Subgroups — C₆₇×#36755 #30716006

Order 17152.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2805	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2804	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2790	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2788	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2788	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2784	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2780	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#2774	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2763	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2755	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2742	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2729	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2720	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2713	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2692	C₂	1	1	yes	maximal, characteristic
19	C₆₇×#2665	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2665	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2612	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2607	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2605	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₇×#2605	C₂	1	1	yes	maximal, characteristic, complemented
25	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
26	C₆₇×#2569	C₂	1	1	yes	maximal, characteristic, complemented
27	C₆₇×#2439	C₂	1	1	yes	maximal, characteristic, complemented
28	C₆₇×#2438	C₂	1	1	yes	maximal, characteristic, complemented
29	C₆₇×#2319	C₂	1	1	yes	maximal, characteristic
30	C₆₇×#2318	C₂	1	1	yes	maximal, characteristic
31	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic
32	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
39	#400×C₆₇	C₂²	1	1	yes	characteristic
40	#400×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	#399×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	#398×C₆₇	C₂²	1	1	yes	characteristic
60	#398×C₆₇	C₂²	1	1	yes	characteristic
61	#398×C₆₇	C₂²	1	1	yes	characteristic
62	#398×C₆₇	C₂²	1	1	yes	characteristic
63	#396×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	#395×C₆₇	C₂²	1	1	yes	characteristic
71	#395×C₆₇	C₂²	1	1	yes	characteristic
72	#395×C₆₇	C₂²	1	1	yes	characteristic
73	#395×C₆₇	C₂²	1	1	yes	characteristic
74	#395×C₆₇	C₂²	1	1	yes	characteristic
75	#395×C₆₇	C₂²	1	1	yes	characteristic
76	#395×C₆₇	C₂²	1	1	yes	characteristic
77	#395×C₆₇	C₂²	1	1	yes	characteristic
78	#395×C₆₇	C₂²	1	1	yes	characteristic
79	#393×C₆₇	C₂²	1	1	yes	characteristic
80	#393×C₆₇	C₂²	1	1	yes	characteristic
81	#393×C₆₇	C₂²	1	1	yes	characteristic
82	#393×C₆₇	C₂²	1	1	yes	characteristic
83	#393×C₆₇	C₂²	1	1	yes	characteristic
84	#393×C₆₇	C₂²	1	1	yes	characteristic
85	#393×C₆₇	C₂²	1	1	yes	characteristic
86	#393×C₆₇	C₂²	1	1	yes	characteristic
87	#391×C₆₇	C₂²	1	1	yes	characteristic
88	#391×C₆₇	C₂²	1	1	yes	characteristic
89	#391×C₆₇	C₂²	1	1	yes	characteristic
90	#391×C₆₇	C₂²	1	1	yes	characteristic
91	#391×C₆₇	C₂²	1	1	yes	characteristic
92	#391×C₆₇	C₂²	1	1	yes	characteristic
93	#391×C₆₇	C₂²	1	1	yes	characteristic
94	#391×C₆₇	C₂²	1	1	yes	characteristic
95	#391×C₆₇	C₂²	1	1	yes	characteristic
96	#391×C₆₇	C₂²	1	1	yes	characteristic
97	#391×C₆₇	C₂²	1	1	yes	characteristic
98	#391×C₆₇	C₂²	1	1	yes	characteristic
99	#391×C₆₇	C₂²	1	1	yes	characteristic
100	#390×C₆₇	C₂²	1	1	yes	characteristic
101	#390×C₆₇	C₂²	1	1	yes	characteristic
102	#389×C₆₇	C₂²	1	1	yes	characteristic
103	#389×C₆₇	C₂²	1	1	yes	characteristic
104	#389×C₆₇	C₂²	1	1	yes	characteristic
105	#389×C₆₇	C₂²	1	1	yes	characteristic
106	#389×C₆₇	C₂²	1	1	yes	characteristic
107	#389×C₆₇	C₂²	1	1	yes	characteristic
108	#389×C₆₇	C₂²	1	1	yes	characteristic
109	#389×C₆₇	C₂²	1	1	yes	characteristic
110	#389×C₆₇	C₂²	1	1	yes	characteristic
111	#389×C₆₇	C₂²	1	1	yes	characteristic
112	#389×C₆₇	C₂²	1	1	yes	characteristic
113	#388×C₆₇	C₂²	1	1	yes	characteristic
114	#388×C₆₇	C₂²	1	1	yes	characteristic
115	#388×C₆₇	C₂²	1	1	yes	characteristic
116	#388×C₆₇	C₂²	1	1	yes	characteristic
117	#388×C₆₇	C₂²	1	1	yes	characteristic
118	#388×C₆₇	C₂²	1	1	yes	characteristic
119	#388×C₆₇	C₂²	1	1	yes	characteristic
120	#388×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	#387×C₆₇	C₂²	1	1	yes	characteristic
144	#387×C₆₇	C₂²	1	1	yes	characteristic
145	#386×C₆₇	C₂²	1	1	yes	characteristic
146	#386×C₆₇	C₂²	1	1	yes	characteristic
147	#386×C₆₇	C₂²	1	1	yes	characteristic
148	#386×C₆₇	C₂²	1	1	yes	characteristic
149	#385×C₆₇	C₂²	1	1	yes	characteristic
150	#385×C₆₇	C₂²	1	1	yes	characteristic
151	#385×C₆₇	C₂²	1	1	yes	characteristic
152	#385×C₆₇	C₂²	1	1	yes	characteristic
153	#385×C₆₇	C₂²	1	1	yes	characteristic
154	#385×C₆₇	C₂²	1	1	yes	characteristic
155	#385×C₆₇	C₂²	1	1	yes	characteristic
156	#385×C₆₇	C₂²	1	1	yes	characteristic
157	#385×C₆₇	C₂²	1	1	yes	characteristic
158	#385×C₆₇	C₂²	1	1	yes	characteristic
159	#385×C₆₇	C₂²	1	1	yes	characteristic
160	#385×C₆₇	C₂²	1	1	yes	characteristic
161	#385×C₆₇	C₂²	1	1	yes	characteristic
162	#385×C₆₇	C₂²	1	1	yes	characteristic
163	#384×C₆₇	C₂²	1	1	yes	characteristic
164	#383×C₆₇	C₂²	1	1	yes	characteristic
165	#382×C₆₇	C₂²	1	1	yes	characteristic
166	#382×C₆₇	C₂²	1	1	yes	characteristic
167	#382×C₆₇	C₂²	1	1	yes	characteristic
168	#382×C₆₇	C₂²	1	1	yes	characteristic
169	#381×C₆₇	C₂²	1	1	yes	characteristic
170	#381×C₆₇	C₂²	1	1	yes	characteristic
171	#381×C₆₇	C₂²	1	1	yes	characteristic
172	#380×C₆₇	C₂²	1	1	yes	characteristic
173	#380×C₆₇	C₂²	1	1	yes	characteristic
174	#380×C₆₇	C₂²	1	1	yes	characteristic
175	#380×C₆₇	C₂²	1	1	yes	characteristic
176	#380×C₆₇	C₂²	1	1	yes	characteristic
177	#380×C₆₇	C₂²	1	1	yes	characteristic
178	#380×C₆₇	C₂²	1	1	yes	characteristic
179	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
180	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
184	#376×C₆₇	C₂²	1	1	yes	characteristic
185	#376×C₆₇	C₂²	1	1	yes	characteristic
186	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
191	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
192	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₄⋊Q₈×C₆₇	—	4	2	no	—
200	#125×C₆₇	—	4	2	no	—
201	C₂²⋊Q₈×C₆₇	—	4	2	no	—
202	C₂²⋊Q₈×C₆₇	—	4	2	no	—
203	C₄×D₄×C₆₇	Q₈	1	8	yes	complemented
204	#117×C₆₇	—	4	2	no	—
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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊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×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₆₇	—	4	2	no	—
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	#95×C₆₇	C₂³	1	1	yes	characteristic
286	#95×C₆₇	C₂³	1	1	yes	characteristic
287	#95×C₆₇	C₂³	1	1	yes	characteristic
288	#95×C₆₇	C₂³	1	1	yes	characteristic
289	#95×C₆₇	C₂³	1	1	yes	characteristic
290	#95×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	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×Q₈×C₆₇	—	2	2	no	—
352	C₂×Q₈×C₆₇	—	4	1	no	—
353	C₂×Q₈×C₆₇	—	4	1	no	—
354	C₂×Q₈×C₆₇	—	4	1	no	—
355	C₂×Q₈×C₆₇	—	4	1	no	—
356	C₂×Q₈×C₆₇	—	4	1	no	—
357	C₂×Q₈×C₆₇	—	4	1	no	—
358	C₂×Q₈×C₆₇	—	4	1	no	—
359	C₂×Q₈×C₆₇	—	4	1	no	—
360	C₂×Q₈×C₆₇	—	4	1	no	—
361	C₂×Q₈×C₆₇	—	4	1	no	—
362	C₂×Q₈×C₆₇	—	4	1	no	—
363	C₂×Q₈×C₆₇	—	4	1	no	—
364	C₂×Q₈×C₆₇	—	4	1	no	—
365	C₂×Q₈×C₆₇	—	4	1	no	—
366	C₂×D₄×C₆₇	—	4	1	no	—
367	C₂×D₄×C₆₇	—	4	1	no	—
368	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	4	1	no	—
371	C₂²×C₄×C₆₇	—	4	1	no	—
372	C₂²×C₄×C₆₇	—	4	1	no	—
373	C₂²×C₄×C₆₇	—	4	1	no	—
374	C₂²×C₄×C₆₇	—	4	1	no	—
375	C₂²×C₄×C₆₇	—	4	1	no	—
376	C₂²×C₄×C₆₇	—	4	1	no	—
377	C₂²×C₄×C₆₇	—	4	1	no	—
378	C₂²×C₄×C₆₇	—	4	1	no	—
379	C₂²×C₄×C₆₇	—	4	1	no	—
380	C₂²×C₄×C₆₇	—	4	1	no	—
381	C₂²×C₄×C₆₇	—	4	1	no	—
382	C₂²×C₄×C₆₇	—	4	1	no	—
383	C₂²×C₄×C₆₇	—	4	1	no	—
384	C₂²×C₄×C₆₇	—	4	1	no	—
385	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
386	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
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	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
421	C₄⋊C₄×C₆₇	—	4	1	no	—
422	C₄⋊C₄×C₆₇	—	4	1	no	—
423	C₄⋊C₄×C₆₇	—	4	1	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	—	4	1	no	—
441	C₄⋊C₄×C₆₇	—	4	1	no	—
442	C₄⋊C₄×C₆₇	—	4	1	no	—
443	C₄⋊C₄×C₆₇	—	4	1	no	—
444	C₄⋊C₄×C₆₇	—	4	1	no	—
445	C₄⋊C₄×C₆₇	—	4	1	no	—
446	C₄⋊C₄×C₆₇	—	4	1	no	—
447	C₄⋊C₄×C₆₇	—	4	1	no	—
448	C₄⋊C₄×C₆₇	—	4	1	no	—
449	C₄⋊C₄×C₆₇	—	4	1	no	—
450	C₄⋊C₄×C₆₇	—	4	1	no	—
451	C₄⋊C₄×C₆₇	—	4	1	no	—
452	C₄⋊C₄×C₆₇	—	4	1	no	—
453	C₄⋊C₄×C₆₇	—	4	1	no	—
454	C₄⋊C₄×C₆₇	—	4	1	no	—
455	C₄⋊C₄×C₆₇	—	4	1	no	—
456	C₄⋊C₄×C₆₇	—	4	1	no	—
457	C₄⋊C₄×C₆₇	—	4	1	no	—
458	C₄⋊C₄×C₆₇	—	4	1	no	—
459	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
460	C₂²⋊C₄×C₆₇	—	2	2	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	—	4	1	no	—
466	C₂²⋊C₄×C₆₇	—	4	1	no	—
467	C₂²⋊C₄×C₆₇	—	4	1	no	—
468	C₂²⋊C₄×C₆₇	—	4	1	no	—
469	C₂²⋊C₄×C₆₇	—	4	1	no	—
470	C₂²⋊C₄×C₆₇	—	4	1	no	—
471	C₂²⋊C₄×C₆₇	—	4	1	no	—
472	C₂²⋊C₄×C₆₇	—	4	1	no	—
473	C₂²⋊C₄×C₆₇	—	4	1	no	—
474	C₂²⋊C₄×C₆₇	—	4	1	no	—
475	C₂²⋊C₄×C₆₇	—	4	1	no	—
476	C₂²⋊C₄×C₆₇	—	4	1	no	—
477	C₂²⋊C₄×C₆₇	—	4	1	no	—
478	C₂²⋊C₄×C₆₇	—	4	1	no	—
479	C₂²⋊C₄×C₆₇	—	4	1	no	—
480	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
481	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
482	C₄²×C₆₇	—	2	2	no	—
483	C₄²×C₆₇	—	2	2	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	C₄²×C₆₇	—	4	1	no	—
490	C₄²×C₆₇	—	4	1	no	—
491	C₄²×C₆₇	—	4	1	no	—
492	C₄²×C₆₇	—	4	1	no	—
493	C₄²×C₆₇	—	4	1	no	—
494	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
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	—	2	1	no	—
503	C₂³×C₆₇	—	2	1	no	—
504	C₂³×C₆₇	—	2	1	no	—
505	C₂³×C₆₇	—	2	1	no	—
506	C₂³×C₆₇	—	2	1	no	—
507	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
508	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
509	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
510	Q₈×C₆₇	—	8	2	no	—
511	Q₈×C₆₇	—	8	2	no	—
512	Q₈×C₆₇	—	8	2	no	—
513	Q₈×C₆₇	—	8	2	no	—
514	Q₈×C₆₇	—	8	2	no	—
515	D₄×C₆₇	—	4	4	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	—	2	1	no	—
585	C₂×C₄×C₆₇	—	2	1	no	—
586	C₂×C₄×C₆₇	—	2	1	no	—
587	C₂×C₄×C₆₇	—	2	1	no	—
588	C₂×C₄×C₆₇	—	2	1	no	—
589	C₂×C₄×C₆₇	—	2	1	no	—
590	C₂×C₄×C₆₇	—	2	1	no	—
591	C₂×C₄×C₆₇	—	2	1	no	—
592	C₂×C₄×C₆₇	—	2	1	no	—
593	C₂×C₄×C₆₇	—	2	1	no	—
594	C₂×C₄×C₆₇	—	2	1	no	—
595	C₂×C₄×C₆₇	—	2	1	no	—
596	C₂×C₄×C₆₇	—	2	1	no	—
597	C₂×C₄×C₆₇	—	4	4	no	—
598	C₂×C₄×C₆₇	—	4	4	no	—
599	C₂×C₄×C₆₇	—	4	4	no	—
600	C₂×C₄×C₆₇	—	4	4	no	—
601	C₂×C₄×C₆₇	—	8	2	no	—
602	C₂×C₄×C₆₇	—	8	2	no	—
603	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
604	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
605	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
606	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
607	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
608	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
609	C₂²×C₆₇	—	2	2	no	—
610	C₂²×C₆₇	—	2	2	no	—
611	C₂²×C₆₇	—	2	2	no	—
612	C₂²×C₆₇	—	2	2	no	—
613	C₂²×C₆₇	—	2	2	no	—
614	C₂²×C₆₇	—	2	2	no	—
615	C₂²×C₆₇	—	4	1	no	—
616	C₂²×C₆₇	—	4	1	no	—
617	C₂²×C₆₇	—	4	1	no	—
618	C₂²×C₆₇	—	4	1	no	—
619	C₂²×C₆₇	—	4	1	no	—
620	C₂²×C₆₇	—	4	1	no	—
621	C₂²×C₆₇	—	4	1	no	—
622	C₂²×C₆₇	—	4	1	no	—
623	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
624	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂²×C₆₇	#585	1	1	yes	characteristic
626	C₂²×C₆₇	#585	1	1	yes	characteristic
627	C₂²×C₆₇	#585	1	1	yes	characteristic
628	C₂²×C₆₇	#585	1	1	yes	characteristic
629	C₂²×C₆₇	#585	1	1	yes	characteristic
630	C₄×C₆₇	—	2	2	no	—
631	C₄×C₆₇	—	2	2	no	—
632	C₄×C₆₇	—	2	2	no	—
633	C₄×C₆₇	—	2	2	no	—
634	C₄×C₆₇	—	2	2	no	—
635	C₄×C₆₇	—	2	2	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	C₄×C₆₇	—	4	1	no	—
648	C₄×C₆₇	—	4	1	no	—
649	C₄×C₆₇	—	4	1	no	—
650	C₄×C₆₇	—	4	1	no	—
651	C₄×C₆₇	—	4	1	no	—
652	C₄×C₆₇	—	4	1	no	—
653	C₄×C₆₇	—	4	1	no	—
654	C₄×C₆₇	—	4	1	no	—
655	C₄×C₆₇	—	4	1	no	—
656	C₄×C₆₇	—	4	1	no	—
657	C₄×C₆₇	—	4	1	no	—
658	C₄×C₆₇	—	4	1	no	—
659	#36755	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
660	C₂×C₆₇	—	4	2	no	—
661	C₂×C₆₇	—	4	2	no	—
662	C₂×C₆₇	#3458	1	1	yes	characteristic
663	C₂×C₆₇	#3501	1	1	yes	characteristic
664	C₂×C₆₇	#3504	1	1	yes	characteristic
665	C₂×C₆₇	#3533	1	1	yes	characteristic
666	C₂×C₆₇	#3540	1	1	yes	characteristic
667	C₂×C₆₇	#3566	1	1	yes	characteristic
668	C₂×C₆₇	#3568	1	1	yes	characteristic
669	#2855	C₂×C₆₇	1	1	yes	characteristic, complemented
670	#2851	C₂×C₆₇	1	1	yes	characteristic, complemented
671	#2805	C₂×C₆₇	1	1	yes	characteristic, complemented
672	#2804	C₂×C₆₇	1	1	yes	characteristic
673	#2790	C₂×C₆₇	1	1	yes	characteristic, complemented
674	#2788	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#2788	C₂×C₆₇	1	1	yes	characteristic, complemented
676	#2784	C₂×C₆₇	1	1	yes	characteristic
677	#2780	C₂×C₆₇	1	1	yes	characteristic
678	#2774	C₂×C₆₇	1	1	yes	characteristic, complemented
679	#2763	C₂×C₆₇	1	1	yes	characteristic, complemented
680	#2763	C₂×C₆₇	1	1	yes	characteristic, complemented
681	#2755	C₂×C₆₇	1	1	yes	characteristic, complemented
682	#2742	C₂×C₆₇	1	1	yes	characteristic, complemented
683	#2729	C₂×C₆₇	1	1	yes	characteristic, complemented
684	#2720	C₂×C₆₇	1	1	yes	characteristic, complemented
685	#2713	C₂×C₆₇	1	1	yes	characteristic, complemented
686	#2692	C₂×C₆₇	1	1	yes	characteristic
687	#2665	C₂×C₆₇	1	1	yes	characteristic, complemented
688	#2665	C₂×C₆₇	1	1	yes	characteristic, complemented
689	#2612	C₂×C₆₇	1	1	yes	characteristic, complemented
690	#2607	C₂×C₆₇	1	1	yes	characteristic, complemented
691	#2605	C₂×C₆₇	1	1	yes	characteristic, complemented
692	#2605	C₂×C₆₇	1	1	yes	characteristic, complemented
693	#2570	C₂×C₆₇	1	1	yes	characteristic, complemented
694	#2569	C₂×C₆₇	1	1	yes	characteristic, complemented
695	#2439	C₂×C₆₇	1	1	yes	characteristic, complemented
696	#2438	C₂×C₆₇	1	1	yes	characteristic, complemented
697	#2319	C₂×C₆₇	1	1	yes	characteristic
698	#2318	C₂×C₆₇	1	1	yes	characteristic
699	#2290	C₂×C₆₇	1	1	yes	characteristic
700	C₆₇	#36755	1	1	yes	characteristic, direct product factor, Sylow
701	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
702	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
703	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
704	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
705	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
706	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
707	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
708	#400	C₂²×C₆₇	1	1	yes	characteristic
709	#400	C₂²×C₆₇	1	1	yes	characteristic
710	#400	C₂²×C₆₇	1	1	yes	characteristic
711	#400	C₂²×C₆₇	1	1	yes	characteristic
712	#400	C₂²×C₆₇	1	1	yes	characteristic
713	#400	C₂²×C₆₇	1	1	yes	characteristic
714	#400	C₂²×C₆₇	1	1	yes	characteristic
715	#400	C₂²×C₆₇	1	1	yes	characteristic
716	#400	C₂²×C₆₇	1	1	yes	characteristic
717	#400	C₂²×C₆₇	1	1	yes	characteristic
718	#400	C₂²×C₆₇	1	1	yes	characteristic
719	#400	C₂²×C₆₇	1	1	yes	characteristic
720	#400	C₂²×C₆₇	1	1	yes	characteristic
721	#400	C₂²×C₆₇	1	1	yes	characteristic
722	#399	C₂²×C₆₇	1	1	yes	characteristic
723	#399	C₂²×C₆₇	1	1	yes	characteristic
724	#398	C₂²×C₆₇	1	1	yes	characteristic
725	#398	C₂²×C₆₇	1	1	yes	characteristic
726	#398	C₂²×C₆₇	1	1	yes	characteristic
727	#398	C₂²×C₆₇	1	1	yes	characteristic
728	#398	C₂²×C₆₇	1	1	yes	characteristic
729	#398	C₂²×C₆₇	1	1	yes	characteristic
730	#398	C₂²×C₆₇	1	1	yes	characteristic
731	#398	C₂²×C₆₇	1	1	yes	characteristic
732	#396	C₂²×C₆₇	1	1	yes	characteristic
733	#396	C₂²×C₆₇	1	1	yes	characteristic
734	#396	C₂²×C₆₇	1	1	yes	characteristic
735	#396	C₂²×C₆₇	1	1	yes	characteristic
736	#396	C₂²×C₆₇	1	1	yes	characteristic
737	#396	C₂²×C₆₇	1	1	yes	characteristic
738	#395	C₂²×C₆₇	1	1	yes	characteristic
739	#395	C₂²×C₆₇	1	1	yes	characteristic
740	#395	C₂²×C₆₇	1	1	yes	characteristic
741	#395	C₂²×C₆₇	1	1	yes	characteristic
742	#395	C₂²×C₆₇	1	1	yes	characteristic
743	#395	C₂²×C₆₇	1	1	yes	characteristic
744	#395	C₂²×C₆₇	1	1	yes	characteristic
745	#395	C₂²×C₆₇	1	1	yes	characteristic
746	#395	C₂²×C₆₇	1	1	yes	characteristic
747	#395	C₂²×C₆₇	1	1	yes	characteristic
748	#393	C₂²×C₆₇	1	1	yes	characteristic
749	#393	C₂²×C₆₇	1	1	yes	characteristic
750	#393	C₂²×C₆₇	1	1	yes	characteristic
751	#393	C₂²×C₆₇	1	1	yes	characteristic
752	#393	C₂²×C₆₇	1	1	yes	characteristic
753	#393	C₂²×C₆₇	1	1	yes	characteristic
754	#393	C₂²×C₆₇	1	1	yes	characteristic
755	#393	C₂²×C₆₇	1	1	yes	characteristic
756	#391	C₂²×C₆₇	1	1	yes	characteristic
757	#391	C₂²×C₆₇	1	1	yes	characteristic
758	#391	C₂²×C₆₇	1	1	yes	characteristic
759	#391	C₂²×C₆₇	1	1	yes	characteristic
760	#391	C₂²×C₆₇	1	1	yes	characteristic
761	#391	C₂²×C₆₇	1	1	yes	characteristic
762	#391	C₂²×C₆₇	1	1	yes	characteristic
763	#391	C₂²×C₆₇	1	1	yes	characteristic
764	#391	C₂²×C₆₇	1	1	yes	characteristic
765	#391	C₂²×C₆₇	1	1	yes	characteristic
766	#391	C₂²×C₆₇	1	1	yes	characteristic
767	#391	C₂²×C₆₇	1	1	yes	characteristic
768	#391	C₂²×C₆₇	1	1	yes	characteristic
769	#390	C₂²×C₆₇	1	1	yes	characteristic
770	#390	C₂²×C₆₇	1	1	yes	characteristic
771	#389	C₂²×C₆₇	1	1	yes	characteristic
772	#389	C₂²×C₆₇	1	1	yes	characteristic
773	#389	C₂²×C₆₇	1	1	yes	characteristic
774	#389	C₂²×C₆₇	1	1	yes	characteristic
775	#389	C₂²×C₆₇	1	1	yes	characteristic
776	#389	C₂²×C₆₇	1	1	yes	characteristic
777	#389	C₂²×C₆₇	1	1	yes	characteristic
778	#389	C₂²×C₆₇	1	1	yes	characteristic
779	#389	C₂²×C₆₇	1	1	yes	characteristic
780	#389	C₂²×C₆₇	1	1	yes	characteristic
781	#389	C₂²×C₆₇	1	1	yes	characteristic
782	#388	C₂²×C₆₇	1	1	yes	characteristic
783	#388	C₂²×C₆₇	1	1	yes	characteristic
784	#388	C₂²×C₆₇	1	1	yes	characteristic
785	#388	C₂²×C₆₇	1	1	yes	characteristic
786	#388	C₂²×C₆₇	1	1	yes	characteristic
787	#388	C₂²×C₆₇	1	1	yes	characteristic
788	#388	C₂²×C₆₇	1	1	yes	characteristic
789	#388	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	#387	C₂²×C₆₇	1	1	yes	characteristic
801	#387	C₂²×C₆₇	1	1	yes	characteristic
802	#387	C₂²×C₆₇	1	1	yes	characteristic
803	#387	C₂²×C₆₇	1	1	yes	characteristic
804	#387	C₂²×C₆₇	1	1	yes	characteristic
805	#387	C₂²×C₆₇	1	1	yes	characteristic
806	#387	C₂²×C₆₇	1	1	yes	characteristic
807	#387	C₂²×C₆₇	1	1	yes	characteristic
808	#387	C₂²×C₆₇	1	1	yes	characteristic
809	#387	C₂²×C₆₇	1	1	yes	characteristic
810	#387	C₂²×C₆₇	1	1	yes	characteristic
811	#387	C₂²×C₆₇	1	1	yes	characteristic
812	#387	C₂²×C₆₇	1	1	yes	characteristic
813	#387	C₂²×C₆₇	1	1	yes	characteristic
814	#386	C₂²×C₆₇	1	1	yes	characteristic
815	#386	C₂²×C₆₇	1	1	yes	characteristic
816	#386	C₂²×C₆₇	1	1	yes	characteristic
817	#386	C₂²×C₆₇	1	1	yes	characteristic
818	#385	C₂²×C₆₇	1	1	yes	characteristic
819	#385	C₂²×C₆₇	1	1	yes	characteristic
820	#385	C₂²×C₆₇	1	1	yes	characteristic
821	#385	C₂²×C₆₇	1	1	yes	characteristic
822	#385	C₂²×C₆₇	1	1	yes	characteristic
823	#385	C₂²×C₆₇	1	1	yes	characteristic
824	#385	C₂²×C₆₇	1	1	yes	characteristic
825	#385	C₂²×C₆₇	1	1	yes	characteristic
826	#385	C₂²×C₆₇	1	1	yes	characteristic
827	#385	C₂²×C₆₇	1	1	yes	characteristic
828	#385	C₂²×C₆₇	1	1	yes	characteristic
829	#385	C₂²×C₆₇	1	1	yes	characteristic
830	#385	C₂²×C₆₇	1	1	yes	characteristic
831	#385	C₂²×C₆₇	1	1	yes	characteristic
832	#384	C₂²×C₆₇	1	1	yes	characteristic
833	#383	C₂²×C₆₇	1	1	yes	characteristic
834	#382	C₂²×C₆₇	1	1	yes	characteristic
835	#382	C₂²×C₆₇	1	1	yes	characteristic
836	#382	C₂²×C₆₇	1	1	yes	characteristic
837	#382	C₂²×C₆₇	1	1	yes	characteristic
838	#381	C₂²×C₆₇	1	1	yes	characteristic
839	#381	C₂²×C₆₇	1	1	yes	characteristic
840	#381	C₂²×C₆₇	1	1	yes	characteristic
841	#380	C₂²×C₆₇	1	1	yes	characteristic
842	#380	C₂²×C₆₇	1	1	yes	characteristic
843	#380	C₂²×C₆₇	1	1	yes	characteristic
844	#380	C₂²×C₆₇	1	1	yes	characteristic
845	#380	C₂²×C₆₇	1	1	yes	characteristic
846	#380	C₂²×C₆₇	1	1	yes	characteristic
847	#380	C₂²×C₆₇	1	1	yes	characteristic
848	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
849	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
850	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
851	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
852	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
853	#376	C₂²×C₆₇	1	1	yes	characteristic
854	#376	C₂²×C₆₇	1	1	yes	characteristic
855	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
856	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
857	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
859	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
860	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
862	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
863	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
864	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
865	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
866	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
867	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
868	C₄⋊Q₈	—	4	2	no	—
869	#125	—	4	2	no	—
870	C₂²⋊Q₈	—	4	2	no	—
871	C₂²⋊Q₈	—	4	2	no	—
872	C₄×D₄	Q₈×C₆₇	1	8	yes	complemented
873	#117	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
913	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₂×C₄⋊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×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
927	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
928	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
929	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
930	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
931	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
932	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
933	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
934	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
935	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
936	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
937	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
938	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
939	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
940	C₂×C₄²	—	4	2	no	—
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	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
949	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
950	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
951	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
952	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
953	C₂×C₄²	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	#95	C₂³×C₆₇	1	1	yes	characteristic
1009	#95	C₂³×C₆₇	1	1	yes	characteristic
1010	#95	C₂³×C₆₇	1	1	yes	characteristic
1011	#95	C₂³×C₆₇	1	1	yes	characteristic
1012	#95	C₂³×C₆₇	1	1	yes	characteristic
1013	#95	C₂³×C₆₇	1	1	yes	characteristic
1014	#95	C₂³×C₆₇	1	1	yes	characteristic
1015	#95	C₂³×C₆₇	1	1	yes	characteristic
1016	#95	C₂³×C₆₇	1	1	yes	characteristic
1017	#95	C₂³×C₆₇	1	1	yes	characteristic
1018	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1019	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1020	C₂×Q₈	—	2	2	no	—
1021	C₂×Q₈	—	4	1	no	—
1022	C₂×Q₈	—	4	1	no	—
1023	C₂×Q₈	—	4	1	no	—
1024	C₂×Q₈	—	4	1	no	—
1025	C₂×Q₈	—	4	1	no	—
1026	C₂×Q₈	—	4	1	no	—
1027	C₂×Q₈	—	4	1	no	—
1028	C₂×Q₈	—	4	1	no	—
1029	C₂×Q₈	—	4	1	no	—
1030	C₂×Q₈	—	4	1	no	—
1031	C₂×Q₈	—	4	1	no	—
1032	C₂×Q₈	—	4	1	no	—
1033	C₂×Q₈	—	4	1	no	—
1034	C₂×Q₈	—	4	1	no	—
1035	C₂×D₄	—	4	1	no	—
1036	C₂×D₄	—	4	1	no	—
1037	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	4	1	no	—
1040	C₂²×C₄	—	4	1	no	—
1041	C₂²×C₄	—	4	1	no	—
1042	C₂²×C₄	—	4	1	no	—
1043	C₂²×C₄	—	4	1	no	—
1044	C₂²×C₄	—	4	1	no	—
1045	C₂²×C₄	—	4	1	no	—
1046	C₂²×C₄	—	4	1	no	—
1047	C₂²×C₄	—	4	1	no	—
1048	C₂²×C₄	—	4	1	no	—
1049	C₂²×C₄	—	4	1	no	—
1050	C₂²×C₄	—	4	1	no	—
1051	C₂²×C₄	—	4	1	no	—
1052	C₂²×C₄	—	4	1	no	—
1053	C₂²×C₄	—	4	1	no	—
1054	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
1055	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
1056	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1058	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1067	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1068	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1069	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1070	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1071	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1072	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1073	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1074	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1075	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1076	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1077	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1078	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1079	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1080	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1081	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1082	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1083	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1084	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	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	—	4	1	no	—
1098	C₄⋊C₄	—	4	1	no	—
1099	C₄⋊C₄	—	4	1	no	—
1100	C₄⋊C₄	—	4	1	no	—
1101	C₄⋊C₄	—	4	1	no	—
1102	C₄⋊C₄	—	4	1	no	—
1103	C₄⋊C₄	—	4	1	no	—
1104	C₄⋊C₄	—	4	1	no	—
1105	C₄⋊C₄	—	4	1	no	—
1106	C₄⋊C₄	—	4	1	no	—
1107	C₄⋊C₄	—	4	1	no	—
1108	C₄⋊C₄	—	4	1	no	—
1109	C₄⋊C₄	—	4	1	no	—
1110	C₄⋊C₄	—	4	1	no	—
1111	C₄⋊C₄	—	4	1	no	—
1112	C₄⋊C₄	—	4	1	no	—
1113	C₄⋊C₄	—	4	1	no	—
1114	C₄⋊C₄	—	4	1	no	—
1115	C₄⋊C₄	—	4	1	no	—
1116	C₄⋊C₄	—	4	1	no	—
1117	C₄⋊C₄	—	4	1	no	—
1118	C₄⋊C₄	—	4	1	no	—
1119	C₄⋊C₄	—	4	1	no	—
1120	C₄⋊C₄	—	4	1	no	—
1121	C₄⋊C₄	—	4	1	no	—
1122	C₄⋊C₄	—	4	1	no	—
1123	C₄⋊C₄	—	4	1	no	—
1124	C₄⋊C₄	—	4	1	no	—
1125	C₄⋊C₄	—	4	1	no	—
1126	C₄⋊C₄	—	4	1	no	—
1127	C₄⋊C₄	—	4	1	no	—
1128	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
1129	C₂²⋊C₄	—	2	2	no	—
1130	C₂²⋊C₄	—	4	1	no	—
1131	C₂²⋊C₄	—	4	1	no	—
1132	C₂²⋊C₄	—	4	1	no	—
1133	C₂²⋊C₄	—	4	1	no	—
1134	C₂²⋊C₄	—	4	1	no	—
1135	C₂²⋊C₄	—	4	1	no	—
1136	C₂²⋊C₄	—	4	1	no	—
1137	C₂²⋊C₄	—	4	1	no	—
1138	C₂²⋊C₄	—	4	1	no	—
1139	C₂²⋊C₄	—	4	1	no	—
1140	C₂²⋊C₄	—	4	1	no	—
1141	C₂²⋊C₄	—	4	1	no	—
1142	C₂²⋊C₄	—	4	1	no	—
1143	C₂²⋊C₄	—	4	1	no	—
1144	C₂²⋊C₄	—	4	1	no	—
1145	C₂²⋊C₄	—	4	1	no	—
1146	C₂²⋊C₄	—	4	1	no	—
1147	C₂²⋊C₄	—	4	1	no	—
1148	C₂²⋊C₄	—	4	1	no	—
1149	C₂²⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
1150	C₂²⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
1151	C₄²	—	2	2	no	—
1152	C₄²	—	2	2	no	—
1153	C₄²	—	4	1	no	—
1154	C₄²	—	4	1	no	—
1155	C₄²	—	4	1	no	—
1156	C₄²	—	4	1	no	—
1157	C₄²	—	4	1	no	—
1158	C₄²	—	4	1	no	—
1159	C₄²	—	4	1	no	—
1160	C₄²	—	4	1	no	—
1161	C₄²	—	4	1	no	—
1162	C₄²	—	4	1	no	—
1163	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
1164	C₂³	—	2	1	no	—
1165	C₂³	—	2	1	no	—
1166	C₂³	—	2	1	no	—
1167	C₂³	—	2	1	no	—
1168	C₂³	—	2	1	no	—
1169	C₂³	—	2	1	no	—
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	1	no	—
1172	C₂³	—	2	1	no	—
1173	C₂³	—	2	1	no	—
1174	C₂³	—	2	1	no	—
1175	C₂³	—	2	1	no	—
1176	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
1177	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
1178	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1179	Q₈	—	8	2	no	—
1180	Q₈	—	8	2	no	—
1181	Q₈	—	8	2	no	—
1182	Q₈	—	8	2	no	—
1183	Q₈	—	8	2	no	—
1184	D₄	—	4	4	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	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	4	4	no	—
1267	C₂×C₄	—	4	4	no	—
1268	C₂×C₄	—	4	4	no	—
1269	C₂×C₄	—	4	4	no	—
1270	C₂×C₄	—	8	2	no	—
1271	C₂×C₄	—	8	2	no	—
1272	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
1273	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
1274	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
1275	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
1276	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
1277	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1278	C₂²	—	2	2	no	—
1279	C₂²	—	2	2	no	—
1280	C₂²	—	2	2	no	—
1281	C₂²	—	2	2	no	—
1282	C₂²	—	2	2	no	—
1283	C₂²	—	2	2	no	—
1284	C₂²	—	4	1	no	—
1285	C₂²	—	4	1	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	1	no	—
1288	C₂²	—	4	1	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	4	1	no	—
1292	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
1293	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1294	C₂²	#585×C₆₇	1	1	yes	characteristic
1295	C₂²	#585×C₆₇	1	1	yes	characteristic
1296	C₂²	#585×C₆₇	1	1	yes	characteristic
1297	C₂²	#585×C₆₇	1	1	yes	characteristic
1298	C₂²	#585×C₆₇	1	1	yes	characteristic
1299	C₄	—	2	2	no	—
1300	C₄	—	2	2	no	—
1301	C₄	—	2	2	no	—
1302	C₄	—	2	2	no	—
1303	C₄	—	2	2	no	—
1304	C₄	—	2	2	no	—
1305	C₄	—	4	1	no	—
1306	C₄	—	4	1	no	—
1307	C₄	—	4	1	no	—
1308	C₄	—	4	1	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	1	no	—
1311	C₄	—	4	1	no	—
1312	C₄	—	4	1	no	—
1313	C₄	—	4	1	no	—
1314	C₄	—	4	1	no	—
1315	C₄	—	4	1	no	—
1316	C₄	—	4	1	no	—
1317	C₄	—	4	1	no	—
1318	C₄	—	4	1	no	—
1319	C₄	—	4	1	no	—
1320	C₄	—	4	1	no	—
1321	C₄	—	4	1	no	—
1322	C₄	—	4	1	no	—
1323	C₄	—	4	1	no	—
1324	C₄	—	4	1	no	—
1325	C₄	—	4	1	no	—
1326	C₄	—	4	1	no	—
1327	C₄	—	4	1	no	—
1328	C₂	—	4	2	no	—
1329	C₂	—	4	2	no	—
1330	C₂	C₆₇×#3458	1	1	yes	characteristic
1331	C₂	C₆₇×#3501	1	1	yes	characteristic
1332	C₂	C₆₇×#3504	1	1	yes	characteristic
1333	C₂	C₆₇×#3533	1	1	yes	characteristic
1334	C₂	C₆₇×#3540	1	1	yes	characteristic
1335	C₂	C₆₇×#3566	1	1	yes	characteristic
1336	C₂	C₆₇×#3568	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×#2855	C₂	semidirect
2. C₆₇×#2851	C₂	semidirect
3. C₆₇×#2805	C₂	semidirect
5. C₆₇×#2790	C₂	semidirect
6. C₆₇×#2788	C₂	semidirect
7. C₆₇×#2788	C₂	semidirect
10. C₆₇×#2774	C₂	semidirect
11. C₆₇×#2763	C₂	semidirect
12. C₆₇×#2763	C₂	semidirect
13. C₆₇×#2755	C₂	semidirect
14. C₆₇×#2742	C₂	semidirect
15. C₆₇×#2729	C₂	semidirect
16. C₆₇×#2720	C₂	semidirect
17. C₆₇×#2713	C₂	semidirect
19. C₆₇×#2665	C₂	semidirect
20. C₆₇×#2665	C₂	semidirect
21. C₆₇×#2612	C₂	semidirect
22. C₆₇×#2607	C₂	semidirect
23. C₆₇×#2605	C₂	semidirect
24. C₆₇×#2605	C₂	semidirect
25. C₆₇×#2570	C₂	semidirect
26. C₆₇×#2569	C₂	semidirect
27. C₆₇×#2439	C₂	semidirect
28. C₆₇×#2438	C₂	semidirect
203. C₄×D₄×C₆₇	Q₈	semidirect
659. #36755	C₆₇	direct (N × H)
669. #2855	C₂×C₆₇	semidirect
670. #2851	C₂×C₆₇	semidirect
671. #2805	C₂×C₆₇	semidirect
673. #2790	C₂×C₆₇	semidirect
674. #2788	C₂×C₆₇	semidirect
675. #2788	C₂×C₆₇	semidirect
678. #2774	C₂×C₆₇	semidirect
679. #2763	C₂×C₆₇	semidirect
680. #2763	C₂×C₆₇	semidirect
681. #2755	C₂×C₆₇	semidirect
682. #2742	C₂×C₆₇	semidirect
683. #2729	C₂×C₆₇	semidirect
684. #2720	C₂×C₆₇	semidirect
685. #2713	C₂×C₆₇	semidirect
687. #2665	C₂×C₆₇	semidirect
688. #2665	C₂×C₆₇	semidirect
689. #2612	C₂×C₆₇	semidirect
690. #2607	C₂×C₆₇	semidirect
691. #2605	C₂×C₆₇	semidirect
692. #2605	C₂×C₆₇	semidirect
693. #2570	C₂×C₆₇	semidirect
694. #2569	C₂×C₆₇	semidirect
695. #2439	C₂×C₆₇	semidirect
696. #2438	C₂×C₆₇	semidirect
700. C₆₇	#36755	direct (N × H)
872. C₄×D₄	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2855	2
C₆₇×#2851	2
C₆₇×#2805	2
C₆₇×#2804	2
C₆₇×#2790	2
C₆₇×#2788	2
C₆₇×#2784	2
C₆₇×#2780	2
C₆₇×#2774	2
C₆₇×#2763	2
C₆₇×#2755	2
C₆₇×#2742	2
C₆₇×#2729	2
C₆₇×#2720	2
C₆₇×#2713	2
C₆₇×#2692	2
C₆₇×#2665	2
C₆₇×#2612	2
C₆₇×#2607	2
C₆₇×#2605	2
C₆₇×#2570	2
C₆₇×#2569	2
C₆₇×#2439	2
C₆₇×#2438	2
C₆₇×#2319	2
C₆₇×#2318	2
C₆₇×#2290	2
#36755	67

Subgroups — C67×#36755 #30716006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#36755 #30716006