Subgroups — C₆₇×#22039 #30701290

Order 17152.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#436×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2388	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1780	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
23	#436×C₆₇	—	2	4	no	—
24	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
27	#408×C₆₇	—	2	4	no	—
28	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#395×C₆₇	C₄	1	1	yes	characteristic
45	#394×C₆₇	C₄	1	1	yes	characteristic
46	#394×C₆₇	C₄	1	1	yes	characteristic
47	#394×C₆₇	C₄	1	1	yes	characteristic
48	#393×C₆₇	C₄	1	1	yes	characteristic
49	#392×C₆₇	C₄	1	1	yes	characteristic
50	#392×C₆₇	C₄	1	1	yes	characteristic
51	#392×C₆₇	C₄	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
55	#336×C₆₇	C₂²	1	1	yes	characteristic
56	#336×C₆₇	C₂²	1	1	yes	characteristic
57	#336×C₆₇	C₂²	1	1	yes	characteristic
58	#336×C₆₇	C₂²	1	1	yes	characteristic
59	#336×C₆₇	C₂²	1	1	yes	characteristic
60	#336×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#41×C₆₇	—	2	2	no	—
62	C₂×#41×C₆₇	—	2	2	no	—
63	C₂×#41×C₆₇	—	4	1	no	—
64	C₂×#41×C₆₇	—	4	1	no	—
65	C₂×#41×C₆₇	—	4	1	no	—
66	C₂×#41×C₆₇	—	4	1	no	—
67	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₆₇	—	2	2	no	—
79	C₂×M₁₆×C₆₇	—	4	1	no	—
80	C₂×M₁₆×C₆₇	—	4	1	no	—
81	C₂×M₁₆×C₆₇	—	4	1	no	—
82	C₂×M₁₆×C₆₇	—	4	1	no	—
83	C₂×M₁₆×C₆₇	D₄	1	4	yes	complemented
84	C₂²×C₈×C₆₇	—	2	2	no	—
85	C₂²×C₈×C₆₇	—	4	1	no	—
86	C₂²×C₈×C₆₇	—	4	1	no	—
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₆₇	—	2	2	no	—
96	C₄×D₄×C₆₇	—	2	2	no	—
97	C₄×D₄×C₆₇	—	4	1	no	—
98	C₄×D₄×C₆₇	—	4	1	no	—
99	C₄×D₄×C₆₇	—	4	1	no	—
100	C₄×D₄×C₆₇	—	4	1	no	—
101	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₆₇	—	2	2	no	—
120	C₄⋊C₈×C₆₇	—	4	1	no	—
121	C₄⋊C₈×C₆₇	—	4	1	no	—
122	C₂²⋊C₈×C₆₇	—	2	2	no	—
123	C₂²⋊C₈×C₆₇	—	2	2	no	—
124	C₂²⋊C₈×C₆₇	—	2	2	no	—
125	C₂²⋊C₈×C₆₇	—	2	2	no	—
126	C₂²⋊C₈×C₆₇	—	2	2	no	—
127	C₂²⋊C₈×C₆₇	—	2	2	no	—
128	C₂²⋊C₈×C₆₇	—	2	2	no	—
129	C₂²⋊C₈×C₆₇	—	4	1	no	—
130	C₂²⋊C₈×C₆₇	—	4	1	no	—
131	C₂²⋊C₈×C₆₇	—	4	1	no	—
132	C₂²⋊C₈×C₆₇	—	4	1	no	—
133	C₂²⋊C₈×C₆₇	—	4	1	no	—
134	C₂²⋊C₈×C₆₇	—	4	1	no	—
135	#97×C₆₇	—	4	1	no	—
136	C₄×C₈×C₆₇	—	2	2	no	—
137	C₄×C₈×C₆₇	—	4	1	no	—
138	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
139	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
140	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
141	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
142	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
143	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
144	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	#41×C₆₇	—	4	4	no	—
149	#41×C₆₇	—	4	4	no	—
150	#41×C₆₇	—	4	4	no	—
151	#41×C₆₇	—	4	4	no	—
152	C₂×Q₈×C₆₇	—	2	2	no	—
153	C₂×Q₈×C₆₇	—	4	1	no	—
154	C₂×Q₈×C₆₇	—	4	1	no	—
155	C₂×D₄×C₆₇	—	2	2	no	—
156	C₂×D₄×C₆₇	—	2	2	no	—
157	C₂×D₄×C₆₇	—	2	2	no	—
158	C₂×D₄×C₆₇	—	2	2	no	—
159	C₂×D₄×C₆₇	—	2	2	no	—
160	C₂×D₄×C₆₇	—	2	2	no	—
161	C₂×D₄×C₆₇	—	4	1	no	—
162	C₂×D₄×C₆₇	—	4	1	no	—
163	C₂×D₄×C₆₇	—	4	1	no	—
164	C₂×D₄×C₆₇	—	4	1	no	—
165	C₂×D₄×C₆₇	—	4	1	no	—
166	C₂×D₄×C₆₇	—	4	1	no	—
167	C₂×D₄×C₆₇	—	4	1	no	—
168	C₂×D₄×C₆₇	—	4	1	no	—
169	C₂×D₄×C₆₇	—	4	1	no	—
170	C₂×D₄×C₆₇	—	4	1	no	—
171	C₂×D₄×C₆₇	—	4	1	no	—
172	C₂×D₄×C₆₇	—	4	1	no	—
173	C₂²×C₄×C₆₇	—	2	1	no	—
174	C₂²×C₄×C₆₇	—	2	1	no	—
175	C₂²×C₄×C₆₇	—	2	1	no	—
176	C₂²×C₄×C₆₇	—	2	1	no	—
177	C₂²×C₄×C₆₇	—	2	1	no	—
178	C₂²×C₄×C₆₇	—	2	1	no	—
179	C₂²×C₄×C₆₇	—	2	1	no	—
180	C₂²×C₄×C₆₇	—	2	1	no	—
181	C₂²×C₄×C₆₇	—	2	1	no	—
182	C₂²×C₄×C₆₇	—	2	1	no	—
183	C₂²×C₄×C₆₇	—	2	1	no	—
184	C₂²×C₄×C₆₇	—	2	1	no	—
185	C₂²×C₄×C₆₇	—	2	1	no	—
186	C₂²×C₄×C₆₇	—	2	1	no	—
187	C₂²×C₄×C₆₇	—	2	1	no	—
188	C₂²×C₄×C₆₇	—	2	1	no	—
189	C₂²×C₄×C₆₇	—	2	1	no	—
190	C₂²×C₄×C₆₇	—	2	1	no	—
191	C₂²×C₄×C₆₇	—	2	1	no	—
192	C₂²×C₄×C₆₇	—	2	1	no	—
193	C₂²×C₄×C₆₇	—	2	1	no	—
194	C₂²×C₄×C₆₇	—	2	1	no	—
195	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₆₇	#41	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	M₁₆×C₆₇	—	4	4	no	—
209	M₁₆×C₆₇	—	4	4	no	—
210	C₂×C₈×C₆₇	—	2	1	no	—
211	C₂×C₈×C₆₇	—	2	1	no	—
212	C₂×C₈×C₆₇	—	2	1	no	—
213	C₂×C₈×C₆₇	—	2	1	no	—
214	C₂×C₈×C₆₇	—	2	1	no	—
215	C₂×C₈×C₆₇	—	2	1	no	—
216	C₂×C₈×C₆₇	—	2	1	no	—
217	C₂×C₈×C₆₇	—	2	1	no	—
218	C₂×C₈×C₆₇	—	2	1	no	—
219	C₂×C₈×C₆₇	—	2	1	no	—
220	C₂×C₈×C₆₇	—	2	1	no	—
221	C₂×C₈×C₆₇	—	2	1	no	—
222	C₂×C₈×C₆₇	—	2	1	no	—
223	C₂×C₈×C₆₇	—	2	1	no	—
224	C₂×C₈×C₆₇	—	2	1	no	—
225	C₂×C₈×C₆₇	—	2	1	no	—
226	C₂×C₈×C₆₇	—	2	1	no	—
227	C₂×C₈×C₆₇	—	2	1	no	—
228	C₂×C₈×C₆₇	—	2	1	no	—
229	C₂×C₈×C₆₇	—	2	1	no	—
230	C₂×C₈×C₆₇	—	2	1	no	—
231	C₂×C₈×C₆₇	—	2	1	no	—
232	C₂×C₈×C₆₇	—	4	4	no	—
233	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	4	1	no	—
237	C₄⋊C₄×C₆₇	—	4	1	no	—
238	C₂²⋊C₄×C₆₇	—	2	2	no	—
239	C₂²⋊C₄×C₆₇	—	2	2	no	—
240	C₂²⋊C₄×C₆₇	—	2	2	no	—
241	C₂²⋊C₄×C₆₇	—	2	2	no	—
242	C₂²⋊C₄×C₆₇	—	2	2	no	—
243	C₂²⋊C₄×C₆₇	—	2	2	no	—
244	C₂²⋊C₄×C₆₇	—	4	1	no	—
245	C₂²⋊C₄×C₆₇	—	4	1	no	—
246	C₂²⋊C₄×C₆₇	—	4	1	no	—
247	C₂²⋊C₄×C₆₇	—	4	1	no	—
248	C₂²⋊C₄×C₆₇	—	4	1	no	—
249	C₂²⋊C₄×C₆₇	—	4	1	no	—
250	C₄²×C₆₇	—	2	1	no	—
251	C₄²×C₆₇	—	2	1	no	—
252	C₄²×C₆₇	—	2	1	no	—
253	C₄²×C₆₇	—	2	1	no	—
254	C₄²×C₆₇	—	2	1	no	—
255	C₄²×C₆₇	—	2	1	no	—
256	C₂³×C₆₇	—	2	1	no	—
257	C₂³×C₆₇	—	2	1	no	—
258	C₂³×C₆₇	—	2	1	no	—
259	C₂³×C₆₇	—	2	1	no	—
260	C₂³×C₆₇	—	2	1	no	—
261	C₂³×C₆₇	—	2	1	no	—
262	C₂³×C₆₇	—	2	1	no	—
263	C₂³×C₆₇	—	2	1	no	—
264	C₂³×C₆₇	—	2	1	no	—
265	C₂³×C₆₇	—	2	1	no	—
266	C₂³×C₆₇	—	2	1	no	—
267	C₂³×C₆₇	—	2	1	no	—
268	C₂³×C₆₇	—	2	1	no	—
269	C₂³×C₆₇	—	2	1	no	—
270	C₂³×C₆₇	—	2	1	no	—
271	C₂³×C₆₇	—	2	1	no	—
272	C₂³×C₆₇	—	2	1	no	—
273	C₂³×C₆₇	—	2	1	no	—
274	C₂³×C₆₇	—	2	1	no	—
275	C₂³×C₆₇	—	2	1	no	—
276	C₂³×C₆₇	—	2	1	no	—
277	C₂³×C₆₇	—	2	1	no	—
278	C₂³×C₆₇	—	2	1	no	—
279	C₂³×C₆₇	—	2	1	no	—
280	C₂³×C₆₇	—	2	1	no	—
281	C₂³×C₆₇	—	2	1	no	—
282	C₂³×C₆₇	—	2	1	no	—
283	C₂³×C₆₇	C₄×D₄	1	2	yes	—
284	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
285	Q₈×C₆₇	—	4	4	no	—
286	D₄×C₆₇	—	4	4	no	—
287	D₄×C₆₇	—	4	4	no	—
288	D₄×C₆₇	—	4	4	no	—
289	D₄×C₆₇	—	4	4	no	—
290	D₄×C₆₇	—	4	4	no	—
291	D₄×C₆₇	—	4	4	no	—
292	C₂×C₄×C₆₇	—	2	1	no	—
293	C₂×C₄×C₆₇	—	2	1	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	1	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	1	no	—
312	C₂×C₄×C₆₇	—	2	1	no	—
313	C₂×C₄×C₆₇	—	2	1	no	—
314	C₂×C₄×C₆₇	—	2	1	no	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	1	no	—
317	C₂×C₄×C₆₇	—	2	1	no	—
318	C₂×C₄×C₆₇	—	2	1	no	—
319	C₂×C₄×C₆₇	—	2	1	no	—
320	C₂×C₄×C₆₇	—	2	1	no	—
321	C₂×C₄×C₆₇	—	2	1	no	—
322	C₂×C₄×C₆₇	—	2	1	no	—
323	C₂×C₄×C₆₇	—	4	1	no	—
324	C₂×C₄×C₆₇	—	4	1	no	—
325	C₂×C₄×C₆₇	—	4	1	no	—
326	C₂×C₄×C₆₇	—	4	1	no	—
327	C₂×C₄×C₆₇	—	4	1	no	—
328	C₂×C₄×C₆₇	—	4	1	no	—
329	C₂×C₄×C₆₇	—	4	1	no	—
330	C₂×C₄×C₆₇	—	4	1	no	—
331	C₂×C₄×C₆₇	—	4	1	no	—
332	C₂×C₄×C₆₇	—	4	1	no	—
333	C₂×C₄×C₆₇	—	4	1	no	—
334	C₂×C₄×C₆₇	—	4	1	no	—
335	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
336	C₂×C₄×C₆₇	#131	1	2	yes	—
337	C₂×C₄×C₆₇	#131	1	2	yes	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
344	C₈×C₆₇	—	2	2	no	—
345	C₈×C₆₇	—	2	2	no	—
346	C₈×C₆₇	—	4	1	no	—
347	C₈×C₆₇	—	4	1	no	—
348	C₈×C₆₇	—	4	1	no	—
349	C₈×C₆₇	—	4	1	no	—
350	C₈×C₆₇	—	4	1	no	—
351	C₈×C₆₇	—	4	1	no	—
352	C₂²×C₆₇	—	2	2	no	—
353	C₂²×C₆₇	—	2	2	no	—
354	C₂²×C₆₇	—	2	2	no	—
355	C₂²×C₆₇	—	4	1	no	—
356	C₂²×C₆₇	—	4	1	no	—
357	C₂²×C₆₇	—	4	1	no	—
358	C₂²×C₆₇	—	4	1	no	—
359	C₂²×C₆₇	—	4	1	no	—
360	C₂²×C₆₇	—	4	1	no	—
361	C₂²×C₆₇	—	4	1	no	—
362	C₂²×C₆₇	—	4	1	no	—
363	C₂²×C₆₇	—	4	1	no	—
364	C₂²×C₆₇	—	4	1	no	—
365	C₂²×C₆₇	—	4	1	no	—
366	C₂²×C₆₇	—	4	1	no	—
367	C₂²×C₆₇	—	4	1	no	—
368	C₂²×C₆₇	—	4	1	no	—
369	C₂²×C₆₇	—	4	1	no	—
370	C₂²×C₆₇	—	4	1	no	—
371	C₂²×C₆₇	—	4	1	no	—
372	C₂²×C₆₇	—	4	1	no	—
373	C₂²×C₆₇	—	4	1	no	—
374	C₂²×C₆₇	—	4	1	no	—
375	C₂²×C₆₇	—	4	1	no	—
376	C₂²×C₆₇	—	4	1	no	—
377	C₂²×C₆₇	—	4	1	no	—
378	C₂²×C₆₇	—	4	1	no	—
379	C₂²×C₆₇	—	4	1	no	—
380	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
381	C₂²×C₆₇	#518	1	1	yes	characteristic
382	C₂²×C₆₇	#518	1	1	yes	characteristic
383	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
384	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
385	C₂²×C₆₇	#568	1	1	yes	characteristic
386	C₂²×C₆₇	#568	1	1	yes	characteristic
387	C₄×C₆₇	—	2	2	no	—
388	C₄×C₆₇	—	2	2	no	—
389	C₄×C₆₇	—	2	2	no	—
390	C₄×C₆₇	—	4	1	no	—
391	C₄×C₆₇	—	4	1	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	1	no	—
397	C₄×C₆₇	#534	1	1	yes	characteristic
398	C₄×C₆₇	#535	1	1	yes	characteristic
399	C₄×C₆₇	#538	1	1	yes	characteristic
400	C₄×C₆₇	#538	1	1	yes	characteristic
401	#22039	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂×C₆₇	—	4	2	no	—
403	C₂×C₆₇	—	8	1	no	—
404	C₂×C₆₇	—	8	1	no	—
405	C₂×C₆₇	—	8	1	no	—
406	C₂×C₆₇	#2321	1	1	yes	characteristic
407	C₂×C₆₇	#2933	1	1	yes	characteristic
408	C₂×C₆₇	#2935	1	1	yes	characteristic
409	C₂×C₆₇	#2976	1	1	yes	characteristic
410	C₂×C₆₇	#2978	1	1	yes	characteristic
411	C₂×C₆₇	#2979	1	1	yes	characteristic
412	C₂×C₆₇	#2981	1	1	yes	characteristic
413	C₂×#436	C₂×C₆₇	1	1	yes	characteristic, complemented
414	C₂×#408	C₂×C₆₇	1	1	yes	characteristic, complemented
415	#2388	C₂×C₆₇	1	1	yes	characteristic
416	#1955	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#1954	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#1924	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#1923	C₂×C₆₇	1	1	yes	characteristic, complemented
420	#1923	C₂×C₆₇	1	1	yes	characteristic, complemented
421	#1923	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#1870	C₂×C₆₇	1	1	yes	characteristic, complemented
423	#1870	C₂×C₆₇	1	1	yes	characteristic, complemented
424	#1869	C₂×C₆₇	1	1	yes	characteristic, complemented
425	#1850	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#1780	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#1753	C₂×C₆₇	1	1	yes	characteristic, complemented
428	C₆₇	#22039	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
430	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
431	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
432	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
436	#436	—	2	4	no	—
437	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
440	#408	—	2	4	no	—
441	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
451	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
457	#395	C₄×C₆₇	1	1	yes	characteristic
458	#394	C₄×C₆₇	1	1	yes	characteristic
459	#394	C₄×C₆₇	1	1	yes	characteristic
460	#394	C₄×C₆₇	1	1	yes	characteristic
461	#393	C₄×C₆₇	1	1	yes	characteristic
462	#392	C₄×C₆₇	1	1	yes	characteristic
463	#392	C₄×C₆₇	1	1	yes	characteristic
464	#392	C₄×C₆₇	1	1	yes	characteristic
465	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
466	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
467	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
468	#336	C₂²×C₆₇	1	1	yes	characteristic
469	#336	C₂²×C₆₇	1	1	yes	characteristic
470	#336	C₂²×C₆₇	1	1	yes	characteristic
471	#336	C₂²×C₆₇	1	1	yes	characteristic
472	#336	C₂²×C₆₇	1	1	yes	characteristic
473	#336	C₂²×C₆₇	1	1	yes	characteristic
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	4	1	no	—
477	C₂×#41	—	4	1	no	—
478	C₂×#41	—	4	1	no	—
479	C₂×#41	—	4	1	no	—
480	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
481	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
482	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
483	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
484	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
485	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
486	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
491	C₂×M₁₆	—	2	2	no	—
492	C₂×M₁₆	—	4	1	no	—
493	C₂×M₁₆	—	4	1	no	—
494	C₂×M₁₆	—	4	1	no	—
495	C₂×M₁₆	—	4	1	no	—
496	C₂×M₁₆	D₄×C₆₇	1	4	yes	complemented
497	C₂²×C₈	—	2	2	no	—
498	C₂²×C₈	—	4	1	no	—
499	C₂²×C₈	—	4	1	no	—
500	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	4	1	no	—
511	C₄×D₄	—	4	1	no	—
512	C₄×D₄	—	4	1	no	—
513	C₄×D₄	—	4	1	no	—
514	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
532	C₄⋊C₈	—	2	2	no	—
533	C₄⋊C₈	—	4	1	no	—
534	C₄⋊C₈	—	4	1	no	—
535	C₂²⋊C₈	—	2	2	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₂²⋊C₈	—	2	2	no	—
538	C₂²⋊C₈	—	2	2	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	C₂²⋊C₈	—	2	2	no	—
542	C₂²⋊C₈	—	4	1	no	—
543	C₂²⋊C₈	—	4	1	no	—
544	C₂²⋊C₈	—	4	1	no	—
545	C₂²⋊C₈	—	4	1	no	—
546	C₂²⋊C₈	—	4	1	no	—
547	C₂²⋊C₈	—	4	1	no	—
548	#97	—	4	1	no	—
549	C₄×C₈	—	2	2	no	—
550	C₄×C₈	—	4	1	no	—
551	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
552	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
553	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
554	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
555	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
556	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
557	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
558	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
559	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
560	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
561	#41	—	4	4	no	—
562	#41	—	4	4	no	—
563	#41	—	4	4	no	—
564	#41	—	4	4	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	4	1	no	—
567	C₂×Q₈	—	4	1	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	—	4	1	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂×D₄	—	4	1	no	—
581	C₂×D₄	—	4	1	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
609	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
610	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
611	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
612	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
613	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
614	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
616	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
619	C₂²×C₄	#41×C₆₇	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
621	M₁₆	—	4	4	no	—
622	M₁₆	—	4	4	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	4	4	no	—
646	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
647	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	4	1	no	—
650	C₄⋊C₄	—	4	1	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	4	1	no	—
658	C₂²⋊C₄	—	4	1	no	—
659	C₂²⋊C₄	—	4	1	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	1	no	—
662	C₂²⋊C₄	—	4	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	C₄×D₄×C₆₇	1	2	yes	—
697	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
698	Q₈	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	4	no	—
703	D₄	—	4	4	no	—
704	D₄	—	4	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
749	C₂×C₄	#131×C₆₇	1	2	yes	—
750	C₂×C₄	#131×C₆₇	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
752	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
753	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
754	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
755	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
756	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	2	2	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₈	—	4	1	no	—
762	C₈	—	4	1	no	—
763	C₈	—	4	1	no	—
764	C₈	—	4	1	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
794	C₂²	#518×C₆₇	1	1	yes	characteristic
795	C₂²	#518×C₆₇	1	1	yes	characteristic
796	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
797	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
798	C₂²	#568×C₆₇	1	1	yes	characteristic
799	C₂²	#568×C₆₇	1	1	yes	characteristic
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	#534×C₆₇	1	1	yes	characteristic
811	C₄	#535×C₆₇	1	1	yes	characteristic
812	C₄	#538×C₆₇	1	1	yes	characteristic
813	C₄	#538×C₆₇	1	1	yes	characteristic
814	C₂	—	4	2	no	—
815	C₂	—	8	1	no	—
816	C₂	—	8	1	no	—
817	C₂	—	8	1	no	—
818	C₂	C₆₇×#2321	1	1	yes	characteristic
819	C₂	C₆₇×#2933	1	1	yes	characteristic
820	C₂	C₆₇×#2935	1	1	yes	characteristic
821	C₂	C₆₇×#2976	1	1	yes	characteristic
822	C₂	C₆₇×#2978	1	1	yes	characteristic
823	C₂	C₆₇×#2979	1	1	yes	characteristic
824	C₂	C₆₇×#2981	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₆₇×#2388	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#436×C₆₇	C₂	semidirect
2. C₂×#408×C₆₇	C₂	semidirect
4. C₆₇×#1955	C₂	semidirect
5. C₆₇×#1954	C₂	semidirect
6. C₆₇×#1924	C₂	semidirect
7. C₆₇×#1923	C₂	semidirect
8. C₆₇×#1923	C₂	semidirect
9. C₆₇×#1923	C₂	semidirect
10. C₆₇×#1870	C₂	semidirect
11. C₆₇×#1870	C₂	semidirect
12. C₆₇×#1869	C₂	semidirect
13. C₆₇×#1850	C₂	semidirect
14. C₆₇×#1780	C₂	semidirect
15. C₆₇×#1753	C₂	semidirect
83. C₂×M₁₆×C₆₇	D₄	semidirect
401. #22039	C₆₇	direct (N × H)
413. C₂×#436	C₂×C₆₇	semidirect
414. C₂×#408	C₂×C₆₇	semidirect
416. #1955	C₂×C₆₇	semidirect
417. #1954	C₂×C₆₇	semidirect
418. #1924	C₂×C₆₇	semidirect
419. #1923	C₂×C₆₇	semidirect
420. #1923	C₂×C₆₇	semidirect
421. #1923	C₂×C₆₇	semidirect
422. #1870	C₂×C₆₇	semidirect
423. #1870	C₂×C₆₇	semidirect
424. #1869	C₂×C₆₇	semidirect
425. #1850	C₂×C₆₇	semidirect
426. #1780	C₂×C₆₇	semidirect
427. #1753	C₂×C₆₇	semidirect
428. C₆₇	#22039	direct (N × H)
496. C₂×M₁₆	D₄×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#436×C₆₇	2
C₂×#408×C₆₇	2
C₆₇×#2388	2
C₆₇×#1955	2
C₆₇×#1954	2
C₆₇×#1924	2
C₆₇×#1923	2
C₆₇×#1870	2
C₆₇×#1869	2
C₆₇×#1850	2
C₆₇×#1780	2
C₆₇×#1753	2
#22039	67

Subgroups — C67×#22039 #30701290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22039 #30701290