Subgroups — C₆₇×#59710 #30738961

Order 17152.

1692 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2800	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2777	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2601	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2523	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#2490	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2469	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2448	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic
19	C₆₇×#2347	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#126×C₆₇	C₂²	1	2	yes	—
27	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#124×C₆₇	C₂²	1	2	yes	—
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
35	#400×C₆₇	C₂²	1	2	yes	—
36	#399×C₆₇	C₂²	1	2	yes	—
37	#399×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	#397×C₆₇	C₂²	1	2	yes	—
44	#396×C₆₇	C₂²	1	2	yes	—
45	#396×C₆₇	C₂²	1	2	yes	—
46	#396×C₆₇	C₂²	1	2	yes	—
47	#395×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	—
49	#394×C₆₇	C₂²	1	2	yes	—
50	#393×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
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	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#390×C₆₇	C₂²	1	1	yes	characteristic
58	#390×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	1	yes	characteristic
61	#389×C₆₇	C₂²	1	1	yes	characteristic
62	#389×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	2	yes	—
65	#389×C₆₇	C₂²	1	2	yes	—
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	1	yes	characteristic
68	#389×C₆₇	C₂²	1	1	yes	characteristic
69	#389×C₆₇	C₂²	1	1	yes	characteristic
70	#389×C₆₇	C₂²	1	1	yes	characteristic
71	#389×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	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	1	yes	characteristic
82	#388×C₆₇	C₂²	1	2	yes	—
83	#388×C₆₇	C₂²	1	1	yes	characteristic
84	#388×C₆₇	C₂²	1	2	yes	—
85	#388×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	1	yes	characteristic
88	#387×C₆₇	C₂²	1	1	yes	characteristic
89	#387×C₆₇	C₂²	1	2	yes	—
90	#387×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	2	yes	—
92	#387×C₆₇	C₂²	1	2	yes	—
93	#387×C₆₇	C₂²	1	1	yes	characteristic
94	#386×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#384×C₆₇	C₂²	1	1	yes	characteristic
97	#383×C₆₇	C₂²	1	2	yes	—
98	#383×C₆₇	C₂²	1	2	yes	—
99	#383×C₆₇	C₂²	1	1	yes	characteristic
100	#382×C₆₇	C₂²	1	1	yes	characteristic
101	#380×C₆₇	C₂²	1	2	yes	—
102	#380×C₆₇	C₂²	1	1	yes	characteristic
103	#380×C₆₇	C₂²	1	1	yes	characteristic
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	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	2	yes	—
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
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	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₆₇	—	2	4	no	—
129	#126×C₆₇	—	2	4	no	—
130	#126×C₆₇	—	4	4	no	—
131	#125×C₆₇	—	2	4	no	—
132	#125×C₆₇	—	2	4	no	—
133	#124×C₆₇	—	4	4	no	—
134	#121×C₆₇	—	2	4	no	—
135	C₄×Q₈×C₆₇	—	4	4	no	—
136	C₄×D₄×C₆₇	—	2	4	no	—
137	#117×C₆₇	—	2	4	no	—
138	#117×C₆₇	—	2	8	no	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
213	#95×C₆₇	C₂³	1	1	yes	characteristic
214	#95×C₆₇	C₂³	1	1	yes	characteristic
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₆₇	—	2	4	no	—
236	C₂×Q₈×C₆₇	—	2	4	no	—
237	C₂×Q₈×C₆₇	—	4	2	no	—
238	C₂×D₄×C₆₇	—	2	2	no	—
239	C₂×D₄×C₆₇	—	2	2	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	2	no	—
242	C₂×D₄×C₆₇	—	4	2	no	—
243	C₂×D₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	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	4	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	4	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	4	2	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	1	no	—
291	C₄⋊C₄×C₆₇	—	4	1	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	2	no	—
294	C₄⋊C₄×C₆₇	—	4	2	no	—
295	C₄⋊C₄×C₆₇	—	4	2	no	—
296	C₄⋊C₄×C₆₇	#41	1	4	yes	—
297	C₄⋊C₄×C₆₇	#41	1	4	yes	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	2	no	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	no	—
306	C₂²⋊C₄×C₆₇	—	2	2	no	—
307	C₂²⋊C₄×C₆₇	—	2	4	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	1	no	—
310	C₂²⋊C₄×C₆₇	—	4	1	no	—
311	C₂²⋊C₄×C₆₇	—	4	2	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	—	4	2	no	—
315	C₂²⋊C₄×C₆₇	—	4	2	no	—
316	C₂²⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₄²×C₆₇	—	2	4	no	—
320	C₄²×C₆₇	—	2	4	no	—
321	C₄²×C₆₇	—	2	2	no	—
322	C₄²×C₆₇	—	2	2	no	—
323	C₄²×C₆₇	—	2	2	no	—
324	C₄²×C₆₇	—	2	2	no	—
325	C₄²×C₆₇	—	2	2	no	—
326	C₄²×C₆₇	—	2	2	no	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	4	1	no	—
329	C₄²×C₆₇	—	4	2	no	—
330	C₄²×C₆₇	—	4	1	no	—
331	C₄²×C₆₇	—	4	2	no	—
332	C₄²×C₆₇	—	4	2	no	—
333	C₄²×C₆₇	—	4	2	no	—
334	C₄²×C₆₇	—	4	2	no	—
335	C₄²×C₆₇	#41	1	4	yes	—
336	C₂³×C₆₇	—	2	1	no	—
337	C₂³×C₆₇	—	2	1	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	1	no	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	2	1	no	—
344	C₂³×C₆₇	—	2	1	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	1	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	1	no	—
350	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
351	Q₈×C₆₇	—	4	8	no	—
352	D₄×C₆₇	—	4	4	no	—
353	D₄×C₆₇	—	8	4	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	1	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	1	no	—
377	C₂×C₄×C₆₇	—	2	1	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	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	1	no	—
386	C₂×C₄×C₆₇	—	2	2	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	1	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	2	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	1	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	1	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	2	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	4	8	no	—
409	C₂×C₄×C₆₇	—	4	4	no	—
410	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
411	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
412	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
413	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
414	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
415	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
416	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
417	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
419	C₂²×C₆₇	—	4	1	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	1	no	—
423	C₂²×C₆₇	—	4	1	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	1	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	—	4	1	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	1	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	1	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
434	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
435	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂²×C₆₇	#585	1	1	yes	characteristic
439	C₂²×C₆₇	#585	1	1	yes	characteristic
440	C₄×C₆₇	—	2	2	no	—
441	C₄×C₆₇	—	2	4	no	—
442	C₄×C₆₇	—	2	2	no	—
443	C₄×C₆₇	—	2	2	no	—
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	4	1	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	1	no	—
450	C₄×C₆₇	—	4	2	no	—
451	C₄×C₆₇	—	4	1	no	—
452	C₄×C₆₇	—	4	1	no	—
453	C₄×C₆₇	—	4	2	no	—
454	C₄×C₆₇	—	4	1	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	1	no	—
457	C₄×C₆₇	—	4	2	no	—
458	C₄×C₆₇	—	4	1	no	—
459	C₄×C₆₇	—	4	1	no	—
460	C₄×C₆₇	#556	1	4	yes	—
461	#59710	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
462	C₂×C₆₇	—	8	1	no	—
463	C₂×C₆₇	—	8	2	no	—
464	C₂×C₆₇	C₂×#556	1	1	yes	characteristic
465	C₂×C₆₇	#3475	1	1	yes	characteristic
466	C₂×C₆₇	#3480	1	1	yes	characteristic
467	C₂×C₆₇	#3511	1	1	yes	characteristic
468	C₂×C₆₇	#3513	1	1	yes	characteristic
469	C₂×C₆₇	#3517	1	1	yes	characteristic
470	C₂×C₆₇	#3565	1	1	yes	characteristic
471	#2800	C₂×C₆₇	1	2	yes	complemented
472	#2777	C₂×C₆₇	1	2	yes	complemented
473	#2601	C₂×C₆₇	1	2	yes	complemented
474	#2550	C₂×C₆₇	1	1	yes	characteristic, complemented
475	#2523	C₂×C₆₇	1	2	yes	complemented
476	#2521	C₂×C₆₇	1	2	yes	complemented
477	#2513	C₂×C₆₇	1	1	yes	characteristic, complemented
478	#2512	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#2495	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#2491	C₂×C₆₇	1	1	yes	characteristic
481	#2490	C₂×C₆₇	1	1	yes	characteristic
482	#2469	C₂×C₆₇	1	2	yes	complemented
483	#2454	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#2448	C₂×C₆₇	1	2	yes	complemented
485	#2441	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#2370	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#2370	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#2363	C₂×C₆₇	1	1	yes	characteristic
489	#2347	C₂×C₆₇	1	2	yes	complemented
490	#2347	C₂×C₆₇	1	1	yes	characteristic, complemented
491	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
492	C₄×#126	C₂×C₆₇	1	1	yes	characteristic, complemented
493	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
494	C₆₇	#59710	1	1	yes	characteristic, direct product factor, Sylow
495	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
496	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×#126	C₂²×C₆₇	1	2	yes	—
498	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
499	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×#124	C₂²×C₆₇	1	2	yes	—
501	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
503	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×#117	C₂²×C₆₇	1	2	yes	—
505	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
506	#400	C₂²×C₆₇	1	2	yes	—
507	#399	C₂²×C₆₇	1	2	yes	—
508	#399	C₂²×C₆₇	1	2	yes	—
509	#398	C₂²×C₆₇	1	2	yes	—
510	#397	C₂²×C₆₇	1	2	yes	—
511	#397	C₂²×C₆₇	1	2	yes	—
512	#397	C₂²×C₆₇	1	2	yes	—
513	#397	C₂²×C₆₇	1	2	yes	—
514	#397	C₂²×C₆₇	1	2	yes	—
515	#396	C₂²×C₆₇	1	2	yes	—
516	#396	C₂²×C₆₇	1	2	yes	—
517	#396	C₂²×C₆₇	1	2	yes	—
518	#395	C₂²×C₆₇	1	2	yes	—
519	#394	C₂²×C₆₇	1	2	yes	—
520	#394	C₂²×C₆₇	1	2	yes	—
521	#393	C₂²×C₆₇	1	2	yes	—
522	#391	C₂²×C₆₇	1	2	yes	—
523	#391	C₂²×C₆₇	1	2	yes	—
524	#390	C₂²×C₆₇	1	2	yes	—
525	#390	C₂²×C₆₇	1	2	yes	—
526	#390	C₂²×C₆₇	1	1	yes	characteristic
527	#390	C₂²×C₆₇	1	1	yes	characteristic
528	#390	C₂²×C₆₇	1	1	yes	characteristic
529	#390	C₂²×C₆₇	1	1	yes	characteristic
530	#390	C₂²×C₆₇	1	1	yes	characteristic
531	#389	C₂²×C₆₇	1	1	yes	characteristic
532	#389	C₂²×C₆₇	1	1	yes	characteristic
533	#389	C₂²×C₆₇	1	2	yes	—
534	#389	C₂²×C₆₇	1	2	yes	—
535	#389	C₂²×C₆₇	1	1	yes	characteristic
536	#389	C₂²×C₆₇	1	2	yes	—
537	#389	C₂²×C₆₇	1	1	yes	characteristic
538	#389	C₂²×C₆₇	1	2	yes	—
539	#389	C₂²×C₆₇	1	1	yes	characteristic
540	#389	C₂²×C₆₇	1	2	yes	—
541	#389	C₂²×C₆₇	1	1	yes	characteristic
542	#389	C₂²×C₆₇	1	1	yes	characteristic
543	#388	C₂²×C₆₇	1	1	yes	characteristic
544	#388	C₂²×C₆₇	1	1	yes	characteristic
545	#388	C₂²×C₆₇	1	1	yes	characteristic
546	#388	C₂²×C₆₇	1	2	yes	—
547	#388	C₂²×C₆₇	1	2	yes	—
548	#388	C₂²×C₆₇	1	2	yes	—
549	#388	C₂²×C₆₇	1	2	yes	—
550	#388	C₂²×C₆₇	1	2	yes	—
551	#388	C₂²×C₆₇	1	2	yes	—
552	#388	C₂²×C₆₇	1	2	yes	—
553	#388	C₂²×C₆₇	1	2	yes	—
554	#388	C₂²×C₆₇	1	2	yes	—
555	#388	C₂²×C₆₇	1	2	yes	—
556	#388	C₂²×C₆₇	1	2	yes	—
557	#387	C₂²×C₆₇	1	1	yes	characteristic
558	#387	C₂²×C₆₇	1	1	yes	characteristic
559	#387	C₂²×C₆₇	1	1	yes	characteristic
560	#387	C₂²×C₆₇	1	2	yes	—
561	#387	C₂²×C₆₇	1	2	yes	—
562	#387	C₂²×C₆₇	1	2	yes	—
563	#387	C₂²×C₆₇	1	2	yes	—
564	#387	C₂²×C₆₇	1	2	yes	—
565	#386	C₂²×C₆₇	1	2	yes	—
566	#385	C₂²×C₆₇	1	2	yes	—
567	#384	C₂²×C₆₇	1	1	yes	characteristic
568	#383	C₂²×C₆₇	1	1	yes	characteristic
569	#383	C₂²×C₆₇	1	2	yes	—
570	#383	C₂²×C₆₇	1	2	yes	—
571	#382	C₂²×C₆₇	1	1	yes	characteristic
572	#380	C₂²×C₆₇	1	2	yes	—
573	#380	C₂²×C₆₇	1	1	yes	characteristic
574	#380	C₂²×C₆₇	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
579	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
582	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
588	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
590	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
593	C₄³	C₂²×C₆₇	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
595	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
597	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
599	C₄⋊Q₈	—	2	4	no	—
600	#126	—	2	4	no	—
601	#126	—	4	4	no	—
602	#125	—	2	4	no	—
603	#125	—	2	4	no	—
604	#124	—	4	4	no	—
605	#121	—	2	4	no	—
606	C₄×Q₈	—	4	4	no	—
607	C₄×D₄	—	2	4	no	—
608	#117	—	2	4	no	—
609	#117	—	2	8	no	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
674	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
675	#95	C₂³×C₆₇	1	1	yes	characteristic
676	#95	C₂³×C₆₇	1	1	yes	characteristic
677	#95	C₂³×C₆₇	1	2	yes	—
678	#95	C₂³×C₆₇	1	1	yes	characteristic
679	#95	C₂³×C₆₇	1	2	yes	—
680	#95	C₂³×C₆₇	1	1	yes	characteristic
681	#95	C₂³×C₆₇	1	1	yes	characteristic
682	#95	C₂³×C₆₇	1	1	yes	characteristic
683	#95	C₂³×C₆₇	1	2	yes	—
684	#95	C₂³×C₆₇	1	1	yes	characteristic
685	#95	C₂³×C₆₇	1	1	yes	characteristic
686	#95	C₂³×C₆₇	1	2	yes	—
687	#95	C₂³×C₆₇	1	2	yes	—
688	#95	C₂³×C₆₇	1	2	yes	—
689	#95	C₂³×C₆₇	1	2	yes	—
690	#95	C₂³×C₆₇	1	1	yes	characteristic
691	#95	C₂³×C₆₇	1	2	yes	—
692	#95	C₂³×C₆₇	1	2	yes	—
693	#95	C₂³×C₆₇	1	1	yes	characteristic
694	#95	C₂³×C₆₇	1	1	yes	characteristic
695	#95	C₂³×C₆₇	1	2	yes	—
696	#95	C₂³×C₆₇	1	2	yes	—
697	#95	C₂³×C₆₇	1	2	yes	—
698	#95	C₂³×C₆₇	1	1	yes	characteristic
699	#95	C₂³×C₆₇	1	2	yes	—
700	#95	C₂³×C₆₇	1	2	yes	—
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	2	yes	—
704	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	2	4	no	—
708	C₂×Q₈	—	4	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	1	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	#41×C₆₇	1	4	yes	—
768	C₄⋊C₄	#41×C₆₇	1	4	yes	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	1	no	—
785	C₂²⋊C₄	—	4	1	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₄²	—	2	4	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₄²	—	4	2	no	—
802	C₄²	—	4	2	no	—
803	C₄²	—	4	1	no	—
804	C₄²	—	4	2	no	—
805	C₄²	—	4	1	no	—
806	C₄²	#41×C₆₇	1	4	yes	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	1	no	—
821	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
822	Q₈	—	4	8	no	—
823	D₄	—	4	4	no	—
824	D₄	—	8	4	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	4	8	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
882	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
883	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
884	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
885	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
886	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
887	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
888	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
889	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
905	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
906	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
907	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
908	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
909	C₂²	#585×C₆₇	1	1	yes	characteristic
910	C₂²	#585×C₆₇	1	1	yes	characteristic
911	C₄	—	2	2	no	—
912	C₄	—	2	4	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	4	no	—
916	C₄	—	2	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	#556×C₆₇	1	4	yes	—
932	C₂	—	8	1	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂×#556×C₆₇	1	1	yes	characteristic
935	C₂	C₆₇×#3475	1	1	yes	characteristic
936	C₂	C₆₇×#3480	1	1	yes	characteristic
937	C₂	C₆₇×#3511	1	1	yes	characteristic
938	C₂	C₆₇×#3513	1	1	yes	characteristic
939	C₂	C₆₇×#3517	1	1	yes	characteristic
940	C₂	C₆₇×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#121×C₆₇	C₂²
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×#2800	C₂	semidirect
2. C₆₇×#2777	C₂	semidirect
3. C₆₇×#2601	C₂	semidirect
4. C₆₇×#2550	C₂	semidirect
5. C₆₇×#2523	C₂	semidirect
6. C₆₇×#2521	C₂	semidirect
7. C₆₇×#2513	C₂	semidirect
8. C₆₇×#2512	C₂	semidirect
9. C₆₇×#2495	C₂	semidirect
12. C₆₇×#2469	C₂	semidirect
13. C₆₇×#2454	C₂	semidirect
14. C₆₇×#2448	C₂	semidirect
15. C₆₇×#2441	C₂	semidirect
16. C₆₇×#2370	C₂	semidirect
17. C₆₇×#2370	C₂	semidirect
19. C₆₇×#2347	C₂	semidirect
20. C₆₇×#2347	C₂	semidirect
21. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#126×C₆₇	C₂	semidirect
23. C₆₇×#2293	C₂	semidirect
461. #59710	C₆₇	direct (N × H)
471. #2800	C₂×C₆₇	semidirect
472. #2777	C₂×C₆₇	semidirect
473. #2601	C₂×C₆₇	semidirect
474. #2550	C₂×C₆₇	semidirect
475. #2523	C₂×C₆₇	semidirect
476. #2521	C₂×C₆₇	semidirect
477. #2513	C₂×C₆₇	semidirect
478. #2512	C₂×C₆₇	semidirect
479. #2495	C₂×C₆₇	semidirect
482. #2469	C₂×C₆₇	semidirect
483. #2454	C₂×C₆₇	semidirect
484. #2448	C₂×C₆₇	semidirect
485. #2441	C₂×C₆₇	semidirect
486. #2370	C₂×C₆₇	semidirect
487. #2370	C₂×C₆₇	semidirect
489. #2347	C₂×C₆₇	semidirect
490. #2347	C₂×C₆₇	semidirect
491. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
492. C₄×#126	C₂×C₆₇	semidirect
493. #2293	C₂×C₆₇	semidirect
494. C₆₇	#59710	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×#2800	2
C₆₇×#2777	2
C₆₇×#2601	2
C₆₇×#2550	2
C₆₇×#2523	2
C₆₇×#2521	2
C₆₇×#2513	2
C₆₇×#2512	2
C₆₇×#2495	2
C₆₇×#2491	2
C₆₇×#2490	2
C₆₇×#2469	2
C₆₇×#2454	2
C₆₇×#2448	2
C₆₇×#2441	2
C₆₇×#2370	2
C₆₇×#2363	2
C₆₇×#2347	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#126×C₆₇	2
C₆₇×#2293	2
#59710	67

Subgroups — C67×#59710 #30738961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59710 #30738961