Subgroups — C₆₇×#59339 #30738590

Order 17152.

1750 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2785	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2783	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2769	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2612	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2609	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2591	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2574	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2529	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2518	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2508	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2425	C₂	1	2	yes	maximal
14	C₆₇×#2413	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2343	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2290	C₂	1	2	yes	maximal, complemented
19	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#123×C₆₇	C₂²	1	2	yes	—
21	C₂×#123×C₆₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
25	C₂×#117×C₆₇	C₂²	1	2	yes	—
26	C₂×#117×C₆₇	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
30	#400×C₆₇	C₂²	1	1	yes	characteristic
31	#400×C₆₇	C₂²	1	2	yes	—
32	#400×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	1	yes	characteristic
34	#398×C₆₇	C₂²	1	2	yes	—
35	#398×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	1	yes	characteristic
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	1	yes	characteristic
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	2	yes	—
41	#396×C₆₇	C₂²	1	2	yes	—
42	#396×C₆₇	C₂²	1	2	yes	—
43	#396×C₆₇	C₂²	1	2	yes	—
44	#395×C₆₇	C₂²	1	1	yes	characteristic
45	#395×C₆₇	C₂²	1	1	yes	characteristic
46	#394×C₆₇	C₂²	1	1	yes	characteristic
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	1	yes	characteristic
49	#393×C₆₇	C₂²	1	2	yes	—
50	#391×C₆₇	C₂²	1	2	yes	—
51	#389×C₆₇	C₂²	1	2	yes	—
52	#389×C₆₇	C₂²	1	2	yes	—
53	#389×C₆₇	C₂²	1	2	yes	—
54	#389×C₆₇	C₂²	1	2	yes	—
55	#389×C₆₇	C₂²	1	2	yes	—
56	#389×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	—
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	#387×C₆₇	C₂²	1	2	yes	—
69	#387×C₆₇	C₂²	1	2	yes	—
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	2	yes	—
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#383×C₆₇	C₂²	1	2	yes	—
85	#382×C₆₇	C₂²	1	2	yes	—
86	#382×C₆₇	C₂²	1	2	yes	—
87	#382×C₆₇	C₂²	1	2	yes	—
88	#382×C₆₇	C₂²	1	1	yes	characteristic
89	#382×C₆₇	C₂²	1	1	yes	characteristic
90	#382×C₆₇	C₂²	1	2	yes	—
91	#382×C₆₇	C₂²	1	1	yes	characteristic
92	#382×C₆₇	C₂²	1	1	yes	characteristic
93	#381×C₆₇	C₂²	1	2	yes	—
94	#380×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₄⋊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	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	#376×C₆₇	C₂²	1	2	yes	—
104	#376×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	#123×C₆₇	—	2	8	no	—
117	#123×C₆₇	—	4	4	no	—
118	C₂²⋊Q₈×C₆₇	—	4	2	no	—
119	#121×C₆₇	—	4	2	no	—
120	C₄×D₄×C₆₇	—	2	8	no	—
121	#117×C₆₇	—	2	8	no	—
122	#117×C₆₇	—	2	8	no	—
123	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
124	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	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	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×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₆₇	—	2	4	no	—
164	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	#95×C₆₇	C₂³	1	2	yes	—
175	#95×C₆₇	C₂³	1	2	yes	—
176	#95×C₆₇	C₂³	1	2	yes	—
177	#95×C₆₇	C₂³	1	2	yes	—
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	1	yes	characteristic
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	1	yes	characteristic
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	1	yes	characteristic
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
205	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	—	4	1	no	—
207	C₂×Q₈×C₆₇	—	4	2	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	4	1	no	—
212	C₂×D₄×C₆₇	—	4	2	no	—
213	C₂²×C₄×C₆₇	—	2	2	no	—
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	2	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	4	2	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	2	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	4	1	no	—
255	C₄⋊C₄×C₆₇	—	4	1	no	—
256	C₄⋊C₄×C₆₇	—	4	1	no	—
257	C₄⋊C₄×C₆₇	—	4	2	no	—
258	C₄⋊C₄×C₆₇	—	4	1	no	—
259	C₄⋊C₄×C₆₇	—	4	1	no	—
260	C₄⋊C₄×C₆₇	—	4	1	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	1	no	—
265	C₄⋊C₄×C₆₇	—	4	1	no	—
266	C₄⋊C₄×C₆₇	—	4	2	no	—
267	C₄⋊C₄×C₆₇	—	4	2	no	—
268	C₄⋊C₄×C₆₇	—	4	2	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	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	#41	1	8	yes	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	—	2	2	no	—
286	C₄²×C₆₇	—	2	4	no	—
287	C₄²×C₆₇	—	2	4	no	—
288	C₄²×C₆₇	—	2	4	no	—
289	C₄²×C₆₇	—	2	4	no	—
290	C₄²×C₆₇	—	4	2	no	—
291	C₄²×C₆₇	—	4	2	no	—
292	C₄²×C₆₇	—	4	2	no	—
293	C₄²×C₆₇	#41	1	4	yes	—
294	C₂³×C₆₇	—	2	1	no	—
295	C₂³×C₆₇	—	2	1	no	—
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	2	no	—
298	C₂³×C₆₇	—	2	2	no	—
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	C₂×#41	1	4	yes	—
305	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
306	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
307	Q₈×C₆₇	—	8	2	no	—
308	D₄×C₆₇	—	4	8	no	—
309	D₄×C₆₇	—	8	2	no	—
310	C₂×C₄×C₆₇	—	2	8	no	—
311	C₂×C₄×C₆₇	—	2	1	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	1	no	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	1	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	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	1	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	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	4	8	no	—
354	C₂×C₄×C₆₇	—	4	8	no	—
355	C₂×C₄×C₆₇	—	4	8	no	—
356	C₂×C₄×C₆₇	—	8	2	no	—
357	C₂×C₄×C₆₇	—	8	2	no	—
358	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
359	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
360	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
361	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
362	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
363	C₂²×C₆₇	—	2	4	no	—
364	C₂²×C₆₇	—	2	2	no	—
365	C₂²×C₆₇	—	2	4	no	—
366	C₂²×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	4	2	no	—
369	C₂²×C₆₇	—	4	2	no	—
370	C₂²×C₆₇	—	4	2	no	—
371	C₂²×C₆₇	—	4	2	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	#555	1	4	yes	—
375	C₂²×C₆₇	C₂²×#41	1	2	yes	—
376	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
377	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
379	C₂²×C₆₇	#585	1	2	yes	—
380	C₄×C₆₇	—	2	4	no	—
381	C₄×C₆₇	—	2	4	no	—
382	C₄×C₆₇	—	2	2	no	—
383	C₄×C₆₇	—	2	2	no	—
384	C₄×C₆₇	—	2	4	no	—
385	C₄×C₆₇	—	4	2	no	—
386	C₄×C₆₇	—	4	2	no	—
387	C₄×C₆₇	—	4	2	no	—
388	C₄×C₆₇	—	4	2	no	—
389	C₄×C₆₇	—	4	2	no	—
390	C₄×C₆₇	—	4	2	no	—
391	C₄×C₆₇	—	4	2	no	—
392	C₄×C₆₇	—	4	1	no	—
393	C₄×C₆₇	—	4	1	no	—
394	C₄×C₆₇	—	4	1	no	—
395	C₄×C₆₇	—	4	1	no	—
396	C₄×C₆₇	—	4	2	no	—
397	#59339	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂×C₆₇	—	2	4	no	—
399	C₂×C₆₇	—	8	2	no	—
400	C₂×C₆₇	C₂×#555	1	1	yes	characteristic
401	C₂×C₆₇	#3475	1	2	yes	—
402	C₂×C₆₇	#3492	1	1	yes	characteristic
403	C₂×C₆₇	#3515	1	2	yes	—
404	C₂×C₆₇	#3545	1	1	yes	characteristic
405	#2785	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#2783	C₂×C₆₇	1	2	yes	complemented
407	#2769	C₂×C₆₇	1	1	yes	characteristic, complemented
408	#2612	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#2609	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#2591	C₂×C₆₇	1	1	yes	characteristic
411	#2583	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#2574	C₂×C₆₇	1	2	yes	complemented
413	#2529	C₂×C₆₇	1	2	yes	complemented
414	#2518	C₂×C₆₇	1	2	yes	complemented
415	#2508	C₂×C₆₇	1	2	yes	complemented
416	#2488	C₂×C₆₇	1	2	yes	complemented
417	#2425	C₂×C₆₇	1	2	yes	—
418	#2413	C₂×C₆₇	1	2	yes	complemented
419	#2359	C₂×C₆₇	1	2	yes	complemented
420	#2346	C₂×C₆₇	1	2	yes	complemented
421	#2343	C₂×C₆₇	1	2	yes	complemented
422	#2290	C₂×C₆₇	1	2	yes	complemented
423	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
424	C₆₇	#59339	1	1	yes	characteristic, direct product factor, Sylow
425	C₂×#123	C₂²×C₆₇	1	2	yes	—
426	C₂×#123	C₂²×C₆₇	1	2	yes	—
427	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
428	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
430	C₂×#117	C₂²×C₆₇	1	2	yes	—
431	C₂×#117	C₂²×C₆₇	1	2	yes	—
432	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
434	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
435	#400	C₂²×C₆₇	1	1	yes	characteristic
436	#400	C₂²×C₆₇	1	1	yes	characteristic
437	#400	C₂²×C₆₇	1	2	yes	—
438	#400	C₂²×C₆₇	1	2	yes	—
439	#398	C₂²×C₆₇	1	2	yes	—
440	#398	C₂²×C₆₇	1	1	yes	characteristic
441	#398	C₂²×C₆₇	1	1	yes	characteristic
442	#398	C₂²×C₆₇	1	2	yes	—
443	#398	C₂²×C₆₇	1	2	yes	—
444	#397	C₂²×C₆₇	1	2	yes	—
445	#397	C₂²×C₆₇	1	2	yes	—
446	#396	C₂²×C₆₇	1	2	yes	—
447	#396	C₂²×C₆₇	1	2	yes	—
448	#396	C₂²×C₆₇	1	2	yes	—
449	#395	C₂²×C₆₇	1	1	yes	characteristic
450	#395	C₂²×C₆₇	1	1	yes	characteristic
451	#394	C₂²×C₆₇	1	1	yes	characteristic
452	#394	C₂²×C₆₇	1	1	yes	characteristic
453	#394	C₂²×C₆₇	1	2	yes	—
454	#393	C₂²×C₆₇	1	2	yes	—
455	#391	C₂²×C₆₇	1	2	yes	—
456	#389	C₂²×C₆₇	1	2	yes	—
457	#389	C₂²×C₆₇	1	2	yes	—
458	#389	C₂²×C₆₇	1	2	yes	—
459	#389	C₂²×C₆₇	1	2	yes	—
460	#389	C₂²×C₆₇	1	2	yes	—
461	#389	C₂²×C₆₇	1	2	yes	—
462	#388	C₂²×C₆₇	1	2	yes	—
463	#388	C₂²×C₆₇	1	2	yes	—
464	#388	C₂²×C₆₇	1	2	yes	—
465	#388	C₂²×C₆₇	1	2	yes	—
466	#388	C₂²×C₆₇	1	2	yes	—
467	#388	C₂²×C₆₇	1	2	yes	—
468	#388	C₂²×C₆₇	1	2	yes	—
469	#388	C₂²×C₆₇	1	2	yes	—
470	#388	C₂²×C₆₇	1	2	yes	—
471	#388	C₂²×C₆₇	1	2	yes	—
472	#388	C₂²×C₆₇	1	2	yes	—
473	#387	C₂²×C₆₇	1	2	yes	—
474	#387	C₂²×C₆₇	1	2	yes	—
475	#387	C₂²×C₆₇	1	2	yes	—
476	#387	C₂²×C₆₇	1	2	yes	—
477	#387	C₂²×C₆₇	1	2	yes	—
478	#387	C₂²×C₆₇	1	2	yes	—
479	#387	C₂²×C₆₇	1	2	yes	—
480	#387	C₂²×C₆₇	1	2	yes	—
481	#386	C₂²×C₆₇	1	2	yes	—
482	#386	C₂²×C₆₇	1	2	yes	—
483	#386	C₂²×C₆₇	1	2	yes	—
484	#386	C₂²×C₆₇	1	2	yes	—
485	#385	C₂²×C₆₇	1	2	yes	—
486	#385	C₂²×C₆₇	1	2	yes	—
487	#385	C₂²×C₆₇	1	2	yes	—
488	#385	C₂²×C₆₇	1	2	yes	—
489	#383	C₂²×C₆₇	1	2	yes	—
490	#382	C₂²×C₆₇	1	2	yes	—
491	#382	C₂²×C₆₇	1	2	yes	—
492	#382	C₂²×C₆₇	1	1	yes	characteristic
493	#382	C₂²×C₆₇	1	2	yes	—
494	#382	C₂²×C₆₇	1	1	yes	characteristic
495	#382	C₂²×C₆₇	1	2	yes	—
496	#382	C₂²×C₆₇	1	1	yes	characteristic
497	#382	C₂²×C₆₇	1	1	yes	characteristic
498	#381	C₂²×C₆₇	1	2	yes	—
499	#380	C₂²×C₆₇	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
506	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
508	#376	C₂²×C₆₇	1	2	yes	—
509	#376	C₂²×C₆₇	1	2	yes	—
510	C₂×#95	C₂²×C₆₇	1	2	yes	—
511	C₂×#95	C₂²×C₆₇	1	2	yes	—
512	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
514	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
517	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
518	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
519	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
521	#123	—	2	8	no	—
522	#123	—	4	4	no	—
523	C₂²⋊Q₈	—	4	2	no	—
524	#121	—	4	2	no	—
525	C₄×D₄	—	2	8	no	—
526	#117	—	2	8	no	—
527	#117	—	2	8	no	—
528	C₂×C₄⋊C₄	—	4	2	no	—
529	C₂×C₄⋊C₄	—	4	2	no	—
530	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₄²	—	2	4	no	—
569	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
570	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
571	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
572	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
573	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
574	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
576	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
577	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
579	#95	C₂³×C₆₇	1	2	yes	—
580	#95	C₂³×C₆₇	1	2	yes	—
581	#95	C₂³×C₆₇	1	2	yes	—
582	#95	C₂³×C₆₇	1	2	yes	—
583	#95	C₂³×C₆₇	1	2	yes	—
584	#95	C₂³×C₆₇	1	2	yes	—
585	#95	C₂³×C₆₇	1	2	yes	—
586	#95	C₂³×C₆₇	1	2	yes	—
587	#95	C₂³×C₆₇	1	2	yes	—
588	#95	C₂³×C₆₇	1	2	yes	—
589	#95	C₂³×C₆₇	1	2	yes	—
590	#95	C₂³×C₆₇	1	2	yes	—
591	#95	C₂³×C₆₇	1	2	yes	—
592	#95	C₂³×C₆₇	1	2	yes	—
593	#95	C₂³×C₆₇	1	1	yes	characteristic
594	#95	C₂³×C₆₇	1	2	yes	—
595	#95	C₂³×C₆₇	1	1	yes	characteristic
596	#95	C₂³×C₆₇	1	2	yes	—
597	#95	C₂³×C₆₇	1	2	yes	—
598	#95	C₂³×C₆₇	1	1	yes	characteristic
599	#95	C₂³×C₆₇	1	2	yes	—
600	#95	C₂³×C₆₇	1	1	yes	characteristic
601	#95	C₂³×C₆₇	1	2	yes	—
602	#95	C₂³×C₆₇	1	2	yes	—
603	#95	C₂³×C₆₇	1	2	yes	—
604	#95	C₂³×C₆₇	1	2	yes	—
605	#95	C₂³×C₆₇	1	2	yes	—
606	#95	C₂³×C₆₇	1	2	yes	—
607	#95	C₂³×C₆₇	1	2	yes	—
608	#95	C₂³×C₆₇	1	2	yes	—
609	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
610	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
611	C₂×Q₈	—	4	1	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	4	1	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	4	1	no	—
660	C₄⋊C₄	—	4	1	no	—
661	C₄⋊C₄	—	4	1	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	1	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	1	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	2	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₄²	#41×C₆₇	1	4	yes	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	C₂×#41×C₆₇	1	4	yes	—
710	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
711	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
712	Q₈	—	8	2	no	—
713	D₄	—	4	8	no	—
714	D₄	—	8	2	no	—
715	C₂×C₄	—	2	8	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	4	8	no	—
759	C₂×C₄	—	4	8	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	8	2	no	—
762	C₂×C₄	—	8	2	no	—
763	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
764	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
765	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
766	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
767	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	#555×C₆₇	1	4	yes	—
780	C₂²	C₂²×#41×C₆₇	1	2	yes	—
781	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
782	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
783	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
784	C₂²	#585×C₆₇	1	2	yes	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	4	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₂	—	2	4	no	—
803	C₂	—	8	2	no	—
804	C₂	C₂×#555×C₆₇	1	1	yes	characteristic
805	C₂	C₆₇×#3475	1	2	yes	—
806	C₂	C₆₇×#3492	1	1	yes	characteristic
807	C₂	C₆₇×#3515	1	2	yes	—
808	C₂	C₆₇×#3545	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×#2785	C₂	semidirect
2. C₆₇×#2783	C₂	semidirect
3. C₆₇×#2769	C₂	semidirect
4. C₆₇×#2612	C₂	semidirect
5. C₆₇×#2609	C₂	semidirect
7. C₆₇×#2583	C₂	semidirect
8. C₆₇×#2574	C₂	semidirect
9. C₆₇×#2529	C₂	semidirect
10. C₆₇×#2518	C₂	semidirect
11. C₆₇×#2508	C₂	semidirect
12. C₆₇×#2488	C₂	semidirect
14. C₆₇×#2413	C₂	semidirect
15. C₆₇×#2359	C₂	semidirect
16. C₆₇×#2346	C₂	semidirect
17. C₆₇×#2343	C₂	semidirect
18. C₆₇×#2290	C₂	semidirect
19. C₂×#382×C₆₇	C₂	semidirect
397. #59339	C₆₇	direct (N × H)
405. #2785	C₂×C₆₇	semidirect
406. #2783	C₂×C₆₇	semidirect
407. #2769	C₂×C₆₇	semidirect
408. #2612	C₂×C₆₇	semidirect
409. #2609	C₂×C₆₇	semidirect
411. #2583	C₂×C₆₇	semidirect
412. #2574	C₂×C₆₇	semidirect
413. #2529	C₂×C₆₇	semidirect
414. #2518	C₂×C₆₇	semidirect
415. #2508	C₂×C₆₇	semidirect
416. #2488	C₂×C₆₇	semidirect
418. #2413	C₂×C₆₇	semidirect
419. #2359	C₂×C₆₇	semidirect
420. #2346	C₂×C₆₇	semidirect
421. #2343	C₂×C₆₇	semidirect
422. #2290	C₂×C₆₇	semidirect
423. C₂×#382	C₂×C₆₇	semidirect
424. C₆₇	#59339	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×#2785	2
C₆₇×#2783	2
C₆₇×#2769	2
C₆₇×#2612	2
C₆₇×#2609	2
C₆₇×#2591	2
C₆₇×#2583	2
C₆₇×#2574	2
C₆₇×#2529	2
C₆₇×#2518	2
C₆₇×#2508	2
C₆₇×#2488	2
C₆₇×#2425	2
C₆₇×#2413	2
C₆₇×#2359	2
C₆₇×#2346	2
C₆₇×#2343	2
C₆₇×#2290	2
C₂×#382×C₆₇	2
#59339	67

Subgroups — C67×#59339 #30738590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59339 #30738590