Subgroups — C₆₇×#34500 #30713751

Order 17152.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2379	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2366	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2337	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2328	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2319	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2318	C₂	1	2	yes	maximal, complemented
21	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₆₇	C₄	1	16	yes	complemented
25	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₇	C₂²	1	2	yes	—
29	C₂×#123×C₆₇	C₂²	1	2	yes	—
30	C₂×#123×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#117×C₆₇	C₂²	1	2	yes	—
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
45	#391×C₆₇	C₂²	1	1	yes	characteristic
46	#391×C₆₇	C₂²	1	1	yes	characteristic
47	#391×C₆₇	C₂²	1	1	yes	characteristic
48	#391×C₆₇	C₂²	1	1	yes	characteristic
49	#391×C₆₇	C₂²	1	2	yes	—
50	#390×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	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	2	yes	—
62	#389×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
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	#387×C₆₇	C₂²	1	1	yes	characteristic
76	#387×C₆₇	C₂²	1	1	yes	characteristic
77	#387×C₆₇	C₂²	1	1	yes	characteristic
78	#387×C₆₇	C₂²	1	1	yes	characteristic
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	#386×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#385×C₆₇	C₂²	1	2	yes	—
91	#385×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#385×C₆₇	C₂²	1	2	yes	—
97	#384×C₆₇	C₂²	1	1	yes	characteristic
98	#383×C₆₇	C₂²	1	2	yes	—
99	#382×C₆₇	C₂²	1	1	yes	characteristic
100	#382×C₆₇	C₂²	1	2	yes	—
101	#382×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
106	#380×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
120	#376×C₆₇	C₂²	1	1	yes	characteristic
121	#376×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₄³×C₆₇	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	#127×C₆₇	C₂×C₄	1	8	yes	—
137	#124×C₆₇	C₂×C₄	1	8	yes	complemented
138	#124×C₆₇	C₂×C₄	1	8	yes	complemented
139	#124×C₆₇	C₂×C₄	1	16	yes	complemented
140	#123×C₆₇	C₂×C₄	1	16	yes	complemented
141	#123×C₆₇	C₂×C₄	1	16	yes	complemented
142	C₄×Q₈×C₆₇	—	4	2	no	—
143	C₄×Q₈×C₆₇	—	4	2	no	—
144	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
145	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₆₇	—	4	2	no	—
147	C₄×D₄×C₆₇	—	4	2	no	—
148	C₄×D₄×C₆₇	—	4	2	no	—
149	C₄×D₄×C₆₇	—	4	2	no	—
150	C₄×D₄×C₆₇	—	4	4	no	—
151	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
152	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
153	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
154	#117×C₆₇	—	4	4	no	—
155	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
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	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
204	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×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	1	yes	characteristic
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	1	yes	characteristic
222	#95×C₆₇	C₂³	1	1	yes	characteristic
223	#95×C₆₇	C₂³	1	1	yes	characteristic
224	#95×C₆₇	C₂³	1	1	yes	characteristic
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
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	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	1	yes	characteristic
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	1	yes	characteristic
242	#95×C₆₇	C₂³	1	2	yes	—
243	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
244	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₆₇	—	2	2	no	—
246	C₂×Q₈×C₆₇	—	2	2	no	—
247	C₂×Q₈×C₆₇	—	4	1	no	—
248	C₂×Q₈×C₆₇	—	4	1	no	—
249	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
250	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	4	2	no	—
256	C₂×D₄×C₆₇	—	4	2	no	—
257	C₂×D₄×C₆₇	—	4	2	no	—
258	C₂×D₄×C₆₇	—	4	2	no	—
259	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
260	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
261	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
262	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
263	C₂²×C₄×C₆₇	—	2	4	no	—
264	C₂²×C₄×C₆₇	—	4	2	no	—
265	C₂²×C₄×C₆₇	—	4	2	no	—
266	C₂²×C₄×C₆₇	—	4	2	no	—
267	C₂²×C₄×C₆₇	—	4	2	no	—
268	C₂²×C₄×C₆₇	—	4	2	no	—
269	C₂²×C₄×C₆₇	—	4	2	no	—
270	C₂²×C₄×C₆₇	—	4	2	no	—
271	C₂²×C₄×C₆₇	—	4	2	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	2	no	—
276	C₂²×C₄×C₆₇	—	4	2	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
280	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
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	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	4	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	4	2	no	—
310	C₄⋊C₄×C₆₇	—	4	2	no	—
311	C₄⋊C₄×C₆₇	—	4	1	no	—
312	C₄⋊C₄×C₆₇	—	4	1	no	—
313	C₄⋊C₄×C₆₇	—	4	2	no	—
314	C₄⋊C₄×C₆₇	—	4	1	no	—
315	C₄⋊C₄×C₆₇	—	4	2	no	—
316	C₄⋊C₄×C₆₇	—	4	1	no	—
317	C₄⋊C₄×C₆₇	—	4	2	no	—
318	C₄⋊C₄×C₆₇	—	4	2	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
321	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
322	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
323	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
324	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	4	2	no	—
327	C₂²⋊C₄×C₆₇	—	4	2	no	—
328	C₂²⋊C₄×C₆₇	—	4	2	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	C₂²⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	4	2	no	—
335	C₂²⋊C₄×C₆₇	—	4	2	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
338	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
339	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
340	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
341	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
342	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
343	C₄²×C₆₇	—	2	2	no	—
344	C₄²×C₆₇	—	2	2	no	—
345	C₄²×C₆₇	—	2	2	no	—
346	C₄²×C₆₇	—	2	2	no	—
347	C₄²×C₆₇	—	2	2	no	—
348	C₄²×C₆₇	—	4	2	no	—
349	C₄²×C₆₇	—	4	1	no	—
350	C₄²×C₆₇	—	4	1	no	—
351	C₄²×C₆₇	—	4	1	no	—
352	C₄²×C₆₇	—	4	2	no	—
353	C₄²×C₆₇	—	4	2	no	—
354	C₄²×C₆₇	—	4	2	no	—
355	C₄²×C₆₇	—	4	2	no	—
356	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
357	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
358	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
359	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	2	no	—
371	C₂³×C₆₇	—	2	2	no	—
372	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
373	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
374	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
375	Q₈×C₆₇	—	2	8	no	—
376	Q₈×C₆₇	—	4	4	no	—
377	D₄×C₆₇	—	2	8	no	—
378	D₄×C₆₇	—	2	8	no	—
379	D₄×C₆₇	—	4	8	no	—
380	D₄×C₆₇	—	4	8	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	1	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	—	2	1	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	2	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	1	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	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	2	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	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	2	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	1	no	—
423	C₂×C₄×C₆₇	—	2	1	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	4	8	no	—
433	C₂×C₄×C₆₇	—	4	8	no	—
434	C₂×C₄×C₆₇	—	8	4	no	—
435	C₂×C₄×C₆₇	—	8	4	no	—
436	C₂×C₄×C₆₇	—	8	4	no	—
437	C₂×C₄×C₆₇	—	8	4	no	—
438	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
440	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
441	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
443	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
444	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
445	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
448	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
449	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
450	C₂²×C₆₇	—	2	4	no	—
451	C₂²×C₆₇	—	2	4	no	—
452	C₂²×C₆₇	—	2	4	no	—
453	C₂²×C₆₇	—	2	4	no	—
454	C₂²×C₆₇	—	2	4	no	—
455	C₂²×C₆₇	—	2	4	no	—
456	C₂²×C₆₇	—	4	2	no	—
457	C₂²×C₆₇	—	4	2	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	2	no	—
461	C₂²×C₆₇	—	4	2	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	2	no	—
464	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
465	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂²×C₆₇	#585	1	1	yes	characteristic
469	C₂²×C₆₇	#585	1	1	yes	characteristic
470	C₂²×C₆₇	#585	1	1	yes	characteristic
471	C₄×C₆₇	—	2	4	no	—
472	C₄×C₆₇	—	2	2	no	—
473	C₄×C₆₇	—	2	2	no	—
474	C₄×C₆₇	—	2	2	no	—
475	C₄×C₆₇	—	2	2	no	—
476	C₄×C₆₇	—	2	2	no	—
477	C₄×C₆₇	—	2	4	no	—
478	C₄×C₆₇	—	2	2	no	—
479	C₄×C₆₇	—	2	2	no	—
480	C₄×C₆₇	—	4	1	no	—
481	C₄×C₆₇	—	4	2	no	—
482	C₄×C₆₇	—	4	1	no	—
483	C₄×C₆₇	—	4	2	no	—
484	C₄×C₆₇	—	4	1	no	—
485	C₄×C₆₇	—	4	1	no	—
486	C₄×C₆₇	—	4	2	no	—
487	C₄×C₆₇	—	4	1	no	—
488	C₄×C₆₇	—	4	1	no	—
489	C₄×C₆₇	—	4	2	no	—
490	C₄×C₆₇	—	4	1	no	—
491	C₄×C₆₇	#520	1	4	yes	—
492	#34500	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
493	C₂×C₆₇	—	4	4	no	—
494	C₂×C₆₇	—	4	4	no	—
495	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
496	C₂×C₆₇	#3428	1	1	yes	characteristic
497	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
498	C₂×C₆₇	#3554	1	1	yes	characteristic
499	C₂×C₆₇	#3557	1	1	yes	characteristic
500	C₂×C₆₇	#3558	1	1	yes	characteristic
501	C₂×C₆₇	#3562	1	1	yes	characteristic
502	C₂×#559	C₂×C₆₇	1	1	yes	characteristic
503	#2379	C₂×C₆₇	1	2	yes	complemented
504	#2376	C₂×C₆₇	1	2	yes	complemented
505	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
506	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
507	#2366	C₂×C₆₇	1	1	yes	characteristic
508	#2359	C₂×C₆₇	1	2	yes	complemented
509	#2355	C₂×C₆₇	1	1	yes	characteristic, complemented
510	#2352	C₂×C₆₇	1	2	yes	complemented
511	#2351	C₂×C₆₇	1	1	yes	characteristic, complemented
512	#2349	C₂×C₆₇	1	1	yes	characteristic, complemented
513	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
514	#2337	C₂×C₆₇	1	2	yes	complemented
515	#2335	C₂×C₆₇	1	2	yes	complemented
516	#2328	C₂×C₆₇	1	1	yes	characteristic
517	#2326	C₂×C₆₇	1	1	yes	characteristic, complemented
518	#2322	C₂×C₆₇	1	2	yes	complemented
519	#2320	C₂×C₆₇	1	1	yes	characteristic, complemented
520	#2319	C₂×C₆₇	1	1	yes	characteristic, complemented
521	#2318	C₂×C₆₇	1	2	yes	complemented
522	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
523	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
524	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
525	C₆₇	#34500	1	1	yes	characteristic, direct product factor, Sylow
526	#559	C₄×C₆₇	1	16	yes	complemented
527	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
528	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
529	C₂×#124	C₂²×C₆₇	1	2	yes	—
530	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
531	C₂×#123	C₂²×C₆₇	1	2	yes	—
532	C₂×#123	C₂²×C₆₇	1	2	yes	—
533	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
534	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
535	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
536	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
537	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
538	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
539	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
540	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
543	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
545	C₂×#117	C₂²×C₆₇	1	2	yes	—
546	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
547	#391	C₂²×C₆₇	1	1	yes	characteristic
548	#391	C₂²×C₆₇	1	1	yes	characteristic
549	#391	C₂²×C₆₇	1	1	yes	characteristic
550	#391	C₂²×C₆₇	1	2	yes	—
551	#391	C₂²×C₆₇	1	1	yes	characteristic
552	#390	C₂²×C₆₇	1	1	yes	characteristic
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	#389	C₂²×C₆₇	1	1	yes	characteristic
558	#389	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	2	yes	—
562	#389	C₂²×C₆₇	1	2	yes	—
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	2	yes	—
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	#387	C₂²×C₆₇	1	1	yes	characteristic
578	#387	C₂²×C₆₇	1	2	yes	—
579	#387	C₂²×C₆₇	1	2	yes	—
580	#387	C₂²×C₆₇	1	2	yes	—
581	#387	C₂²×C₆₇	1	2	yes	—
582	#387	C₂²×C₆₇	1	1	yes	characteristic
583	#387	C₂²×C₆₇	1	1	yes	characteristic
584	#387	C₂²×C₆₇	1	1	yes	characteristic
585	#386	C₂²×C₆₇	1	2	yes	—
586	#386	C₂²×C₆₇	1	2	yes	—
587	#386	C₂²×C₆₇	1	2	yes	—
588	#386	C₂²×C₆₇	1	2	yes	—
589	#386	C₂²×C₆₇	1	2	yes	—
590	#386	C₂²×C₆₇	1	2	yes	—
591	#385	C₂²×C₆₇	1	2	yes	—
592	#385	C₂²×C₆₇	1	2	yes	—
593	#385	C₂²×C₆₇	1	2	yes	—
594	#385	C₂²×C₆₇	1	2	yes	—
595	#385	C₂²×C₆₇	1	2	yes	—
596	#385	C₂²×C₆₇	1	2	yes	—
597	#385	C₂²×C₆₇	1	2	yes	—
598	#385	C₂²×C₆₇	1	2	yes	—
599	#384	C₂²×C₆₇	1	1	yes	characteristic
600	#383	C₂²×C₆₇	1	2	yes	—
601	#382	C₂²×C₆₇	1	2	yes	—
602	#382	C₂²×C₆₇	1	2	yes	—
603	#382	C₂²×C₆₇	1	1	yes	characteristic
604	#382	C₂²×C₆₇	1	1	yes	characteristic
605	#381	C₂²×C₆₇	1	2	yes	—
606	#380	C₂²×C₆₇	1	2	yes	—
607	#380	C₂²×C₆₇	1	2	yes	—
608	#380	C₂²×C₆₇	1	2	yes	—
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	2	yes	—
612	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
613	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
614	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
615	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
616	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
617	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
618	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
619	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
620	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
621	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
622	#376	C₂²×C₆₇	1	1	yes	characteristic
623	#376	C₂²×C₆₇	1	1	yes	characteristic
624	C₂×#95	C₂²×C₆₇	1	2	yes	—
625	C₄³	C₂²×C₆₇	1	1	yes	characteristic
626	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
627	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
628	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
629	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
631	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
632	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
633	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
634	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
635	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
636	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
637	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
638	#127	C₂×C₄×C₆₇	1	8	yes	—
639	#124	C₂×C₄×C₆₇	1	8	yes	complemented
640	#124	C₂×C₄×C₆₇	1	8	yes	complemented
641	#124	C₂×C₄×C₆₇	1	16	yes	complemented
642	#123	C₂×C₄×C₆₇	1	16	yes	complemented
643	#123	C₂×C₄×C₆₇	1	16	yes	complemented
644	C₄×Q₈	—	4	2	no	—
645	C₄×Q₈	—	4	2	no	—
646	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
647	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
648	C₄×D₄	—	4	2	no	—
649	C₄×D₄	—	4	2	no	—
650	C₄×D₄	—	4	2	no	—
651	C₄×D₄	—	4	2	no	—
652	C₄×D₄	—	4	4	no	—
653	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
654	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
655	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
656	#117	—	4	4	no	—
657	C₂×C₄⋊C₄	—	4	4	no	—
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	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
705	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
706	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
707	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
708	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
712	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
715	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
716	#95	C₂³×C₆₇	1	1	yes	characteristic
717	#95	C₂³×C₆₇	1	2	yes	—
718	#95	C₂³×C₆₇	1	2	yes	—
719	#95	C₂³×C₆₇	1	2	yes	—
720	#95	C₂³×C₆₇	1	1	yes	characteristic
721	#95	C₂³×C₆₇	1	1	yes	characteristic
722	#95	C₂³×C₆₇	1	1	yes	characteristic
723	#95	C₂³×C₆₇	1	1	yes	characteristic
724	#95	C₂³×C₆₇	1	1	yes	characteristic
725	#95	C₂³×C₆₇	1	1	yes	characteristic
726	#95	C₂³×C₆₇	1	1	yes	characteristic
727	#95	C₂³×C₆₇	1	1	yes	characteristic
728	#95	C₂³×C₆₇	1	1	yes	characteristic
729	#95	C₂³×C₆₇	1	1	yes	characteristic
730	#95	C₂³×C₆₇	1	2	yes	—
731	#95	C₂³×C₆₇	1	2	yes	—
732	#95	C₂³×C₆₇	1	2	yes	—
733	#95	C₂³×C₆₇	1	2	yes	—
734	#95	C₂³×C₆₇	1	2	yes	—
735	#95	C₂³×C₆₇	1	2	yes	—
736	#95	C₂³×C₆₇	1	2	yes	—
737	#95	C₂³×C₆₇	1	1	yes	characteristic
738	#95	C₂³×C₆₇	1	2	yes	—
739	#95	C₂³×C₆₇	1	2	yes	—
740	#95	C₂³×C₆₇	1	1	yes	characteristic
741	#95	C₂³×C₆₇	1	2	yes	—
742	#95	C₂³×C₆₇	1	2	yes	—
743	#95	C₂³×C₆₇	1	1	yes	characteristic
744	#95	C₂³×C₆₇	1	2	yes	—
745	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
746	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	—	4	1	no	—
750	C₂×Q₈	—	4	1	no	—
751	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
752	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
762	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
763	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
764	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
782	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
783	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	1	no	—
817	C₄⋊C₄	—	4	1	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	1	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	1	no	—
822	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
823	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
824	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
825	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
826	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
840	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
841	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
842	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
843	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
844	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	4	2	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	2	no	—
853	C₄²	—	4	2	no	—
854	C₄²	—	4	2	no	—
855	C₄²	—	4	1	no	—
856	C₄²	—	4	1	no	—
857	C₄²	—	4	1	no	—
858	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
859	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
860	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
861	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
875	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
876	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
877	Q₈	—	2	8	no	—
878	Q₈	—	4	4	no	—
879	D₄	—	2	8	no	—
880	D₄	—	2	8	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	8	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	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	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	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	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	4	8	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	—	8	4	no	—
938	C₂×C₄	—	8	4	no	—
939	C₂×C₄	—	8	4	no	—
940	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
941	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
942	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
943	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
944	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
945	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
946	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
947	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
948	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
949	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
950	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
951	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
952	C₂²	—	2	4	no	—
953	C₂²	—	2	4	no	—
954	C₂²	—	2	4	no	—
955	C₂²	—	2	4	no	—
956	C₂²	—	2	4	no	—
957	C₂²	—	2	4	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
967	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
968	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
969	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
970	C₂²	#585×C₆₇	1	1	yes	characteristic
971	C₂²	#585×C₆₇	1	1	yes	characteristic
972	C₂²	#585×C₆₇	1	1	yes	characteristic
973	C₄	—	2	2	no	—
974	C₄	—	2	4	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	4	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	1	no	—
993	C₄	#520×C₆₇	1	4	yes	—
994	C₂	—	4	4	no	—
995	C₂	—	4	4	no	—
996	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
997	C₂	C₆₇×#3428	1	1	yes	characteristic
998	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
999	C₂	C₆₇×#3554	1	1	yes	characteristic
1000	C₂	C₆₇×#3557	1	1	yes	characteristic
1001	C₂	C₆₇×#3558	1	1	yes	characteristic
1002	C₂	C₆₇×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₆₇×#2379	C₂	semidirect
3. C₆₇×#2376	C₂	semidirect
4. C₆₇×#2367	C₂	semidirect
5. C₆₇×#2367	C₂	semidirect
7. C₆₇×#2359	C₂	semidirect
8. C₆₇×#2355	C₂	semidirect
9. C₆₇×#2352	C₂	semidirect
10. C₆₇×#2351	C₂	semidirect
11. C₆₇×#2349	C₂	semidirect
12. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
13. C₆₇×#2337	C₂	semidirect
14. C₆₇×#2335	C₂	semidirect
16. C₆₇×#2326	C₂	semidirect
17. C₆₇×#2322	C₂	semidirect
18. C₆₇×#2320	C₂	semidirect
19. C₆₇×#2319	C₂	semidirect
20. C₆₇×#2318	C₂	semidirect
21. C₄×#124×C₆₇	C₂	semidirect
22. C₆₇×#2295	C₂	semidirect
23. C₆₇×#2293	C₂	semidirect
24. #559×C₆₇	C₄	semidirect
137. #124×C₆₇	C₂×C₄	semidirect
138. #124×C₆₇	C₂×C₄	semidirect
139. #124×C₆₇	C₂×C₄	semidirect
140. #123×C₆₇	C₂×C₄	semidirect
141. #123×C₆₇	C₂×C₄	semidirect
144. C₄×Q₈×C₆₇	C₂×C₄	semidirect
145. C₄×Q₈×C₆₇	C₂×C₄	semidirect
151. C₄×D₄×C₆₇	C₂×C₄	semidirect
152. C₄×D₄×C₆₇	C₂×C₄	semidirect
153. C₄×D₄×C₆₇	C₂×C₄	semidirect
492. #34500	C₆₇	direct (N × H)
503. #2379	C₂×C₆₇	semidirect
504. #2376	C₂×C₆₇	semidirect
505. #2367	C₂×C₆₇	semidirect
506. #2367	C₂×C₆₇	semidirect
508. #2359	C₂×C₆₇	semidirect
509. #2355	C₂×C₆₇	semidirect
510. #2352	C₂×C₆₇	semidirect
511. #2351	C₂×C₆₇	semidirect
512. #2349	C₂×C₆₇	semidirect
513. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
514. #2337	C₂×C₆₇	semidirect
515. #2335	C₂×C₆₇	semidirect
517. #2326	C₂×C₆₇	semidirect
518. #2322	C₂×C₆₇	semidirect
519. #2320	C₂×C₆₇	semidirect
520. #2319	C₂×C₆₇	semidirect
521. #2318	C₂×C₆₇	semidirect
522. C₄×#124	C₂×C₆₇	semidirect
523. #2295	C₂×C₆₇	semidirect
524. #2293	C₂×C₆₇	semidirect
525. C₆₇	#34500	direct (N × H)
526. #559	C₄×C₆₇	semidirect
639. #124	C₂×C₄×C₆₇	semidirect
640. #124	C₂×C₄×C₆₇	semidirect
641. #124	C₂×C₄×C₆₇	semidirect
642. #123	C₂×C₄×C₆₇	semidirect
643. #123	C₂×C₄×C₆₇	semidirect
646. C₄×Q₈	C₂×C₄×C₆₇	semidirect
647. C₄×Q₈	C₂×C₄×C₆₇	semidirect
653. C₄×D₄	C₂×C₄×C₆₇	semidirect
654. C₄×D₄	C₂×C₄×C₆₇	semidirect
655. C₄×D₄	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₆₇	2
C₆₇×#2379	2
C₆₇×#2376	2
C₆₇×#2367	2
C₆₇×#2366	2
C₆₇×#2359	2
C₆₇×#2355	2
C₆₇×#2352	2
C₆₇×#2351	2
C₆₇×#2349	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2337	2
C₆₇×#2335	2
C₆₇×#2328	2
C₆₇×#2326	2
C₆₇×#2322	2
C₆₇×#2320	2
C₆₇×#2319	2
C₆₇×#2318	2
C₄×#124×C₆₇	2
C₆₇×#2295	2
C₆₇×#2293	2
#34500	67

Subgroups — C67×#34500 #30713751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34500 #30713751