Subgroups — C₆₇×#34502 #30713753

Order 17152.

2156 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2378	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2375	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2374	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2372	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2334	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2323	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2321	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2319	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2312	C₂	1	2	yes	maximal, complemented
18	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2298	C₂	1	2	yes	maximal, complemented
20	#551×C₆₇	C₄	1	16	yes	complemented
21	C₂×#126×C₆₇	C₂²	1	2	yes	—
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×#117×C₆₇	C₂²	1	2	yes	—
31	C₂×#117×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
35	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#391×C₆₇	C₂²	1	2	yes	complemented
37	#390×C₆₇	C₂²	1	1	yes	characteristic
38	#390×C₆₇	C₂²	1	2	yes	—
39	#390×C₆₇	C₂²	1	2	yes	—
40	#389×C₆₇	C₂²	1	2	yes	complemented
41	#389×C₆₇	C₂²	1	2	yes	complemented
42	#389×C₆₇	C₂²	1	2	yes	complemented
43	#389×C₆₇	C₂²	1	2	yes	complemented
44	#389×C₆₇	C₂²	1	2	yes	complemented
45	#388×C₆₇	C₂²	1	2	yes	—
46	#388×C₆₇	C₂²	1	2	yes	—
47	#388×C₆₇	C₂²	1	2	yes	—
48	#388×C₆₇	C₂²	1	2	yes	—
49	#388×C₆₇	C₂²	1	2	yes	—
50	#388×C₆₇	C₂²	1	2	yes	—
51	#388×C₆₇	C₂²	1	2	yes	—
52	#388×C₆₇	C₂²	1	2	yes	—
53	#388×C₆₇	C₂²	1	2	yes	—
54	#388×C₆₇	C₂²	1	2	yes	—
55	#388×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
61	#388×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	complemented
63	#388×C₆₇	C₂²	1	2	yes	complemented
64	#388×C₆₇	C₂²	1	2	yes	complemented
65	#387×C₆₇	C₂²	1	2	yes	complemented
66	#387×C₆₇	C₂²	1	2	yes	complemented
67	#387×C₆₇	C₂²	1	2	yes	complemented
68	#387×C₆₇	C₂²	1	2	yes	complemented
69	#387×C₆₇	C₂²	1	2	yes	complemented
70	#387×C₆₇	C₂²	1	2	yes	complemented
71	#387×C₆₇	C₂²	1	2	yes	complemented
72	#387×C₆₇	C₂²	1	2	yes	complemented
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	1	yes	characteristic
75	#386×C₆₇	C₂²	1	1	yes	characteristic
76	#386×C₆₇	C₂²	1	2	yes	—
77	#385×C₆₇	C₂²	1	1	yes	characteristic
78	#385×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#382×C₆₇	C₂²	1	2	yes	complemented
83	#381×C₆₇	C₂²	1	2	yes	—
84	#381×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#380×C₆₇	C₂²	1	2	yes	—
86	#380×C₆₇	C₂²	1	2	yes	—
87	#380×C₆₇	C₂²	1	2	yes	—
88	#380×C₆₇	C₂²	1	2	yes	complemented
89	#379×C₆₇	C₂²	1	1	yes	characteristic
90	#379×C₆₇	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	#376×C₆₇	C₂²	1	2	yes	complemented
106	#376×C₆₇	C₂²	1	2	yes	complemented
107	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	#126×C₆₇	C₂×C₄	1	16	yes	complemented
120	#124×C₆₇	C₂×C₄	1	8	yes	—
121	#123×C₆₇	C₂×C₄	1	8	yes	—
122	#123×C₆₇	C₂×C₄	1	16	yes	complemented
123	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
124	#120×C₆₇	C₂×C₄	1	8	yes	—
125	C₄×Q₈×C₆₇	—	4	2	no	—
126	C₄×D₄×C₆₇	—	4	2	no	—
127	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
128	#117×C₆₇	—	4	4	no	—
129	#117×C₆₇	C₂×C₄	1	16	yes	complemented
130	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
148	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊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	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	C₂⁴×C₆₇	—	4	1	no	—
210	C₂⁴×C₆₇	—	4	2	no	—
211	C₂⁴×C₆₇	—	4	2	no	—
212	C₂⁴×C₆₇	—	4	1	no	—
213	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
214	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
215	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
217	C₂×Q₈×C₆₇	—	4	1	no	—
218	C₂×Q₈×C₆₇	—	4	1	no	—
219	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
220	C₂×D₄×C₆₇	—	4	1	no	—
221	C₂×D₄×C₆₇	—	4	2	no	—
222	C₂×D₄×C₆₇	—	4	2	no	—
223	C₂×D₄×C₆₇	—	4	1	no	—
224	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
225	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
226	C₂²×C₄×C₆₇	—	2	2	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	4	1	no	—
229	C₂²×C₄×C₆₇	—	4	2	no	—
230	C₂²×C₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	4	2	no	—
232	C₂²×C₄×C₆₇	—	4	1	no	—
233	C₂²×C₄×C₆₇	—	4	2	no	—
234	C₂²×C₄×C₆₇	—	4	1	no	—
235	C₂²×C₄×C₆₇	—	4	1	no	—
236	C₂²×C₄×C₆₇	—	4	2	no	—
237	C₂²×C₄×C₆₇	—	4	2	no	—
238	C₂²×C₄×C₆₇	—	4	2	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
241	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
242	C₂²×C₄×C₆₇	C₂²×C₄	1	4	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	2	yes	—
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	2	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₆₇	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	4	2	no	—
261	C₄⋊C₄×C₆₇	—	4	2	no	—
262	C₄⋊C₄×C₆₇	—	4	2	no	—
263	C₄⋊C₄×C₆₇	—	4	2	no	—
264	C₄⋊C₄×C₆₇	—	4	2	no	—
265	C₄⋊C₄×C₆₇	—	4	2	no	—
266	C₄⋊C₄×C₆₇	—	4	2	no	—
267	C₄⋊C₄×C₆₇	—	4	2	no	—
268	C₄⋊C₄×C₆₇	—	4	1	no	—
269	C₄⋊C₄×C₆₇	—	4	2	no	—
270	C₄⋊C₄×C₆₇	—	4	1	no	—
271	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
272	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
273	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
274	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
275	C₂²⋊C₄×C₆₇	—	2	4	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	—	4	2	no	—
280	C₂²⋊C₄×C₆₇	—	4	2	no	—
281	C₂²⋊C₄×C₆₇	—	4	2	no	—
282	C₂²⋊C₄×C₆₇	—	4	2	no	—
283	C₂²⋊C₄×C₆₇	—	4	2	no	—
284	C₂²⋊C₄×C₆₇	—	4	2	no	—
285	C₂²⋊C₄×C₆₇	—	4	2	no	—
286	C₂²⋊C₄×C₆₇	—	4	1	no	—
287	C₂²⋊C₄×C₆₇	—	4	1	no	—
288	C₂²⋊C₄×C₆₇	—	4	2	no	—
289	C₂²⋊C₄×C₆₇	—	4	1	no	—
290	C₂²⋊C₄×C₆₇	—	4	1	no	—
291	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
292	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
293	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
294	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
295	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
296	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
297	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
298	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
299	C₄²×C₆₇	—	2	4	no	—
300	C₄²×C₆₇	—	2	2	no	—
301	C₄²×C₆₇	—	4	2	no	—
302	C₄²×C₆₇	—	4	2	no	—
303	C₄²×C₆₇	—	4	2	no	—
304	C₄²×C₆₇	—	4	2	no	—
305	C₄²×C₆₇	—	4	2	no	—
306	C₄²×C₆₇	—	4	2	no	—
307	C₄²×C₆₇	—	4	2	no	—
308	C₄²×C₆₇	—	4	2	no	—
309	C₄²×C₆₇	—	4	1	no	—
310	C₄²×C₆₇	—	4	2	no	—
311	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
312	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	—	2	1	no	—
315	C₂³×C₆₇	—	2	1	no	—
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	1	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	1	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	4	8	no	—
328	C₂³×C₆₇	—	4	4	no	—
329	C₂³×C₆₇	—	8	2	no	—
330	C₂³×C₆₇	—	8	2	no	—
331	C₂³×C₆₇	—	8	4	no	—
332	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
333	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
334	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
335	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
336	Q₈×C₆₇	—	4	4	no	—
337	D₄×C₆₇	—	4	8	no	—
338	D₄×C₆₇	—	4	4	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	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	1	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	1	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	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	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	4	8	no	—
377	C₂×C₄×C₆₇	—	4	4	no	—
378	C₂×C₄×C₆₇	—	4	8	no	—
379	C₂×C₄×C₆₇	—	8	2	no	—
380	C₂×C₄×C₆₇	—	8	2	no	—
381	C₂×C₄×C₆₇	—	8	2	no	—
382	C₂×C₄×C₆₇	—	8	2	no	—
383	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
384	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
385	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
387	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
388	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
389	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
390	C₂²×C₆₇	—	2	4	no	—
391	C₂²×C₆₇	—	2	4	no	—
392	C₂²×C₆₇	—	2	4	no	—
393	C₂²×C₆₇	—	2	4	no	—
394	C₂²×C₆₇	—	2	2	no	—
395	C₂²×C₆₇	—	2	4	no	—
396	C₂²×C₆₇	—	2	2	no	—
397	C₂²×C₆₇	—	4	1	no	—
398	C₂²×C₆₇	—	4	1	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	4	1	no	—
401	C₂²×C₆₇	—	4	1	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	—	8	8	no	—
408	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
409	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂²×C₆₇	#585	1	2	yes	—
411	C₂²×C₆₇	#585	1	2	yes	—
412	C₂²×C₆₇	#585	1	1	yes	characteristic
413	C₄×C₆₇	—	2	4	no	—
414	C₄×C₆₇	—	2	4	no	—
415	C₄×C₆₇	—	2	4	no	—
416	C₄×C₆₇	—	2	4	no	—
417	C₄×C₆₇	—	2	4	no	—
418	C₄×C₆₇	—	2	2	no	—
419	C₄×C₆₇	—	2	2	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	—	4	1	no	—
423	C₄×C₆₇	—	4	1	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	2	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	2	no	—
429	#34502	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₂×C₆₇	—	4	2	no	—
431	C₂×C₆₇	—	4	4	no	—
432	C₂×C₆₇	—	4	2	no	—
433	C₂×C₆₇	#3428	1	2	yes	—
434	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×C₆₇	#3545	1	1	yes	characteristic
436	C₂×C₆₇	#3551	1	1	yes	characteristic
437	C₂×C₆₇	#3566	1	2	yes	—
438	C₂×#551	C₂×C₆₇	1	1	yes	characteristic
439	#2378	C₂×C₆₇	1	2	yes	complemented
440	#2376	C₂×C₆₇	1	1	yes	characteristic, complemented
441	#2375	C₂×C₆₇	1	1	yes	characteristic
442	#2374	C₂×C₆₇	1	2	yes	complemented
443	#2373	C₂×C₆₇	1	2	yes	complemented
444	#2372	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#2352	C₂×C₆₇	1	2	yes	complemented
446	#2346	C₂×C₆₇	1	2	yes	complemented
447	#2342	C₂×C₆₇	1	2	yes	complemented
448	#2335	C₂×C₆₇	1	2	yes	complemented
449	#2334	C₂×C₆₇	1	2	yes	complemented
450	#2323	C₂×C₆₇	1	2	yes	complemented
451	#2322	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#2321	C₂×C₆₇	1	1	yes	characteristic
453	#2319	C₂×C₆₇	1	2	yes	complemented
454	#2312	C₂×C₆₇	1	2	yes	complemented
455	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#2298	C₂×C₆₇	1	2	yes	complemented
457	C₆₇	#34502	1	1	yes	characteristic, direct product factor, Sylow
458	#551	C₄×C₆₇	1	16	yes	complemented
459	C₂×#126	C₂²×C₆₇	1	2	yes	—
460	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×#123	C₂²×C₆₇	1	2	yes	—
463	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
464	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
466	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
468	C₂×#117	C₂²×C₆₇	1	2	yes	—
469	C₂×#117	C₂²×C₆₇	1	2	yes	—
470	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
473	#391	C₂²×C₆₇	1	2	yes	complemented
474	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
475	#390	C₂²×C₆₇	1	2	yes	—
476	#390	C₂²×C₆₇	1	2	yes	—
477	#390	C₂²×C₆₇	1	1	yes	characteristic
478	#389	C₂²×C₆₇	1	2	yes	complemented
479	#389	C₂²×C₆₇	1	2	yes	complemented
480	#389	C₂²×C₆₇	1	2	yes	complemented
481	#389	C₂²×C₆₇	1	2	yes	complemented
482	#389	C₂²×C₆₇	1	2	yes	complemented
483	#388	C₂²×C₆₇	1	2	yes	—
484	#388	C₂²×C₆₇	1	2	yes	—
485	#388	C₂²×C₆₇	1	2	yes	—
486	#388	C₂²×C₆₇	1	2	yes	—
487	#388	C₂²×C₆₇	1	2	yes	—
488	#388	C₂²×C₆₇	1	2	yes	—
489	#388	C₂²×C₆₇	1	2	yes	—
490	#388	C₂²×C₆₇	1	2	yes	—
491	#388	C₂²×C₆₇	1	2	yes	—
492	#388	C₂²×C₆₇	1	2	yes	—
493	#388	C₂²×C₆₇	1	2	yes	—
494	#388	C₂²×C₆₇	1	2	yes	—
495	#388	C₂²×C₆₇	1	2	yes	—
496	#388	C₂²×C₆₇	1	2	yes	—
497	#388	C₂²×C₆₇	1	2	yes	—
498	#388	C₂²×C₆₇	1	2	yes	—
499	#388	C₂²×C₆₇	1	2	yes	—
500	#388	C₂²×C₆₇	1	2	yes	complemented
501	#388	C₂²×C₆₇	1	2	yes	complemented
502	#388	C₂²×C₆₇	1	2	yes	complemented
503	#387	C₂²×C₆₇	1	2	yes	complemented
504	#387	C₂²×C₆₇	1	2	yes	complemented
505	#387	C₂²×C₆₇	1	2	yes	complemented
506	#387	C₂²×C₆₇	1	2	yes	complemented
507	#387	C₂²×C₆₇	1	2	yes	complemented
508	#387	C₂²×C₆₇	1	2	yes	complemented
509	#387	C₂²×C₆₇	1	2	yes	complemented
510	#387	C₂²×C₆₇	1	2	yes	complemented
511	#386	C₂²×C₆₇	1	2	yes	—
512	#386	C₂²×C₆₇	1	1	yes	characteristic
513	#386	C₂²×C₆₇	1	1	yes	characteristic
514	#386	C₂²×C₆₇	1	2	yes	—
515	#385	C₂²×C₆₇	1	1	yes	characteristic
516	#385	C₂²×C₆₇	1	2	yes	—
517	#385	C₂²×C₆₇	1	2	yes	—
518	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
519	#382	C₂²×C₆₇	1	2	yes	complemented
520	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
521	#381	C₂²×C₆₇	1	2	yes	—
522	#381	C₂²×C₆₇	1	1	yes	characteristic, complemented
523	#380	C₂²×C₆₇	1	2	yes	—
524	#380	C₂²×C₆₇	1	2	yes	—
525	#380	C₂²×C₆₇	1	2	yes	—
526	#380	C₂²×C₆₇	1	2	yes	complemented
527	#379	C₂²×C₆₇	1	1	yes	characteristic
528	#379	C₂²×C₆₇	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
530	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
531	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
532	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
533	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
534	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
537	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
539	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
542	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
543	#376	C₂²×C₆₇	1	2	yes	complemented
544	#376	C₂²×C₆₇	1	2	yes	complemented
545	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
546	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
550	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
555	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
556	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
557	#126	C₂×C₄×C₆₇	1	16	yes	complemented
558	#124	C₂×C₄×C₆₇	1	8	yes	—
559	#123	C₂×C₄×C₆₇	1	8	yes	—
560	#123	C₂×C₄×C₆₇	1	16	yes	complemented
561	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
562	#120	C₂×C₄×C₆₇	1	8	yes	—
563	C₄×Q₈	—	4	2	no	—
564	C₄×D₄	—	4	2	no	—
565	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
566	#117	—	4	4	no	—
567	#117	C₂×C₄×C₆₇	1	16	yes	complemented
568	C₂×C₄⋊C₄	—	4	2	no	—
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
585	C₂×C₂²⋊C₄	—	4	2	no	—
586	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
587	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
616	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
623	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
625	#95	C₂³×C₆₇	1	2	yes	—
626	#95	C₂³×C₆₇	1	2	yes	—
627	#95	C₂³×C₆₇	1	2	yes	—
628	#95	C₂³×C₆₇	1	2	yes	—
629	#95	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	2	yes	—
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
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	C₂⁴	—	4	1	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	—	4	2	no	—
650	C₂⁴	—	4	1	no	—
651	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
652	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
653	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
654	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
655	C₂×Q₈	—	4	1	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
658	C₂×D₄	—	4	1	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	1	no	—
662	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
663	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
679	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
680	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
681	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
710	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
711	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
712	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	1	no	—
728	C₂²⋊C₄	—	4	1	no	—
729	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
730	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
731	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
732	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
733	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
734	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
735	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
736	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	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	1	no	—
749	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
750	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	8	2	no	—
768	C₂³	—	8	2	no	—
769	C₂³	—	8	4	no	—
770	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
771	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
772	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
773	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
774	Q₈	—	4	4	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	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	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
822	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
823	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
824	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
825	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
826	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
827	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	8	8	no	—
846	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
847	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
848	C₂²	#585×C₆₇	1	2	yes	—
849	C₂²	#585×C₆₇	1	2	yes	—
850	C₂²	#585×C₆₇	1	1	yes	characteristic
851	C₄	—	2	2	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	4	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₂	—	4	4	no	—
868	C₂	—	4	2	no	—
869	C₂	—	4	2	no	—
870	C₂	C₆₇×#3428	1	2	yes	—
871	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
872	C₂	C₆₇×#3545	1	1	yes	characteristic
873	C₂	C₆₇×#3551	1	1	yes	characteristic
874	C₂	C₆₇×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#120×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×#2378	C₂	semidirect
3. C₆₇×#2376	C₂	semidirect
5. C₆₇×#2374	C₂	semidirect
6. C₆₇×#2373	C₂	semidirect
7. C₆₇×#2372	C₂	semidirect
8. C₆₇×#2352	C₂	semidirect
9. C₆₇×#2346	C₂	semidirect
10. C₆₇×#2342	C₂	semidirect
11. C₆₇×#2335	C₂	semidirect
12. C₆₇×#2334	C₂	semidirect
13. C₆₇×#2323	C₂	semidirect
14. C₆₇×#2322	C₂	semidirect
16. C₆₇×#2319	C₂	semidirect
17. C₆₇×#2312	C₂	semidirect
18. C₄×#124×C₆₇	C₂	semidirect
19. C₆₇×#2298	C₂	semidirect
20. #551×C₆₇	C₄	semidirect
27. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
35. #391×C₆₇	C₂²	semidirect
36. #391×C₆₇	C₂²	semidirect
40. #389×C₆₇	C₂²	semidirect
41. #389×C₆₇	C₂²	semidirect
42. #389×C₆₇	C₂²	semidirect
43. #389×C₆₇	C₂²	semidirect
44. #389×C₆₇	C₂²	semidirect
62. #388×C₆₇	C₂²	semidirect
63. #388×C₆₇	C₂²	semidirect
64. #388×C₆₇	C₂²	semidirect
65. #387×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
67. #387×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
69. #387×C₆₇	C₂²	semidirect
70. #387×C₆₇	C₂²	semidirect
71. #387×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
80. #385×C₆₇	C₂²	semidirect
81. #382×C₆₇	C₂²	semidirect
82. #382×C₆₇	C₂²	semidirect
84. #381×C₆₇	C₂²	semidirect
88. #380×C₆₇	C₂²	semidirect
91. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
92. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
93. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
94. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
95. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. #376×C₆₇	C₂²	semidirect
106. #376×C₆₇	C₂²	semidirect
107. C₄³×C₆₇	C₂²	semidirect
119. #126×C₆₇	C₂×C₄	semidirect
122. #123×C₆₇	C₂×C₄	semidirect
123. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
127. C₄×D₄×C₆₇	C₂×C₄	semidirect
129. #117×C₆₇	C₂×C₄	semidirect
148. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
429. #34502	C₆₇	direct (N × H)
439. #2378	C₂×C₆₇	semidirect
440. #2376	C₂×C₆₇	semidirect
442. #2374	C₂×C₆₇	semidirect
443. #2373	C₂×C₆₇	semidirect
444. #2372	C₂×C₆₇	semidirect
445. #2352	C₂×C₆₇	semidirect
446. #2346	C₂×C₆₇	semidirect
447. #2342	C₂×C₆₇	semidirect
448. #2335	C₂×C₆₇	semidirect
449. #2334	C₂×C₆₇	semidirect
450. #2323	C₂×C₆₇	semidirect
451. #2322	C₂×C₆₇	semidirect
453. #2319	C₂×C₆₇	semidirect
454. #2312	C₂×C₆₇	semidirect
455. C₄×#124	C₂×C₆₇	semidirect
456. #2298	C₂×C₆₇	semidirect
457. C₆₇	#34502	direct (N × H)
458. #551	C₄×C₆₇	semidirect
465. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
470. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
473. #391	C₂²×C₆₇	semidirect
474. #391	C₂²×C₆₇	semidirect
478. #389	C₂²×C₆₇	semidirect
479. #389	C₂²×C₆₇	semidirect
480. #389	C₂²×C₆₇	semidirect
481. #389	C₂²×C₆₇	semidirect
482. #389	C₂²×C₆₇	semidirect
500. #388	C₂²×C₆₇	semidirect
501. #388	C₂²×C₆₇	semidirect
502. #388	C₂²×C₆₇	semidirect
503. #387	C₂²×C₆₇	semidirect
504. #387	C₂²×C₆₇	semidirect
505. #387	C₂²×C₆₇	semidirect
506. #387	C₂²×C₆₇	semidirect
507. #387	C₂²×C₆₇	semidirect
508. #387	C₂²×C₆₇	semidirect
509. #387	C₂²×C₆₇	semidirect
510. #387	C₂²×C₆₇	semidirect
518. #385	C₂²×C₆₇	semidirect
519. #382	C₂²×C₆₇	semidirect
520. #382	C₂²×C₆₇	semidirect
522. #381	C₂²×C₆₇	semidirect
526. #380	C₂²×C₆₇	semidirect
529. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
530. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
531. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
532. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
533. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
540. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
541. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
542. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
543. #376	C₂²×C₆₇	semidirect
544. #376	C₂²×C₆₇	semidirect
545. C₄³	C₂²×C₆₇	semidirect
557. #126	C₂×C₄×C₆₇	semidirect
560. #123	C₂×C₄×C₆₇	semidirect
561. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
565. C₄×D₄	C₂×C₄×C₆₇	semidirect
567. #117	C₂×C₄×C₆₇	semidirect
586. C₂×C₂²⋊C₄	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×#551×C₆₇	2
C₆₇×#2378	2
C₆₇×#2376	2
C₆₇×#2375	2
C₆₇×#2374	2
C₆₇×#2373	2
C₆₇×#2372	2
C₆₇×#2352	2
C₆₇×#2346	2
C₆₇×#2342	2
C₆₇×#2335	2
C₆₇×#2334	2
C₆₇×#2323	2
C₆₇×#2322	2
C₆₇×#2321	2
C₆₇×#2319	2
C₆₇×#2312	2
C₄×#124×C₆₇	2
C₆₇×#2298	2
#34502	67

Subgroups — C67×#34502 #30713753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34502 #30713753