Subgroups — C₆₇×#60933 #30740184

Order 17152.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1188 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	C₆₇×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3260	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3259	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3258	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3257	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3256	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3251	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3250	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3247	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#478×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2906	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	1	yes	characteristic
26	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	#553×C₆₇	—	2	2	no	—
31	#553×C₆₇	—	2	2	no	—
32	#553×C₆₇	—	2	1	no	—
33	#553×C₆₇	—	2	1	no	—
34	#552×C₆₇	—	2	1	no	—
35	#552×C₆₇	—	2	1	no	—
36	#544×C₆₇	C₂²	1	1	yes	characteristic
37	#542×C₆₇	—	2	1	no	—
38	#542×C₆₇	C₂²	1	2	yes	—
39	#541×C₆₇	C₂²	1	2	yes	complemented
40	#540×C₆₇	—	2	1	no	—
41	#540×C₆₇	C₂²	1	2	yes	—
42	#540×C₆₇	C₂²	1	2	yes	complemented
43	#538×C₆₇	—	2	2	no	—
44	#537×C₆₇	C₂²	1	1	yes	characteristic
45	#537×C₆₇	C₂²	1	1	yes	characteristic
46	#537×C₆₇	C₂²	1	1	yes	characteristic
47	#535×C₆₇	C₂²	1	1	yes	characteristic
48	#535×C₆₇	C₂²	1	1	yes	characteristic
49	#532×C₆₇	—	2	1	no	—
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	C₂²	1	2	yes	—
52	#529×C₆₇	—	2	1	no	—
53	#529×C₆₇	C₂²	1	2	yes	—
54	#529×C₆₇	C₂²	1	2	yes	complemented
55	#529×C₆₇	C₂²	1	2	yes	complemented
56	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
57	#525×C₆₇	—	2	2	no	—
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	C₂²	1	1	yes	characteristic
60	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
61	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
63	#479×C₆₇	C₂²	1	2	yes	complemented
64	#479×C₆₇	C₂²	1	2	yes	complemented
65	#479×C₆₇	C₂²	1	2	yes	complemented
66	#479×C₆₇	C₂²	1	2	yes	complemented
67	#478×C₆₇	C₂²	1	2	yes	—
68	#478×C₆₇	C₂²	1	2	yes	—
69	#478×C₆₇	C₂²	1	2	yes	—
70	#478×C₆₇	C₂²	1	2	yes	—
71	#478×C₆₇	C₂²	1	2	yes	complemented
72	#478×C₆₇	C₂²	1	2	yes	complemented
73	#478×C₆₇	C₂²	1	2	yes	complemented
74	#478×C₆₇	C₂²	1	2	yes	complemented
75	#477×C₆₇	C₂²	1	2	yes	complemented
76	#476×C₆₇	C₂²	1	2	yes	complemented
77	#475×C₆₇	C₂²	1	2	yes	complemented
78	#474×C₆₇	C₂²	1	2	yes	complemented
79	#470×C₆₇	C₂²	1	2	yes	complemented
80	#469×C₆₇	C₂²	1	2	yes	—
81	#469×C₆₇	C₂²	1	2	yes	—
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#468×C₆₇	C₂²	1	2	yes	—
84	#468×C₆₇	C₂²	1	2	yes	—
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#468×C₆₇	C₂²	1	2	yes	complemented
87	#467×C₆₇	C₂²	1	2	yes	complemented
88	#466×C₆₇	C₂²	1	2	yes	—
89	#466×C₆₇	C₂²	1	2	yes	—
90	#466×C₆₇	C₂²	1	2	yes	complemented
91	#465×C₆₇	C₂²	1	2	yes	—
92	#465×C₆₇	C₂²	1	2	yes	—
93	#465×C₆₇	C₂²	1	2	yes	complemented
94	#465×C₆₇	C₂²	1	2	yes	complemented
95	#464×C₆₇	C₂²	1	2	yes	—
96	#464×C₆₇	C₂²	1	2	yes	—
97	#464×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#464×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#463×C₆₇	C₂²	1	2	yes	—
100	#463×C₆₇	C₂²	1	2	yes	—
101	#463×C₆₇	C₂²	1	2	yes	—
102	#463×C₆₇	C₂²	1	2	yes	—
103	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#461×C₆₇	C₂²	1	2	yes	—
107	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#460×C₆₇	C₂²	1	2	yes	—
109	#460×C₆₇	C₂²	1	2	yes	—
110	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#459×C₆₇	C₂²	1	2	yes	—
112	#459×C₆₇	C₂²	1	2	yes	—
113	#459×C₆₇	C₂²	1	2	yes	—
114	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#428×C₆₇	C₂²	1	1	yes	characteristic
116	#428×C₆₇	C₂²	1	1	yes	characteristic
117	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
118	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
119	#424×C₆₇	C₂²	1	1	yes	characteristic
120	#424×C₆₇	C₂²	1	1	yes	characteristic
121	#424×C₆₇	C₂²	1	2	yes	complemented
122	#424×C₆₇	C₂²	1	2	yes	complemented
123	#423×C₆₇	C₂²	1	1	yes	characteristic
124	#423×C₆₇	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
127	#417×C₆₇	C₂²	1	1	yes	characteristic
128	#417×C₆₇	C₂²	1	1	yes	characteristic
129	#417×C₆₇	C₂²	1	1	yes	characteristic
130	#417×C₆₇	C₂²	1	1	yes	characteristic
131	#416×C₆₇	C₂²	1	1	yes	characteristic
132	#416×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
134	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₇	—	2	1	no	—
142	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
143	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
144	#135×C₆₇	—	4	2	no	—
145	#135×C₆₇	—	4	2	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
153	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	#131×C₆₇	—	4	2	no	—
159	#131×C₆₇	—	4	2	no	—
160	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
167	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₇	—	2	1	no	—
169	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
171	#127×C₆₇	—	2	1	no	—
172	#127×C₆₇	C₂³	1	1	yes	characteristic
173	#127×C₆₇	C₂³	1	2	yes	—
174	#126×C₆₇	—	2	2	no	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	2	no	—
177	#126×C₆₇	—	2	2	no	—
178	#126×C₆₇	—	2	2	no	—
179	#126×C₆₇	—	2	2	no	—
180	#125×C₆₇	—	2	1	no	—
181	#125×C₆₇	—	2	2	no	—
182	#125×C₆₇	—	2	2	no	—
183	#125×C₆₇	—	2	1	no	—
184	#125×C₆₇	—	2	1	no	—
185	#125×C₆₇	C₂³	1	2	yes	—
186	#125×C₆₇	C₂³	1	2	yes	—
187	#125×C₆₇	C₂³	1	2	yes	—
188	#124×C₆₇	—	2	1	no	—
189	#124×C₆₇	—	2	2	no	—
190	#124×C₆₇	—	2	2	no	—
191	#124×C₆₇	C₂³	1	1	yes	characteristic
192	#124×C₆₇	C₂³	1	1	yes	characteristic
193	#124×C₆₇	C₂³	1	2	yes	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	2	no	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	1	no	—
203	C₂²⋊Q₈×C₆₇	—	2	1	no	—
204	C₂²⋊Q₈×C₆₇	—	2	1	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	1	no	—
214	#121×C₆₇	—	2	2	no	—
215	#121×C₆₇	—	2	2	no	—
216	#121×C₆₇	—	2	2	no	—
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	1	no	—
219	#121×C₆₇	—	2	1	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	—	2	2	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	C₂³	1	2	yes	—
226	#121×C₆₇	C₂³	1	2	yes	—
227	#121×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#121×C₆₇	C₂³	1	2	yes	—
230	#120×C₆₇	—	2	2	no	—
231	#120×C₆₇	—	2	2	no	—
232	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
233	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
235	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
236	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	2	no	—
241	C₄×D₄×C₆₇	—	2	2	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	—	2	2	no	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	1	no	—
247	C₄×D₄×C₆₇	—	2	2	no	—
248	C₄×D₄×C₆₇	—	2	1	no	—
249	C₄×D₄×C₆₇	—	2	1	no	—
250	C₄×D₄×C₆₇	D₄	1	2	yes	—
251	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
252	C₄×D₄×C₆₇	D₄	1	2	yes	—
253	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
254	C₄×D₄×C₆₇	C₂³	1	2	yes	—
255	C₄×D₄×C₆₇	C₂³	1	2	yes	—
256	C₄×D₄×C₆₇	C₂³	1	2	yes	—
257	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	C₂³	1	2	yes	—
259	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
260	#117×C₆₇	—	2	1	no	—
261	#117×C₆₇	—	2	1	no	—
262	#117×C₆₇	—	2	1	no	—
263	#117×C₆₇	—	2	2	no	—
264	#117×C₆₇	—	2	2	no	—
265	#117×C₆₇	—	2	2	no	—
266	#117×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	C₂³	1	1	yes	characteristic
268	#117×C₆₇	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
277	C₂×C₄²×C₆₇	—	2	1	no	—
278	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
280	#107×C₆₇	C₂³	1	2	yes	—
281	#107×C₆₇	C₂³	1	2	yes	—
282	#107×C₆₇	C₂³	1	2	yes	—
283	#107×C₆₇	C₂³	1	2	yes	—
284	#106×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	2	yes	—
286	#106×C₆₇	C₂³	1	2	yes	—
287	#106×C₆₇	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
289	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
290	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
291	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
293	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
294	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
295	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
296	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
297	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	1	yes	characteristic
301	#103×C₆₇	C₂³	1	1	yes	characteristic
302	#103×C₆₇	C₂³	1	1	yes	characteristic
303	#103×C₆₇	C₂³	1	1	yes	characteristic
304	#103×C₆₇	C₂³	1	2	yes	—
305	#103×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	#102×C₆₇	C₂³	1	2	yes	—
309	#102×C₆₇	C₂³	1	2	yes	—
310	#102×C₆₇	C₂³	1	2	yes	—
311	#102×C₆₇	C₂³	1	2	yes	—
312	#102×C₆₇	C₂³	1	1	yes	characteristic
313	#102×C₆₇	C₂³	1	1	yes	characteristic
314	#102×C₆₇	C₂³	1	2	yes	—
315	#102×C₆₇	C₂³	1	2	yes	—
316	#102×C₆₇	C₂³	1	1	yes	characteristic
317	#102×C₆₇	C₂³	1	1	yes	characteristic
318	C₂⁴×C₆₇	—	2	1	no	—
319	#41×C₆₇	—	2	2	no	—
320	#41×C₆₇	—	2	2	no	—
321	#41×C₆₇	—	2	2	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	—	8	4	no	—
328	C₂×Q₈×C₆₇	—	2	2	no	—
329	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	1	no	—
335	C₂×D₄×C₆₇	—	2	1	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	2	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	2	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
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	2	no	—
346	C₂×D₄×C₆₇	—	2	2	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
353	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₆₇	—	2	1	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	1	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	2	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	2	no	—
366	C₂²×C₄×C₆₇	—	8	2	no	—
367	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	Q₁₆×C₆₇	—	4	1	no	—
374	Q₁₆×C₆₇	—	4	1	no	—
375	SD₁₆×C₆₇	—	4	1	no	—
376	SD₁₆×C₆₇	—	4	1	no	—
377	SD₁₆×C₆₇	—	4	1	no	—
378	SD₁₆×C₆₇	—	4	1	no	—
379	SD₁₆×C₆₇	—	4	2	no	—
380	SD₁₆×C₆₇	—	4	2	no	—
381	D₈×C₆₇	—	4	1	no	—
382	D₈×C₆₇	—	4	1	no	—
383	D₈×C₆₇	—	4	2	no	—
384	D₈×C₆₇	—	4	2	no	—
385	M₁₆×C₆₇	—	2	2	no	—
386	M₁₆×C₆₇	—	2	2	no	—
387	M₁₆×C₆₇	—	4	2	no	—
388	M₁₆×C₆₇	—	4	2	no	—
389	C₂×C₈×C₆₇	—	2	2	no	—
390	C₂×C₈×C₆₇	—	2	2	no	—
391	C₂×C₈×C₆₇	—	4	2	no	—
392	C₂×C₈×C₆₇	—	4	2	no	—
393	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
398	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	—	2	1	no	—
408	C₄⋊C₄×C₆₇	—	2	1	no	—
409	C₄⋊C₄×C₆₇	—	2	1	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	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	1	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	1	no	—
444	C₂²⋊C₄×C₆₇	—	2	1	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
451	C₄²×C₆₇	—	2	1	no	—
452	C₄²×C₆₇	—	2	1	no	—
453	C₄²×C₆₇	—	2	1	no	—
454	C₄²×C₆₇	—	2	2	no	—
455	C₄²×C₆₇	—	2	2	no	—
456	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
461	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
462	C₄²×C₆₇	C₂⁴	1	2	yes	—
463	C₂³×C₆₇	—	2	1	no	—
464	C₂³×C₆₇	—	2	1	no	—
465	C₂³×C₆₇	—	2	2	no	—
466	C₂³×C₆₇	—	2	1	no	—
467	C₂³×C₆₇	—	4	2	no	—
468	C₂³×C₆₇	—	8	1	no	—
469	C₂³×C₆₇	—	8	1	no	—
470	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
471	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₆₇	—	2	2	no	—
473	Q₈×C₆₇	—	2	1	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	—	2	1	no	—
479	Q₈×C₆₇	—	8	2	no	—
480	D₄×C₆₇	—	2	4	no	—
481	D₄×C₆₇	—	2	2	no	—
482	D₄×C₆₇	—	2	1	no	—
483	D₄×C₆₇	—	2	1	no	—
484	D₄×C₆₇	—	2	2	no	—
485	D₄×C₆₇	—	2	1	no	—
486	D₄×C₆₇	—	2	2	no	—
487	D₄×C₆₇	—	2	1	no	—
488	D₄×C₆₇	—	2	1	no	—
489	D₄×C₆₇	—	2	1	no	—
490	D₄×C₆₇	—	4	2	no	—
491	D₄×C₆₇	—	4	2	no	—
492	D₄×C₆₇	—	4	2	no	—
493	D₄×C₆₇	—	4	2	no	—
494	D₄×C₆₇	—	8	1	no	—
495	D₄×C₆₇	—	8	2	no	—
496	D₄×C₆₇	—	8	1	no	—
497	D₄×C₆₇	—	8	2	no	—
498	D₄×C₆₇	—	8	2	no	—
499	D₄×C₆₇	—	8	2	no	—
500	D₄×C₆₇	—	8	2	no	—
501	D₄×C₆₇	—	8	2	no	—
502	D₄×C₆₇	—	8	2	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	2	no	—
511	C₂×C₄×C₆₇	—	2	2	no	—
512	C₂×C₄×C₆₇	—	2	2	no	—
513	C₂×C₄×C₆₇	—	4	1	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	4	no	—
518	C₂×C₄×C₆₇	—	4	2	no	—
519	C₂×C₄×C₆₇	—	4	2	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	4	2	no	—
522	C₂×C₄×C₆₇	—	8	2	no	—
523	C₂×C₄×C₆₇	—	8	1	no	—
524	C₂×C₄×C₆₇	—	8	2	no	—
525	C₂×C₄×C₆₇	—	8	2	no	—
526	C₂×C₄×C₆₇	—	8	1	no	—
527	C₂×C₄×C₆₇	—	8	1	no	—
528	C₂×C₄×C₆₇	—	8	1	no	—
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
539	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
540	C₈×C₆₇	—	2	1	no	—
541	C₈×C₆₇	—	2	1	no	—
542	C₈×C₆₇	—	2	1	no	—
543	C₈×C₆₇	—	2	1	no	—
544	C₈×C₆₇	—	2	2	no	—
545	C₈×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	2	1	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	2	no	—
550	C₂²×C₆₇	—	2	2	no	—
551	C₂²×C₆₇	—	4	1	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	4	2	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	1	no	—
559	C₂²×C₆₇	—	4	1	no	—
560	C₂²×C₆₇	—	4	1	no	—
561	C₂²×C₆₇	—	4	1	no	—
562	C₂²×C₆₇	—	4	2	no	—
563	C₂²×C₆₇	—	8	4	no	—
564	C₂²×C₆₇	#537	1	2	yes	—
565	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₆₇	—	2	1	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	2	no	—
569	C₄×C₆₇	—	2	1	no	—
570	C₄×C₆₇	—	2	1	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	4	2	no	—
574	C₄×C₆₇	—	4	1	no	—
575	C₄×C₆₇	—	4	2	no	—
576	C₄×C₆₇	—	4	1	no	—
577	C₄×C₆₇	—	4	2	no	—
578	C₄×C₆₇	—	4	1	no	—
579	C₄×C₆₇	—	4	1	no	—
580	C₄×C₆₇	—	4	1	no	—
581	C₄×C₆₇	#537	1	2	yes	—
582	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
584	#60933	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
585	C₂×C₆₇	—	2	2	no	—
586	C₂×C₆₇	—	4	2	no	—
587	C₂×C₆₇	—	8	1	no	—
588	C₂×C₆₇	—	8	1	no	—
589	C₂×C₆₇	—	8	1	no	—
590	C₂×C₆₇	—	8	2	no	—
591	C₂×C₆₇	C₂×#537	1	1	yes	characteristic
592	C₂×C₆₇	#3584	1	1	yes	characteristic
593	C₂×C₆₇	#3585	1	1	yes	characteristic
594	#3512	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#3460	C₂×C₆₇	1	1	yes	characteristic, complemented
596	#3260	C₂×C₆₇	1	2	yes	complemented
597	#3259	C₂×C₆₇	1	2	yes	complemented
598	#3258	C₂×C₆₇	1	2	yes	complemented
599	#3257	C₂×C₆₇	1	2	yes	complemented
600	#3256	C₂×C₆₇	1	2	yes	complemented
601	#3251	C₂×C₆₇	1	2	yes	complemented
602	#3250	C₂×C₆₇	1	2	yes	complemented
603	#3247	C₂×C₆₇	1	2	yes	complemented
604	#3084	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#3080	C₂×C₆₇	1	1	yes	characteristic, complemented
607	C₂×#478	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#3061	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#3060	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#2906	C₂×C₆₇	1	1	yes	characteristic, complemented
617	C₆₇	#60933	1	1	yes	characteristic, direct product factor, Sylow
618	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
619	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
620	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
621	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
622	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
623	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
624	#553	—	2	2	no	—
625	#553	—	2	2	no	—
626	#553	—	2	1	no	—
627	#553	—	2	1	no	—
628	#552	—	2	1	no	—
629	#552	—	2	1	no	—
630	#544	C₂²×C₆₇	1	1	yes	characteristic
631	#542	—	2	1	no	—
632	#542	C₂²×C₆₇	1	2	yes	—
633	#541	C₂²×C₆₇	1	2	yes	complemented
634	#540	—	2	1	no	—
635	#540	C₂²×C₆₇	1	2	yes	—
636	#540	C₂²×C₆₇	1	2	yes	complemented
637	#538	—	2	2	no	—
638	#537	C₂²×C₆₇	1	1	yes	characteristic
639	#537	C₂²×C₆₇	1	1	yes	characteristic
640	#537	C₂²×C₆₇	1	1	yes	characteristic
641	#535	C₂²×C₆₇	1	1	yes	characteristic
642	#535	C₂²×C₆₇	1	1	yes	characteristic
643	#532	—	2	1	no	—
644	#532	C₂²×C₆₇	1	1	yes	characteristic
645	#532	C₂²×C₆₇	1	2	yes	—
646	#529	—	2	1	no	—
647	#529	C₂²×C₆₇	1	2	yes	—
648	#529	C₂²×C₆₇	1	2	yes	complemented
649	#529	C₂²×C₆₇	1	2	yes	complemented
650	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
651	#525	—	2	2	no	—
652	#520	C₂²×C₆₇	1	1	yes	characteristic
653	#520	C₂²×C₆₇	1	1	yes	characteristic
654	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
655	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
656	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
657	#479	C₂²×C₆₇	1	2	yes	complemented
658	#479	C₂²×C₆₇	1	2	yes	complemented
659	#479	C₂²×C₆₇	1	2	yes	complemented
660	#479	C₂²×C₆₇	1	2	yes	complemented
661	#478	C₂²×C₆₇	1	2	yes	—
662	#478	C₂²×C₆₇	1	2	yes	—
663	#478	C₂²×C₆₇	1	2	yes	—
664	#478	C₂²×C₆₇	1	2	yes	—
665	#478	C₂²×C₆₇	1	2	yes	complemented
666	#478	C₂²×C₆₇	1	2	yes	complemented
667	#478	C₂²×C₆₇	1	2	yes	complemented
668	#478	C₂²×C₆₇	1	2	yes	complemented
669	#477	C₂²×C₆₇	1	2	yes	complemented
670	#476	C₂²×C₆₇	1	2	yes	complemented
671	#475	C₂²×C₆₇	1	2	yes	complemented
672	#474	C₂²×C₆₇	1	2	yes	complemented
673	#470	C₂²×C₆₇	1	2	yes	complemented
674	#469	C₂²×C₆₇	1	2	yes	—
675	#469	C₂²×C₆₇	1	2	yes	—
676	#469	C₂²×C₆₇	1	2	yes	complemented
677	#468	C₂²×C₆₇	1	2	yes	—
678	#468	C₂²×C₆₇	1	2	yes	—
679	#468	C₂²×C₆₇	1	2	yes	complemented
680	#468	C₂²×C₆₇	1	2	yes	complemented
681	#467	C₂²×C₆₇	1	2	yes	complemented
682	#466	C₂²×C₆₇	1	2	yes	—
683	#466	C₂²×C₆₇	1	2	yes	—
684	#466	C₂²×C₆₇	1	2	yes	complemented
685	#465	C₂²×C₆₇	1	2	yes	—
686	#465	C₂²×C₆₇	1	2	yes	—
687	#465	C₂²×C₆₇	1	2	yes	complemented
688	#465	C₂²×C₆₇	1	2	yes	complemented
689	#464	C₂²×C₆₇	1	2	yes	—
690	#464	C₂²×C₆₇	1	2	yes	—
691	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#463	C₂²×C₆₇	1	2	yes	—
694	#463	C₂²×C₆₇	1	2	yes	—
695	#463	C₂²×C₆₇	1	2	yes	—
696	#463	C₂²×C₆₇	1	2	yes	—
697	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
700	#461	C₂²×C₆₇	1	2	yes	—
701	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#460	C₂²×C₆₇	1	2	yes	—
703	#460	C₂²×C₆₇	1	2	yes	—
704	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
705	#459	C₂²×C₆₇	1	2	yes	—
706	#459	C₂²×C₆₇	1	2	yes	—
707	#459	C₂²×C₆₇	1	2	yes	—
708	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#428	C₂²×C₆₇	1	1	yes	characteristic
710	#428	C₂²×C₆₇	1	1	yes	characteristic
711	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
712	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
713	#424	C₂²×C₆₇	1	1	yes	characteristic
714	#424	C₂²×C₆₇	1	1	yes	characteristic
715	#424	C₂²×C₆₇	1	2	yes	complemented
716	#424	C₂²×C₆₇	1	2	yes	complemented
717	#423	C₂²×C₆₇	1	1	yes	characteristic
718	#423	C₂²×C₆₇	1	2	yes	complemented
719	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
720	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
721	#417	C₂²×C₆₇	1	1	yes	characteristic
722	#417	C₂²×C₆₇	1	1	yes	characteristic
723	#417	C₂²×C₆₇	1	1	yes	characteristic
724	#417	C₂²×C₆₇	1	1	yes	characteristic
725	#416	C₂²×C₆₇	1	1	yes	characteristic
726	#416	C₂²×C₆₇	1	1	yes	characteristic
727	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
728	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
729	C₂×#41	—	2	2	no	—
730	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
734	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
735	C₂³×C₄	—	2	1	no	—
736	AGL(1,ℤ/8)	—	4	2	no	—
737	AGL(1,ℤ/8)	—	4	2	no	—
738	#135	—	4	2	no	—
739	#135	—	4	2	no	—
740	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
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×D₈	C₂³×C₆₇	1	2	yes	—
751	C₂×D₈	C₂³×C₆₇	1	2	yes	—
752	#131	—	4	2	no	—
753	#131	—	4	2	no	—
754	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
757	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
758	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
759	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
760	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
761	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
762	C₄⋊Q₈	—	2	1	no	—
763	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
765	#127	—	2	1	no	—
766	#127	C₂³×C₆₇	1	2	yes	—
767	#127	C₂³×C₆₇	1	1	yes	characteristic
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	—	2	2	no	—
774	#125	—	2	1	no	—
775	#125	—	2	2	no	—
776	#125	—	2	2	no	—
777	#125	—	2	1	no	—
778	#125	—	2	1	no	—
779	#125	C₂³×C₆₇	1	2	yes	—
780	#125	C₂³×C₆₇	1	2	yes	—
781	#125	C₂³×C₆₇	1	2	yes	—
782	#124	—	2	1	no	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	C₂³×C₆₇	1	2	yes	—
786	#124	C₂³×C₆₇	1	1	yes	characteristic
787	#124	C₂³×C₆₇	1	1	yes	characteristic
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	C₂³×C₆₇	1	2	yes	—
820	#121	C₂³×C₆₇	1	2	yes	—
821	#121	C₂³×C₆₇	1	2	yes	—
822	#121	C₂³×C₆₇	1	2	yes	—
823	#121	C₂³×C₆₇	1	2	yes	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
827	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
828	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
829	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
830	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
831	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	D₄×C₆₇	1	2	yes	—
845	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
846	C₄×D₄	D₄×C₆₇	1	2	yes	—
847	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₆₇	1	2	yes	—
849	C₄×D₄	C₂³×C₆₇	1	2	yes	—
850	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₆₇	1	2	yes	—
853	C₄×D₄	C₂³×C₆₇	1	2	yes	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	—	2	2	no	—
858	#117	—	2	2	no	—
859	#117	—	2	2	no	—
860	#117	C₂³×C₆₇	1	1	yes	characteristic
861	#117	C₂³×C₆₇	1	1	yes	characteristic
862	#117	C₂³×C₆₇	1	2	yes	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	—	2	1	no	—
866	C₂×C₄⋊C₄	—	2	1	no	—
867	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₂×C₂²⋊C₄	—	2	1	no	—
871	C₂×C₄²	—	2	1	no	—
872	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
873	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
874	#107	C₂³×C₆₇	1	2	yes	—
875	#107	C₂³×C₆₇	1	2	yes	—
876	#107	C₂³×C₆₇	1	2	yes	—
877	#107	C₂³×C₆₇	1	2	yes	—
878	#106	C₂³×C₆₇	1	2	yes	—
879	#106	C₂³×C₆₇	1	2	yes	—
880	#106	C₂³×C₆₇	1	2	yes	—
881	#106	C₂³×C₆₇	1	2	yes	—
882	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
887	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
888	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
889	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
890	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
891	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
892	#103	C₂³×C₆₇	1	1	yes	characteristic
893	#103	C₂³×C₆₇	1	1	yes	characteristic
894	#103	C₂³×C₆₇	1	1	yes	characteristic
895	#103	C₂³×C₆₇	1	1	yes	characteristic
896	#103	C₂³×C₆₇	1	2	yes	—
897	#103	C₂³×C₆₇	1	2	yes	—
898	#103	C₂³×C₆₇	1	2	yes	—
899	#103	C₂³×C₆₇	1	2	yes	—
900	#102	C₂³×C₆₇	1	2	yes	—
901	#102	C₂³×C₆₇	1	2	yes	—
902	#102	C₂³×C₆₇	1	2	yes	—
903	#102	C₂³×C₆₇	1	2	yes	—
904	#102	C₂³×C₆₇	1	1	yes	characteristic
905	#102	C₂³×C₆₇	1	1	yes	characteristic
906	#102	C₂³×C₆₇	1	1	yes	characteristic
907	#102	C₂³×C₆₇	1	1	yes	characteristic
908	#102	C₂³×C₆₇	1	2	yes	—
909	#102	C₂³×C₆₇	1	2	yes	—
910	#102	C₂³×C₆₇	1	2	yes	—
911	#102	C₂³×C₆₇	1	2	yes	—
912	C₂⁴	—	2	1	no	—
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	—	2	2	no	—
921	#41	—	8	4	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
924	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
947	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
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	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	8	2	no	—
961	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
962	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
964	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
966	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
967	Q₁₆	—	4	1	no	—
968	Q₁₆	—	4	1	no	—
969	SD₁₆	—	4	1	no	—
970	SD₁₆	—	4	1	no	—
971	SD₁₆	—	4	1	no	—
972	SD₁₆	—	4	1	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	D₈	—	4	1	no	—
976	D₈	—	4	1	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	2	no	—
979	M₁₆	—	2	2	no	—
980	M₁₆	—	2	2	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	—	2	2	no	—
985	C₂×C₈	—	4	2	no	—
986	C₂×C₈	—	4	2	no	—
987	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
991	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
992	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	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	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1013	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1051	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1052	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1053	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1054	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₆₇	1	2	yes	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	4	2	no	—
1062	C₂³	—	8	1	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1065	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	8	2	no	—
1074	D₄	—	2	4	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	1	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	—	8	1	no	—
1122	C₂×C₄	—	8	1	no	—
1123	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1131	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1132	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1133	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	2	2	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	8	4	no	—
1158	C₂²	#537×C₆₇	1	2	yes	—
1159	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	1	no	—
1175	C₄	#537×C₆₇	1	2	yes	—
1176	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1177	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1178	C₂	—	2	2	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	1	no	—
1184	C₂	C₂×#537×C₆₇	1	1	yes	characteristic
1185	C₂	C₆₇×#3584	1	1	yes	characteristic
1186	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 ◁ 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. C₆₇×#3460	C₂	semidirect
3. C₆₇×#3260	C₂	semidirect
4. C₆₇×#3259	C₂	semidirect
5. C₆₇×#3258	C₂	semidirect
6. C₆₇×#3257	C₂	semidirect
7. C₆₇×#3256	C₂	semidirect
8. C₆₇×#3251	C₂	semidirect
9. C₆₇×#3250	C₂	semidirect
10. C₆₇×#3247	C₂	semidirect
11. C₆₇×#3084	C₂	semidirect
12. C₆₇×#3083	C₂	semidirect
13. C₆₇×#3080	C₂	semidirect
14. C₂×#478×C₆₇	C₂	semidirect
15. C₆₇×#3062	C₂	semidirect
16. C₆₇×#3062	C₂	semidirect
17. C₆₇×#3061	C₂	semidirect
18. C₆₇×#3060	C₂	semidirect
19. C₆₇×#3045	C₂	semidirect
20. C₆₇×#3045	C₂	semidirect
21. C₆₇×#3036	C₂	semidirect
22. C₆₇×#3035	C₂	semidirect
23. C₆₇×#2906	C₂	semidirect
39. #541×C₆₇	C₂²	semidirect
42. #540×C₆₇	C₂²	semidirect
54. #529×C₆₇	C₂²	semidirect
55. #529×C₆₇	C₂²	semidirect
63. #479×C₆₇	C₂²	semidirect
64. #479×C₆₇	C₂²	semidirect
65. #479×C₆₇	C₂²	semidirect
66. #479×C₆₇	C₂²	semidirect
71. #478×C₆₇	C₂²	semidirect
72. #478×C₆₇	C₂²	semidirect
73. #478×C₆₇	C₂²	semidirect
74. #478×C₆₇	C₂²	semidirect
75. #477×C₆₇	C₂²	semidirect
76. #476×C₆₇	C₂²	semidirect
77. #475×C₆₇	C₂²	semidirect
78. #474×C₆₇	C₂²	semidirect
79. #470×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #468×C₆₇	C₂²	semidirect
87. #467×C₆₇	C₂²	semidirect
90. #466×C₆₇	C₂²	semidirect
93. #465×C₆₇	C₂²	semidirect
94. #465×C₆₇	C₂²	semidirect
97. #464×C₆₇	C₂²	semidirect
98. #464×C₆₇	C₂²	semidirect
103. #463×C₆₇	C₂²	semidirect
104. #463×C₆₇	C₂²	semidirect
105. #462×C₆₇	C₂²	semidirect
107. #461×C₆₇	C₂²	semidirect
110. #460×C₆₇	C₂²	semidirect
114. #459×C₆₇	C₂²	semidirect
121. #424×C₆₇	C₂²	semidirect
122. #424×C₆₇	C₂²	semidirect
124. #423×C₆₇	C₂²	semidirect
126. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
584. #60933	C₆₇	direct (N × H)
594. #3512	C₂×C₆₇	semidirect
595. #3460	C₂×C₆₇	semidirect
596. #3260	C₂×C₆₇	semidirect
597. #3259	C₂×C₆₇	semidirect
598. #3258	C₂×C₆₇	semidirect
599. #3257	C₂×C₆₇	semidirect
600. #3256	C₂×C₆₇	semidirect
601. #3251	C₂×C₆₇	semidirect
602. #3250	C₂×C₆₇	semidirect
603. #3247	C₂×C₆₇	semidirect
604. #3084	C₂×C₆₇	semidirect
605. #3083	C₂×C₆₇	semidirect
606. #3080	C₂×C₆₇	semidirect
607. C₂×#478	C₂×C₆₇	semidirect
608. #3062	C₂×C₆₇	semidirect
609. #3062	C₂×C₆₇	semidirect
610. #3061	C₂×C₆₇	semidirect
611. #3060	C₂×C₆₇	semidirect
612. #3045	C₂×C₆₇	semidirect
613. #3045	C₂×C₆₇	semidirect
614. #3036	C₂×C₆₇	semidirect
615. #3035	C₂×C₆₇	semidirect
616. #2906	C₂×C₆₇	semidirect
617. C₆₇	#60933	direct (N × H)
633. #541	C₂²×C₆₇	semidirect
636. #540	C₂²×C₆₇	semidirect
648. #529	C₂²×C₆₇	semidirect
649. #529	C₂²×C₆₇	semidirect
657. #479	C₂²×C₆₇	semidirect
658. #479	C₂²×C₆₇	semidirect
659. #479	C₂²×C₆₇	semidirect
660. #479	C₂²×C₆₇	semidirect
665. #478	C₂²×C₆₇	semidirect
666. #478	C₂²×C₆₇	semidirect
667. #478	C₂²×C₆₇	semidirect
668. #478	C₂²×C₆₇	semidirect
669. #477	C₂²×C₆₇	semidirect
670. #476	C₂²×C₆₇	semidirect
671. #475	C₂²×C₆₇	semidirect
672. #474	C₂²×C₆₇	semidirect
673. #470	C₂²×C₆₇	semidirect
676. #469	C₂²×C₆₇	semidirect
679. #468	C₂²×C₆₇	semidirect
680. #468	C₂²×C₆₇	semidirect
681. #467	C₂²×C₆₇	semidirect
684. #466	C₂²×C₆₇	semidirect
687. #465	C₂²×C₆₇	semidirect
688. #465	C₂²×C₆₇	semidirect
691. #464	C₂²×C₆₇	semidirect
692. #464	C₂²×C₆₇	semidirect
697. #463	C₂²×C₆₇	semidirect
698. #463	C₂²×C₆₇	semidirect
699. #462	C₂²×C₆₇	semidirect
701. #461	C₂²×C₆₇	semidirect
704. #460	C₂²×C₆₇	semidirect
708. #459	C₂²×C₆₇	semidirect
715. #424	C₂²×C₆₇	semidirect
716. #424	C₂²×C₆₇	semidirect
718. #423	C₂²×C₆₇	semidirect
720. C₂×C₄⋊C₈	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×#3512	2
C₆₇×#3460	2
C₆₇×#3260	2
C₆₇×#3259	2
C₆₇×#3258	2
C₆₇×#3257	2
C₆₇×#3256	2
C₆₇×#3251	2
C₆₇×#3250	2
C₆₇×#3247	2
C₆₇×#3084	2
C₆₇×#3083	2
C₆₇×#3080	2
C₂×#478×C₆₇	2
C₆₇×#3062	2
C₆₇×#3061	2
C₆₇×#3060	2
C₆₇×#3045	2
C₆₇×#3036	2
C₆₇×#3035	2
C₆₇×#2906	2
#60933	67

Subgroups — C67×#60933 #30740184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60933 #30740184