Subgroups — C₆₇×#36761 #30716012

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2856	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2800	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2791	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2786	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2780	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2761	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2740	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2709	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2707	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2618	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2618	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2443	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2425	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2425	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#387×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#121×C₆₇	C₂²	1	2	yes	—
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
34	#400×C₆₇	C₂²	1	2	yes	—
35	#399×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#398×C₆₇	C₂²	1	2	yes	—
40	#398×C₆₇	C₂²	1	2	yes	—
41	#397×C₆₇	C₂²	1	2	yes	—
42	#397×C₆₇	C₂²	1	2	yes	—
43	#397×C₆₇	C₂²	1	2	yes	—
44	#397×C₆₇	C₂²	1	2	yes	—
45	#397×C₆₇	C₂²	1	2	yes	—
46	#396×C₆₇	C₂²	1	2	yes	—
47	#396×C₆₇	C₂²	1	2	yes	—
48	#396×C₆₇	C₂²	1	2	yes	—
49	#396×C₆₇	C₂²	1	2	yes	—
50	#396×C₆₇	C₂²	1	2	yes	—
51	#396×C₆₇	C₂²	1	2	yes	—
52	#394×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#394×C₆₇	C₂²	1	2	yes	—
55	#394×C₆₇	C₂²	1	2	yes	—
56	#394×C₆₇	C₂²	1	2	yes	—
57	#394×C₆₇	C₂²	1	2	yes	—
58	#390×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	2	yes	—
60	#390×C₆₇	C₂²	1	1	yes	characteristic
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	2	yes	—
65	#389×C₆₇	C₂²	1	1	yes	characteristic
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	#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	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#385×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#384×C₆₇	C₂²	1	1	yes	characteristic
97	#382×C₆₇	C₂²	1	1	yes	characteristic
98	#381×C₆₇	C₂²	1	2	yes	—
99	#380×C₆₇	C₂²	1	2	yes	—
100	#380×C₆₇	C₂²	1	2	yes	—
101	#380×C₆₇	C₂²	1	1	yes	characteristic
102	#380×C₆₇	C₂²	1	1	yes	characteristic
103	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
104	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
105	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
106	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
107	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	#127×C₆₇	—	4	2	no	—
123	#125×C₆₇	—	4	2	no	—
124	#123×C₆₇	—	4	4	no	—
125	#123×C₆₇	—	4	4	no	—
126	#123×C₆₇	—	4	4	no	—
127	#121×C₆₇	—	2	4	no	—
128	#121×C₆₇	—	2	4	no	—
129	#121×C₆₇	—	4	4	no	—
130	#121×C₆₇	—	4	4	no	—
131	C₄×D₄×C₆₇	—	4	4	no	—
132	C₄×D₄×C₆₇	—	4	4	no	—
133	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
134	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	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×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊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×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	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	—	4	2	no	—
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×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	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
209	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
210	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	4	no	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	2	4	no	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	2	no	—
218	C₂×D₄×C₆₇	—	2	2	no	—
219	C₂×D₄×C₆₇	—	2	4	no	—
220	C₂×D₄×C₆₇	—	2	4	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	—	4	2	no	—
225	C₂×D₄×C₆₇	—	4	1	no	—
226	C₂×D₄×C₆₇	—	4	1	no	—
227	C₂×D₄×C₆₇	—	4	2	no	—
228	C₂×D₄×C₆₇	—	4	1	no	—
229	C₂²×C₄×C₆₇	—	2	2	no	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	2	no	—
238	C₂²×C₄×C₆₇	—	2	2	no	—
239	C₂²×C₄×C₆₇	—	4	1	no	—
240	C₂²×C₄×C₆₇	—	4	1	no	—
241	C₂²×C₄×C₆₇	—	4	1	no	—
242	C₂²×C₄×C₆₇	—	4	1	no	—
243	C₂²×C₄×C₆₇	—	4	1	no	—
244	C₂²×C₄×C₆₇	—	4	1	no	—
245	C₂²×C₄×C₆₇	—	4	1	no	—
246	C₂²×C₄×C₆₇	—	4	2	no	—
247	C₂²×C₄×C₆₇	—	4	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	1	no	—
253	C₂²×C₄×C₆₇	—	4	1	no	—
254	C₂²×C₄×C₆₇	—	4	1	no	—
255	C₂²×C₄×C₆₇	#41	1	4	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	1	no	—
281	C₄⋊C₄×C₆₇	—	4	1	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₄⋊C₄×C₆₇	—	4	2	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	2	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₄⋊C₄×C₆₇	—	4	1	no	—
292	C₄⋊C₄×C₆₇	—	4	1	no	—
293	C₄⋊C₄×C₆₇	—	4	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	4	2	no	—
299	C₂²⋊C₄×C₆₇	—	4	2	no	—
300	C₂²⋊C₄×C₆₇	—	4	2	no	—
301	C₂²⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	2	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₂²⋊C₄×C₆₇	—	4	2	no	—
311	C₂²⋊C₄×C₆₇	—	4	2	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	—	4	2	no	—
315	C₂²⋊C₄×C₆₇	—	4	2	no	—
316	C₄²×C₆₇	—	2	2	no	—
317	C₄²×C₆₇	—	2	2	no	—
318	C₄²×C₆₇	—	4	1	no	—
319	C₄²×C₆₇	—	4	1	no	—
320	C₄²×C₆₇	—	4	2	no	—
321	C₄²×C₆₇	—	4	2	no	—
322	C₂³×C₆₇	—	2	1	no	—
323	C₂³×C₆₇	—	2	1	no	—
324	C₂³×C₆₇	—	2	1	no	—
325	C₂³×C₆₇	—	2	1	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	2	2	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	C₂×#41	1	2	yes	—
341	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
342	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
343	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
344	D₄×C₆₇	—	4	8	no	—
345	D₄×C₆₇	—	4	8	no	—
346	D₄×C₆₇	—	8	2	no	—
347	D₄×C₆₇	—	8	2	no	—
348	D₄×C₆₇	—	8	4	no	—
349	D₄×C₆₇	—	8	4	no	—
350	C₂×C₄×C₆₇	—	2	1	no	—
351	C₂×C₄×C₆₇	—	2	1	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	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	1	no	—
363	C₂×C₄×C₆₇	—	2	1	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	1	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	4	4	no	—
395	C₂×C₄×C₆₇	—	4	4	no	—
396	C₂×C₄×C₆₇	—	4	4	no	—
397	C₂×C₄×C₆₇	—	4	4	no	—
398	C₂×C₄×C₆₇	—	4	4	no	—
399	C₂×C₄×C₆₇	—	8	2	no	—
400	C₂×C₄×C₆₇	—	8	2	no	—
401	C₂×C₄×C₆₇	—	8	4	no	—
402	C₂×C₄×C₆₇	—	8	4	no	—
403	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
404	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
405	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
407	C₂²×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	2	2	no	—
412	C₂²×C₆₇	—	2	2	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	2	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	#540	1	4	yes	—
428	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂²×C₆₇	#585	1	1	yes	characteristic
434	C₂²×C₆₇	#585	1	1	yes	characteristic
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	2	no	—
437	C₄×C₆₇	—	2	2	no	—
438	C₄×C₆₇	—	2	2	no	—
439	C₄×C₆₇	—	4	2	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	1	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	2	no	—
451	#36761	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂×C₆₇	—	2	4	no	—
453	C₂×C₆₇	—	8	2	no	—
454	C₂×C₆₇	—	8	2	no	—
455	C₂×C₆₇	C₂×#540	1	1	yes	characteristic
456	C₂×C₆₇	#3505	1	1	yes	characteristic
457	C₂×C₆₇	#3507	1	1	yes	characteristic
458	C₂×C₆₇	#3534	1	1	yes	characteristic
459	C₂×C₆₇	#3536	1	1	yes	characteristic
460	C₂×C₆₇	#3559	1	1	yes	characteristic
461	C₂×C₆₇	#3560	1	1	yes	characteristic
462	#2856	C₂×C₆₇	1	1	yes	characteristic
463	#2851	C₂×C₆₇	1	1	yes	characteristic, complemented
464	#2800	C₂×C₆₇	1	2	yes	complemented
465	#2791	C₂×C₆₇	1	2	yes	complemented
466	#2786	C₂×C₆₇	1	2	yes	complemented
467	#2780	C₂×C₆₇	1	2	yes	complemented
468	#2761	C₂×C₆₇	1	2	yes	complemented
469	#2740	C₂×C₆₇	1	2	yes	complemented
470	#2709	C₂×C₆₇	1	2	yes	complemented
471	#2707	C₂×C₆₇	1	2	yes	complemented
472	#2618	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#2618	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#2444	C₂×C₆₇	1	2	yes	complemented
475	#2443	C₂×C₆₇	1	2	yes	complemented
476	#2425	C₂×C₆₇	1	2	yes	complemented
477	#2425	C₂×C₆₇	1	2	yes	complemented
478	#2325	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#2325	C₂×C₆₇	1	1	yes	characteristic, complemented
480	C₂×#387	C₂×C₆₇	1	1	yes	characteristic, complemented
481	C₆₇	#36761	1	1	yes	characteristic, direct product factor, Sylow
482	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
484	C₂×#123	C₂²×C₆₇	1	2	yes	—
485	C₂×#123	C₂²×C₆₇	1	2	yes	—
486	C₂×#123	C₂²×C₆₇	1	2	yes	—
487	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×#121	C₂²×C₆₇	1	2	yes	—
490	C₂×#121	C₂²×C₆₇	1	2	yes	—
491	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
492	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
493	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
494	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
495	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
496	#400	C₂²×C₆₇	1	2	yes	—
497	#399	C₂²×C₆₇	1	2	yes	—
498	#398	C₂²×C₆₇	1	2	yes	—
499	#398	C₂²×C₆₇	1	2	yes	—
500	#398	C₂²×C₆₇	1	2	yes	—
501	#398	C₂²×C₆₇	1	2	yes	—
502	#398	C₂²×C₆₇	1	2	yes	—
503	#397	C₂²×C₆₇	1	2	yes	—
504	#397	C₂²×C₆₇	1	2	yes	—
505	#397	C₂²×C₆₇	1	2	yes	—
506	#397	C₂²×C₆₇	1	2	yes	—
507	#397	C₂²×C₆₇	1	2	yes	—
508	#396	C₂²×C₆₇	1	2	yes	—
509	#396	C₂²×C₆₇	1	2	yes	—
510	#396	C₂²×C₆₇	1	2	yes	—
511	#396	C₂²×C₆₇	1	2	yes	—
512	#396	C₂²×C₆₇	1	2	yes	—
513	#396	C₂²×C₆₇	1	2	yes	—
514	#394	C₂²×C₆₇	1	2	yes	—
515	#394	C₂²×C₆₇	1	2	yes	—
516	#394	C₂²×C₆₇	1	2	yes	—
517	#394	C₂²×C₆₇	1	2	yes	—
518	#394	C₂²×C₆₇	1	2	yes	—
519	#394	C₂²×C₆₇	1	2	yes	—
520	#390	C₂²×C₆₇	1	2	yes	—
521	#390	C₂²×C₆₇	1	1	yes	characteristic
522	#390	C₂²×C₆₇	1	2	yes	—
523	#390	C₂²×C₆₇	1	1	yes	characteristic
524	#389	C₂²×C₆₇	1	1	yes	characteristic
525	#389	C₂²×C₆₇	1	1	yes	characteristic
526	#389	C₂²×C₆₇	1	2	yes	—
527	#389	C₂²×C₆₇	1	2	yes	—
528	#388	C₂²×C₆₇	1	2	yes	—
529	#388	C₂²×C₆₇	1	2	yes	—
530	#388	C₂²×C₆₇	1	2	yes	—
531	#388	C₂²×C₆₇	1	2	yes	—
532	#388	C₂²×C₆₇	1	2	yes	—
533	#388	C₂²×C₆₇	1	2	yes	—
534	#387	C₂²×C₆₇	1	2	yes	—
535	#387	C₂²×C₆₇	1	2	yes	—
536	#387	C₂²×C₆₇	1	2	yes	—
537	#387	C₂²×C₆₇	1	2	yes	—
538	#387	C₂²×C₆₇	1	2	yes	—
539	#387	C₂²×C₆₇	1	2	yes	—
540	#387	C₂²×C₆₇	1	2	yes	—
541	#387	C₂²×C₆₇	1	2	yes	—
542	#387	C₂²×C₆₇	1	2	yes	—
543	#387	C₂²×C₆₇	1	2	yes	—
544	#386	C₂²×C₆₇	1	2	yes	—
545	#386	C₂²×C₆₇	1	2	yes	—
546	#386	C₂²×C₆₇	1	2	yes	—
547	#386	C₂²×C₆₇	1	2	yes	—
548	#386	C₂²×C₆₇	1	2	yes	—
549	#386	C₂²×C₆₇	1	2	yes	—
550	#386	C₂²×C₆₇	1	2	yes	—
551	#386	C₂²×C₆₇	1	2	yes	—
552	#386	C₂²×C₆₇	1	2	yes	—
553	#385	C₂²×C₆₇	1	2	yes	—
554	#385	C₂²×C₆₇	1	2	yes	—
555	#385	C₂²×C₆₇	1	2	yes	—
556	#385	C₂²×C₆₇	1	2	yes	—
557	#385	C₂²×C₆₇	1	2	yes	—
558	#384	C₂²×C₆₇	1	1	yes	characteristic
559	#382	C₂²×C₆₇	1	1	yes	characteristic
560	#381	C₂²×C₆₇	1	2	yes	—
561	#380	C₂²×C₆₇	1	1	yes	characteristic
562	#380	C₂²×C₆₇	1	1	yes	characteristic
563	#380	C₂²×C₆₇	1	2	yes	—
564	#380	C₂²×C₆₇	1	2	yes	—
565	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
566	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
568	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
570	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
571	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
572	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
582	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
583	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
584	#127	—	4	2	no	—
585	#125	—	4	2	no	—
586	#123	—	4	4	no	—
587	#123	—	4	4	no	—
588	#123	—	4	4	no	—
589	#121	—	2	4	no	—
590	#121	—	2	4	no	—
591	#121	—	4	4	no	—
592	#121	—	4	4	no	—
593	C₄×D₄	—	4	4	no	—
594	C₄×D₄	—	4	4	no	—
595	C₂×C₄⋊C₄	—	2	4	no	—
596	C₂×C₄⋊C₄	—	4	2	no	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄²	—	4	2	no	—
642	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	#95	C₂³×C₆₇	1	2	yes	—
670	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
671	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
672	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	1	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	C₂²×C₄	—	4	1	no	—
715	C₂²×C₄	—	4	1	no	—
716	C₂²×C₄	—	4	1	no	—
717	C₂²×C₄	#41×C₆₇	1	4	yes	—
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	1	no	—
751	C₄⋊C₄	—	4	1	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	1	no	—
754	C₄⋊C₄	—	4	1	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	4	1	no	—
781	C₄²	—	4	1	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	2	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	C₂×#41×C₆₇	1	2	yes	—
803	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
804	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
805	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
806	D₄	—	4	8	no	—
807	D₄	—	4	8	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	2	no	—
811	D₄	—	8	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	—	8	4	no	—
864	C₂×C₄	—	8	4	no	—
865	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
866	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
867	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
868	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	#540×C₆₇	1	4	yes	—
890	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
891	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
892	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
893	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
894	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
895	C₂²	#585×C₆₇	1	1	yes	characteristic
896	C₂²	#585×C₆₇	1	1	yes	characteristic
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₂	—	2	4	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	C₂×#540×C₆₇	1	1	yes	characteristic
917	C₂	C₆₇×#3505	1	1	yes	characteristic
918	C₂	C₆₇×#3507	1	1	yes	characteristic
919	C₂	C₆₇×#3534	1	1	yes	characteristic
920	C₂	C₆₇×#3536	1	1	yes	characteristic
921	C₂	C₆₇×#3559	1	1	yes	characteristic
922	C₂	C₆₇×#3560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2856	C₂
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×#2851	C₂	semidirect
3. C₆₇×#2800	C₂	semidirect
4. C₆₇×#2791	C₂	semidirect
5. C₆₇×#2786	C₂	semidirect
6. C₆₇×#2780	C₂	semidirect
7. C₆₇×#2761	C₂	semidirect
8. C₆₇×#2740	C₂	semidirect
9. C₆₇×#2709	C₂	semidirect
10. C₆₇×#2707	C₂	semidirect
11. C₆₇×#2618	C₂	semidirect
12. C₆₇×#2618	C₂	semidirect
13. C₆₇×#2444	C₂	semidirect
14. C₆₇×#2443	C₂	semidirect
15. C₆₇×#2425	C₂	semidirect
16. C₆₇×#2425	C₂	semidirect
17. C₆₇×#2325	C₂	semidirect
18. C₆₇×#2325	C₂	semidirect
19. C₂×#387×C₆₇	C₂	semidirect
451. #36761	C₆₇	direct (N × H)
463. #2851	C₂×C₆₇	semidirect
464. #2800	C₂×C₆₇	semidirect
465. #2791	C₂×C₆₇	semidirect
466. #2786	C₂×C₆₇	semidirect
467. #2780	C₂×C₆₇	semidirect
468. #2761	C₂×C₆₇	semidirect
469. #2740	C₂×C₆₇	semidirect
470. #2709	C₂×C₆₇	semidirect
471. #2707	C₂×C₆₇	semidirect
472. #2618	C₂×C₆₇	semidirect
473. #2618	C₂×C₆₇	semidirect
474. #2444	C₂×C₆₇	semidirect
475. #2443	C₂×C₆₇	semidirect
476. #2425	C₂×C₆₇	semidirect
477. #2425	C₂×C₆₇	semidirect
478. #2325	C₂×C₆₇	semidirect
479. #2325	C₂×C₆₇	semidirect
480. C₂×#387	C₂×C₆₇	semidirect
481. C₆₇	#36761	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×#2856	2
C₆₇×#2851	2
C₆₇×#2800	2
C₆₇×#2791	2
C₆₇×#2786	2
C₆₇×#2780	2
C₆₇×#2761	2
C₆₇×#2740	2
C₆₇×#2709	2
C₆₇×#2707	2
C₆₇×#2618	2
C₆₇×#2444	2
C₆₇×#2443	2
C₆₇×#2425	2
C₆₇×#2325	2
C₂×#387×C₆₇	2
#36761	67

Subgroups — C67×#36761 #30716012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#36761 #30716012