Subgroups — C₆₇×#59877 #30739128

Order 17152.

1564 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2808	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2805	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2727	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2726	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2611	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2596	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2594	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2594	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2593	C₂	1	2	yes	maximal
10	C₆₇×#2574	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2528	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2469	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2460	C₂	1	2	yes	maximal
14	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2370	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
17	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#125×C₆₇	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₆₇	C₂²	1	2	yes	—
26	#401×C₆₇	C₂²	1	2	yes	—
27	#400×C₆₇	C₂²	1	2	yes	—
28	#400×C₆₇	C₂²	1	2	yes	—
29	#400×C₆₇	C₂²	1	2	yes	—
30	#399×C₆₇	C₂²	1	2	yes	—
31	#398×C₆₇	C₂²	1	2	yes	—
32	#398×C₆₇	C₂²	1	2	yes	—
33	#398×C₆₇	C₂²	1	2	yes	—
34	#397×C₆₇	C₂²	1	2	yes	—
35	#397×C₆₇	C₂²	1	2	yes	—
36	#396×C₆₇	C₂²	1	2	yes	—
37	#396×C₆₇	C₂²	1	2	yes	—
38	#395×C₆₇	C₂²	1	2	yes	—
39	#394×C₆₇	C₂²	1	2	yes	—
40	#394×C₆₇	C₂²	1	2	yes	—
41	#393×C₆₇	C₂²	1	2	yes	—
42	#391×C₆₇	C₂²	1	1	yes	characteristic
43	#391×C₆₇	C₂²	1	1	yes	characteristic
44	#390×C₆₇	C₂²	1	1	yes	characteristic
45	#390×C₆₇	C₂²	1	1	yes	characteristic
46	#389×C₆₇	C₂²	1	2	yes	—
47	#389×C₆₇	C₂²	1	1	yes	characteristic
48	#389×C₆₇	C₂²	1	1	yes	characteristic
49	#389×C₆₇	C₂²	1	1	yes	characteristic
50	#389×C₆₇	C₂²	1	2	yes	—
51	#389×C₆₇	C₂²	1	1	yes	characteristic
52	#389×C₆₇	C₂²	1	1	yes	characteristic
53	#389×C₆₇	C₂²	1	1	yes	characteristic
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	#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	#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	#387×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	2	yes	—
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#382×C₆₇	C₂²	1	2	yes	—
89	#382×C₆₇	C₂²	1	1	yes	characteristic
90	#380×C₆₇	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	#376×C₆₇	C₂²	1	2	yes	—
105	#376×C₆₇	C₂²	1	2	yes	—
106	C₄³×C₆₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
110	#126×C₆₇	—	2	8	no	—
111	#125×C₆₇	—	2	8	no	—
112	#125×C₆₇	—	2	4	no	—
113	C₄×Q₈×C₆₇	—	2	4	no	—
114	C₄×D₄×C₆₇	—	2	4	no	—
115	#117×C₆₇	—	2	8	no	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊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×C₄²×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
172	#95×C₆₇	C₂³	1	2	yes	—
173	#95×C₆₇	C₂³	1	2	yes	—
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	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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
201	C₂×Q₈×C₆₇	—	2	2	no	—
202	C₂×Q₈×C₆₇	—	4	1	no	—
203	C₂×Q₈×C₆₇	—	4	1	no	—
204	C₂×D₄×C₆₇	—	2	2	no	—
205	C₂×D₄×C₆₇	—	4	1	no	—
206	C₂×D₄×C₆₇	—	4	1	no	—
207	C₂²×C₄×C₆₇	—	2	4	no	—
208	C₂²×C₄×C₆₇	—	2	4	no	—
209	C₂²×C₄×C₆₇	—	4	2	no	—
210	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₆₇	—	2	4	no	—
229	C₄⋊C₄×C₆₇	—	2	4	no	—
230	C₄⋊C₄×C₆₇	—	2	4	no	—
231	C₄⋊C₄×C₆₇	—	2	4	no	—
232	C₄⋊C₄×C₆₇	—	2	4	no	—
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	4	no	—
236	C₄⋊C₄×C₆₇	—	2	4	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	2	no	—
239	C₄⋊C₄×C₆₇	—	2	2	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	4	no	—
243	C₄⋊C₄×C₆₇	—	4	1	no	—
244	C₄⋊C₄×C₆₇	—	4	1	no	—
245	C₄⋊C₄×C₆₇	—	4	2	no	—
246	C₄⋊C₄×C₆₇	—	4	1	no	—
247	C₄⋊C₄×C₆₇	—	4	1	no	—
248	C₄⋊C₄×C₆₇	—	4	1	no	—
249	C₄⋊C₄×C₆₇	—	4	1	no	—
250	C₄⋊C₄×C₆₇	—	4	2	no	—
251	C₄⋊C₄×C₆₇	—	4	2	no	—
252	C₄⋊C₄×C₆₇	—	4	2	no	—
253	C₄⋊C₄×C₆₇	#41	1	4	yes	—
254	C₄⋊C₄×C₆₇	#41	1	4	yes	—
255	C₂²⋊C₄×C₆₇	—	2	4	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	4	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	2	4	no	—
261	C₂²⋊C₄×C₆₇	—	2	4	no	—
262	C₂²⋊C₄×C₆₇	—	4	2	no	—
263	C₂²⋊C₄×C₆₇	—	4	2	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	C₄²×C₆₇	—	2	4	no	—
269	C₄²×C₆₇	—	2	2	no	—
270	C₄²×C₆₇	—	2	2	no	—
271	C₄²×C₆₇	—	2	4	no	—
272	C₄²×C₆₇	—	2	4	no	—
273	C₄²×C₆₇	—	2	4	no	—
274	C₄²×C₆₇	—	2	2	no	—
275	C₄²×C₆₇	—	4	1	no	—
276	C₄²×C₆₇	—	4	1	no	—
277	C₄²×C₆₇	—	4	2	no	—
278	C₄²×C₆₇	—	4	2	no	—
279	C₄²×C₆₇	—	4	2	no	—
280	C₄²×C₆₇	—	4	1	no	—
281	C₄²×C₆₇	—	4	2	no	—
282	C₄²×C₆₇	—	4	2	no	—
283	C₄²×C₆₇	#41	1	4	yes	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	2	no	—
291	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
292	Q₈×C₆₇	—	4	4	no	—
293	D₄×C₆₇	—	4	4	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	1	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	1	no	—
301	C₂×C₄×C₆₇	—	2	1	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	1	no	—
306	C₂×C₄×C₆₇	—	2	1	no	—
307	C₂×C₄×C₆₇	—	2	1	no	—
308	C₂×C₄×C₆₇	—	2	1	no	—
309	C₂×C₄×C₆₇	—	2	1	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	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	1	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	2	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	2	no	—
340	C₂×C₄×C₆₇	—	4	8	no	—
341	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
342	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
343	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
344	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
345	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
346	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
347	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
348	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	2	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	2	no	—
356	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
357	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂²×C₆₇	#585	1	1	yes	characteristic
361	C₂²×C₆₇	#585	1	1	yes	characteristic
362	C₂²×C₆₇	#585	1	1	yes	characteristic
363	C₄×C₆₇	—	2	2	no	—
364	C₄×C₆₇	—	2	4	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	2	2	no	—
368	C₄×C₆₇	—	2	2	no	—
369	C₄×C₆₇	—	2	2	no	—
370	C₄×C₆₇	—	2	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	1	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	#59877	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂×C₆₇	—	8	2	no	—
383	C₂×C₆₇	#3475	1	1	yes	characteristic
384	C₂×C₆₇	#3480	1	1	yes	characteristic
385	C₂×C₆₇	#3482	1	1	yes	characteristic
386	C₂×C₆₇	#3493	1	1	yes	characteristic
387	C₂×C₆₇	#3493	1	1	yes	characteristic
388	C₂×C₆₇	#3507	1	1	yes	characteristic
389	C₂×C₆₇	#3553	1	1	yes	characteristic
390	#2808	C₂×C₆₇	1	1	yes	characteristic
391	#2805	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#2727	C₂×C₆₇	1	1	yes	characteristic
393	#2726	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#2611	C₂×C₆₇	1	2	yes	complemented
395	#2596	C₂×C₆₇	1	2	yes	complemented
396	#2594	C₂×C₆₇	1	2	yes	complemented
397	#2594	C₂×C₆₇	1	2	yes	complemented
398	#2593	C₂×C₆₇	1	2	yes	—
399	#2574	C₂×C₆₇	1	2	yes	complemented
400	#2528	C₂×C₆₇	1	2	yes	complemented
401	#2469	C₂×C₆₇	1	2	yes	complemented
402	#2460	C₂×C₆₇	1	2	yes	—
403	#2373	C₂×C₆₇	1	2	yes	complemented
404	#2370	C₂×C₆₇	1	2	yes	complemented
405	#2346	C₂×C₆₇	1	2	yes	complemented
406	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
408	#2293	C₂×C₆₇	1	1	yes	characteristic
409	C₆₇	#59877	1	1	yes	characteristic, direct product factor, Sylow
410	C₂×#126	C₂²×C₆₇	1	2	yes	—
411	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×#125	C₂²×C₆₇	1	2	yes	—
413	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×#117	C₂²×C₆₇	1	2	yes	—
416	#401	C₂²×C₆₇	1	2	yes	—
417	#400	C₂²×C₆₇	1	2	yes	—
418	#400	C₂²×C₆₇	1	2	yes	—
419	#400	C₂²×C₆₇	1	2	yes	—
420	#399	C₂²×C₆₇	1	2	yes	—
421	#398	C₂²×C₆₇	1	2	yes	—
422	#398	C₂²×C₆₇	1	2	yes	—
423	#398	C₂²×C₆₇	1	2	yes	—
424	#397	C₂²×C₆₇	1	2	yes	—
425	#397	C₂²×C₆₇	1	2	yes	—
426	#396	C₂²×C₆₇	1	2	yes	—
427	#396	C₂²×C₆₇	1	2	yes	—
428	#395	C₂²×C₆₇	1	2	yes	—
429	#394	C₂²×C₆₇	1	2	yes	—
430	#394	C₂²×C₆₇	1	2	yes	—
431	#393	C₂²×C₆₇	1	2	yes	—
432	#391	C₂²×C₆₇	1	1	yes	characteristic
433	#391	C₂²×C₆₇	1	1	yes	characteristic
434	#390	C₂²×C₆₇	1	1	yes	characteristic
435	#390	C₂²×C₆₇	1	1	yes	characteristic
436	#389	C₂²×C₆₇	1	1	yes	characteristic
437	#389	C₂²×C₆₇	1	1	yes	characteristic
438	#389	C₂²×C₆₇	1	2	yes	—
439	#389	C₂²×C₆₇	1	2	yes	—
440	#389	C₂²×C₆₇	1	2	yes	—
441	#389	C₂²×C₆₇	1	2	yes	—
442	#389	C₂²×C₆₇	1	1	yes	characteristic
443	#389	C₂²×C₆₇	1	2	yes	—
444	#389	C₂²×C₆₇	1	1	yes	characteristic
445	#389	C₂²×C₆₇	1	1	yes	characteristic
446	#389	C₂²×C₆₇	1	1	yes	characteristic
447	#388	C₂²×C₆₇	1	2	yes	—
448	#388	C₂²×C₆₇	1	2	yes	—
449	#388	C₂²×C₆₇	1	2	yes	—
450	#388	C₂²×C₆₇	1	2	yes	—
451	#388	C₂²×C₆₇	1	2	yes	—
452	#388	C₂²×C₆₇	1	2	yes	—
453	#388	C₂²×C₆₇	1	2	yes	—
454	#388	C₂²×C₆₇	1	2	yes	—
455	#388	C₂²×C₆₇	1	2	yes	—
456	#388	C₂²×C₆₇	1	2	yes	—
457	#388	C₂²×C₆₇	1	2	yes	—
458	#388	C₂²×C₆₇	1	2	yes	—
459	#388	C₂²×C₆₇	1	2	yes	—
460	#388	C₂²×C₆₇	1	2	yes	—
461	#388	C₂²×C₆₇	1	2	yes	—
462	#387	C₂²×C₆₇	1	2	yes	—
463	#387	C₂²×C₆₇	1	2	yes	—
464	#387	C₂²×C₆₇	1	2	yes	—
465	#387	C₂²×C₆₇	1	2	yes	—
466	#387	C₂²×C₆₇	1	2	yes	—
467	#387	C₂²×C₆₇	1	2	yes	—
468	#387	C₂²×C₆₇	1	2	yes	—
469	#387	C₂²×C₆₇	1	2	yes	—
470	#387	C₂²×C₆₇	1	2	yes	—
471	#387	C₂²×C₆₇	1	2	yes	—
472	#387	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	#385	C₂²×C₆₇	1	2	yes	—
477	#385	C₂²×C₆₇	1	2	yes	—
478	#382	C₂²×C₆₇	1	1	yes	characteristic
479	#382	C₂²×C₆₇	1	2	yes	—
480	#380	C₂²×C₆₇	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
484	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
485	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
492	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
494	#376	C₂²×C₆₇	1	2	yes	—
495	#376	C₂²×C₆₇	1	2	yes	—
496	C₄³	C₂²×C₆₇	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
500	#126	—	2	8	no	—
501	#125	—	2	8	no	—
502	#125	—	2	4	no	—
503	C₄×Q₈	—	2	4	no	—
504	C₄×D₄	—	2	4	no	—
505	#117	—	2	8	no	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
546	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
552	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
557	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
558	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
559	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
560	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
561	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
562	#95	C₂³×C₆₇	1	2	yes	—
563	#95	C₂³×C₆₇	1	2	yes	—
564	#95	C₂³×C₆₇	1	2	yes	—
565	#95	C₂³×C₆₇	1	2	yes	—
566	#95	C₂³×C₆₇	1	2	yes	—
567	#95	C₂³×C₆₇	1	2	yes	—
568	#95	C₂³×C₆₇	1	2	yes	—
569	#95	C₂³×C₆₇	1	2	yes	—
570	#95	C₂³×C₆₇	1	2	yes	—
571	#95	C₂³×C₆₇	1	2	yes	—
572	#95	C₂³×C₆₇	1	2	yes	—
573	#95	C₂³×C₆₇	1	2	yes	—
574	#95	C₂³×C₆₇	1	2	yes	—
575	#95	C₂³×C₆₇	1	2	yes	—
576	#95	C₂³×C₆₇	1	2	yes	—
577	#95	C₂³×C₆₇	1	2	yes	—
578	#95	C₂³×C₆₇	1	2	yes	—
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	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	4	1	no	—
593	C₂×Q₈	—	4	1	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	4	1	no	—
596	C₂×D₄	—	4	1	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	4	1	no	—
634	C₄⋊C₄	—	4	1	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	1	no	—
637	C₄⋊C₄	—	4	1	no	—
638	C₄⋊C₄	—	4	1	no	—
639	C₄⋊C₄	—	4	1	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	#41×C₆₇	1	4	yes	—
644	C₄⋊C₄	#41×C₆₇	1	4	yes	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	2	no	—
665	C₄²	—	4	1	no	—
666	C₄²	—	4	1	no	—
667	C₄²	—	4	2	no	—
668	C₄²	—	4	2	no	—
669	C₄²	—	4	2	no	—
670	C₄²	—	4	1	no	—
671	C₄²	—	4	2	no	—
672	C₄²	—	4	2	no	—
673	C₄²	#41×C₆₇	1	4	yes	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
682	Q₈	—	4	4	no	—
683	D₄	—	4	4	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	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	—	4	8	no	—
731	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
732	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
733	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
734	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
735	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
736	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
737	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
738	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
747	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
748	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
749	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
750	C₂²	#585×C₆₇	1	1	yes	characteristic
751	C₂²	#585×C₆₇	1	1	yes	characteristic
752	C₂²	#585×C₆₇	1	1	yes	characteristic
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	4	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₆₇×#3475	1	1	yes	characteristic
773	C₂	C₆₇×#3480	1	1	yes	characteristic
774	C₂	C₆₇×#3482	1	1	yes	characteristic
775	C₂	C₆₇×#3493	1	1	yes	characteristic
776	C₂	C₆₇×#3493	1	1	yes	characteristic
777	C₂	C₆₇×#3507	1	1	yes	characteristic
778	C₂	C₆₇×#3553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
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
2. C₆₇×#2805	C₂	semidirect
4. C₆₇×#2726	C₂	semidirect
5. C₆₇×#2611	C₂	semidirect
6. C₆₇×#2596	C₂	semidirect
7. C₆₇×#2594	C₂	semidirect
8. C₆₇×#2594	C₂	semidirect
10. C₆₇×#2574	C₂	semidirect
11. C₆₇×#2528	C₂	semidirect
12. C₆₇×#2469	C₂	semidirect
14. C₆₇×#2373	C₂	semidirect
15. C₆₇×#2370	C₂	semidirect
16. C₆₇×#2346	C₂	semidirect
17. C₄×#125×C₆₇	C₂	semidirect
18. C₆₇×#2295	C₂	semidirect
381. #59877	C₆₇	direct (N × H)
391. #2805	C₂×C₆₇	semidirect
393. #2726	C₂×C₆₇	semidirect
394. #2611	C₂×C₆₇	semidirect
395. #2596	C₂×C₆₇	semidirect
396. #2594	C₂×C₆₇	semidirect
397. #2594	C₂×C₆₇	semidirect
399. #2574	C₂×C₆₇	semidirect
400. #2528	C₂×C₆₇	semidirect
401. #2469	C₂×C₆₇	semidirect
403. #2373	C₂×C₆₇	semidirect
404. #2370	C₂×C₆₇	semidirect
405. #2346	C₂×C₆₇	semidirect
406. C₄×#125	C₂×C₆₇	semidirect
407. #2295	C₂×C₆₇	semidirect
409. C₆₇	#59877	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×#2808	2
C₆₇×#2805	2
C₆₇×#2727	2
C₆₇×#2726	2
C₆₇×#2611	2
C₆₇×#2596	2
C₆₇×#2594	2
C₆₇×#2593	2
C₆₇×#2574	2
C₆₇×#2528	2
C₆₇×#2469	2
C₆₇×#2460	2
C₆₇×#2373	2
C₆₇×#2370	2
C₆₇×#2346	2
C₄×#125×C₆₇	2
C₆₇×#2295	2
C₆₇×#2293	2
#59877	67

Subgroups — C67×#59877 #30739128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59877 #30739128