Subgroups — C₆₇×#60015 #30739266

Order 17152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2758	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2738	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2725	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2702	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2590	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2587	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2556	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2533	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2530	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2529	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2526	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2523	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2516	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2515	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2509	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2481	C₂	1	1	yes	maximal, characteristic
20	C₆₇×#2470	C₂	1	1	yes	maximal, characteristic
21	C₆₇×#2470	C₂	1	1	yes	maximal, characteristic
22	C₆₇×#2469	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2374	C₂	1	1	yes	maximal, characteristic
24	C₆₇×#2373	C₂	1	1	yes	maximal, characteristic, complemented
25	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
26	C₆₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
27	C₆₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
28	C₆₇×#2344	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
30	C₆₇×#2298	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	#400×C₆₇	C₂²	1	1	yes	characteristic
42	#400×C₆₇	C₂²	1	1	yes	characteristic
43	#400×C₆₇	C₂²	1	1	yes	characteristic
44	#400×C₆₇	C₂²	1	1	yes	characteristic
45	#400×C₆₇	C₂²	1	1	yes	characteristic
46	#400×C₆₇	C₂²	1	1	yes	characteristic
47	#400×C₆₇	C₂²	1	1	yes	characteristic
48	#400×C₆₇	C₂²	1	1	yes	characteristic
49	#400×C₆₇	C₂²	1	1	yes	characteristic
50	#400×C₆₇	C₂²	1	1	yes	characteristic
51	#400×C₆₇	C₂²	1	1	yes	characteristic
52	#400×C₆₇	C₂²	1	1	yes	characteristic
53	#399×C₆₇	C₂²	1	1	yes	characteristic
54	#398×C₆₇	C₂²	1	1	yes	characteristic
55	#398×C₆₇	C₂²	1	1	yes	characteristic
56	#398×C₆₇	C₂²	1	1	yes	characteristic
57	#398×C₆₇	C₂²	1	1	yes	characteristic
58	#398×C₆₇	C₂²	1	1	yes	characteristic
59	#397×C₆₇	C₂²	1	1	yes	characteristic
60	#397×C₆₇	C₂²	1	1	yes	characteristic
61	#397×C₆₇	C₂²	1	1	yes	characteristic
62	#397×C₆₇	C₂²	1	1	yes	characteristic
63	#397×C₆₇	C₂²	1	1	yes	characteristic
64	#396×C₆₇	C₂²	1	1	yes	characteristic
65	#396×C₆₇	C₂²	1	1	yes	characteristic
66	#396×C₆₇	C₂²	1	1	yes	characteristic
67	#396×C₆₇	C₂²	1	1	yes	characteristic
68	#396×C₆₇	C₂²	1	1	yes	characteristic
69	#395×C₆₇	C₂²	1	1	yes	characteristic
70	#394×C₆₇	C₂²	1	1	yes	characteristic
71	#394×C₆₇	C₂²	1	1	yes	characteristic
72	#393×C₆₇	C₂²	1	1	yes	characteristic
73	#391×C₆₇	C₂²	1	1	yes	characteristic
74	#391×C₆₇	C₂²	1	1	yes	characteristic
75	#391×C₆₇	C₂²	1	1	yes	characteristic
76	#390×C₆₇	C₂²	1	1	yes	characteristic
77	#389×C₆₇	C₂²	1	1	yes	characteristic
78	#389×C₆₇	C₂²	1	1	yes	characteristic
79	#389×C₆₇	C₂²	1	1	yes	characteristic
80	#389×C₆₇	C₂²	1	1	yes	characteristic
81	#389×C₆₇	C₂²	1	1	yes	characteristic
82	#389×C₆₇	C₂²	1	1	yes	characteristic
83	#389×C₆₇	C₂²	1	1	yes	characteristic
84	#389×C₆₇	C₂²	1	1	yes	characteristic
85	#389×C₆₇	C₂²	1	1	yes	characteristic
86	#389×C₆₇	C₂²	1	1	yes	characteristic
87	#389×C₆₇	C₂²	1	1	yes	characteristic
88	#389×C₆₇	C₂²	1	1	yes	characteristic
89	#389×C₆₇	C₂²	1	1	yes	characteristic
90	#389×C₆₇	C₂²	1	1	yes	characteristic
91	#389×C₆₇	C₂²	1	1	yes	characteristic
92	#389×C₆₇	C₂²	1	1	yes	characteristic
93	#389×C₆₇	C₂²	1	1	yes	characteristic
94	#388×C₆₇	C₂²	1	1	yes	characteristic
95	#388×C₆₇	C₂²	1	1	yes	characteristic
96	#388×C₆₇	C₂²	1	1	yes	characteristic
97	#388×C₆₇	C₂²	1	1	yes	characteristic
98	#388×C₆₇	C₂²	1	1	yes	characteristic
99	#388×C₆₇	C₂²	1	1	yes	characteristic
100	#388×C₆₇	C₂²	1	1	yes	characteristic
101	#388×C₆₇	C₂²	1	1	yes	characteristic
102	#388×C₆₇	C₂²	1	1	yes	characteristic
103	#388×C₆₇	C₂²	1	1	yes	characteristic
104	#388×C₆₇	C₂²	1	1	yes	characteristic
105	#388×C₆₇	C₂²	1	1	yes	characteristic
106	#388×C₆₇	C₂²	1	1	yes	characteristic
107	#388×C₆₇	C₂²	1	1	yes	characteristic
108	#388×C₆₇	C₂²	1	1	yes	characteristic
109	#388×C₆₇	C₂²	1	1	yes	characteristic
110	#388×C₆₇	C₂²	1	1	yes	characteristic
111	#388×C₆₇	C₂²	1	1	yes	characteristic
112	#388×C₆₇	C₂²	1	1	yes	characteristic
113	#388×C₆₇	C₂²	1	1	yes	characteristic
114	#387×C₆₇	C₂²	1	1	yes	characteristic
115	#387×C₆₇	C₂²	1	1	yes	characteristic
116	#387×C₆₇	C₂²	1	1	yes	characteristic
117	#387×C₆₇	C₂²	1	1	yes	characteristic
118	#387×C₆₇	C₂²	1	1	yes	characteristic
119	#387×C₆₇	C₂²	1	1	yes	characteristic
120	#387×C₆₇	C₂²	1	1	yes	characteristic
121	#387×C₆₇	C₂²	1	1	yes	characteristic
122	#387×C₆₇	C₂²	1	1	yes	characteristic
123	#387×C₆₇	C₂²	1	1	yes	characteristic
124	#387×C₆₇	C₂²	1	1	yes	characteristic
125	#387×C₆₇	C₂²	1	1	yes	characteristic
126	#387×C₆₇	C₂²	1	1	yes	characteristic
127	#387×C₆₇	C₂²	1	1	yes	characteristic
128	#387×C₆₇	C₂²	1	1	yes	characteristic
129	#387×C₆₇	C₂²	1	1	yes	characteristic
130	#387×C₆₇	C₂²	1	1	yes	characteristic
131	#387×C₆₇	C₂²	1	1	yes	characteristic
132	#387×C₆₇	C₂²	1	1	yes	characteristic
133	#387×C₆₇	C₂²	1	1	yes	characteristic
134	#387×C₆₇	C₂²	1	1	yes	characteristic
135	#387×C₆₇	C₂²	1	1	yes	characteristic
136	#387×C₆₇	C₂²	1	1	yes	characteristic
137	#387×C₆₇	C₂²	1	1	yes	characteristic
138	#387×C₆₇	C₂²	1	1	yes	characteristic
139	#387×C₆₇	C₂²	1	1	yes	characteristic
140	#387×C₆₇	C₂²	1	1	yes	characteristic
141	#387×C₆₇	C₂²	1	1	yes	characteristic
142	#387×C₆₇	C₂²	1	1	yes	characteristic
143	#386×C₆₇	C₂²	1	1	yes	characteristic
144	#386×C₆₇	C₂²	1	1	yes	characteristic
145	#386×C₆₇	C₂²	1	1	yes	characteristic
146	#385×C₆₇	C₂²	1	1	yes	characteristic
147	#385×C₆₇	C₂²	1	1	yes	characteristic
148	#385×C₆₇	C₂²	1	1	yes	characteristic
149	#385×C₆₇	C₂²	1	1	yes	characteristic
150	#385×C₆₇	C₂²	1	1	yes	characteristic
151	#383×C₆₇	C₂²	1	1	yes	characteristic
152	#383×C₆₇	C₂²	1	1	yes	characteristic
153	#383×C₆₇	C₂²	1	1	yes	characteristic
154	#383×C₆₇	C₂²	1	1	yes	characteristic
155	#382×C₆₇	C₂²	1	1	yes	characteristic
156	#381×C₆₇	C₂²	1	1	yes	characteristic
157	#381×C₆₇	C₂²	1	1	yes	characteristic
158	#380×C₆₇	C₂²	1	1	yes	characteristic
159	#380×C₆₇	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
171	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
172	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
173	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
183	#376×C₆₇	C₂²	1	1	yes	characteristic
184	#376×C₆₇	C₂²	1	1	yes	characteristic
185	#376×C₆₇	C₂²	1	1	yes	characteristic
186	C₄³×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
188	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
193	#126×C₆₇	—	2	4	no	—
194	#126×C₆₇	—	2	4	no	—
195	#125×C₆₇	—	2	4	no	—
196	#123×C₆₇	—	2	4	no	—
197	C₂²⋊Q₈×C₆₇	—	2	4	no	—
198	C₄×Q₈×C₆₇	—	2	4	no	—
199	#117×C₆₇	—	2	4	no	—
200	#117×C₆₇	—	2	4	no	—
201	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
278	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
281	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
288	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
291	#95×C₆₇	C₂³	1	1	yes	characteristic
292	#95×C₆₇	C₂³	1	1	yes	characteristic
293	#95×C₆₇	C₂³	1	1	yes	characteristic
294	#95×C₆₇	C₂³	1	1	yes	characteristic
295	#95×C₆₇	C₂³	1	1	yes	characteristic
296	#95×C₆₇	C₂³	1	1	yes	characteristic
297	#95×C₆₇	C₂³	1	1	yes	characteristic
298	#95×C₆₇	C₂³	1	1	yes	characteristic
299	#95×C₆₇	C₂³	1	1	yes	characteristic
300	#95×C₆₇	C₂³	1	1	yes	characteristic
301	#95×C₆₇	C₂³	1	1	yes	characteristic
302	#95×C₆₇	C₂³	1	1	yes	characteristic
303	#95×C₆₇	C₂³	1	1	yes	characteristic
304	#95×C₆₇	C₂³	1	1	yes	characteristic
305	#95×C₆₇	C₂³	1	1	yes	characteristic
306	#95×C₆₇	C₂³	1	1	yes	characteristic
307	#95×C₆₇	C₂³	1	1	yes	characteristic
308	#95×C₆₇	C₂³	1	1	yes	characteristic
309	#95×C₆₇	C₂³	1	1	yes	characteristic
310	#95×C₆₇	C₂³	1	1	yes	characteristic
311	#95×C₆₇	C₂³	1	1	yes	characteristic
312	#95×C₆₇	C₂³	1	1	yes	characteristic
313	#95×C₆₇	C₂³	1	1	yes	characteristic
314	#95×C₆₇	C₂³	1	1	yes	characteristic
315	#95×C₆₇	C₂³	1	1	yes	characteristic
316	#95×C₆₇	C₂³	1	1	yes	characteristic
317	#95×C₆₇	C₂³	1	1	yes	characteristic
318	#95×C₆₇	C₂³	1	1	yes	characteristic
319	#95×C₆₇	C₂³	1	1	yes	characteristic
320	#95×C₆₇	C₂³	1	1	yes	characteristic
321	#95×C₆₇	C₂³	1	1	yes	characteristic
322	#95×C₆₇	C₂³	1	1	yes	characteristic
323	#95×C₆₇	C₂³	1	1	yes	characteristic
324	#95×C₆₇	C₂³	1	1	yes	characteristic
325	#95×C₆₇	C₂³	1	1	yes	characteristic
326	#95×C₆₇	C₂³	1	1	yes	characteristic
327	#95×C₆₇	C₂³	1	1	yes	characteristic
328	#95×C₆₇	C₂³	1	1	yes	characteristic
329	#95×C₆₇	C₂³	1	1	yes	characteristic
330	#95×C₆₇	C₂³	1	1	yes	characteristic
331	#95×C₆₇	C₂³	1	1	yes	characteristic
332	#95×C₆₇	C₂³	1	1	yes	characteristic
333	#95×C₆₇	C₂³	1	1	yes	characteristic
334	#95×C₆₇	C₂³	1	1	yes	characteristic
335	#95×C₆₇	C₂³	1	1	yes	characteristic
336	#95×C₆₇	C₂³	1	1	yes	characteristic
337	#95×C₆₇	C₂³	1	1	yes	characteristic
338	#95×C₆₇	C₂³	1	1	yes	characteristic
339	#95×C₆₇	C₂³	1	1	yes	characteristic
340	#95×C₆₇	C₂³	1	1	yes	characteristic
341	#95×C₆₇	C₂³	1	1	yes	characteristic
342	#95×C₆₇	C₂³	1	1	yes	characteristic
343	#95×C₆₇	C₂³	1	1	yes	characteristic
344	#95×C₆₇	C₂³	1	1	yes	characteristic
345	#95×C₆₇	C₂³	1	1	yes	characteristic
346	#95×C₆₇	C₂³	1	1	yes	characteristic
347	#95×C₆₇	C₂³	1	1	yes	characteristic
348	#95×C₆₇	C₂³	1	1	yes	characteristic
349	#95×C₆₇	C₂³	1	1	yes	characteristic
350	#95×C₆₇	C₂³	1	1	yes	characteristic
351	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₆₇	—	2	2	no	—
354	C₂×Q₈×C₆₇	—	2	2	no	—
355	C₂×Q₈×C₆₇	—	4	1	no	—
356	C₂×D₄×C₆₇	—	2	2	no	—
357	C₂×D₄×C₆₇	—	4	1	no	—
358	C₂×D₄×C₆₇	—	4	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	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	2	no	—
366	C₂²×C₄×C₆₇	—	4	1	no	—
367	C₂²×C₄×C₆₇	—	4	1	no	—
368	C₂²×C₄×C₆₇	—	4	1	no	—
369	C₂²×C₄×C₆₇	—	4	1	no	—
370	C₂²×C₄×C₆₇	—	4	1	no	—
371	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	—	2	2	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	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	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	4	1	no	—
425	C₄⋊C₄×C₆₇	—	4	1	no	—
426	C₄⋊C₄×C₆₇	—	4	1	no	—
427	C₄⋊C₄×C₆₇	—	4	1	no	—
428	C₄⋊C₄×C₆₇	—	4	1	no	—
429	C₄⋊C₄×C₆₇	—	4	1	no	—
430	C₄⋊C₄×C₆₇	—	4	1	no	—
431	C₄⋊C₄×C₆₇	—	4	1	no	—
432	C₄⋊C₄×C₆₇	—	4	1	no	—
433	C₄⋊C₄×C₆₇	—	4	1	no	—
434	C₄⋊C₄×C₆₇	—	4	1	no	—
435	C₄⋊C₄×C₆₇	—	4	1	no	—
436	C₄⋊C₄×C₆₇	—	4	1	no	—
437	C₄⋊C₄×C₆₇	—	4	1	no	—
438	C₄⋊C₄×C₆₇	—	4	1	no	—
439	C₄⋊C₄×C₆₇	—	4	1	no	—
440	C₄⋊C₄×C₆₇	#41	1	4	yes	—
441	C₄⋊C₄×C₆₇	#41	1	4	yes	—
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	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	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	2	no	—
456	C₂²⋊C₄×C₆₇	—	4	1	no	—
457	C₂²⋊C₄×C₆₇	—	4	1	no	—
458	C₂²⋊C₄×C₆₇	—	4	1	no	—
459	C₂²⋊C₄×C₆₇	—	4	1	no	—
460	C₂²⋊C₄×C₆₇	—	4	1	no	—
461	C₂²⋊C₄×C₆₇	—	4	1	no	—
462	C₂²⋊C₄×C₆₇	—	4	1	no	—
463	C₂²⋊C₄×C₆₇	—	4	1	no	—
464	C₂²⋊C₄×C₆₇	—	4	1	no	—
465	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
466	C₄²×C₆₇	—	2	2	no	—
467	C₄²×C₆₇	—	2	2	no	—
468	C₄²×C₆₇	—	2	2	no	—
469	C₄²×C₆₇	—	2	2	no	—
470	C₄²×C₆₇	—	2	2	no	—
471	C₄²×C₆₇	—	2	2	no	—
472	C₄²×C₆₇	—	2	2	no	—
473	C₄²×C₆₇	—	2	2	no	—
474	C₄²×C₆₇	—	2	2	no	—
475	C₄²×C₆₇	—	2	2	no	—
476	C₄²×C₆₇	—	2	2	no	—
477	C₄²×C₆₇	—	4	1	no	—
478	C₄²×C₆₇	—	4	1	no	—
479	C₄²×C₆₇	—	4	1	no	—
480	C₄²×C₆₇	—	4	1	no	—
481	C₄²×C₆₇	—	4	1	no	—
482	C₄²×C₆₇	—	4	1	no	—
483	C₄²×C₆₇	—	4	1	no	—
484	C₄²×C₆₇	—	4	1	no	—
485	C₄²×C₆₇	—	4	1	no	—
486	C₄²×C₆₇	—	4	1	no	—
487	C₄²×C₆₇	—	4	1	no	—
488	C₄²×C₆₇	—	4	1	no	—
489	C₂³×C₆₇	—	2	1	no	—
490	C₂³×C₆₇	—	2	1	no	—
491	C₂³×C₆₇	—	2	1	no	—
492	C₂³×C₆₇	—	2	1	no	—
493	C₂³×C₆₇	—	2	1	no	—
494	C₂³×C₆₇	—	2	1	no	—
495	C₂³×C₆₇	—	2	1	no	—
496	C₂³×C₆₇	—	2	1	no	—
497	C₂³×C₆₇	—	2	1	no	—
498	C₂³×C₆₇	—	2	1	no	—
499	C₂³×C₆₇	—	2	1	no	—
500	C₂³×C₆₇	—	2	1	no	—
501	C₂³×C₆₇	—	2	1	no	—
502	C₂³×C₆₇	C₂×#41	1	2	yes	—
503	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
504	Q₈×C₆₇	—	4	4	no	—
505	D₄×C₆₇	—	8	2	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	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	1	no	—
516	C₂×C₄×C₆₇	—	2	1	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	2	1	no	—
519	C₂×C₄×C₆₇	—	2	1	no	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	1	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	1	no	—
545	C₂×C₄×C₆₇	—	2	1	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	2	1	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	2	1	no	—
567	C₂×C₄×C₆₇	—	2	1	no	—
568	C₂×C₄×C₆₇	—	2	1	no	—
569	C₂×C₄×C₆₇	—	2	1	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	1	no	—
574	C₂×C₄×C₆₇	—	2	1	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	2	1	no	—
577	C₂×C₄×C₆₇	—	2	1	no	—
578	C₂×C₄×C₆₇	—	2	1	no	—
579	C₂×C₄×C₆₇	—	2	1	no	—
580	C₂×C₄×C₆₇	—	2	1	no	—
581	C₂×C₄×C₆₇	—	2	1	no	—
582	C₂×C₄×C₆₇	—	2	1	no	—
583	C₂×C₄×C₆₇	—	2	1	no	—
584	C₂×C₄×C₆₇	—	4	4	no	—
585	C₂×C₄×C₆₇	—	4	4	no	—
586	C₂×C₄×C₆₇	—	4	4	no	—
587	C₂×C₄×C₆₇	—	8	2	no	—
588	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
589	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
590	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
591	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
592	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
593	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
594	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
595	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
596	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
597	C₂²×C₆₇	—	2	2	no	—
598	C₂²×C₆₇	—	2	2	no	—
599	C₂²×C₆₇	—	2	2	no	—
600	C₂²×C₆₇	—	4	1	no	—
601	C₂²×C₆₇	—	4	1	no	—
602	C₂²×C₆₇	—	4	1	no	—
603	C₂²×C₆₇	—	4	1	no	—
604	C₂²×C₆₇	—	4	1	no	—
605	C₂²×C₆₇	—	4	1	no	—
606	C₂²×C₆₇	—	4	1	no	—
607	C₂²×C₆₇	—	4	1	no	—
608	C₂²×C₆₇	—	4	1	no	—
609	C₂²×C₆₇	—	4	1	no	—
610	C₂²×C₆₇	—	4	1	no	—
611	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
612	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
613	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
614	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
615	C₂²×C₆₇	#585	1	1	yes	characteristic
616	C₂²×C₆₇	#585	1	1	yes	characteristic
617	C₂²×C₆₇	#585	1	1	yes	characteristic
618	C₄×C₆₇	—	2	2	no	—
619	C₄×C₆₇	—	2	2	no	—
620	C₄×C₆₇	—	2	2	no	—
621	C₄×C₆₇	—	2	2	no	—
622	C₄×C₆₇	—	2	2	no	—
623	C₄×C₆₇	—	2	2	no	—
624	C₄×C₆₇	—	2	2	no	—
625	C₄×C₆₇	—	2	2	no	—
626	C₄×C₆₇	—	2	2	no	—
627	C₄×C₆₇	—	4	1	no	—
628	C₄×C₆₇	—	4	1	no	—
629	C₄×C₆₇	—	4	1	no	—
630	C₄×C₆₇	—	4	1	no	—
631	C₄×C₆₇	—	4	1	no	—
632	C₄×C₆₇	—	4	1	no	—
633	C₄×C₆₇	—	4	1	no	—
634	C₄×C₆₇	—	4	1	no	—
635	C₄×C₆₇	—	4	1	no	—
636	C₄×C₆₇	—	4	1	no	—
637	C₄×C₆₇	—	4	1	no	—
638	C₄×C₆₇	—	4	1	no	—
639	C₄×C₆₇	—	4	1	no	—
640	C₄×C₆₇	—	4	1	no	—
641	C₄×C₆₇	—	4	1	no	—
642	C₄×C₆₇	—	4	1	no	—
643	C₄×C₆₇	—	4	1	no	—
644	C₄×C₆₇	—	4	1	no	—
645	C₄×C₆₇	—	4	1	no	—
646	C₄×C₆₇	—	4	1	no	—
647	#60015	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
648	C₂×C₆₇	—	4	2	no	—
649	C₂×C₆₇	—	8	1	no	—
650	C₂×C₆₇	#3475	1	1	yes	characteristic
651	C₂×C₆₇	#3475	1	1	yes	characteristic
652	C₂×C₆₇	#3482	1	1	yes	characteristic
653	C₂×C₆₇	#3512	1	1	yes	characteristic
654	C₂×C₆₇	#3516	1	1	yes	characteristic
655	C₂×C₆₇	#3521	1	1	yes	characteristic
656	C₂×C₆₇	#3557	1	1	yes	characteristic
657	#2758	C₂×C₆₇	1	1	yes	characteristic, complemented
658	#2738	C₂×C₆₇	1	1	yes	characteristic, complemented
659	#2725	C₂×C₆₇	1	1	yes	characteristic, complemented
660	#2702	C₂×C₆₇	1	1	yes	characteristic
661	#2590	C₂×C₆₇	1	1	yes	characteristic, complemented
662	#2590	C₂×C₆₇	1	1	yes	characteristic, complemented
663	#2587	C₂×C₆₇	1	1	yes	characteristic, complemented
664	#2556	C₂×C₆₇	1	1	yes	characteristic, complemented
665	#2533	C₂×C₆₇	1	1	yes	characteristic, complemented
666	#2533	C₂×C₆₇	1	1	yes	characteristic, complemented
667	#2530	C₂×C₆₇	1	1	yes	characteristic, complemented
668	#2529	C₂×C₆₇	1	1	yes	characteristic, complemented
669	#2526	C₂×C₆₇	1	1	yes	characteristic
670	#2525	C₂×C₆₇	1	1	yes	characteristic, complemented
671	#2523	C₂×C₆₇	1	1	yes	characteristic, complemented
672	#2516	C₂×C₆₇	1	1	yes	characteristic
673	#2515	C₂×C₆₇	1	1	yes	characteristic, complemented
674	#2509	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#2481	C₂×C₆₇	1	1	yes	characteristic
676	#2470	C₂×C₆₇	1	1	yes	characteristic
677	#2470	C₂×C₆₇	1	1	yes	characteristic
678	#2469	C₂×C₆₇	1	1	yes	characteristic, complemented
679	#2374	C₂×C₆₇	1	1	yes	characteristic
680	#2373	C₂×C₆₇	1	1	yes	characteristic, complemented
681	#2370	C₂×C₆₇	1	1	yes	characteristic, complemented
682	#2360	C₂×C₆₇	1	1	yes	characteristic, complemented
683	#2347	C₂×C₆₇	1	1	yes	characteristic, complemented
684	#2344	C₂×C₆₇	1	1	yes	characteristic, complemented
685	C₄×#126	C₂×C₆₇	1	1	yes	characteristic, complemented
686	#2298	C₂×C₆₇	1	1	yes	characteristic, complemented
687	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
688	C₆₇	#60015	1	1	yes	characteristic, direct product factor, Sylow
689	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
690	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
691	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
692	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
693	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
694	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
695	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
696	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
697	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
698	#400	C₂²×C₆₇	1	1	yes	characteristic
699	#400	C₂²×C₆₇	1	1	yes	characteristic
700	#400	C₂²×C₆₇	1	1	yes	characteristic
701	#400	C₂²×C₆₇	1	1	yes	characteristic
702	#400	C₂²×C₆₇	1	1	yes	characteristic
703	#400	C₂²×C₆₇	1	1	yes	characteristic
704	#400	C₂²×C₆₇	1	1	yes	characteristic
705	#400	C₂²×C₆₇	1	1	yes	characteristic
706	#400	C₂²×C₆₇	1	1	yes	characteristic
707	#400	C₂²×C₆₇	1	1	yes	characteristic
708	#400	C₂²×C₆₇	1	1	yes	characteristic
709	#400	C₂²×C₆₇	1	1	yes	characteristic
710	#399	C₂²×C₆₇	1	1	yes	characteristic
711	#398	C₂²×C₆₇	1	1	yes	characteristic
712	#398	C₂²×C₆₇	1	1	yes	characteristic
713	#398	C₂²×C₆₇	1	1	yes	characteristic
714	#398	C₂²×C₆₇	1	1	yes	characteristic
715	#398	C₂²×C₆₇	1	1	yes	characteristic
716	#397	C₂²×C₆₇	1	1	yes	characteristic
717	#397	C₂²×C₆₇	1	1	yes	characteristic
718	#397	C₂²×C₆₇	1	1	yes	characteristic
719	#397	C₂²×C₆₇	1	1	yes	characteristic
720	#397	C₂²×C₆₇	1	1	yes	characteristic
721	#396	C₂²×C₆₇	1	1	yes	characteristic
722	#396	C₂²×C₆₇	1	1	yes	characteristic
723	#396	C₂²×C₆₇	1	1	yes	characteristic
724	#396	C₂²×C₆₇	1	1	yes	characteristic
725	#396	C₂²×C₆₇	1	1	yes	characteristic
726	#395	C₂²×C₆₇	1	1	yes	characteristic
727	#394	C₂²×C₆₇	1	1	yes	characteristic
728	#394	C₂²×C₆₇	1	1	yes	characteristic
729	#393	C₂²×C₆₇	1	1	yes	characteristic
730	#391	C₂²×C₆₇	1	1	yes	characteristic
731	#391	C₂²×C₆₇	1	1	yes	characteristic
732	#391	C₂²×C₆₇	1	1	yes	characteristic
733	#390	C₂²×C₆₇	1	1	yes	characteristic
734	#389	C₂²×C₆₇	1	1	yes	characteristic
735	#389	C₂²×C₆₇	1	1	yes	characteristic
736	#389	C₂²×C₆₇	1	1	yes	characteristic
737	#389	C₂²×C₆₇	1	1	yes	characteristic
738	#389	C₂²×C₆₇	1	1	yes	characteristic
739	#389	C₂²×C₆₇	1	1	yes	characteristic
740	#389	C₂²×C₆₇	1	1	yes	characteristic
741	#389	C₂²×C₆₇	1	1	yes	characteristic
742	#389	C₂²×C₆₇	1	1	yes	characteristic
743	#389	C₂²×C₆₇	1	1	yes	characteristic
744	#389	C₂²×C₆₇	1	1	yes	characteristic
745	#389	C₂²×C₆₇	1	1	yes	characteristic
746	#389	C₂²×C₆₇	1	1	yes	characteristic
747	#389	C₂²×C₆₇	1	1	yes	characteristic
748	#389	C₂²×C₆₇	1	1	yes	characteristic
749	#389	C₂²×C₆₇	1	1	yes	characteristic
750	#389	C₂²×C₆₇	1	1	yes	characteristic
751	#388	C₂²×C₆₇	1	1	yes	characteristic
752	#388	C₂²×C₆₇	1	1	yes	characteristic
753	#388	C₂²×C₆₇	1	1	yes	characteristic
754	#388	C₂²×C₆₇	1	1	yes	characteristic
755	#388	C₂²×C₆₇	1	1	yes	characteristic
756	#388	C₂²×C₆₇	1	1	yes	characteristic
757	#388	C₂²×C₆₇	1	1	yes	characteristic
758	#388	C₂²×C₆₇	1	1	yes	characteristic
759	#388	C₂²×C₆₇	1	1	yes	characteristic
760	#388	C₂²×C₆₇	1	1	yes	characteristic
761	#388	C₂²×C₆₇	1	1	yes	characteristic
762	#388	C₂²×C₆₇	1	1	yes	characteristic
763	#388	C₂²×C₆₇	1	1	yes	characteristic
764	#388	C₂²×C₆₇	1	1	yes	characteristic
765	#388	C₂²×C₆₇	1	1	yes	characteristic
766	#388	C₂²×C₆₇	1	1	yes	characteristic
767	#388	C₂²×C₆₇	1	1	yes	characteristic
768	#388	C₂²×C₆₇	1	1	yes	characteristic
769	#388	C₂²×C₆₇	1	1	yes	characteristic
770	#388	C₂²×C₆₇	1	1	yes	characteristic
771	#387	C₂²×C₆₇	1	1	yes	characteristic
772	#387	C₂²×C₆₇	1	1	yes	characteristic
773	#387	C₂²×C₆₇	1	1	yes	characteristic
774	#387	C₂²×C₆₇	1	1	yes	characteristic
775	#387	C₂²×C₆₇	1	1	yes	characteristic
776	#387	C₂²×C₆₇	1	1	yes	characteristic
777	#387	C₂²×C₆₇	1	1	yes	characteristic
778	#387	C₂²×C₆₇	1	1	yes	characteristic
779	#387	C₂²×C₆₇	1	1	yes	characteristic
780	#387	C₂²×C₆₇	1	1	yes	characteristic
781	#387	C₂²×C₆₇	1	1	yes	characteristic
782	#387	C₂²×C₆₇	1	1	yes	characteristic
783	#387	C₂²×C₆₇	1	1	yes	characteristic
784	#387	C₂²×C₆₇	1	1	yes	characteristic
785	#387	C₂²×C₆₇	1	1	yes	characteristic
786	#387	C₂²×C₆₇	1	1	yes	characteristic
787	#387	C₂²×C₆₇	1	1	yes	characteristic
788	#387	C₂²×C₆₇	1	1	yes	characteristic
789	#387	C₂²×C₆₇	1	1	yes	characteristic
790	#387	C₂²×C₆₇	1	1	yes	characteristic
791	#387	C₂²×C₆₇	1	1	yes	characteristic
792	#387	C₂²×C₆₇	1	1	yes	characteristic
793	#387	C₂²×C₆₇	1	1	yes	characteristic
794	#387	C₂²×C₆₇	1	1	yes	characteristic
795	#387	C₂²×C₆₇	1	1	yes	characteristic
796	#387	C₂²×C₆₇	1	1	yes	characteristic
797	#387	C₂²×C₆₇	1	1	yes	characteristic
798	#387	C₂²×C₆₇	1	1	yes	characteristic
799	#387	C₂²×C₆₇	1	1	yes	characteristic
800	#386	C₂²×C₆₇	1	1	yes	characteristic
801	#386	C₂²×C₆₇	1	1	yes	characteristic
802	#386	C₂²×C₆₇	1	1	yes	characteristic
803	#385	C₂²×C₆₇	1	1	yes	characteristic
804	#385	C₂²×C₆₇	1	1	yes	characteristic
805	#385	C₂²×C₆₇	1	1	yes	characteristic
806	#385	C₂²×C₆₇	1	1	yes	characteristic
807	#385	C₂²×C₆₇	1	1	yes	characteristic
808	#383	C₂²×C₆₇	1	1	yes	characteristic
809	#383	C₂²×C₆₇	1	1	yes	characteristic
810	#383	C₂²×C₆₇	1	1	yes	characteristic
811	#383	C₂²×C₆₇	1	1	yes	characteristic
812	#382	C₂²×C₆₇	1	1	yes	characteristic
813	#381	C₂²×C₆₇	1	1	yes	characteristic
814	#381	C₂²×C₆₇	1	1	yes	characteristic
815	#380	C₂²×C₆₇	1	1	yes	characteristic
816	#380	C₂²×C₆₇	1	1	yes	characteristic
817	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
818	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
819	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
820	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
821	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
822	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
823	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
824	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
825	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
826	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
827	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
828	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
829	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
830	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
831	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
832	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
833	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
834	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
835	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
836	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
837	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
838	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
839	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
840	#376	C₂²×C₆₇	1	1	yes	characteristic
841	#376	C₂²×C₆₇	1	1	yes	characteristic
842	#376	C₂²×C₆₇	1	1	yes	characteristic
843	C₄³	C₂²×C₆₇	1	1	yes	characteristic
844	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
846	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
847	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
848	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
849	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
850	#126	—	2	4	no	—
851	#126	—	2	4	no	—
852	#125	—	2	4	no	—
853	#123	—	2	4	no	—
854	C₂²⋊Q₈	—	2	4	no	—
855	C₄×Q₈	—	2	4	no	—
856	#117	—	2	4	no	—
857	#117	—	2	4	no	—
858	C₂×C₄⋊C₄	—	2	4	no	—
859	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
861	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
863	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
864	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
898	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
900	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
901	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
902	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
903	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
904	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
905	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
906	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
907	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
908	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
909	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
910	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
912	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
913	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
914	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
915	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
918	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
919	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
920	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
921	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
922	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
923	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
925	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
926	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
927	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
928	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
929	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
930	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
931	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
932	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
933	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
934	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
935	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
936	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
937	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
938	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
939	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
940	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
941	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
942	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
943	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
944	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
945	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
946	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
947	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
948	#95	C₂³×C₆₇	1	1	yes	characteristic
949	#95	C₂³×C₆₇	1	1	yes	characteristic
950	#95	C₂³×C₆₇	1	1	yes	characteristic
951	#95	C₂³×C₆₇	1	1	yes	characteristic
952	#95	C₂³×C₆₇	1	1	yes	characteristic
953	#95	C₂³×C₆₇	1	1	yes	characteristic
954	#95	C₂³×C₆₇	1	1	yes	characteristic
955	#95	C₂³×C₆₇	1	1	yes	characteristic
956	#95	C₂³×C₆₇	1	1	yes	characteristic
957	#95	C₂³×C₆₇	1	1	yes	characteristic
958	#95	C₂³×C₆₇	1	1	yes	characteristic
959	#95	C₂³×C₆₇	1	1	yes	characteristic
960	#95	C₂³×C₆₇	1	1	yes	characteristic
961	#95	C₂³×C₆₇	1	1	yes	characteristic
962	#95	C₂³×C₆₇	1	1	yes	characteristic
963	#95	C₂³×C₆₇	1	1	yes	characteristic
964	#95	C₂³×C₆₇	1	1	yes	characteristic
965	#95	C₂³×C₆₇	1	1	yes	characteristic
966	#95	C₂³×C₆₇	1	1	yes	characteristic
967	#95	C₂³×C₆₇	1	1	yes	characteristic
968	#95	C₂³×C₆₇	1	1	yes	characteristic
969	#95	C₂³×C₆₇	1	1	yes	characteristic
970	#95	C₂³×C₆₇	1	1	yes	characteristic
971	#95	C₂³×C₆₇	1	1	yes	characteristic
972	#95	C₂³×C₆₇	1	1	yes	characteristic
973	#95	C₂³×C₆₇	1	1	yes	characteristic
974	#95	C₂³×C₆₇	1	1	yes	characteristic
975	#95	C₂³×C₆₇	1	1	yes	characteristic
976	#95	C₂³×C₆₇	1	1	yes	characteristic
977	#95	C₂³×C₆₇	1	1	yes	characteristic
978	#95	C₂³×C₆₇	1	1	yes	characteristic
979	#95	C₂³×C₆₇	1	1	yes	characteristic
980	#95	C₂³×C₆₇	1	1	yes	characteristic
981	#95	C₂³×C₆₇	1	1	yes	characteristic
982	#95	C₂³×C₆₇	1	1	yes	characteristic
983	#95	C₂³×C₆₇	1	1	yes	characteristic
984	#95	C₂³×C₆₇	1	1	yes	characteristic
985	#95	C₂³×C₆₇	1	1	yes	characteristic
986	#95	C₂³×C₆₇	1	1	yes	characteristic
987	#95	C₂³×C₆₇	1	1	yes	characteristic
988	#95	C₂³×C₆₇	1	1	yes	characteristic
989	#95	C₂³×C₆₇	1	1	yes	characteristic
990	#95	C₂³×C₆₇	1	1	yes	characteristic
991	#95	C₂³×C₆₇	1	1	yes	characteristic
992	#95	C₂³×C₆₇	1	1	yes	characteristic
993	#95	C₂³×C₆₇	1	1	yes	characteristic
994	#95	C₂³×C₆₇	1	1	yes	characteristic
995	#95	C₂³×C₆₇	1	1	yes	characteristic
996	#95	C₂³×C₆₇	1	1	yes	characteristic
997	#95	C₂³×C₆₇	1	1	yes	characteristic
998	#95	C₂³×C₆₇	1	1	yes	characteristic
999	#95	C₂³×C₆₇	1	1	yes	characteristic
1000	#95	C₂³×C₆₇	1	1	yes	characteristic
1001	#95	C₂³×C₆₇	1	1	yes	characteristic
1002	#95	C₂³×C₆₇	1	1	yes	characteristic
1003	#95	C₂³×C₆₇	1	1	yes	characteristic
1004	#95	C₂³×C₆₇	1	1	yes	characteristic
1005	#95	C₂³×C₆₇	1	1	yes	characteristic
1006	#95	C₂³×C₆₇	1	1	yes	characteristic
1007	#95	C₂³×C₆₇	1	1	yes	characteristic
1008	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1009	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1010	C₂×Q₈	—	2	2	no	—
1011	C₂×Q₈	—	2	2	no	—
1012	C₂×Q₈	—	4	1	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	4	1	no	—
1015	C₂×D₄	—	4	1	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	2	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	4	1	no	—
1024	C₂²×C₄	—	4	1	no	—
1025	C₂²×C₄	—	4	1	no	—
1026	C₂²×C₄	—	4	1	no	—
1027	C₂²×C₄	—	4	1	no	—
1028	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1030	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1031	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1032	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1033	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1034	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1035	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1036	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1037	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1041	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1042	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1043	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1044	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1045	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1046	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1047	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1048	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1055	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	4	1	no	—
1082	C₄⋊C₄	—	4	1	no	—
1083	C₄⋊C₄	—	4	1	no	—
1084	C₄⋊C₄	—	4	1	no	—
1085	C₄⋊C₄	—	4	1	no	—
1086	C₄⋊C₄	—	4	1	no	—
1087	C₄⋊C₄	—	4	1	no	—
1088	C₄⋊C₄	—	4	1	no	—
1089	C₄⋊C₄	—	4	1	no	—
1090	C₄⋊C₄	—	4	1	no	—
1091	C₄⋊C₄	—	4	1	no	—
1092	C₄⋊C₄	—	4	1	no	—
1093	C₄⋊C₄	—	4	1	no	—
1094	C₄⋊C₄	—	4	1	no	—
1095	C₄⋊C₄	—	4	1	no	—
1096	C₄⋊C₄	—	4	1	no	—
1097	C₄⋊C₄	#41×C₆₇	1	4	yes	—
1098	C₄⋊C₄	#41×C₆₇	1	4	yes	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	4	1	no	—
1114	C₂²⋊C₄	—	4	1	no	—
1115	C₂²⋊C₄	—	4	1	no	—
1116	C₂²⋊C₄	—	4	1	no	—
1117	C₂²⋊C₄	—	4	1	no	—
1118	C₂²⋊C₄	—	4	1	no	—
1119	C₂²⋊C₄	—	4	1	no	—
1120	C₂²⋊C₄	—	4	1	no	—
1121	C₂²⋊C₄	—	4	1	no	—
1122	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
1123	C₄²	—	2	2	no	—
1124	C₄²	—	2	2	no	—
1125	C₄²	—	2	2	no	—
1126	C₄²	—	2	2	no	—
1127	C₄²	—	2	2	no	—
1128	C₄²	—	2	2	no	—
1129	C₄²	—	2	2	no	—
1130	C₄²	—	2	2	no	—
1131	C₄²	—	2	2	no	—
1132	C₄²	—	2	2	no	—
1133	C₄²	—	2	2	no	—
1134	C₄²	—	4	1	no	—
1135	C₄²	—	4	1	no	—
1136	C₄²	—	4	1	no	—
1137	C₄²	—	4	1	no	—
1138	C₄²	—	4	1	no	—
1139	C₄²	—	4	1	no	—
1140	C₄²	—	4	1	no	—
1141	C₄²	—	4	1	no	—
1142	C₄²	—	4	1	no	—
1143	C₄²	—	4	1	no	—
1144	C₄²	—	4	1	no	—
1145	C₄²	—	4	1	no	—
1146	C₂³	—	2	1	no	—
1147	C₂³	—	2	1	no	—
1148	C₂³	—	2	1	no	—
1149	C₂³	—	2	1	no	—
1150	C₂³	—	2	1	no	—
1151	C₂³	—	2	1	no	—
1152	C₂³	—	2	1	no	—
1153	C₂³	—	2	1	no	—
1154	C₂³	—	2	1	no	—
1155	C₂³	—	2	1	no	—
1156	C₂³	—	2	1	no	—
1157	C₂³	—	2	1	no	—
1158	C₂³	—	2	1	no	—
1159	C₂³	C₂×#41×C₆₇	1	2	yes	—
1160	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1161	Q₈	—	4	4	no	—
1162	D₄	—	8	2	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	4	4	no	—
1242	C₂×C₄	—	4	4	no	—
1243	C₂×C₄	—	4	4	no	—
1244	C₂×C₄	—	8	2	no	—
1245	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1246	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1247	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1248	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1249	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1250	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1251	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1252	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1253	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1254	C₂²	—	2	2	no	—
1255	C₂²	—	2	2	no	—
1256	C₂²	—	2	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	4	1	no	—
1261	C₂²	—	4	1	no	—
1262	C₂²	—	4	1	no	—
1263	C₂²	—	4	1	no	—
1264	C₂²	—	4	1	no	—
1265	C₂²	—	4	1	no	—
1266	C₂²	—	4	1	no	—
1267	C₂²	—	4	1	no	—
1268	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1269	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1270	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1271	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1272	C₂²	#585×C₆₇	1	1	yes	characteristic
1273	C₂²	#585×C₆₇	1	1	yes	characteristic
1274	C₂²	#585×C₆₇	1	1	yes	characteristic
1275	C₄	—	2	2	no	—
1276	C₄	—	2	2	no	—
1277	C₄	—	2	2	no	—
1278	C₄	—	2	2	no	—
1279	C₄	—	2	2	no	—
1280	C₄	—	2	2	no	—
1281	C₄	—	2	2	no	—
1282	C₄	—	2	2	no	—
1283	C₄	—	2	2	no	—
1284	C₄	—	4	1	no	—
1285	C₄	—	4	1	no	—
1286	C₄	—	4	1	no	—
1287	C₄	—	4	1	no	—
1288	C₄	—	4	1	no	—
1289	C₄	—	4	1	no	—
1290	C₄	—	4	1	no	—
1291	C₄	—	4	1	no	—
1292	C₄	—	4	1	no	—
1293	C₄	—	4	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	1	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	8	1	no	—
1306	C₂	C₆₇×#3475	1	1	yes	characteristic
1307	C₂	C₆₇×#3475	1	1	yes	characteristic
1308	C₂	C₆₇×#3482	1	1	yes	characteristic
1309	C₂	C₆₇×#3512	1	1	yes	characteristic
1310	C₂	C₆₇×#3516	1	1	yes	characteristic
1311	C₂	C₆₇×#3521	1	1	yes	characteristic
1312	C₂	C₆₇×#3557	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2758	C₂	semidirect
2. C₆₇×#2738	C₂	semidirect
3. C₆₇×#2725	C₂	semidirect
5. C₆₇×#2590	C₂	semidirect
6. C₆₇×#2590	C₂	semidirect
7. C₆₇×#2587	C₂	semidirect
8. C₆₇×#2556	C₂	semidirect
9. C₆₇×#2533	C₂	semidirect
10. C₆₇×#2533	C₂	semidirect
11. C₆₇×#2530	C₂	semidirect
12. C₆₇×#2529	C₂	semidirect
14. C₆₇×#2525	C₂	semidirect
15. C₆₇×#2523	C₂	semidirect
17. C₆₇×#2515	C₂	semidirect
18. C₆₇×#2509	C₂	semidirect
22. C₆₇×#2469	C₂	semidirect
24. C₆₇×#2373	C₂	semidirect
25. C₆₇×#2370	C₂	semidirect
26. C₆₇×#2360	C₂	semidirect
27. C₆₇×#2347	C₂	semidirect
28. C₆₇×#2344	C₂	semidirect
29. C₄×#126×C₆₇	C₂	semidirect
30. C₆₇×#2298	C₂	semidirect
31. C₆₇×#2295	C₂	semidirect
647. #60015	C₆₇	direct (N × H)
657. #2758	C₂×C₆₇	semidirect
658. #2738	C₂×C₆₇	semidirect
659. #2725	C₂×C₆₇	semidirect
661. #2590	C₂×C₆₇	semidirect
662. #2590	C₂×C₆₇	semidirect
663. #2587	C₂×C₆₇	semidirect
664. #2556	C₂×C₆₇	semidirect
665. #2533	C₂×C₆₇	semidirect
666. #2533	C₂×C₆₇	semidirect
667. #2530	C₂×C₆₇	semidirect
668. #2529	C₂×C₆₇	semidirect
670. #2525	C₂×C₆₇	semidirect
671. #2523	C₂×C₆₇	semidirect
673. #2515	C₂×C₆₇	semidirect
674. #2509	C₂×C₆₇	semidirect
678. #2469	C₂×C₆₇	semidirect
680. #2373	C₂×C₆₇	semidirect
681. #2370	C₂×C₆₇	semidirect
682. #2360	C₂×C₆₇	semidirect
683. #2347	C₂×C₆₇	semidirect
684. #2344	C₂×C₆₇	semidirect
685. C₄×#126	C₂×C₆₇	semidirect
686. #2298	C₂×C₆₇	semidirect
687. #2295	C₂×C₆₇	semidirect
688. C₆₇	#60015	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×#2758	2
C₆₇×#2738	2
C₆₇×#2725	2
C₆₇×#2702	2
C₆₇×#2590	2
C₆₇×#2587	2
C₆₇×#2556	2
C₆₇×#2533	2
C₆₇×#2530	2
C₆₇×#2529	2
C₆₇×#2526	2
C₆₇×#2525	2
C₆₇×#2523	2
C₆₇×#2516	2
C₆₇×#2515	2
C₆₇×#2509	2
C₆₇×#2481	2
C₆₇×#2470	2
C₆₇×#2469	2
C₆₇×#2374	2
C₆₇×#2373	2
C₆₇×#2370	2
C₆₇×#2360	2
C₆₇×#2347	2
C₆₇×#2344	2
C₄×#126×C₆₇	2
C₆₇×#2298	2
C₆₇×#2295	2
#60015	67

Subgroups — C67×#60015 #30739266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60015 #30739266