	C₂	semidirect
23. C₆₇×#2925	C₂	semidirect
578. #60598	C₆₇	direct (N × H)
587. #3512	C₂×C₆₇	semidirect
588. C₄×2₋¹⁺⁴	C₂×C₆₇	semidirect
589. #3127	C₂×C₆₇	semidirect
590. #3126	C₂×C₆₇	semidirect
591. #3120	C₂×C₆₇	semidirect
592. #3119	C₂×C₆₇	semidirect
593. #3117	C₂×C₆₇	semidirect
594. #3111	C₂×C₆₇	semidirect
595. #3108	C₂×C₆₇	semidirect
596. #3102	C₂×C₆₇	semidirect
597. #3099	C₂×C₆₇	semidirect
598. #3098	C₂×C₆₇	semidirect
599. #3080	C₂×C₆₇	semidirect
600. C₂×#479	C₂×C₆₇	semidirect
601. #3037	C₂×C₆₇	semidirect
602. #3035	C₂×C₆₇	semidirect
603. #3013	C₂×C₆₇	semidirect
604. #3013	C₂×C₆₇	semidirect
605. #2952	C₂×C₆₇	semidirect
606. #2951	C₂×C₆₇	semidirect
607. #2947	C₂×C₆₇	semidirect
608. #2947	C₂×C₆₇	semidirect
609. #2925	C₂×C₆₇	semidirect
610. C₆₇	#60598	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3512	2
C₄×2₋¹⁺⁴×C₆₇	2
C₆₇×#3127	2
C₆₇×#3126	2
C₆₇×#3120	2
C₆₇×#3119	2
C₆₇×#3117	2
C₆₇×#3111	2
C₆₇×#3108	2
C₆₇×#3102	2
C₆₇×#3099	2
C₆₇×#3098	2
C₆₇×#3080	2
C₂×#479×C₆₇	2
C₆₇×#3037	2
C₆₇×#3035	2
C₆₇×#3013	2
C₆₇×#2952	2
C₆₇×#2951	2
C₆₇×#2947	2
C₆₇×#2925	2
#60598	67

Subgroups — C67×#60598 #30739849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60598 #30739849