Subgroups — C₆₇×#59670 #30738921

Order 17152.

1580 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2755	C₂	1	2	yes	maximal
2	C₆₇×#2713	C₂	1	2	yes	maximal
3	C₆₇×#2590	C₂	1	2	yes	maximal
4	C₆₇×#2588	C₂	1	2	yes	maximal
5	C₆₇×#2585	C₂	1	2	yes	maximal
6	C₆₇×#2584	C₂	1	2	yes	maximal
7	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2551	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#2509	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2507	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2507	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2506	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2462	C₂	1	2	yes	maximal
16	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic
19	C₆₇×#2365	C₂	1	2	yes	maximal
20	C₆₇×#2365	C₂	1	1	yes	maximal, characteristic
21	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
22	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic
23	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×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×#125×C₆₇	C₂²	1	2	yes	—
30	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#400×C₆₇	C₂²	1	2	yes	—
36	#400×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	#398×C₆₇	C₂²	1	2	yes	—
41	#398×C₆₇	C₂²	1	2	yes	—
42	#398×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#398×C₆₇	C₂²	1	2	yes	—
45	#395×C₆₇	C₂²	1	2	yes	—
46	#395×C₆₇	C₂²	1	2	yes	—
47	#395×C₆₇	C₂²	1	2	yes	—
48	#395×C₆₇	C₂²	1	2	yes	—
49	#391×C₆₇	C₂²	1	2	yes	—
50	#391×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
53	#389×C₆₇	C₂²	1	2	yes	—
54	#389×C₆₇	C₂²	1	2	yes	—
55	#389×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	1	yes	characteristic
60	#389×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	2	yes	—
68	#389×C₆₇	C₂²	1	2	yes	—
69	#389×C₆₇	C₂²	1	2	yes	—
70	#389×C₆₇	C₂²	1	2	yes	—
71	#389×C₆₇	C₂²	1	1	yes	characteristic
72	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	2	yes	—
74	#389×C₆₇	C₂²	1	1	yes	characteristic
75	#389×C₆₇	C₂²	1	2	yes	—
76	#389×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	1	yes	characteristic
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	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	#387×C₆₇	C₂²	1	2	yes	—
94	#387×C₆₇	C₂²	1	2	yes	—
95	#387×C₆₇	C₂²	1	2	yes	—
96	#387×C₆₇	C₂²	1	2	yes	—
97	#384×C₆₇	C₂²	1	1	yes	characteristic
98	#384×C₆₇	C₂²	1	1	yes	characteristic
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	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×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	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×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
124	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₆₇	—	2	4	no	—
126	C₄⋊Q₈×C₆₇	—	2	4	no	—
127	C₄⋊Q₈×C₆₇	—	2	8	no	—
128	#125×C₆₇	—	2	4	no	—
129	#125×C₆₇	—	2	4	no	—
130	#125×C₆₇	—	4	4	no	—
131	#125×C₆₇	Q₈	1	8	yes	complemented
132	C₄×Q₈×C₆₇	—	4	4	no	—
133	C₄×Q₈×C₆₇	—	4	4	no	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
195	#95×C₆₇	C₂³	1	1	yes	characteristic
196	#95×C₆₇	C₂³	1	1	yes	characteristic
197	#95×C₆₇	C₂³	1	1	yes	characteristic
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	1	yes	characteristic
200	#95×C₆₇	C₂³	1	1	yes	characteristic
201	#95×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
221	#95×C₆₇	C₂³	1	2	yes	—
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	C₂×Q₈×C₆₇	—	2	4	no	—
232	C₂×Q₈×C₆₇	—	2	4	no	—
233	C₂×Q₈×C₆₇	—	2	4	no	—
234	C₂×Q₈×C₆₇	—	2	4	no	—
235	C₂×Q₈×C₆₇	—	4	2	no	—
236	C₂×Q₈×C₆₇	—	4	2	no	—
237	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	2	yes	—
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	C₄⋊C₄×C₆₇	—	2	2	no	—
261	C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₄⋊C₄×C₆₇	—	2	2	no	—
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	2	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	4	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
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	2	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	4	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	2	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	1	no	—
288	C₄⋊C₄×C₆₇	—	4	2	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	—	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	C₂×Q₈	1	8	yes	—
297	C₄⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
298	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
299	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
300	C₄⋊C₄×C₆₇	#41	1	4	yes	—
301	C₄⋊C₄×C₆₇	#41	1	4	yes	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	—	2	2	no	—
304	C₄²×C₆₇	—	2	4	no	—
305	C₄²×C₆₇	—	2	2	no	—
306	C₄²×C₆₇	—	2	2	no	—
307	C₄²×C₆₇	—	2	2	no	—
308	C₄²×C₆₇	—	2	4	no	—
309	C₄²×C₆₇	—	2	2	no	—
310	C₄²×C₆₇	—	2	2	no	—
311	C₄²×C₆₇	—	2	2	no	—
312	C₄²×C₆₇	—	2	2	no	—
313	C₄²×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	4	1	no	—
315	C₄²×C₆₇	—	4	2	no	—
316	C₄²×C₆₇	—	4	2	no	—
317	C₄²×C₆₇	—	4	2	no	—
318	C₄²×C₆₇	—	4	2	no	—
319	C₄²×C₆₇	—	4	2	no	—
320	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
321	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
322	Q₈×C₆₇	—	4	8	no	—
323	Q₈×C₆₇	—	4	8	no	—
324	C₂×C₄×C₆₇	—	2	1	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	2	1	no	—
328	C₂×C₄×C₆₇	—	2	1	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	1	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	1	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	1	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	2	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	1	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	2	no	—
354	C₂×C₄×C₆₇	—	2	2	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	1	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	1	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	2	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	1	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
381	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
382	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
383	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
384	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
385	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
386	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
387	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
388	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
389	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
390	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
391	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
392	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
393	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
394	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
399	C₂²×C₆₇	#585	1	1	yes	characteristic
400	C₄×C₆₇	—	2	4	no	—
401	C₄×C₆₇	—	2	2	no	—
402	C₄×C₆₇	—	2	2	no	—
403	C₄×C₆₇	—	2	2	no	—
404	C₄×C₆₇	—	2	4	no	—
405	C₄×C₆₇	—	2	2	no	—
406	C₄×C₆₇	—	2	4	no	—
407	C₄×C₆₇	—	2	2	no	—
408	C₄×C₆₇	—	2	2	no	—
409	C₄×C₆₇	—	2	2	no	—
410	C₄×C₆₇	—	4	1	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	2	no	—
413	C₄×C₆₇	—	4	1	no	—
414	C₄×C₆₇	—	4	1	no	—
415	C₄×C₆₇	—	4	1	no	—
416	C₄×C₆₇	—	4	1	no	—
417	C₄×C₆₇	—	4	2	no	—
418	C₄×C₆₇	—	4	1	no	—
419	C₄×C₆₇	—	4	2	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	#557	1	4	yes	—
423	#59670	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₆₇	C₂×#557	1	1	yes	characteristic
425	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
426	C₂×C₆₇	#3481	1	1	yes	characteristic
427	C₂×C₆₇	#3503	1	1	yes	characteristic
428	C₂×C₆₇	#3509	1	1	yes	characteristic
429	C₂×C₆₇	#3516	1	1	yes	characteristic
430	C₂×C₆₇	#3559	1	1	yes	characteristic
431	#2755	C₂×C₆₇	1	2	yes	—
432	#2713	C₂×C₆₇	1	2	yes	—
433	#2590	C₂×C₆₇	1	2	yes	—
434	#2588	C₂×C₆₇	1	2	yes	—
435	#2585	C₂×C₆₇	1	2	yes	—
436	#2584	C₂×C₆₇	1	2	yes	—
437	#2570	C₂×C₆₇	1	1	yes	characteristic
438	#2551	C₂×C₆₇	1	1	yes	characteristic
439	#2550	C₂×C₆₇	1	1	yes	characteristic
440	#2550	C₂×C₆₇	1	1	yes	characteristic
441	#2509	C₂×C₆₇	1	1	yes	characteristic
442	#2507	C₂×C₆₇	1	1	yes	characteristic
443	#2507	C₂×C₆₇	1	1	yes	characteristic
444	#2506	C₂×C₆₇	1	1	yes	characteristic
445	#2462	C₂×C₆₇	1	2	yes	—
446	#2370	C₂×C₆₇	1	1	yes	characteristic
447	#2370	C₂×C₆₇	1	1	yes	characteristic
448	#2370	C₂×C₆₇	1	1	yes	characteristic
449	#2365	C₂×C₆₇	1	2	yes	—
450	#2365	C₂×C₆₇	1	1	yes	characteristic
451	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic
452	C₄×#125	C₂×C₆₇	1	1	yes	characteristic
453	C₄×#125	C₂×C₆₇	1	1	yes	characteristic
454	C₆₇	#59670	1	1	yes	characteristic, direct product factor, Sylow
455	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
457	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
458	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×#125	C₂²×C₆₇	1	2	yes	—
461	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
463	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
464	#400	C₂²×C₆₇	1	2	yes	—
465	#400	C₂²×C₆₇	1	2	yes	—
466	#400	C₂²×C₆₇	1	2	yes	—
467	#400	C₂²×C₆₇	1	2	yes	—
468	#398	C₂²×C₆₇	1	2	yes	—
469	#398	C₂²×C₆₇	1	2	yes	—
470	#398	C₂²×C₆₇	1	2	yes	—
471	#398	C₂²×C₆₇	1	2	yes	—
472	#398	C₂²×C₆₇	1	2	yes	—
473	#398	C₂²×C₆₇	1	2	yes	—
474	#398	C₂²×C₆₇	1	2	yes	—
475	#398	C₂²×C₆₇	1	2	yes	—
476	#395	C₂²×C₆₇	1	2	yes	—
477	#395	C₂²×C₆₇	1	2	yes	—
478	#395	C₂²×C₆₇	1	2	yes	—
479	#395	C₂²×C₆₇	1	2	yes	—
480	#391	C₂²×C₆₇	1	2	yes	—
481	#391	C₂²×C₆₇	1	2	yes	—
482	#391	C₂²×C₆₇	1	2	yes	—
483	#391	C₂²×C₆₇	1	2	yes	—
484	#389	C₂²×C₆₇	1	1	yes	characteristic
485	#389	C₂²×C₆₇	1	1	yes	characteristic
486	#389	C₂²×C₆₇	1	1	yes	characteristic
487	#389	C₂²×C₆₇	1	1	yes	characteristic
488	#389	C₂²×C₆₇	1	2	yes	—
489	#389	C₂²×C₆₇	1	1	yes	characteristic
490	#389	C₂²×C₆₇	1	1	yes	characteristic
491	#389	C₂²×C₆₇	1	1	yes	characteristic
492	#389	C₂²×C₆₇	1	1	yes	characteristic
493	#389	C₂²×C₆₇	1	2	yes	—
494	#389	C₂²×C₆₇	1	2	yes	—
495	#389	C₂²×C₆₇	1	2	yes	—
496	#389	C₂²×C₆₇	1	2	yes	—
497	#389	C₂²×C₆₇	1	2	yes	—
498	#389	C₂²×C₆₇	1	2	yes	—
499	#389	C₂²×C₆₇	1	2	yes	—
500	#389	C₂²×C₆₇	1	2	yes	—
501	#389	C₂²×C₆₇	1	2	yes	—
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	#387	C₂²×C₆₇	1	1	yes	characteristic
509	#387	C₂²×C₆₇	1	2	yes	—
510	#387	C₂²×C₆₇	1	1	yes	characteristic
511	#387	C₂²×C₆₇	1	1	yes	characteristic
512	#387	C₂²×C₆₇	1	2	yes	—
513	#387	C₂²×C₆₇	1	1	yes	characteristic
514	#387	C₂²×C₆₇	1	2	yes	—
515	#387	C₂²×C₆₇	1	2	yes	—
516	#387	C₂²×C₆₇	1	2	yes	—
517	#387	C₂²×C₆₇	1	2	yes	—
518	#387	C₂²×C₆₇	1	2	yes	—
519	#387	C₂²×C₆₇	1	2	yes	—
520	#387	C₂²×C₆₇	1	2	yes	—
521	#387	C₂²×C₆₇	1	2	yes	—
522	#387	C₂²×C₆₇	1	2	yes	—
523	#387	C₂²×C₆₇	1	2	yes	—
524	#387	C₂²×C₆₇	1	2	yes	—
525	#387	C₂²×C₆₇	1	2	yes	—
526	#387	C₂²×C₆₇	1	2	yes	—
527	#387	C₂²×C₆₇	1	2	yes	—
528	#384	C₂²×C₆₇	1	1	yes	characteristic
529	#384	C₂²×C₆₇	1	1	yes	characteristic
530	#382	C₂²×C₆₇	1	1	yes	characteristic
531	#382	C₂²×C₆₇	1	1	yes	characteristic
532	#382	C₂²×C₆₇	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
536	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
541	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
542	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
543	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
545	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
546	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
548	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
549	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
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	C₄³	C₂²×C₆₇	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
555	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
556	C₄⋊Q₈	—	2	4	no	—
557	C₄⋊Q₈	—	2	8	no	—
558	C₄⋊Q₈	—	2	4	no	—
559	#125	—	2	4	no	—
560	#125	—	2	4	no	—
561	#125	—	4	4	no	—
562	#125	Q₈×C₆₇	1	8	yes	complemented
563	C₄×Q₈	—	4	4	no	—
564	C₄×Q₈	—	4	4	no	—
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
626	#95	C₂³×C₆₇	1	1	yes	characteristic
627	#95	C₂³×C₆₇	1	1	yes	characteristic
628	#95	C₂³×C₆₇	1	1	yes	characteristic
629	#95	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	1	yes	characteristic
631	#95	C₂³×C₆₇	1	1	yes	characteristic
632	#95	C₂³×C₆₇	1	1	yes	characteristic
633	#95	C₂³×C₆₇	1	1	yes	characteristic
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	1	yes	characteristic
636	#95	C₂³×C₆₇	1	1	yes	characteristic
637	#95	C₂³×C₆₇	1	1	yes	characteristic
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	#95	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
651	#95	C₂³×C₆₇	1	1	yes	characteristic
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	C₂×Q₈	—	2	4	no	—
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	4	no	—
666	C₂×Q₈	—	4	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	1	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
728	C₄⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
729	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
730	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
731	C₄⋊C₄	#41×C₆₇	1	4	yes	—
732	C₄⋊C₄	#41×C₆₇	1	4	yes	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	2	no	—
746	C₄²	—	4	2	no	—
747	C₄²	—	4	2	no	—
748	C₄²	—	4	2	no	—
749	C₄²	—	4	1	no	—
750	C₄²	—	4	2	no	—
751	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
752	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
753	Q₈	—	4	8	no	—
754	Q₈	—	4	8	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	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	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
812	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
813	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
814	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
815	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
816	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
817	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
818	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
819	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
820	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
821	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
822	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
823	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
824	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
825	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
826	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
828	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
829	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
830	C₂²	#585×C₆₇	1	1	yes	characteristic
831	C₄	—	2	2	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	4	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	#557×C₆₇	1	4	yes	—
854	C₂	C₂×#557×C₆₇	1	1	yes	characteristic
855	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
856	C₂	C₆₇×#3481	1	1	yes	characteristic
857	C₂	C₆₇×#3503	1	1	yes	characteristic
858	C₂	C₆₇×#3509	1	1	yes	characteristic
859	C₂	C₆₇×#3516	1	1	yes	characteristic
860	C₂	C₆₇×#3559	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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
131. #125×C₆₇	Q₈	semidirect
423. #59670	C₆₇	direct (N × H)
454. C₆₇	#59670	direct (N × H)
562. #125	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×#2755	2
C₆₇×#2713	2
C₆₇×#2590	2
C₆₇×#2588	2
C₆₇×#2585	2
C₆₇×#2584	2
C₆₇×#2570	2
C₆₇×#2551	2
C₆₇×#2550	2
C₆₇×#2509	2
C₆₇×#2507	2
C₆₇×#2506	2
C₆₇×#2462	2
C₆₇×#2370	2
C₆₇×#2365	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#125×C₆₇	2
#59670	67

Subgroups — C67×#59670 #30738921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59670 #30738921