Subgroups — C₆₇×#59449 #30738700

Order 17152.

1564 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2777	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2772	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2575	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2571	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2566	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2529	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2519	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2517	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2515	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2512	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2448	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2448	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2357	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
24	C₂×#126×C₆₇	C₂²	1	2	yes	—
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	#400×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#399×C₆₇	C₂²	1	2	yes	—
36	#399×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#398×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	#397×C₆₇	C₂²	1	2	yes	—
44	#397×C₆₇	C₂²	1	2	yes	—
45	#396×C₆₇	C₂²	1	2	yes	—
46	#396×C₆₇	C₂²	1	2	yes	—
47	#396×C₆₇	C₂²	1	2	yes	—
48	#391×C₆₇	C₂²	1	1	yes	characteristic
49	#391×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	1	yes	characteristic
51	#390×C₆₇	C₂²	1	1	yes	characteristic
52	#390×C₆₇	C₂²	1	1	yes	characteristic
53	#390×C₆₇	C₂²	1	1	yes	characteristic
54	#390×C₆₇	C₂²	1	1	yes	characteristic
55	#390×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	1	yes	characteristic
58	#389×C₆₇	C₂²	1	1	yes	characteristic
59	#389×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	1	yes	characteristic
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	1	yes	characteristic
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	2	yes	—
81	#387×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	1	yes	characteristic
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic
89	#387×C₆₇	C₂²	1	1	yes	characteristic
90	#385×C₆₇	C₂²	1	2	yes	—
91	#385×C₆₇	C₂²	1	2	yes	—
92	#384×C₆₇	C₂²	1	1	yes	characteristic
93	#384×C₆₇	C₂²	1	1	yes	characteristic
94	#383×C₆₇	C₂²	1	2	yes	—
95	#382×C₆₇	C₂²	1	1	yes	characteristic
96	#382×C₆₇	C₂²	1	2	yes	—
97	#382×C₆₇	C₂²	1	2	yes	—
98	#382×C₆₇	C₂²	1	2	yes	—
99	#382×C₆₇	C₂²	1	1	yes	characteristic
100	#382×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	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
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×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	#376×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
126	#126×C₆₇	—	2	8	no	—
127	#125×C₆₇	—	2	4	no	—
128	#125×C₆₇	—	2	4	no	—
129	#124×C₆₇	—	2	4	no	—
130	C₄×Q₈×C₆₇	—	2	4	no	—
131	C₄×Q₈×C₆₇	—	2	4	no	—
132	C₄×Q₈×C₆₇	—	2	4	no	—
133	C₄×D₄×C₆₇	—	2	4	no	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	#95×C₆₇	C₂³	1	1	yes	characteristic
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	1	yes	characteristic
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
216	#95×C₆₇	C₂³	1	1	yes	characteristic
217	#95×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
222	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₆₇	—	2	2	no	—
232	C₂×Q₈×C₆₇	—	2	2	no	—
233	C₂×Q₈×C₆₇	#41	1	4	yes	—
234	C₂×D₄×C₆₇	—	2	2	no	—
235	C₂×D₄×C₆₇	—	2	2	no	—
236	C₂×D₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	4	2	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₄⋊C₄×C₆₇	—	2	2	no	—
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	4	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	4	1	no	—
281	C₄⋊C₄×C₆₇	—	4	1	no	—
282	C₄⋊C₄×C₆₇	—	4	1	no	—
283	C₄⋊C₄×C₆₇	—	4	1	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	1	no	—
286	C₄⋊C₄×C₆₇	—	4	2	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	1	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₄⋊C₄×C₆₇	—	4	2	no	—
292	C₄⋊C₄×C₆₇	#41	1	4	yes	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	4	2	no	—
300	C₂²⋊C₄×C₆₇	—	4	2	no	—
301	C₂²⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₄²×C₆₇	—	2	4	no	—
307	C₄²×C₆₇	—	2	2	no	—
308	C₄²×C₆₇	—	2	4	no	—
309	C₄²×C₆₇	—	2	4	no	—
310	C₄²×C₆₇	—	2	2	no	—
311	C₄²×C₆₇	—	2	2	no	—
312	C₄²×C₆₇	—	2	2	no	—
313	C₄²×C₆₇	—	2	4	no	—
314	C₄²×C₆₇	—	2	2	no	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₄²×C₆₇	—	2	2	no	—
317	C₄²×C₆₇	—	4	1	no	—
318	C₄²×C₆₇	—	4	2	no	—
319	C₄²×C₆₇	—	4	2	no	—
320	C₄²×C₆₇	—	4	1	no	—
321	C₄²×C₆₇	—	4	1	no	—
322	C₄²×C₆₇	—	4	2	no	—
323	C₄²×C₆₇	#41	1	4	yes	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
332	Q₈×C₆₇	—	2	8	no	—
333	D₄×C₆₇	—	4	4	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	1	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	1	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	1	no	—
344	C₂×C₄×C₆₇	—	2	1	no	—
345	C₂×C₄×C₆₇	—	2	1	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	2	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	1	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	8	4	no	—
392	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
393	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
394	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
395	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
396	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
397	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
398	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
399	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
400	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	2	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
409	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂²×C₆₇	#585	1	1	yes	characteristic
413	C₂²×C₆₇	#585	1	1	yes	characteristic
414	C₂²×C₆₇	#585	1	1	yes	characteristic
415	C₄×C₆₇	—	2	4	no	—
416	C₄×C₆₇	—	2	2	no	—
417	C₄×C₆₇	—	2	2	no	—
418	C₄×C₆₇	—	2	2	no	—
419	C₄×C₆₇	—	2	2	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	—	4	2	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	1	no	—
426	C₄×C₆₇	—	4	2	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	1	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	1	no	—
433	C₄×C₆₇	—	4	1	no	—
434	C₄×C₆₇	—	4	1	no	—
435	C₄×C₆₇	—	4	1	no	—
436	C₄×C₆₇	#552	1	4	yes	—
437	#59449	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂×C₆₇	—	8	2	no	—
439	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
440	C₂×C₆₇	#3480	1	1	yes	characteristic
441	C₂×C₆₇	#3480	1	1	yes	characteristic
442	C₂×C₆₇	#3510	1	1	yes	characteristic
443	C₂×C₆₇	#3515	1	1	yes	characteristic
444	C₂×C₆₇	#3524	1	1	yes	characteristic
445	C₂×C₆₇	#3565	1	1	yes	characteristic
446	#2777	C₂×C₆₇	1	2	yes	complemented
447	#2772	C₂×C₆₇	1	2	yes	complemented
448	#2575	C₂×C₆₇	1	2	yes	complemented
449	#2571	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2570	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#2566	C₂×C₆₇	1	1	yes	characteristic
452	#2565	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#2529	C₂×C₆₇	1	2	yes	complemented
454	#2519	C₂×C₆₇	1	2	yes	complemented
455	#2517	C₂×C₆₇	1	2	yes	complemented
456	#2515	C₂×C₆₇	1	2	yes	complemented
457	#2513	C₂×C₆₇	1	1	yes	characteristic
458	#2512	C₂×C₆₇	1	1	yes	characteristic
459	#2448	C₂×C₆₇	1	1	yes	characteristic
460	#2448	C₂×C₆₇	1	1	yes	characteristic
461	#2373	C₂×C₆₇	1	2	yes	complemented
462	#2357	C₂×C₆₇	1	1	yes	characteristic
463	#2356	C₂×C₆₇	1	1	yes	characteristic, complemented
464	#2355	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#2351	C₂×C₆₇	1	1	yes	characteristic, complemented
466	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
467	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
468	C₄×#124	C₂×C₆₇	1	1	yes	characteristic
469	C₆₇	#59449	1	1	yes	characteristic, direct product factor, Sylow
470	C₂×#126	C₂²×C₆₇	1	2	yes	—
471	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
474	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
478	#400	C₂²×C₆₇	1	2	yes	—
479	#400	C₂²×C₆₇	1	2	yes	—
480	#400	C₂²×C₆₇	1	2	yes	—
481	#399	C₂²×C₆₇	1	2	yes	—
482	#399	C₂²×C₆₇	1	2	yes	—
483	#398	C₂²×C₆₇	1	2	yes	—
484	#398	C₂²×C₆₇	1	2	yes	—
485	#398	C₂²×C₆₇	1	2	yes	—
486	#397	C₂²×C₆₇	1	2	yes	—
487	#397	C₂²×C₆₇	1	2	yes	—
488	#397	C₂²×C₆₇	1	2	yes	—
489	#397	C₂²×C₆₇	1	2	yes	—
490	#397	C₂²×C₆₇	1	2	yes	—
491	#396	C₂²×C₆₇	1	2	yes	—
492	#396	C₂²×C₆₇	1	2	yes	—
493	#396	C₂²×C₆₇	1	2	yes	—
494	#391	C₂²×C₆₇	1	1	yes	characteristic
495	#391	C₂²×C₆₇	1	1	yes	characteristic
496	#391	C₂²×C₆₇	1	1	yes	characteristic
497	#390	C₂²×C₆₇	1	1	yes	characteristic
498	#390	C₂²×C₆₇	1	1	yes	characteristic
499	#390	C₂²×C₆₇	1	1	yes	characteristic
500	#390	C₂²×C₆₇	1	1	yes	characteristic
501	#390	C₂²×C₆₇	1	1	yes	characteristic
502	#389	C₂²×C₆₇	1	1	yes	characteristic
503	#389	C₂²×C₆₇	1	1	yes	characteristic
504	#389	C₂²×C₆₇	1	1	yes	characteristic
505	#389	C₂²×C₆₇	1	1	yes	characteristic
506	#389	C₂²×C₆₇	1	1	yes	characteristic
507	#389	C₂²×C₆₇	1	1	yes	characteristic
508	#389	C₂²×C₆₇	1	2	yes	—
509	#389	C₂²×C₆₇	1	2	yes	—
510	#389	C₂²×C₆₇	1	2	yes	—
511	#388	C₂²×C₆₇	1	2	yes	—
512	#388	C₂²×C₆₇	1	2	yes	—
513	#388	C₂²×C₆₇	1	2	yes	—
514	#388	C₂²×C₆₇	1	2	yes	—
515	#388	C₂²×C₆₇	1	2	yes	—
516	#388	C₂²×C₆₇	1	2	yes	—
517	#388	C₂²×C₆₇	1	2	yes	—
518	#388	C₂²×C₆₇	1	2	yes	—
519	#388	C₂²×C₆₇	1	2	yes	—
520	#388	C₂²×C₆₇	1	2	yes	—
521	#388	C₂²×C₆₇	1	2	yes	—
522	#387	C₂²×C₆₇	1	1	yes	characteristic
523	#387	C₂²×C₆₇	1	1	yes	characteristic
524	#387	C₂²×C₆₇	1	1	yes	characteristic
525	#387	C₂²×C₆₇	1	2	yes	—
526	#387	C₂²×C₆₇	1	2	yes	—
527	#387	C₂²×C₆₇	1	1	yes	characteristic
528	#387	C₂²×C₆₇	1	2	yes	—
529	#387	C₂²×C₆₇	1	2	yes	—
530	#387	C₂²×C₆₇	1	2	yes	—
531	#387	C₂²×C₆₇	1	2	yes	—
532	#387	C₂²×C₆₇	1	2	yes	—
533	#387	C₂²×C₆₇	1	2	yes	—
534	#387	C₂²×C₆₇	1	2	yes	—
535	#387	C₂²×C₆₇	1	2	yes	—
536	#385	C₂²×C₆₇	1	2	yes	—
537	#385	C₂²×C₆₇	1	2	yes	—
538	#384	C₂²×C₆₇	1	1	yes	characteristic
539	#384	C₂²×C₆₇	1	1	yes	characteristic
540	#383	C₂²×C₆₇	1	2	yes	—
541	#382	C₂²×C₆₇	1	1	yes	characteristic
542	#382	C₂²×C₆₇	1	1	yes	characteristic
543	#382	C₂²×C₆₇	1	1	yes	characteristic
544	#382	C₂²×C₆₇	1	1	yes	characteristic
545	#382	C₂²×C₆₇	1	1	yes	characteristic
546	#382	C₂²×C₆₇	1	2	yes	—
547	#382	C₂²×C₆₇	1	2	yes	—
548	#382	C₂²×C₆₇	1	2	yes	—
549	#381	C₂²×C₆₇	1	2	yes	—
550	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
553	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
555	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
564	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
565	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
567	#376	C₂²×C₆₇	1	2	yes	—
568	C₄³	C₂²×C₆₇	1	1	yes	characteristic
569	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
572	#126	—	2	8	no	—
573	#125	—	2	4	no	—
574	#125	—	2	4	no	—
575	#124	—	2	4	no	—
576	C₄×Q₈	—	2	4	no	—
577	C₄×Q₈	—	2	4	no	—
578	C₄×Q₈	—	2	4	no	—
579	C₄×D₄	—	2	4	no	—
580	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
642	#95	C₂³×C₆₇	1	1	yes	characteristic
643	#95	C₂³×C₆₇	1	2	yes	—
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	1	yes	characteristic
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	1	yes	characteristic
652	#95	C₂³×C₆₇	1	1	yes	characteristic
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	1	yes	characteristic
656	#95	C₂³×C₆₇	1	1	yes	characteristic
657	#95	C₂³×C₆₇	1	1	yes	characteristic
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	1	yes	characteristic
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	1	yes	characteristic
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	1	yes	characteristic
665	#95	C₂³×C₆₇	1	1	yes	characteristic
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	1	yes	characteristic
669	#95	C₂³×C₆₇	1	2	yes	—
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	#95	C₂³×C₆₇	1	2	yes	—
673	#95	C₂³×C₆₇	1	2	yes	—
674	#95	C₂³×C₆₇	1	2	yes	—
675	#95	C₂³×C₆₇	1	2	yes	—
676	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	#41×C₆₇	1	4	yes	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	1	no	—
728	C₄⋊C₄	—	4	1	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	#41×C₆₇	1	4	yes	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	4	1	no	—
764	C₄²	—	4	2	no	—
765	C₄²	—	4	2	no	—
766	C₄²	—	4	1	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	2	no	—
769	C₄²	#41×C₆₇	1	4	yes	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
778	Q₈	—	2	8	no	—
779	D₄	—	4	4	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
839	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
840	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
841	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
842	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
843	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
844	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
845	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
846	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
855	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
856	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
857	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
858	C₂²	#585×C₆₇	1	1	yes	characteristic
859	C₂²	#585×C₆₇	1	1	yes	characteristic
860	C₂²	#585×C₆₇	1	1	yes	characteristic
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	1	no	—
882	C₄	#552×C₆₇	1	4	yes	—
883	C₂	—	8	2	no	—
884	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
885	C₂	C₆₇×#3480	1	1	yes	characteristic
886	C₂	C₆₇×#3480	1	1	yes	characteristic
887	C₂	C₆₇×#3510	1	1	yes	characteristic
888	C₂	C₆₇×#3515	1	1	yes	characteristic
889	C₂	C₆₇×#3524	1	1	yes	characteristic
890	C₂	C₆₇×#3565	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×#2777	C₂	semidirect
2. C₆₇×#2772	C₂	semidirect
3. C₆₇×#2575	C₂	semidirect
4. C₆₇×#2571	C₂	semidirect
5. C₆₇×#2570	C₂	semidirect
7. C₆₇×#2565	C₂	semidirect
8. C₆₇×#2529	C₂	semidirect
9. C₆₇×#2519	C₂	semidirect
10. C₆₇×#2517	C₂	semidirect
11. C₆₇×#2515	C₂	semidirect
16. C₆₇×#2373	C₂	semidirect
18. C₆₇×#2356	C₂	semidirect
19. C₆₇×#2355	C₂	semidirect
20. C₆₇×#2351	C₂	semidirect
21. C₄×#125×C₆₇	C₂	semidirect
22. C₄×#125×C₆₇	C₂	semidirect
437. #59449	C₆₇	direct (N × H)
446. #2777	C₂×C₆₇	semidirect
447. #2772	C₂×C₆₇	semidirect
448. #2575	C₂×C₆₇	semidirect
449. #2571	C₂×C₆₇	semidirect
450. #2570	C₂×C₆₇	semidirect
452. #2565	C₂×C₆₇	semidirect
453. #2529	C₂×C₆₇	semidirect
454. #2519	C₂×C₆₇	semidirect
455. #2517	C₂×C₆₇	semidirect
456. #2515	C₂×C₆₇	semidirect
461. #2373	C₂×C₆₇	semidirect
463. #2356	C₂×C₆₇	semidirect
464. #2355	C₂×C₆₇	semidirect
465. #2351	C₂×C₆₇	semidirect
466. C₄×#125	C₂×C₆₇	semidirect
467. C₄×#125	C₂×C₆₇	semidirect
469. C₆₇	#59449	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×#2777	2
C₆₇×#2772	2
C₆₇×#2575	2
C₆₇×#2571	2
C₆₇×#2570	2
C₆₇×#2566	2
C₆₇×#2565	2
C₆₇×#2529	2
C₆₇×#2519	2
C₆₇×#2517	2
C₆₇×#2515	2
C₆₇×#2513	2
C₆₇×#2512	2
C₆₇×#2448	2
C₆₇×#2373	2
C₆₇×#2357	2
C₆₇×#2356	2
C₆₇×#2355	2
C₆₇×#2351	2
C₄×#125×C₆₇	2
C₄×#124×C₆₇	2
#59449	67

Subgroups — C67×#59449 #30738700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59449 #30738700