Subgroups — C₆₇×#59873 #30739124

Order 17152.

1750 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2810	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2808	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2805	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2727	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2596	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2591	C₂	1	2	yes	maximal
7	C₆₇×#2573	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2564	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2533	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2481	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2481	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2469	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2466	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2345	C₂	1	2	yes	maximal, complemented
17	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
19	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#126×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×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×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	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#400×C₆₇	C₂²	1	2	yes	—
36	#400×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	2	yes	—
38	#399×C₆₇	C₂²	1	2	yes	—
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	#395×C₆₇	C₂²	1	2	yes	—
44	#394×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#393×C₆₇	C₂²	1	2	yes	—
47	#391×C₆₇	C₂²	1	1	yes	characteristic
48	#390×C₆₇	C₂²	1	1	yes	characteristic
49	#389×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	1	yes	characteristic
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	#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	#386×C₆₇	C₂²	1	2	yes	—
82	#386×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	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#385×C₆₇	C₂²	1	2	yes	—
89	#383×C₆₇	C₂²	1	2	yes	—
90	#381×C₆₇	C₂²	1	2	yes	—
91	#380×C₆₇	C₂²	1	1	yes	characteristic
92	#380×C₆₇	C₂²	1	1	yes	characteristic
93	#380×C₆₇	C₂²	1	2	yes	—
94	#380×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
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×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊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	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	#376×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	#126×C₆₇	—	2	8	no	—
117	#126×C₆₇	—	4	4	no	—
118	C₂²⋊Q₈×C₆₇	—	2	4	no	—
119	#121×C₆₇	—	2	4	no	—
120	C₄×Q₈×C₆₇	—	4	2	no	—
121	C₄×D₄×C₆₇	—	2	8	no	—
122	C₄×D₄×C₆₇	—	4	2	no	—
123	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
124	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
125	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
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	1	yes	characteristic
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	—	4	2	no	—
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×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	#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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
206	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂×Q₈×C₆₇	—	2	2	no	—
208	C₂×Q₈×C₆₇	—	4	1	no	—
209	C₂×Q₈×C₆₇	—	4	1	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	4	no	—
213	C₂×D₄×C₆₇	—	2	2	no	—
214	C₂×D₄×C₆₇	—	4	1	no	—
215	C₂×D₄×C₆₇	—	4	1	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	2	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	4	1	no	—
224	C₂²×C₄×C₆₇	—	4	1	no	—
225	C₂²×C₄×C₆₇	—	4	1	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	1	no	—
228	C₂²×C₄×C₆₇	—	4	2	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	#41	1	4	yes	—
233	C₂²×C₄×C₆₇	#41	1	4	yes	—
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	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	2	no	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	4	no	—
262	C₄⋊C₄×C₆₇	—	2	4	no	—
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	4	1	no	—
266	C₄⋊C₄×C₆₇	—	4	1	no	—
267	C₄⋊C₄×C₆₇	—	4	2	no	—
268	C₄⋊C₄×C₆₇	—	4	1	no	—
269	C₄⋊C₄×C₆₇	—	4	1	no	—
270	C₄⋊C₄×C₆₇	—	4	2	no	—
271	C₄⋊C₄×C₆₇	—	4	1	no	—
272	C₄⋊C₄×C₆₇	—	4	1	no	—
273	C₄⋊C₄×C₆₇	—	4	2	no	—
274	C₄⋊C₄×C₆₇	#41	1	4	yes	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	no	—
277	C₂²⋊C₄×C₆₇	—	2	4	no	—
278	C₂²⋊C₄×C₆₇	—	2	4	no	—
279	C₂²⋊C₄×C₆₇	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	2	4	no	—
281	C₂²⋊C₄×C₆₇	—	2	4	no	—
282	C₂²⋊C₄×C₆₇	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	4	2	no	—
285	C₂²⋊C₄×C₆₇	—	4	2	no	—
286	C₂²⋊C₄×C₆₇	—	4	2	no	—
287	C₂²⋊C₄×C₆₇	—	4	2	no	—
288	C₂²⋊C₄×C₆₇	—	4	2	no	—
289	C₂²⋊C₄×C₆₇	—	4	2	no	—
290	C₄²×C₆₇	—	2	4	no	—
291	C₄²×C₆₇	—	2	4	no	—
292	C₄²×C₆₇	—	2	2	no	—
293	C₄²×C₆₇	—	2	2	no	—
294	C₄²×C₆₇	—	4	1	no	—
295	C₄²×C₆₇	—	4	1	no	—
296	C₄²×C₆₇	—	4	2	no	—
297	C₄²×C₆₇	—	4	2	no	—
298	C₄²×C₆₇	—	4	2	no	—
299	C₄²×C₆₇	—	4	2	no	—
300	C₄²×C₆₇	—	4	2	no	—
301	C₂³×C₆₇	—	2	1	no	—
302	C₂³×C₆₇	—	2	1	no	—
303	C₂³×C₆₇	—	2	1	no	—
304	C₂³×C₆₇	—	2	1	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	2	2	no	—
310	C₂³×C₆₇	—	2	2	no	—
311	C₂³×C₆₇	—	2	2	no	—
312	C₂³×C₆₇	C₂×#41	1	2	yes	—
313	C₂³×C₆₇	C₂×#41	1	2	yes	—
314	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
315	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
316	Q₈×C₆₇	—	4	4	no	—
317	D₄×C₆₇	—	4	4	no	—
318	D₄×C₆₇	—	4	8	no	—
319	C₂×C₄×C₆₇	—	2	8	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	1	no	—
322	C₂×C₄×C₆₇	—	2	1	no	—
323	C₂×C₄×C₆₇	—	2	1	no	—
324	C₂×C₄×C₆₇	—	2	1	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	2	1	no	—
328	C₂×C₄×C₆₇	—	2	1	no	—
329	C₂×C₄×C₆₇	—	2	1	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	1	no	—
332	C₂×C₄×C₆₇	—	2	1	no	—
333	C₂×C₄×C₆₇	—	2	1	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	—	2	2	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	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	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	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	—	4	4	no	—
365	C₂×C₄×C₆₇	—	4	4	no	—
366	C₂×C₄×C₆₇	—	4	8	no	—
367	C₂×C₄×C₆₇	—	8	4	no	—
368	C₂×C₄×C₆₇	—	8	4	no	—
369	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
370	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
371	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
372	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
373	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
374	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
375	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
376	C₂²×C₆₇	—	2	2	no	—
377	C₂²×C₆₇	—	2	2	no	—
378	C₂²×C₆₇	—	2	2	no	—
379	C₂²×C₆₇	—	2	2	no	—
380	C₂²×C₆₇	—	2	2	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	4	2	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	4	2	no	—
389	C₂²×C₆₇	#556	1	4	yes	—
390	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
392	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
393	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
395	C₂²×C₆₇	#585	1	1	yes	characteristic
396	C₂²×C₆₇	#585	1	1	yes	characteristic
397	C₄×C₆₇	—	2	4	no	—
398	C₄×C₆₇	—	2	2	no	—
399	C₄×C₆₇	—	2	2	no	—
400	C₄×C₆₇	—	2	2	no	—
401	C₄×C₆₇	—	2	2	no	—
402	C₄×C₆₇	—	2	2	no	—
403	C₄×C₆₇	—	2	2	no	—
404	C₄×C₆₇	—	4	2	no	—
405	C₄×C₆₇	—	4	2	no	—
406	C₄×C₆₇	—	4	2	no	—
407	C₄×C₆₇	—	4	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	—	4	2	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	2	no	—
413	C₄×C₆₇	—	4	2	no	—
414	#59873	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂×C₆₇	—	2	4	no	—
416	C₂×C₆₇	—	8	2	no	—
417	C₂×C₆₇	C₂×#556	1	1	yes	characteristic
418	C₂×C₆₇	#3475	1	1	yes	characteristic
419	C₂×C₆₇	#3480	1	1	yes	characteristic
420	C₂×C₆₇	#3492	1	1	yes	characteristic
421	C₂×C₆₇	#3505	1	1	yes	characteristic
422	C₂×C₆₇	#3505	1	1	yes	characteristic
423	C₂×C₆₇	#3553	1	1	yes	characteristic
424	#2810	C₂×C₆₇	1	1	yes	characteristic, complemented
425	#2808	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#2805	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#2727	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#2596	C₂×C₆₇	1	2	yes	complemented
429	#2591	C₂×C₆₇	1	2	yes	—
430	#2573	C₂×C₆₇	1	2	yes	complemented
431	#2564	C₂×C₆₇	1	2	yes	complemented
432	#2533	C₂×C₆₇	1	2	yes	complemented
433	#2481	C₂×C₆₇	1	2	yes	complemented
434	#2481	C₂×C₆₇	1	2	yes	complemented
435	#2469	C₂×C₆₇	1	2	yes	complemented
436	#2466	C₂×C₆₇	1	2	yes	complemented
437	#2373	C₂×C₆₇	1	2	yes	complemented
438	#2353	C₂×C₆₇	1	2	yes	complemented
439	#2345	C₂×C₆₇	1	2	yes	complemented
440	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
441	C₄×#121	C₂×C₆₇	1	1	yes	characteristic
442	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
443	C₆₇	#59873	1	1	yes	characteristic, direct product factor, Sylow
444	C₂×#126	C₂²×C₆₇	1	2	yes	—
445	C₂×#126	C₂²×C₆₇	1	2	yes	—
446	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
451	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
452	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
453	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
454	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
455	#400	C₂²×C₆₇	1	2	yes	—
456	#400	C₂²×C₆₇	1	2	yes	—
457	#400	C₂²×C₆₇	1	2	yes	—
458	#400	C₂²×C₆₇	1	2	yes	—
459	#400	C₂²×C₆₇	1	2	yes	—
460	#400	C₂²×C₆₇	1	2	yes	—
461	#400	C₂²×C₆₇	1	2	yes	—
462	#399	C₂²×C₆₇	1	2	yes	—
463	#397	C₂²×C₆₇	1	2	yes	—
464	#397	C₂²×C₆₇	1	2	yes	—
465	#396	C₂²×C₆₇	1	2	yes	—
466	#396	C₂²×C₆₇	1	2	yes	—
467	#395	C₂²×C₆₇	1	2	yes	—
468	#394	C₂²×C₆₇	1	2	yes	—
469	#394	C₂²×C₆₇	1	2	yes	—
470	#393	C₂²×C₆₇	1	2	yes	—
471	#391	C₂²×C₆₇	1	1	yes	characteristic
472	#390	C₂²×C₆₇	1	1	yes	characteristic
473	#389	C₂²×C₆₇	1	1	yes	characteristic
474	#389	C₂²×C₆₇	1	2	yes	—
475	#389	C₂²×C₆₇	1	2	yes	—
476	#389	C₂²×C₆₇	1	2	yes	—
477	#389	C₂²×C₆₇	1	1	yes	characteristic
478	#389	C₂²×C₆₇	1	2	yes	—
479	#389	C₂²×C₆₇	1	1	yes	characteristic
480	#389	C₂²×C₆₇	1	1	yes	characteristic
481	#389	C₂²×C₆₇	1	1	yes	characteristic
482	#389	C₂²×C₆₇	1	1	yes	characteristic
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	#387	C₂²×C₆₇	1	2	yes	—
493	#387	C₂²×C₆₇	1	2	yes	—
494	#387	C₂²×C₆₇	1	2	yes	—
495	#387	C₂²×C₆₇	1	2	yes	—
496	#387	C₂²×C₆₇	1	2	yes	—
497	#387	C₂²×C₆₇	1	2	yes	—
498	#387	C₂²×C₆₇	1	2	yes	—
499	#387	C₂²×C₆₇	1	2	yes	—
500	#387	C₂²×C₆₇	1	2	yes	—
501	#387	C₂²×C₆₇	1	2	yes	—
502	#387	C₂²×C₆₇	1	2	yes	—
503	#387	C₂²×C₆₇	1	2	yes	—
504	#387	C₂²×C₆₇	1	2	yes	—
505	#386	C₂²×C₆₇	1	2	yes	—
506	#386	C₂²×C₆₇	1	2	yes	—
507	#386	C₂²×C₆₇	1	2	yes	—
508	#386	C₂²×C₆₇	1	2	yes	—
509	#386	C₂²×C₆₇	1	2	yes	—
510	#385	C₂²×C₆₇	1	2	yes	—
511	#385	C₂²×C₆₇	1	2	yes	—
512	#385	C₂²×C₆₇	1	2	yes	—
513	#383	C₂²×C₆₇	1	2	yes	—
514	#381	C₂²×C₆₇	1	2	yes	—
515	#380	C₂²×C₆₇	1	2	yes	—
516	#380	C₂²×C₆₇	1	2	yes	—
517	#380	C₂²×C₆₇	1	1	yes	characteristic
518	#380	C₂²×C₆₇	1	1	yes	characteristic
519	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
521	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
524	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
529	#376	C₂²×C₆₇	1	2	yes	—
530	C₂×#95	C₂²×C₆₇	1	2	yes	—
531	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
533	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
536	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
537	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
538	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
540	#126	—	2	8	no	—
541	#126	—	4	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	#121	—	2	4	no	—
544	C₄×Q₈	—	4	2	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	4	2	no	—
547	C₂×C₄⋊C₄	—	2	8	no	—
548	C₂×C₄⋊C₄	—	2	4	no	—
549	C₂×C₄⋊C₄	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄²	—	4	2	no	—
590	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄²	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	#95	C₂³×C₆₇	1	2	yes	—
610	#95	C₂³×C₆₇	1	2	yes	—
611	#95	C₂³×C₆₇	1	2	yes	—
612	#95	C₂³×C₆₇	1	2	yes	—
613	#95	C₂³×C₆₇	1	2	yes	—
614	#95	C₂³×C₆₇	1	2	yes	—
615	#95	C₂³×C₆₇	1	2	yes	—
616	#95	C₂³×C₆₇	1	2	yes	—
617	#95	C₂³×C₆₇	1	2	yes	—
618	#95	C₂³×C₆₇	1	2	yes	—
619	#95	C₂³×C₆₇	1	2	yes	—
620	#95	C₂³×C₆₇	1	2	yes	—
621	#95	C₂³×C₆₇	1	2	yes	—
622	#95	C₂³×C₆₇	1	2	yes	—
623	#95	C₂³×C₆₇	1	2	yes	—
624	#95	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	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
630	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	4	1	no	—
633	C₂×Q₈	—	4	1	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	4	1	no	—
639	C₂×D₄	—	4	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	1	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	#41×C₆₇	1	4	yes	—
657	C₂²×C₄	#41×C₆₇	1	4	yes	—
658	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	#41×C₆₇	1	4	yes	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	4	1	no	—
719	C₄²	—	4	1	no	—
720	C₄²	—	4	2	no	—
721	C₄²	—	4	2	no	—
722	C₄²	—	4	2	no	—
723	C₄²	—	4	2	no	—
724	C₄²	—	4	2	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	C₂×#41×C₆₇	1	2	yes	—
737	C₂³	C₂×#41×C₆₇	1	2	yes	—
738	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
739	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
740	Q₈	—	4	4	no	—
741	D₄	—	4	4	no	—
742	D₄	—	4	8	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	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	2	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	8	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	—	8	4	no	—
793	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
794	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
795	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
796	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
797	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
798	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
799	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	#556×C₆₇	1	4	yes	—
814	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
815	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
816	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
817	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
818	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
819	C₂²	#585×C₆₇	1	1	yes	characteristic
820	C₂²	#585×C₆₇	1	1	yes	characteristic
821	C₄	—	2	4	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₂	—	2	4	no	—
839	C₂	—	8	2	no	—
840	C₂	C₂×#556×C₆₇	1	1	yes	characteristic
841	C₂	C₆₇×#3475	1	1	yes	characteristic
842	C₂	C₆₇×#3480	1	1	yes	characteristic
843	C₂	C₆₇×#3492	1	1	yes	characteristic
844	C₂	C₆₇×#3505	1	1	yes	characteristic
845	C₂	C₆₇×#3505	1	1	yes	characteristic
846	C₂	C₆₇×#3553	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×#2810	C₂	semidirect
2. C₆₇×#2808	C₂	semidirect
3. C₆₇×#2805	C₂	semidirect
4. C₆₇×#2727	C₂	semidirect
5. C₆₇×#2596	C₂	semidirect
7. C₆₇×#2573	C₂	semidirect
8. C₆₇×#2564	C₂	semidirect
9. C₆₇×#2533	C₂	semidirect
10. C₆₇×#2481	C₂	semidirect
11. C₆₇×#2481	C₂	semidirect
12. C₆₇×#2469	C₂	semidirect
13. C₆₇×#2466	C₂	semidirect
14. C₆₇×#2373	C₂	semidirect
15. C₆₇×#2353	C₂	semidirect
16. C₆₇×#2345	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
19. C₂×#389×C₆₇	C₂	semidirect
414. #59873	C₆₇	direct (N × H)
424. #2810	C₂×C₆₇	semidirect
425. #2808	C₂×C₆₇	semidirect
426. #2805	C₂×C₆₇	semidirect
427. #2727	C₂×C₆₇	semidirect
428. #2596	C₂×C₆₇	semidirect
430. #2573	C₂×C₆₇	semidirect
431. #2564	C₂×C₆₇	semidirect
432. #2533	C₂×C₆₇	semidirect
433. #2481	C₂×C₆₇	semidirect
434. #2481	C₂×C₆₇	semidirect
435. #2469	C₂×C₆₇	semidirect
436. #2466	C₂×C₆₇	semidirect
437. #2373	C₂×C₆₇	semidirect
438. #2353	C₂×C₆₇	semidirect
439. #2345	C₂×C₆₇	semidirect
440. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
442. C₂×#389	C₂×C₆₇	semidirect
443. C₆₇	#59873	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×#2810	2
C₆₇×#2808	2
C₆₇×#2805	2
C₆₇×#2727	2
C₆₇×#2596	2
C₆₇×#2591	2
C₆₇×#2573	2
C₆₇×#2564	2
C₆₇×#2533	2
C₆₇×#2481	2
C₆₇×#2469	2
C₆₇×#2466	2
C₆₇×#2373	2
C₆₇×#2353	2
C₆₇×#2345	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×#389×C₆₇	2
#59873	67

Subgroups — C67×#59873 #30739124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59873 #30739124