Subgroups — C₆₇×#35164 #30714415

Order 17152.

1766 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2866	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2861	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2653	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2648	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2531	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2527	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2506	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2500	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2485	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2460	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2459	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2439	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2414	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2319	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	2	yes	—
26	C₂×#124×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
36	#401×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	2	yes	—
41	#397×C₆₇	C₂²	1	2	yes	—
42	#397×C₆₇	C₂²	1	2	yes	—
43	#396×C₆₇	C₂²	1	2	yes	—
44	#394×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	—
49	#393×C₆₇	C₂²	1	2	yes	—
50	#393×C₆₇	C₂²	1	2	yes	—
51	#392×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
53	#391×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	1	yes	characteristic
56	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#390×C₆₇	C₂²	1	1	yes	characteristic
58	#390×C₆₇	C₂²	1	1	yes	characteristic
59	#390×C₆₇	C₂²	1	2	yes	—
60	#390×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	1	yes	characteristic
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	1	yes	characteristic
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	2	yes	—
71	#388×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	1	yes	characteristic
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	1	yes	characteristic
76	#388×C₆₇	C₂²	1	2	yes	—
77	#388×C₆₇	C₂²	1	2	yes	—
78	#388×C₆₇	C₂²	1	2	yes	—
79	#388×C₆₇	C₂²	1	2	yes	—
80	#388×C₆₇	C₂²	1	2	yes	—
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	1	yes	characteristic
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#387×C₆₇	C₂²	1	1	yes	characteristic
90	#387×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	2	yes	—
92	#387×C₆₇	C₂²	1	2	yes	—
93	#386×C₆₇	C₂²	1	2	yes	—
94	#386×C₆₇	C₂²	1	1	yes	characteristic
95	#386×C₆₇	C₂²	1	1	yes	characteristic
96	#386×C₆₇	C₂²	1	2	yes	—
97	#385×C₆₇	C₂²	1	2	yes	—
98	#385×C₆₇	C₂²	1	1	yes	characteristic
99	#385×C₆₇	C₂²	1	1	yes	characteristic
100	#384×C₆₇	C₂²	1	1	yes	characteristic
101	#382×C₆₇	C₂²	1	1	yes	characteristic
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#381×C₆₇	C₂²	1	2	yes	—
104	#380×C₆₇	C₂²	1	2	yes	—
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	1	yes	characteristic
107	#380×C₆₇	C₂²	1	1	yes	characteristic
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	#376×C₆₇	C₂²	1	2	yes	—
121	#376×C₆₇	C₂²	1	1	yes	characteristic
122	C₄³×C₆₇	C₂²	1	2	yes	—
123	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₆₇	—	2	4	no	—
134	#125×C₆₇	—	4	4	no	—
135	#124×C₆₇	—	4	4	no	—
136	#121×C₆₇	—	2	4	no	—
137	#121×C₆₇	—	2	4	no	—
138	C₄×D₄×C₆₇	—	2	4	no	—
139	C₄×D₄×C₆₇	—	2	4	no	—
140	C₄×D₄×C₆₇	—	4	4	no	—
141	#117×C₆₇	—	2	4	no	—
142	#117×C₆₇	—	2	4	no	—
143	#117×C₆₇	—	2	4	no	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	—	2	4	no	—
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	1	yes	characteristic
210	#95×C₆₇	C₂³	1	1	yes	characteristic
211	#95×C₆₇	C₂³	1	1	yes	characteristic
212	#95×C₆₇	C₂³	1	1	yes	characteristic
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	1	yes	characteristic
215	#95×C₆₇	C₂³	1	1	yes	characteristic
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	1	yes	characteristic
218	#95×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	1	yes	characteristic
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
236	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₆₇	—	2	4	no	—
238	C₂×Q₈×C₆₇	—	4	2	no	—
239	C₂×Q₈×C₆₇	—	4	2	no	—
240	C₂×D₄×C₆₇	—	2	2	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	4	2	no	—
247	C₂×D₄×C₆₇	—	4	1	no	—
248	C₂×D₄×C₆₇	—	4	2	no	—
249	C₂×D₄×C₆₇	—	4	1	no	—
250	C₂×D₄×C₆₇	—	4	2	no	—
251	C₂×D₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	2	no	—
258	C₂²×C₄×C₆₇	—	2	2	no	—
259	C₂²×C₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	4	no	—
261	C₂²×C₄×C₆₇	—	4	1	no	—
262	C₂²×C₄×C₆₇	—	4	1	no	—
263	C₂²×C₄×C₆₇	—	4	1	no	—
264	C₂²×C₄×C₆₇	—	4	2	no	—
265	C₂²×C₄×C₆₇	—	4	2	no	—
266	C₂²×C₄×C₆₇	#41	1	4	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	2	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	4	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	4	no	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	4	2	no	—
300	C₄⋊C₄×C₆₇	—	4	2	no	—
301	C₄⋊C₄×C₆₇	—	4	2	no	—
302	C₄⋊C₄×C₆₇	—	4	1	no	—
303	C₄⋊C₄×C₆₇	—	4	2	no	—
304	C₄⋊C₄×C₆₇	—	4	2	no	—
305	C₄⋊C₄×C₆₇	—	4	2	no	—
306	C₄⋊C₄×C₆₇	—	4	2	no	—
307	C₄⋊C₄×C₆₇	#41	1	4	yes	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	4	2	no	—
320	C₂²⋊C₄×C₆₇	—	4	2	no	—
321	C₂²⋊C₄×C₆₇	—	4	2	no	—
322	C₂²⋊C₄×C₆₇	—	4	2	no	—
323	C₂²⋊C₄×C₆₇	—	4	2	no	—
324	C₂²⋊C₄×C₆₇	—	4	2	no	—
325	C₂²⋊C₄×C₆₇	—	4	2	no	—
326	C₂²⋊C₄×C₆₇	—	4	1	no	—
327	C₂²⋊C₄×C₆₇	—	4	1	no	—
328	C₂²⋊C₄×C₆₇	—	4	1	no	—
329	C₂²⋊C₄×C₆₇	—	4	2	no	—
330	C₂²⋊C₄×C₆₇	—	4	2	no	—
331	C₂²⋊C₄×C₆₇	—	4	2	no	—
332	C₂²⋊C₄×C₆₇	—	4	2	no	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	2	no	—
335	C₄²×C₆₇	—	2	2	no	—
336	C₄²×C₆₇	—	2	4	no	—
337	C₄²×C₆₇	—	2	4	no	—
338	C₄²×C₆₇	—	2	2	no	—
339	C₄²×C₆₇	—	2	2	no	—
340	C₄²×C₆₇	—	2	2	no	—
341	C₄²×C₆₇	—	2	4	no	—
342	C₄²×C₆₇	—	4	2	no	—
343	C₄²×C₆₇	—	4	2	no	—
344	C₄²×C₆₇	—	4	2	no	—
345	C₄²×C₆₇	—	4	2	no	—
346	C₄²×C₆₇	#41	1	4	yes	—
347	C₂³×C₆₇	—	2	1	no	—
348	C₂³×C₆₇	—	2	1	no	—
349	C₂³×C₆₇	—	2	1	no	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	1	no	—
359	C₂³×C₆₇	—	2	1	no	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	1	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	1	no	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	1	no	—
367	C₂³×C₆₇	C₂×#41	1	2	yes	—
368	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
369	Q₈×C₆₇	—	8	4	no	—
370	D₄×C₆₇	—	4	4	no	—
371	D₄×C₆₇	—	4	8	no	—
372	D₄×C₆₇	—	4	4	no	—
373	D₄×C₆₇	—	8	4	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	8	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	1	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	4	4	no	—
428	C₂×C₄×C₆₇	—	4	4	no	—
429	C₂×C₄×C₆₇	—	4	4	no	—
430	C₂×C₄×C₆₇	—	8	4	no	—
431	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
432	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
433	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
434	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
435	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
436	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
437	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
438	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
439	C₂²×C₆₇	—	2	2	no	—
440	C₂²×C₆₇	—	2	2	no	—
441	C₂²×C₆₇	—	2	2	no	—
442	C₂²×C₆₇	—	4	1	no	—
443	C₂²×C₆₇	—	4	1	no	—
444	C₂²×C₆₇	—	4	1	no	—
445	C₂²×C₆₇	—	4	1	no	—
446	C₂²×C₆₇	—	4	1	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	1	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	4	1	no	—
452	C₂²×C₆₇	—	4	1	no	—
453	C₂²×C₆₇	—	4	2	no	—
454	C₂²×C₆₇	—	4	2	no	—
455	C₂²×C₆₇	—	4	1	no	—
456	C₂²×C₆₇	—	4	1	no	—
457	C₂²×C₆₇	—	4	2	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	1	no	—
460	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
461	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
462	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
463	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
464	C₂²×C₆₇	#585	1	1	yes	characteristic
465	C₂²×C₆₇	#585	1	1	yes	characteristic
466	C₂²×C₆₇	#585	1	1	yes	characteristic
467	C₄×C₆₇	—	2	2	no	—
468	C₄×C₆₇	—	2	2	no	—
469	C₄×C₆₇	—	2	2	no	—
470	C₄×C₆₇	—	2	2	no	—
471	C₄×C₆₇	—	2	4	no	—
472	C₄×C₆₇	—	4	1	no	—
473	C₄×C₆₇	—	4	2	no	—
474	C₄×C₆₇	—	4	1	no	—
475	C₄×C₆₇	—	4	1	no	—
476	C₄×C₆₇	—	4	2	no	—
477	C₄×C₆₇	—	4	2	no	—
478	C₄×C₆₇	—	4	1	no	—
479	C₄×C₆₇	—	4	1	no	—
480	C₄×C₆₇	—	4	1	no	—
481	C₄×C₆₇	—	4	2	no	—
482	C₄×C₆₇	—	4	2	no	—
483	C₄×C₆₇	—	4	1	no	—
484	C₄×C₆₇	—	4	2	no	—
485	C₄×C₆₇	—	4	1	no	—
486	C₄×C₆₇	#529	1	4	yes	—
487	#35164	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
488	C₂×C₆₇	—	4	2	no	—
489	C₂×C₆₇	—	8	1	no	—
490	C₂×C₆₇	—	8	2	no	—
491	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
492	C₂×C₆₇	#3455	1	1	yes	characteristic
493	C₂×C₆₇	#3460	1	1	yes	characteristic
494	C₂×C₆₇	#3493	1	1	yes	characteristic
495	C₂×C₆₇	#3494	1	1	yes	characteristic
496	C₂×C₆₇	#3514	1	1	yes	characteristic
497	C₂×C₆₇	#3524	1	1	yes	characteristic
498	#2866	C₂×C₆₇	1	2	yes	complemented
499	#2861	C₂×C₆₇	1	2	yes	complemented
500	#2653	C₂×C₆₇	1	2	yes	complemented
501	#2648	C₂×C₆₇	1	2	yes	complemented
502	#2531	C₂×C₆₇	1	2	yes	complemented
503	#2527	C₂×C₆₇	1	2	yes	complemented
504	#2513	C₂×C₆₇	1	1	yes	characteristic, complemented
505	#2506	C₂×C₆₇	1	1	yes	characteristic, complemented
506	#2500	C₂×C₆₇	1	1	yes	characteristic, complemented
507	#2494	C₂×C₆₇	1	1	yes	characteristic, complemented
508	#2491	C₂×C₆₇	1	1	yes	characteristic, complemented
509	#2485	C₂×C₆₇	1	1	yes	characteristic, complemented
510	#2460	C₂×C₆₇	1	2	yes	complemented
511	#2459	C₂×C₆₇	1	2	yes	complemented
512	#2439	C₂×C₆₇	1	1	yes	characteristic, complemented
513	#2414	C₂×C₆₇	1	1	yes	characteristic
514	#2331	C₂×C₆₇	1	1	yes	characteristic, complemented
515	#2324	C₂×C₆₇	1	1	yes	characteristic, complemented
516	#2319	C₂×C₆₇	1	1	yes	characteristic, complemented
517	#2314	C₂×C₆₇	1	1	yes	characteristic, complemented
518	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
519	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
520	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
521	C₆₇	#35164	1	1	yes	characteristic, direct product factor, Sylow
522	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
523	C₂×#125	C₂²×C₆₇	1	2	yes	—
524	C₂×#124	C₂²×C₆₇	1	2	yes	—
525	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
527	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
528	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
529	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
530	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
531	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
532	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
533	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
534	#401	C₂²×C₆₇	1	2	yes	—
535	#400	C₂²×C₆₇	1	2	yes	—
536	#398	C₂²×C₆₇	1	2	yes	—
537	#397	C₂²×C₆₇	1	2	yes	—
538	#397	C₂²×C₆₇	1	2	yes	—
539	#397	C₂²×C₆₇	1	2	yes	—
540	#397	C₂²×C₆₇	1	2	yes	—
541	#396	C₂²×C₆₇	1	2	yes	—
542	#394	C₂²×C₆₇	1	2	yes	—
543	#394	C₂²×C₆₇	1	2	yes	—
544	#394	C₂²×C₆₇	1	2	yes	—
545	#394	C₂²×C₆₇	1	2	yes	—
546	#394	C₂²×C₆₇	1	2	yes	—
547	#393	C₂²×C₆₇	1	2	yes	—
548	#393	C₂²×C₆₇	1	2	yes	—
549	#392	C₂²×C₆₇	1	2	yes	—
550	#391	C₂²×C₆₇	1	2	yes	—
551	#391	C₂²×C₆₇	1	2	yes	—
552	#391	C₂²×C₆₇	1	2	yes	—
553	#390	C₂²×C₆₇	1	1	yes	characteristic
554	#390	C₂²×C₆₇	1	1	yes	characteristic
555	#390	C₂²×C₆₇	1	2	yes	—
556	#390	C₂²×C₆₇	1	1	yes	characteristic
557	#390	C₂²×C₆₇	1	2	yes	—
558	#390	C₂²×C₆₇	1	1	yes	characteristic
559	#389	C₂²×C₆₇	1	1	yes	characteristic
560	#389	C₂²×C₆₇	1	1	yes	characteristic
561	#389	C₂²×C₆₇	1	1	yes	characteristic
562	#389	C₂²×C₆₇	1	1	yes	characteristic
563	#389	C₂²×C₆₇	1	1	yes	characteristic
564	#389	C₂²×C₆₇	1	1	yes	characteristic
565	#388	C₂²×C₆₇	1	2	yes	—
566	#388	C₂²×C₆₇	1	2	yes	—
567	#388	C₂²×C₆₇	1	2	yes	—
568	#388	C₂²×C₆₇	1	2	yes	—
569	#388	C₂²×C₆₇	1	2	yes	—
570	#388	C₂²×C₆₇	1	1	yes	characteristic
571	#388	C₂²×C₆₇	1	2	yes	—
572	#388	C₂²×C₆₇	1	2	yes	—
573	#388	C₂²×C₆₇	1	2	yes	—
574	#388	C₂²×C₆₇	1	2	yes	—
575	#388	C₂²×C₆₇	1	2	yes	—
576	#388	C₂²×C₆₇	1	2	yes	—
577	#388	C₂²×C₆₇	1	2	yes	—
578	#388	C₂²×C₆₇	1	2	yes	—
579	#388	C₂²×C₆₇	1	2	yes	—
580	#388	C₂²×C₆₇	1	1	yes	characteristic
581	#387	C₂²×C₆₇	1	2	yes	—
582	#387	C₂²×C₆₇	1	2	yes	—
583	#387	C₂²×C₆₇	1	2	yes	—
584	#387	C₂²×C₆₇	1	2	yes	—
585	#387	C₂²×C₆₇	1	1	yes	characteristic
586	#387	C₂²×C₆₇	1	2	yes	—
587	#387	C₂²×C₆₇	1	2	yes	—
588	#387	C₂²×C₆₇	1	2	yes	—
589	#387	C₂²×C₆₇	1	2	yes	—
590	#387	C₂²×C₆₇	1	1	yes	characteristic
591	#386	C₂²×C₆₇	1	2	yes	—
592	#386	C₂²×C₆₇	1	1	yes	characteristic
593	#386	C₂²×C₆₇	1	2	yes	—
594	#386	C₂²×C₆₇	1	1	yes	characteristic
595	#385	C₂²×C₆₇	1	2	yes	—
596	#385	C₂²×C₆₇	1	1	yes	characteristic
597	#385	C₂²×C₆₇	1	1	yes	characteristic
598	#384	C₂²×C₆₇	1	1	yes	characteristic
599	#382	C₂²×C₆₇	1	1	yes	characteristic
600	#382	C₂²×C₆₇	1	1	yes	characteristic
601	#381	C₂²×C₆₇	1	2	yes	—
602	#380	C₂²×C₆₇	1	1	yes	characteristic
603	#380	C₂²×C₆₇	1	1	yes	characteristic
604	#380	C₂²×C₆₇	1	2	yes	—
605	#380	C₂²×C₆₇	1	1	yes	characteristic
606	#380	C₂²×C₆₇	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
608	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
610	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
611	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
612	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
614	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
615	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
616	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
617	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
618	#376	C₂²×C₆₇	1	1	yes	characteristic
619	#376	C₂²×C₆₇	1	2	yes	—
620	C₄³	C₂²×C₆₇	1	2	yes	—
621	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
622	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
624	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
626	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
630	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₄⋊Q₈	—	2	4	no	—
632	#125	—	4	4	no	—
633	#124	—	4	4	no	—
634	#121	—	2	4	no	—
635	#121	—	2	4	no	—
636	C₄×D₄	—	2	4	no	—
637	C₄×D₄	—	2	4	no	—
638	C₄×D₄	—	4	4	no	—
639	#117	—	2	4	no	—
640	#117	—	2	4	no	—
641	#117	—	2	4	no	—
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₄²	—	2	4	no	—
689	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
700	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
701	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
703	#95	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	#95	C₂³×C₆₇	1	2	yes	—
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	1	yes	characteristic
708	#95	C₂³×C₆₇	1	1	yes	characteristic
709	#95	C₂³×C₆₇	1	1	yes	characteristic
710	#95	C₂³×C₆₇	1	1	yes	characteristic
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	1	yes	characteristic
713	#95	C₂³×C₆₇	1	1	yes	characteristic
714	#95	C₂³×C₆₇	1	2	yes	—
715	#95	C₂³×C₆₇	1	1	yes	characteristic
716	#95	C₂³×C₆₇	1	1	yes	characteristic
717	#95	C₂³×C₆₇	1	1	yes	characteristic
718	#95	C₂³×C₆₇	1	2	yes	—
719	#95	C₂³×C₆₇	1	1	yes	characteristic
720	#95	C₂³×C₆₇	1	2	yes	—
721	#95	C₂³×C₆₇	1	2	yes	—
722	#95	C₂³×C₆₇	1	2	yes	—
723	#95	C₂³×C₆₇	1	2	yes	—
724	#95	C₂³×C₆₇	1	2	yes	—
725	#95	C₂³×C₆₇	1	2	yes	—
726	#95	C₂³×C₆₇	1	2	yes	—
727	#95	C₂³×C₆₇	1	2	yes	—
728	#95	C₂³×C₆₇	1	2	yes	—
729	#95	C₂³×C₆₇	1	2	yes	—
730	#95	C₂³×C₆₇	1	2	yes	—
731	#95	C₂³×C₆₇	1	2	yes	—
732	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
734	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
735	C₂×Q₈	—	2	4	no	—
736	C₂×Q₈	—	4	2	no	—
737	C₂×Q₈	—	4	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	1	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	1	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	#41×C₆₇	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₄⋊C₄	#41×C₆₇	1	4	yes	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	1	no	—
828	C₂²⋊C₄	—	4	1	no	—
829	C₂²⋊C₄	—	4	1	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	4	no	—
835	C₄²	—	2	4	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	4	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	#41×C₆₇	1	4	yes	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	1	no	—
865	C₂³	C₂×#41×C₆₇	1	2	yes	—
866	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
867	Q₈	—	8	4	no	—
868	D₄	—	4	4	no	—
869	D₄	—	4	8	no	—
870	D₄	—	4	4	no	—
871	D₄	—	8	4	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	8	4	no	—
929	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
930	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
931	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
932	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
933	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
934	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
935	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
936	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	2	no	—
958	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
959	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
960	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
961	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
962	C₂²	#585×C₆₇	1	1	yes	characteristic
963	C₂²	#585×C₆₇	1	1	yes	characteristic
964	C₂²	#585×C₆₇	1	1	yes	characteristic
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	4	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	#529×C₆₇	1	4	yes	—
985	C₂	—	4	2	no	—
986	C₂	—	8	1	no	—
987	C₂	—	8	2	no	—
988	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
989	C₂	C₆₇×#3455	1	1	yes	characteristic
990	C₂	C₆₇×#3460	1	1	yes	characteristic
991	C₂	C₆₇×#3493	1	1	yes	characteristic
992	C₂	C₆₇×#3494	1	1	yes	characteristic
993	C₂	C₆₇×#3514	1	1	yes	characteristic
994	C₂	C₆₇×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2414	C₂
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×#2866	C₂	semidirect
2. C₆₇×#2861	C₂	semidirect
3. C₆₇×#2653	C₂	semidirect
4. C₆₇×#2648	C₂	semidirect
5. C₆₇×#2531	C₂	semidirect
6. C₆₇×#2527	C₂	semidirect
7. C₆₇×#2513	C₂	semidirect
8. C₆₇×#2506	C₂	semidirect
9. C₆₇×#2500	C₂	semidirect
10. C₆₇×#2494	C₂	semidirect
11. C₆₇×#2491	C₂	semidirect
12. C₆₇×#2485	C₂	semidirect
13. C₆₇×#2460	C₂	semidirect
14. C₆₇×#2459	C₂	semidirect
15. C₆₇×#2439	C₂	semidirect
17. C₆₇×#2331	C₂	semidirect
18. C₆₇×#2324	C₂	semidirect
19. C₆₇×#2319	C₂	semidirect
20. C₆₇×#2314	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₆₇×#2290	C₂	semidirect
23. C₄×#117×C₆₇	C₂	semidirect
487. #35164	C₆₇	direct (N × H)
498. #2866	C₂×C₆₇	semidirect
499. #2861	C₂×C₆₇	semidirect
500. #2653	C₂×C₆₇	semidirect
501. #2648	C₂×C₆₇	semidirect
502. #2531	C₂×C₆₇	semidirect
503. #2527	C₂×C₆₇	semidirect
504. #2513	C₂×C₆₇	semidirect
505. #2506	C₂×C₆₇	semidirect
506. #2500	C₂×C₆₇	semidirect
507. #2494	C₂×C₆₇	semidirect
508. #2491	C₂×C₆₇	semidirect
509. #2485	C₂×C₆₇	semidirect
510. #2460	C₂×C₆₇	semidirect
511. #2459	C₂×C₆₇	semidirect
512. #2439	C₂×C₆₇	semidirect
514. #2331	C₂×C₆₇	semidirect
515. #2324	C₂×C₆₇	semidirect
516. #2319	C₂×C₆₇	semidirect
517. #2314	C₂×C₆₇	semidirect
518. C₄×#121	C₂×C₆₇	semidirect
519. #2290	C₂×C₆₇	semidirect
520. C₄×#117	C₂×C₆₇	semidirect
521. C₆₇	#35164	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×#2866	2
C₆₇×#2861	2
C₆₇×#2653	2
C₆₇×#2648	2
C₆₇×#2531	2
C₆₇×#2527	2
C₆₇×#2513	2
C₆₇×#2506	2
C₆₇×#2500	2
C₆₇×#2494	2
C₆₇×#2491	2
C₆₇×#2485	2
C₆₇×#2460	2
C₆₇×#2459	2
C₆₇×#2439	2
C₆₇×#2414	2
C₆₇×#2331	2
C₆₇×#2324	2
C₆₇×#2319	2
C₆₇×#2314	2
C₄×#121×C₆₇	2
C₆₇×#2290	2
C₄×#117×C₆₇	2
#35164	67

Subgroups — C67×#35164 #30714415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35164 #30714415