Subgroups — C₂×#22574481 #31763129

Order 17152.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574481	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864138	C₂	1	2	yes	maximal, complemented
3	C₂×#16864136	C₂	1	2	yes	maximal, complemented
4	C₂×#16864128	C₂	1	2	yes	maximal, complemented
5	C₂×#16864120	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864119	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864112	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16864111	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864069	C₂	1	2	yes	maximal, complemented
10	C₂×#16864058	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16864041	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16864019	C₂	1	2	yes	maximal, complemented
15	C₂×#16864017	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16864012	C₂	1	2	yes	maximal, complemented
17	C₂×#16863986	C₂	1	2	yes	maximal, complemented
18	C₂×#16863985	C₂	1	2	yes	maximal, complemented
19	C₂×#16863969	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16863962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16863909	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863908	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#16863906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761629	C₂²	1	1	yes	characteristic
26	C₂²×#11761628	C₂²	1	1	yes	characteristic
27	C₂²×#11761627	C₂²	1	1	yes	characteristic
28	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
31	#16864138	C₂²	1	32	yes	complemented
32	#16864136	C₂²	1	32	yes	complemented
33	#16864128	C₂²	1	32	yes	complemented
34	#16864120	C₂²	1	16	yes	complemented
35	#16864119	C₂²	1	16	yes	complemented
36	#16864112	C₂²	1	16	yes	complemented
37	#16864111	C₂²	1	16	yes	complemented
38	#16864069	C₂²	1	32	yes	complemented
39	#16864058	C₂²	1	16	yes	complemented
40	#16864054	C₂²	1	16	yes	complemented
41	#16864041	C₂²	1	16	yes	complemented
42	#16864039	C₂²	1	16	yes	complemented
43	#16864019	C₂²	1	32	yes	complemented
44	#16864017	C₂²	1	16	yes	complemented
45	#16864012	C₂²	1	32	yes	complemented
46	#16863986	C₂²	1	32	yes	complemented
47	#16863985	C₂²	1	32	yes	complemented
48	#16863969	C₂²	1	16	yes	complemented
49	#16863962	C₂²	1	16	yes	complemented
50	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
51	C₂×#14524042	C₂²	1	2	yes	complemented
52	C₂×#14524039	C₂²	1	2	yes	—
53	C₂×#14524038	C₂²	1	2	yes	complemented
54	C₂×#14524038	C₂²	1	2	yes	complemented
55	C₂×#14524038	C₂²	1	2	yes	complemented
56	C₂×#14524038	C₂²	1	2	yes	complemented
57	C₂×#14524038	C₂²	1	2	yes	complemented
58	C₂×#14524032	C₂²	1	2	yes	—
59	C₂×#14524032	C₂²	1	2	yes	complemented
60	C₂×#14524032	C₂²	1	2	yes	complemented
61	C₂×#14524031	C₂²	1	2	yes	—
62	C₂×#14524031	C₂²	1	2	yes	complemented
63	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
64	C₂×#14524029	C₂²	1	2	yes	—
65	C₂×#14524029	C₂²	1	2	yes	complemented
66	C₂×#14524029	C₂²	1	2	yes	complemented
67	C₂×#14524029	C₂²	1	2	yes	complemented
68	C₂×#14524029	C₂²	1	2	yes	complemented
69	C₂×#14524029	C₂²	1	2	yes	complemented
70	#16863909	C₂²	1	16	yes	complemented
71	#16863908	C₂²	1	16	yes	complemented
72	#16863906	C₂²	1	16	yes	complemented
73	C₂×#14524028	C₂²	1	2	yes	complemented
74	C₂×#14524028	C₂²	1	2	yes	complemented
75	C₂×#14524027	C₂²	1	1	yes	characteristic
76	C₂×#14524027	C₂²	1	2	yes	complemented
77	C₂×#14524027	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14524025	C₂²	1	2	yes	complemented
79	C₂×#14524025	C₂²	1	2	yes	complemented
80	C₂×#14524025	C₂²	1	2	yes	complemented
81	C₂×#14524025	C₂²	1	2	yes	complemented
82	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
83	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
84	C₂×#14524023	C₂²	1	2	yes	complemented
85	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
86	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
87	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
88	C₂×#14524021	C₂²	1	2	yes	complemented
89	C₂×#14524020	C₂²	1	2	yes	complemented
90	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
91	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
92	C₂×#14524018	C₂²	1	1	yes	characteristic
93	C₂×#14524018	C₂²	1	1	yes	characteristic
94	C₂×#14524018	C₂²	1	1	yes	characteristic
95	C₂×#14524018	C₂²	1	1	yes	characteristic, complemented
96	C₂×#14524018	C₂²	1	2	yes	complemented
97	C₂×#14524018	C₂²	1	2	yes	complemented
98	C₂×#14524017	C₂²	1	1	yes	characteristic
99	C₂×#14524017	C₂²	1	2	yes	—
100	C₂×#14524017	C₂²	1	2	yes	complemented
101	C₂×#14524016	C₂²	1	2	yes	—
102	C₂×#14524016	C₂²	1	2	yes	complemented
103	C₂×#14524014	C₂²	1	1	yes	characteristic
104	C₂×#14524014	C₂²	1	1	yes	characteristic, complemented
105	C₂×#14524013	C₂²	1	2	yes	—
106	C₂×#14524013	C₂²	1	2	yes	—
107	C₂×#14524013	C₂²	1	1	yes	characteristic
108	C₂×#14524013	C₂²	1	1	yes	characteristic, complemented
109	C₂×#14524013	C₂²	1	2	yes	complemented
110	C₂×#14524013	C₂²	1	2	yes	complemented
111	C₂×#14524011	C₂²	1	2	yes	—
112	C₂×#14524011	C₂²	1	2	yes	complemented
113	C₂×Q₈×Dic₆₇	C₂²	1	2	yes	complemented
114	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
115	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
117	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
118	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
122	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
123	C₂×#14524005	C₂²	1	2	yes	complemented
124	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
125	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
126	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
127	C₂×#14524002	C₂²	1	2	yes	complemented
128	C₂×#14524001	C₂²	1	2	yes	complemented
129	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
130	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
131	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
132	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
133	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
135	#542×C₆₇	C₂²	1	16	yes	complemented
136	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
138	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
140	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
141	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
142	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
143	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
144	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
146	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
149	C₂×#11761629	—	4	4	no	—
150	C₂×#11761629	C₂³	1	8	yes	—
151	C₂×#11761628	—	4	4	no	—
152	C₂×#11761628	C₂³	1	8	yes	—
153	C₂×#11761627	—	4	4	no	—
154	C₂×#11761627	C₂³	1	8	yes	—
155	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
156	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
157	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
158	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
159	C₂×Q₈×D₆₇	—	4	4	no	—
160	C₂×Q₈×D₆₇	C₂³	1	8	yes	complemented
161	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
162	C₂²×D₂₆₈	C₂³	1	2	yes	—
163	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
164	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
165	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
166	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
167	C₂²×D₂₆₈	C₂³	1	2	yes	—
168	C₂²×D₂₆₈	C₂³	1	2	yes	—
169	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
170	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
171	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
172	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
173	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
175	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
176	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
177	C₂×D₄×D₆₇	—	4	4	no	—
178	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
179	C₂³×Dic₆₇	C₂³	1	2	yes	—
180	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₆₇	—	4	4	no	—
182	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
185	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
186	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
187	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
188	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
189	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
190	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
192	#14524043	C₂³	1	8	yes	complemented
193	#14524042	C₂³	1	16	yes	complemented
194	#14524039	C₂³	1	16	yes	—
195	#14524038	C₂³	1	16	yes	complemented
196	#14524038	C₂³	1	16	yes	complemented
197	#14524038	C₂³	1	16	yes	complemented
198	#14524038	C₂³	1	16	yes	complemented
199	#14524038	C₂³	1	16	yes	complemented
200	#14524032	C₂³	1	16	yes	—
201	#14524032	C₂³	1	16	yes	complemented
202	#14524032	C₂³	1	16	yes	complemented
203	#14524031	C₂³	1	16	yes	—
204	#14524031	C₂³	1	16	yes	complemented
205	#14524031	C₂³	1	8	yes	complemented
206	#14524029	C₂³	1	16	yes	—
207	#14524029	C₂³	1	16	yes	complemented
208	#14524029	C₂³	1	16	yes	complemented
209	#14524029	C₂³	1	16	yes	complemented
210	#14524029	C₂³	1	16	yes	complemented
211	#14524029	C₂³	1	16	yes	complemented
212	#14524028	C₂³	1	16	yes	complemented
213	#14524028	C₂³	1	16	yes	complemented
214	#14524027	C₂³	1	8	yes	—
215	#14524027	C₂³	1	16	yes	complemented
216	#14524027	C₂³	1	8	yes	complemented
217	#14524025	C₂³	1	16	yes	complemented
218	#14524025	C₂³	1	16	yes	complemented
219	#14524025	C₂³	1	16	yes	complemented
220	#14524025	C₂³	1	16	yes	complemented
221	#14524023	C₂³	1	8	yes	complemented
222	#14524023	C₂³	1	8	yes	complemented
223	#14524023	C₂³	1	16	yes	complemented
224	#14524023	C₂³	1	8	yes	complemented
225	#14524023	C₂³	1	8	yes	complemented
226	#14524022	C₂³	1	8	yes	complemented
227	#14524021	C₂³	1	16	yes	complemented
228	#14524020	C₂³	1	16	yes	complemented
229	#14524019	C₂³	1	8	yes	complemented
230	#14524019	C₂³	1	8	yes	complemented
231	#14524018	C₂³	1	8	yes	—
232	#14524018	C₂³	1	8	yes	—
233	#14524018	C₂³	1	8	yes	—
234	#14524018	C₂³	1	8	yes	complemented
235	#14524018	C₂³	1	16	yes	complemented
236	#14524018	C₂³	1	16	yes	complemented
237	#14524017	C₂³	1	8	yes	—
238	#14524017	C₂³	1	16	yes	—
239	#14524017	C₂³	1	16	yes	complemented
240	#14524016	C₂³	1	16	yes	—
241	#14524016	C₂³	1	16	yes	complemented
242	#14524014	C₂³	1	8	yes	—
243	#14524014	C₂³	1	8	yes	complemented
244	#14524013	C₂³	1	16	yes	—
245	#14524013	C₂³	1	16	yes	—
246	#14524013	C₂³	1	8	yes	—
247	#14524013	C₂³	1	8	yes	complemented
248	#14524013	C₂³	1	16	yes	complemented
249	#14524013	C₂³	1	16	yes	complemented
250	#14524011	C₂³	1	16	yes	—
251	#14524011	C₂³	1	16	yes	complemented
252	Q₈×Dic₆₇	C₂³	1	16	yes	complemented
253	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
254	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
255	C₄×D₂₆₈	C₂³	1	8	yes	—
256	C₄×D₂₆₈	C₂³	1	8	yes	—
257	C₄×D₂₆₈	C₂³	1	8	yes	complemented
258	C₄×D₂₆₈	C₂³	1	8	yes	complemented
259	C₄×D₂₆₈	C₂³	1	8	yes	complemented
260	C₄×D₂₆₈	C₂³	1	16	yes	complemented
261	D₄×Dic₆₇	C₂³	1	16	yes	complemented
262	#14524005	C₂³	1	16	yes	complemented
263	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
264	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
265	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
266	#14524002	C₂³	1	16	yes	complemented
267	#14524001	C₂³	1	16	yes	complemented
268	#14524001	C₂³	1	8	yes	complemented
269	#14524001	C₂³	1	8	yes	complemented
270	#14524001	C₂³	1	8	yes	complemented
271	#14524001	C₂³	1	8	yes	complemented
272	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
277	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
278	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
281	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
282	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
283	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
284	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
285	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
286	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
287	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
288	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
290	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
292	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
293	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
294	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
295	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
296	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
297	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
298	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
299	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
301	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
302	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
303	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
304	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
305	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
306	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
307	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
308	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
309	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
310	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
311	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
312	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
313	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
314	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
315	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
316	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
317	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
319	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
321	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
323	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
324	#126×C₆₇	C₂³	1	16	yes	complemented
325	#124×C₆₇	C₂³	1	8	yes	complemented
326	#124×C₆₇	C₂³	1	16	yes	complemented
327	#123×C₆₇	C₂³	1	16	yes	complemented
328	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
329	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
330	#121×C₆₇	C₂³	1	8	yes	—
331	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
332	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
333	#117×C₆₇	C₂³	1	8	yes	complemented
334	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
339	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
340	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
341	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
345	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
348	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
351	C₂³×D₆₇	—	4	2	no	—
352	C₂³×D₆₇	—	4	2	no	—
353	C₂³×D₆₇	—	4	2	no	—
354	C₂³×D₆₇	—	4	4	no	—
355	C₂³×D₆₇	—	4	4	no	—
356	C₂³×D₆₇	—	4	4	no	—
357	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
358	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
359	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
360	C₂³×D₆₇	C₂⁴	1	2	yes	—
361	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
362	C₂³×D₆₇	C₂⁴	1	8	yes	—
363	C₂³×D₆₇	C₂⁴	1	4	yes	—
364	#11761629	—	4	16	no	—
365	#11761628	—	4	16	no	—
366	#11761627	—	4	16	no	—
367	C₂×Dic₁₃₄	—	2	4	no	—
368	C₂×Dic₁₃₄	—	4	4	no	—
369	C₂×Dic₁₃₄	—	4	4	no	—
370	C₂×Dic₁₃₄	—	4	2	no	—
371	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
372	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
373	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
374	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
375	Q₈×D₆₇	—	4	16	no	—
376	C₂×D₂₆₈	—	2	4	no	—
377	C₂×D₂₆₈	—	4	2	no	—
378	C₂×D₂₆₈	—	4	4	no	—
379	C₂×D₂₆₈	—	4	4	no	—
380	C₂×D₂₆₈	—	4	2	no	—
381	C₂×D₂₆₈	—	4	2	no	—
382	C₂×D₂₆₈	—	4	2	no	—
383	C₂×D₂₆₈	—	4	2	no	—
384	C₂×D₂₆₈	—	4	4	no	—
385	C₂×D₂₆₈	C₂⁴	1	4	yes	—
386	C₂×D₂₆₈	C₂⁴	1	8	yes	—
387	C₂×D₂₆₈	C₂⁴	1	4	yes	—
388	C₂×D₂₆₈	C₂⁴	1	4	yes	—
389	C₂×D₂₆₈	C₂⁴	1	4	yes	—
390	C₂×D₂₆₈	C₂⁴	1	4	yes	—
391	C₂×D₂₆₈	C₂⁴	1	8	yes	—
392	C₂×D₂₆₈	C₂⁴	1	8	yes	—
393	C₂×D₂₆₈	C₂⁴	1	4	yes	—
394	C₂×C₂²⋊D₆₇	—	4	4	no	—
395	C₂×C₂²⋊D₆₇	—	4	4	no	—
396	C₂×C₂²⋊D₆₇	—	4	4	no	—
397	C₂×C₂²⋊D₆₇	—	4	4	no	—
398	C₂×C₂²⋊D₆₇	—	4	4	no	—
399	C₂×C₂²⋊D₆₇	—	4	2	no	—
400	C₂×C₂²⋊D₆₇	—	4	2	no	—
401	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
402	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
403	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
404	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
405	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
406	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
407	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
408	D₄×D₆₇	—	4	16	no	—
409	C₂²×Dic₆₇	—	4	2	no	—
410	C₂²×Dic₆₇	—	4	4	no	—
411	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
412	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
413	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
418	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
419	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
420	C₂×C₄×D₆₇	—	2	4	no	—
421	C₂×C₄×D₆₇	—	2	4	no	—
422	C₂×C₄×D₆₇	—	2	4	no	—
423	C₂×C₄×D₆₇	—	2	4	no	—
424	C₂×C₄×D₆₇	—	4	16	no	—
425	C₂×C₄×D₆₇	—	4	2	no	—
426	C₂×C₄×D₆₇	—	4	2	no	—
427	C₂×C₄×D₆₇	—	4	4	no	—
428	C₂×C₄×D₆₇	—	4	4	no	—
429	C₂×C₄×D₆₇	—	4	4	no	—
430	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
431	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
432	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
433	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
434	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
435	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
436	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
437	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
438	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
439	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
440	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
441	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
442	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
443	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
444	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
445	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
446	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
447	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
448	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
449	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
450	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
451	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
452	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
453	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
454	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
455	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
456	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
457	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
458	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
459	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
460	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
461	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
462	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
463	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
464	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
465	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
466	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
467	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
468	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
469	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
470	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
471	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
472	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
473	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
474	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
475	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
476	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
477	C₄×Dic₆₇	C₂⁴	1	8	yes	—
478	C₄×Dic₆₇	C₂⁴	1	8	yes	—
479	C₄×Dic₆₇	C₂⁴	1	8	yes	—
480	C₄×Dic₆₇	C₂⁴	1	8	yes	—
481	C₄×Dic₆₇	C₂⁴	1	8	yes	—
482	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
483	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
484	C₂×Q₈×C₆₇	—	2	4	no	—
485	C₂×Q₈×C₆₇	—	4	4	no	—
486	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
487	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
488	C₂×D₄×C₆₇	—	2	4	no	—
489	C₂×D₄×C₆₇	—	4	4	no	—
490	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
491	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
492	C₂²×C₄×C₆₇	—	2	4	no	—
493	C₂²×C₄×C₆₇	—	4	4	no	—
494	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
497	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
500	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
502	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
503	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
504	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
506	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
507	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
508	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
509	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
510	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
511	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
512	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
513	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
514	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
515	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
516	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
517	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
518	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
519	C₄²×C₆₇	C₂⁴	1	4	yes	—
520	C₄²×C₆₇	C₂⁴	1	4	yes	—
521	C₄²×C₆₇	C₂⁴	1	8	yes	—
522	C₂³×C₆₇	—	2	2	no	—
523	C₂³×C₆₇	—	2	4	no	—
524	C₂³×C₆₇	—	2	4	no	—
525	C₂³×C₆₇	—	2	2	no	—
526	C₂³×C₆₇	—	2	2	no	—
527	C₂³×C₆₇	—	2	4	no	—
528	C₂³×C₆₇	C₂⁵	1	2	yes	—
529	C₂³×C₆₇	C₂⁵	1	4	yes	—
530	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
531	C₂²×D₆₇	—	2	2	no	—
532	C₂²×D₆₇	—	2	2	no	—
533	C₂²×D₆₇	—	2	2	no	—
534	C₂²×D₆₇	—	2	2	no	—
535	C₂²×D₆₇	—	2	4	no	—
536	C₂²×D₆₇	—	2	4	no	—
537	C₂²×D₆₇	—	2	2	no	—
538	C₂²×D₆₇	—	2	2	no	—
539	C₂²×D₆₇	—	2	2	no	—
540	C₂²×D₆₇	—	2	2	no	—
541	C₂²×D₆₇	—	2	2	no	—
542	C₂²×D₆₇	—	2	4	no	—
543	C₂²×D₆₇	—	2	2	no	—
544	C₂²×D₆₇	—	2	2	no	—
545	C₂²×D₆₇	—	2	2	no	—
546	C₂²×D₆₇	—	4	4	no	—
547	C₂²×D₆₇	—	4	4	no	—
548	C₂²×D₆₇	—	4	4	no	—
549	C₂²×D₆₇	—	4	8	no	—
550	C₂²×D₆₇	—	4	8	no	—
551	C₂²×D₆₇	—	4	8	no	—
552	C₂²×D₆₇	—	4	16	no	—
553	C₂²×D₆₇	—	8	16	no	—
554	C₂²×D₆₇	C₂⁵	1	2	yes	—
555	C₂²×D₆₇	C₂⁵	1	2	yes	—
556	C₂²×D₆₇	C₂⁵	1	2	yes	—
557	C₂²×D₆₇	C₂⁵	1	4	yes	—
558	C₂²×D₆₇	C₂⁵	1	2	yes	—
559	Q₈×C₆₇	—	2	8	no	—
560	Q₈×C₆₇	—	4	8	no	—
561	D₄×C₆₇	—	2	8	no	—
562	D₄×C₆₇	—	4	8	no	—
563	C₂×C₄×C₆₇	—	2	2	no	—
564	C₂×C₄×C₆₇	—	2	4	no	—
565	C₂×C₄×C₆₇	—	2	2	no	—
566	C₂×C₄×C₆₇	—	2	4	no	—
567	C₂×C₄×C₆₇	—	2	4	no	—
568	C₂×C₄×C₆₇	—	2	2	no	—
569	C₂×C₄×C₆₇	—	2	2	no	—
570	C₂×C₄×C₆₇	—	2	2	no	—
571	C₂×C₄×C₆₇	—	2	8	no	—
572	C₂×C₄×C₆₇	—	4	8	no	—
573	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
574	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
575	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
576	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
577	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
578	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
579	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
580	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
581	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
582	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
583	C₂²⋊D₆₇	—	4	8	no	—
584	C₂²⋊D₆₇	—	4	8	no	—
585	C₂²⋊D₆₇	—	4	8	no	—
586	C₂²⋊D₆₇	—	4	8	no	—
587	C₂²⋊D₆₇	—	4	8	no	—
588	C₂²⋊D₆₇	—	4	4	no	—
589	C₂²⋊D₆₇	—	4	4	no	—
590	C₂×Dic₆₇	—	2	2	no	—
591	C₂×Dic₆₇	—	2	2	no	—
592	C₂×Dic₆₇	—	2	2	no	—
593	C₂×Dic₆₇	—	2	2	no	—
594	C₂×Dic₆₇	—	2	4	no	—
595	C₂×Dic₆₇	—	2	4	no	—
596	C₂×Dic₆₇	—	2	4	no	—
597	C₂×Dic₆₇	—	4	4	no	—
598	C₂×Dic₆₇	—	4	8	no	—
599	C₂×Dic₆₇	C₂⁵	1	4	yes	—
600	C₂×Dic₆₇	C₂⁵	1	4	yes	—
601	C₂×Dic₆₇	C₂⁵	1	2	yes	—
602	C₂×Dic₆₇	C₂⁵	1	2	yes	—
603	C₂×Dic₆₇	C₂⁵	1	2	yes	—
604	C₂×Dic₆₇	C₂⁵	1	2	yes	—
605	C₂×Dic₆₇	C₂⁵	1	4	yes	—
606	D₂₆₈	—	2	8	no	—
607	D₂₆₈	—	4	4	no	—
608	D₂₆₈	—	4	4	no	—
609	D₂₆₈	—	4	4	no	—
610	D₂₆₈	—	4	8	no	—
611	D₂₆₈	—	4	8	no	—
612	D₂₆₈	—	4	4	no	—
613	D₂₆₈	—	4	4	no	—
614	D₂₆₈	—	4	8	no	—
615	C₄×D₆₇	—	2	8	no	—
616	C₄×D₆₇	—	2	8	no	—
617	C₄×D₆₇	—	2	8	no	—
618	C₄×D₆₇	—	2	8	no	—
619	C₄×D₆₇	—	4	4	no	—
620	C₄×D₆₇	—	4	4	no	—
621	C₄×D₆₇	—	4	8	no	—
622	C₄×D₆₇	—	4	8	no	—
623	C₄×D₆₇	—	4	8	no	—
624	Dic₁₃₄	—	2	8	no	—
625	Dic₁₃₄	—	4	8	no	—
626	Dic₁₃₄	—	4	8	no	—
627	Dic₁₃₄	—	4	4	no	—
628	C₂²×C₆₇	—	2	2	no	—
629	C₂²×C₆₇	—	2	4	no	—
630	C₂²×C₆₇	—	2	2	no	—
631	C₂²×C₆₇	—	2	4	no	—
632	C₂²×C₆₇	—	2	4	no	—
633	C₂²×C₆₇	—	2	2	no	—
634	C₂²×C₆₇	—	4	4	no	—
635	C₂²×C₆₇	—	4	8	no	—
636	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
637	C₂²×C₆₇	#585	1	2	yes	—
638	C₂²×C₆₇	#585	1	2	yes	—
639	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
640	C₂×D₆₇	—	2	2	no	—
641	C₂×D₆₇	—	2	2	no	—
642	C₂×D₆₇	—	2	2	no	—
643	C₂×D₆₇	—	2	2	no	—
644	C₂×D₆₇	—	2	4	no	—
645	C₂×D₆₇	—	2	4	no	—
646	C₂×D₆₇	—	2	2	no	—
647	C₂×D₆₇	—	2	2	no	—
648	C₂×D₆₇	—	2	2	no	—
649	C₂×D₆₇	—	2	4	no	—
650	C₂×D₆₇	—	2	2	no	—
651	C₂×D₆₇	—	2	2	no	—
652	C₂×D₆₇	—	2	2	no	—
653	C₂×D₆₇	—	2	2	no	—
654	C₂×D₆₇	—	2	2	no	—
655	C₂×D₆₇	—	4	16	no	—
656	C₂×D₆₇	—	4	4	no	—
657	C₂×D₆₇	—	4	4	no	—
658	C₂×D₆₇	—	4	4	no	—
659	C₂×D₆₇	—	4	8	no	—
660	C₂×D₆₇	—	4	4	no	—
661	C₂×D₆₇	—	8	16	no	—
662	C₄×C₆₇	—	2	2	no	—
663	C₄×C₆₇	—	2	4	no	—
664	C₄×C₆₇	—	2	2	no	—
665	C₄×C₆₇	—	2	2	no	—
666	C₄×C₆₇	—	2	2	no	—
667	C₄×C₆₇	—	2	4	no	—
668	C₄×C₆₇	—	2	4	no	—
669	C₄×C₆₇	—	2	2	no	—
670	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
671	Dic₆₇	—	2	4	no	—
672	Dic₆₇	—	2	2	no	—
673	Dic₆₇	—	2	2	no	—
674	Dic₆₇	—	2	2	no	—
675	Dic₆₇	—	2	2	no	—
676	Dic₆₇	—	2	4	no	—
677	Dic₆₇	—	2	4	no	—
678	C₂×#3540	—	67	1	no	maximal, Sylow
679	C₂×C₆₇	—	4	2	no	—
680	C₂×C₆₇	—	4	4	no	—
681	C₂×C₆₇	#3540	1	4	yes	complemented
682	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
684	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
685	D₆₇	—	4	2	no	—
686	D₆₇	—	4	2	no	—
687	D₆₇	—	4	2	no	—
688	D₆₇	—	4	4	no	—
689	D₆₇	—	4	2	no	—
690	#3540	—	67	32	no	—
691	C₂×H(3,𝔽₄)	—	67	2	no	—
692	C₂×#560	—	67	2	no	—
693	C₂×#559	—	67	2	no	—
694	C₂×#556	—	67	1	no	—
695	C₂×#556	—	67	1	no	—
696	C₂×#555	—	67	1	no	—
697	C₂×#555	—	67	1	no	—
698	C₂×#551	—	67	2	no	—
699	C₂×#548	—	67	1	no	—
700	C₂×#548	—	67	1	no	—
701	C₂×#546	—	67	1	no	—
702	C₂×#546	—	67	1	no	—
703	C₂×#542	—	67	2	no	—
704	C₂×#542	—	67	2	no	—
705	C₂×#542	—	67	1	no	—
706	C₂×#542	D₆₇	1	1	yes	characteristic, complemented
707	C₂×#538	—	67	2	no	—
708	C₂×#538	—	67	2	no	—
709	C₂×#536	—	67	1	no	—
710	C₂×#535	—	67	1	no	—
711	C₂×#525	—	67	1	no	—
712	C₂×#525	—	67	1	no	—
713	C₂×#525	—	67	1	no	—
714	C₆₇	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
715	C₂²×#41	—	67	1	no	—
716	C₂²×#41	—	67	1	no	—
717	C₂²×#41	—	67	1	no	—
718	C₂³×Q₈	—	67	1	no	—
719	C₂³×D₄	—	67	1	no	—
720	C₂⁴×C₄	—	67	1	no	—
721	H(3,𝔽₄)	—	67	32	no	—
722	#560	—	67	32	no	—
723	#559	—	67	32	no	—
724	#556	—	67	16	no	—
725	#556	—	67	16	no	—
726	#555	—	67	16	no	—
727	#555	—	67	16	no	—
728	#551	—	67	32	no	—
729	#548	—	67	16	no	—
730	#548	—	67	16	no	—
731	#546	—	67	16	no	—
732	#546	—	67	16	no	—
733	#542	—	67	32	no	—
734	#542	—	67	32	no	—
735	#542	—	67	16	no	—
736	#542	C₂×D₆₇	1	16	yes	complemented
737	#538	—	67	32	no	—
738	#538	—	67	32	no	—
739	#536	—	67	16	no	—
740	#535	—	67	16	no	—
741	C₂×C₄⋊Q₈	—	67	2	no	—
742	C₂×C₄⋊Q₈	—	67	1	no	—
743	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
744	C₂×#127	—	67	2	no	—
745	C₂×#126	—	67	2	no	—
746	C₂×#126	—	67	2	no	—
747	C₂×#126	—	67	2	no	—
748	C₂×#126	—	67	2	no	—
749	C₂×#126	—	67	2	no	—
750	C₂×#126	C₂×D₆₇	1	2	yes	complemented
751	C₂×#124	—	67	2	no	—
752	C₂×#124	—	67	2	no	—
753	C₂×#124	—	67	2	no	—
754	C₂×#124	—	67	2	no	—
755	C₂×#124	—	67	2	no	—
756	C₂×#124	—	67	2	no	—
757	C₂×#124	—	67	2	no	—
758	C₂×#124	—	67	2	no	—
759	C₂×#124	—	67	2	no	—
760	C₂×#124	—	67	2	no	—
761	C₂×#124	—	67	1	no	—
762	C₂×#124	—	67	2	no	—
763	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
764	C₂×#124	C₂×D₆₇	1	2	yes	complemented
765	#525	—	67	16	no	—
766	#525	—	67	16	no	—
767	#525	—	67	16	no	—
768	C₂×#123	—	67	2	no	—
769	C₂×#123	—	67	2	no	—
770	C₂×#123	—	67	2	no	—
771	C₂×#123	—	67	1	no	—
772	C₂×#123	—	67	1	no	—
773	C₂×#123	—	67	2	no	—
774	C₂×#123	—	67	2	no	—
775	C₂×#123	—	67	2	no	—
776	C₂×#123	—	67	2	no	—
777	C₂×#123	C₂×D₆₇	1	2	yes	complemented
778	C₂×C₂²⋊Q₈	—	67	1	no	—
779	C₂×C₂²⋊Q₈	—	67	1	no	—
780	C₂×C₂²⋊Q₈	—	67	1	no	—
781	C₂×C₂²⋊Q₈	—	67	1	no	—
782	C₂×C₂²⋊Q₈	—	67	1	no	—
783	C₂×C₂²⋊Q₈	—	67	1	no	—
784	C₂×C₂²⋊Q₈	—	67	1	no	—
785	C₂×C₂²⋊Q₈	—	67	2	no	—
786	C₂×C₂²⋊Q₈	—	67	2	no	—
787	C₂×C₂²⋊Q₈	—	67	2	no	—
788	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
789	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
790	C₂×#121	—	67	1	no	—
791	C₂×#121	—	67	1	no	—
792	C₂×#121	—	67	1	no	—
793	C₂×#121	—	67	2	no	—
794	C₂×#121	—	67	2	no	—
795	C₂×#121	—	67	1	no	—
796	C₂×#121	—	67	1	no	—
797	C₂×#121	—	67	1	no	—
798	C₂×#121	—	67	1	no	—
799	C₂×#121	—	67	2	no	—
800	C₂×#121	—	67	2	no	—
801	C₂×#121	—	67	2	no	—
802	C₂×#121	—	67	2	no	—
803	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
804	C₂×#120	—	67	2	no	—
805	C₂×#120	—	67	2	no	—
806	C₂×#120	—	67	1	no	—
807	C₂×#120	—	67	1	no	—
808	C₂×#120	—	67	2	no	—
809	C₂×#120	—	67	2	no	—
810	C₂×#120	—	67	2	no	—
811	C₂×#120	—	67	2	no	—
812	C₂×C₄×Q₈	—	67	2	no	—
813	C₂×C₄×Q₈	—	67	1	no	—
814	C₂×C₄×Q₈	—	67	2	no	—
815	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
816	C₂×C₄×D₄	—	67	2	no	—
817	C₂×C₄×D₄	—	67	2	no	—
818	C₂×C₄×D₄	—	67	2	no	—
819	C₂×C₄×D₄	—	67	2	no	—
820	C₂×C₄×D₄	—	67	2	no	—
821	C₂×C₄×D₄	—	67	1	no	—
822	C₂×C₄×D₄	—	67	1	no	—
823	C₂×C₄×D₄	—	67	1	no	—
824	C₂×C₄×D₄	—	67	1	no	—
825	C₂×C₄×D₄	—	67	2	no	—
826	C₂×C₄×D₄	—	67	1	no	—
827	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
828	C₂×#117	—	67	2	no	—
829	C₂×#117	—	67	1	no	—
830	C₂×#117	—	67	1	no	—
831	C₂×#117	—	67	1	no	—
832	C₂×#117	—	67	1	no	—
833	C₂×#117	—	67	2	no	—
834	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
835	C₂²×C₂²⋊C₄	—	67	2	no	—
836	C₂²×C₂²⋊C₄	—	67	2	no	—
837	C₂⁵	—	67	2	no	—
838	C₂⁵	—	67	1	no	—
839	C₂×#41	—	268	4	no	—
840	C₂×#41	—	268	4	no	—
841	C₂×#41	—	268	4	no	—
842	C₂×#41	—	67	8	no	—
843	C₂×#41	—	67	8	no	—
844	C₂×#41	—	67	8	no	—
845	C₂²×Q₈	—	268	4	no	—
846	C₂²×Q₈	—	67	8	no	—
847	C₂²×Q₈	—	67	2	no	—
848	C₂²×Q₈	—	67	2	no	—
849	C₂²×Q₈	—	67	1	no	—
850	C₂²×Q₈	—	67	1	no	—
851	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
852	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
853	C₂²×D₄	—	268	4	no	—
854	C₂²×D₄	—	67	2	no	—
855	C₂²×D₄	—	67	2	no	—
856	C₂²×D₄	—	67	2	no	—
857	C₂²×D₄	—	67	1	no	—
858	C₂²×D₄	—	67	2	no	—
859	C₂²×D₄	—	67	1	no	—
860	C₂²×D₄	—	67	2	no	—
861	C₂²×D₄	—	67	8	no	—
862	C₂²×D₄	—	67	1	no	—
863	C₂²×D₄	—	67	1	no	—
864	C₂²×D₄	—	67	2	no	—
865	C₂²×D₄	—	67	1	no	—
866	C₂²×D₄	—	67	1	no	—
867	C₂²×D₄	—	67	2	no	—
868	C₂²×D₄	—	67	1	no	—
869	C₂²×D₄	—	67	2	no	—
870	C₂²×D₄	—	67	1	no	—
871	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
872	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
873	C₂³×C₄	—	268	4	no	—
874	C₂³×C₄	—	67	2	no	—
875	C₂³×C₄	—	67	1	no	—
876	C₂³×C₄	—	67	2	no	—
877	C₂³×C₄	—	67	2	no	—
878	C₂³×C₄	—	67	2	no	—
879	C₂³×C₄	—	67	1	no	—
880	C₂³×C₄	—	67	1	no	—
881	C₂³×C₄	—	67	8	no	—
882	C₂³×C₄	—	67	1	no	—
883	C₂³×C₄	—	67	1	no	—
884	C₂³×C₄	—	67	1	no	—
885	C₂³×C₄	—	67	1	no	—
886	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
887	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
888	C₄⋊Q₈	—	67	16	no	—
889	C₄⋊Q₈	—	67	8	no	—
890	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
891	#127	—	67	16	no	—
892	#126	—	67	16	no	—
893	#126	—	67	16	no	—
894	#126	—	67	16	no	—
895	#126	—	67	16	no	—
896	#126	—	67	16	no	—
897	#126	C₂²×D₆₇	1	16	yes	complemented
898	#124	—	67	16	no	—
899	#124	—	67	16	no	—
900	#124	—	67	16	no	—
901	#124	—	67	16	no	—
902	#124	—	67	16	no	—
903	#124	—	67	16	no	—
904	#124	—	67	16	no	—
905	#124	—	67	16	no	—
906	#124	—	67	16	no	—
907	#124	—	67	16	no	—
908	#124	—	67	8	no	—
909	#124	—	67	16	no	—
910	#124	C₂²×D₆₇	1	8	yes	complemented
911	#124	C₂²×D₆₇	1	16	yes	complemented
912	#123	—	67	16	no	—
913	#123	—	67	16	no	—
914	#123	—	67	16	no	—
915	#123	—	67	8	no	—
916	#123	—	67	8	no	—
917	#123	—	67	16	no	—
918	#123	—	67	16	no	—
919	#123	—	67	16	no	—
920	#123	—	67	16	no	—
921	#123	C₂²×D₆₇	1	16	yes	complemented
922	C₂²⋊Q₈	—	67	8	no	—
923	C₂²⋊Q₈	—	67	8	no	—
924	C₂²⋊Q₈	—	67	8	no	—
925	C₂²⋊Q₈	—	67	8	no	—
926	C₂²⋊Q₈	—	67	8	no	—
927	C₂²⋊Q₈	—	67	8	no	—
928	C₂²⋊Q₈	—	67	8	no	—
929	C₂²⋊Q₈	—	67	16	no	—
930	C₂²⋊Q₈	—	67	16	no	—
931	C₂²⋊Q₈	—	67	16	no	—
932	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
933	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
934	#121	—	67	8	no	—
935	#121	—	67	8	no	—
936	#121	—	67	8	no	—
937	#121	—	67	16	no	—
938	#121	—	67	16	no	—
939	#121	—	67	8	no	—
940	#121	—	67	8	no	—
941	#121	—	67	8	no	—
942	#121	—	67	8	no	—
943	#121	—	67	16	no	—
944	#121	—	67	16	no	—
945	#121	—	67	16	no	—
946	#121	—	67	16	no	—
947	#121	C₂²×D₆₇	1	8	yes	—
948	#120	—	67	16	no	—
949	#120	—	67	16	no	—
950	#120	—	67	8	no	—
951	#120	—	67	16	no	—
952	#120	—	67	8	no	—
953	#120	—	67	16	no	—
954	#120	—	67	16	no	—
955	#120	—	67	16	no	—
956	C₄×Q₈	—	67	16	no	—
957	C₄×Q₈	—	67	8	no	—
958	C₄×Q₈	—	67	16	no	—
959	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
960	C₄×D₄	—	67	16	no	—
961	C₄×D₄	—	67	16	no	—
962	C₄×D₄	—	67	16	no	—
963	C₄×D₄	—	67	16	no	—
964	C₄×D₄	—	67	16	no	—
965	C₄×D₄	—	67	8	no	—
966	C₄×D₄	—	67	8	no	—
967	C₄×D₄	—	67	8	no	—
968	C₄×D₄	—	67	8	no	—
969	C₄×D₄	—	67	16	no	—
970	C₄×D₄	—	67	8	no	—
971	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
972	#117	—	67	16	no	—
973	#117	—	67	8	no	—
974	#117	—	67	8	no	—
975	#117	—	67	8	no	—
976	#117	—	67	8	no	—
977	#117	—	67	16	no	—
978	#117	C₂²×D₆₇	1	8	yes	complemented
979	C₂×C₄⋊C₄	—	67	1	no	—
980	C₂×C₄⋊C₄	—	67	1	no	—
981	C₂×C₄⋊C₄	—	67	1	no	—
982	C₂×C₄⋊C₄	—	67	1	no	—
983	C₂×C₄⋊C₄	—	67	2	no	—
984	C₂×C₄⋊C₄	—	67	2	no	—
985	C₂×C₄⋊C₄	—	67	2	no	—
986	C₂×C₄⋊C₄	—	67	1	no	—
987	C₂×C₄⋊C₄	—	67	1	no	—
988	C₂×C₄⋊C₄	—	67	2	no	—
989	C₂×C₄⋊C₄	—	67	2	no	—
990	C₂×C₄⋊C₄	—	67	2	no	—
991	C₂×C₄⋊C₄	—	67	2	no	—
992	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
995	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
998	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
999	C₂×C₂²⋊C₄	—	67	2	no	—
1000	C₂×C₂²⋊C₄	—	67	2	no	—
1001	C₂×C₂²⋊C₄	—	67	2	no	—
1002	C₂×C₂²⋊C₄	—	67	1	no	—
1003	C₂×C₂²⋊C₄	—	67	1	no	—
1004	C₂×C₂²⋊C₄	—	67	2	no	—
1005	C₂×C₂²⋊C₄	—	67	2	no	—
1006	C₂×C₂²⋊C₄	—	67	2	no	—
1007	C₂×C₂²⋊C₄	—	67	2	no	—
1008	C₂×C₂²⋊C₄	—	67	16	no	—
1009	C₂×C₂²⋊C₄	—	67	2	no	—
1010	C₂×C₂²⋊C₄	—	67	2	no	—
1011	C₂×C₂²⋊C₄	—	67	2	no	—
1012	C₂×C₂²⋊C₄	—	67	2	no	—
1013	C₂×C₂²⋊C₄	—	67	2	no	—
1014	C₂×C₂²⋊C₄	—	67	1	no	—
1015	C₂×C₂²⋊C₄	—	67	1	no	—
1016	C₂×C₂²⋊C₄	—	67	1	no	—
1017	C₂×C₂²⋊C₄	—	67	1	no	—
1018	C₂×C₂²⋊C₄	—	67	2	no	—
1019	C₂×C₂²⋊C₄	—	67	2	no	—
1020	C₂×C₂²⋊C₄	—	67	2	no	—
1021	C₂×C₂²⋊C₄	—	67	2	no	—
1022	C₂×C₂²⋊C₄	—	67	1	no	—
1023	C₂×C₂²⋊C₄	—	67	1	no	—
1024	C₂×C₂²⋊C₄	—	67	2	no	—
1025	C₂×C₂²⋊C₄	—	67	16	no	—
1026	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1027	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1030	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1031	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1032	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1033	C₂×C₄²	—	67	2	no	—
1034	C₂×C₄²	—	67	2	no	—
1035	C₂×C₄²	—	67	2	no	—
1036	C₂×C₄²	—	67	2	no	—
1037	C₂×C₄²	—	67	2	no	—
1038	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1039	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1040	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1041	C₂⁴	—	268	2	no	—
1042	C₂⁴	—	268	2	no	—
1043	C₂⁴	—	268	2	no	—
1044	C₂⁴	—	268	4	no	—
1045	C₂⁴	—	268	4	no	—
1046	C₂⁴	—	268	4	no	—
1047	C₂⁴	—	67	8	no	—
1048	C₂⁴	—	67	4	no	—
1049	C₂⁴	—	67	1	no	—
1050	C₂⁴	—	67	1	no	—
1051	C₂⁴	—	67	1	no	—
1052	C₂⁴	—	67	2	no	—
1053	C₂⁴	—	67	1	no	—
1054	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1055	C₂⁴	C₂³×D₆₇	1	2	yes	—
1056	#41	—	268	16	no	—
1057	#41	—	268	16	no	—
1058	#41	—	268	16	no	—
1059	C₂×Q₈	—	2	4	no	—
1060	C₂×Q₈	—	4	4	no	—
1061	C₂×Q₈	—	268	4	no	—
1062	C₂×Q₈	—	268	2	no	—
1063	C₂×Q₈	—	268	4	no	—
1064	C₂×Q₈	—	268	16	no	—
1065	C₂×Q₈	—	67	8	no	—
1066	C₂×Q₈	—	67	8	no	—
1067	C₂×Q₈	—	67	4	no	—
1068	C₂×Q₈	—	67	4	no	—
1069	C₂×Q₈	—	134	4	no	—
1070	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1071	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
1072	C₂×D₄	—	2	4	no	—
1073	C₂×D₄	—	4	4	no	—
1074	C₂×D₄	—	268	2	no	—
1075	C₂×D₄	—	268	4	no	—
1076	C₂×D₄	—	268	2	no	—
1077	C₂×D₄	—	268	4	no	—
1078	C₂×D₄	—	268	4	no	—
1079	C₂×D₄	—	268	2	no	—
1080	C₂×D₄	—	268	2	no	—
1081	C₂×D₄	—	268	2	no	—
1082	C₂×D₄	—	268	16	no	—
1083	C₂×D₄	—	268	4	no	—
1084	C₂×D₄	—	268	4	no	—
1085	C₂×D₄	—	268	2	no	—
1086	C₂×D₄	—	268	2	no	—
1087	C₂×D₄	—	268	4	no	—
1088	C₂×D₄	—	268	4	no	—
1089	C₂×D₄	—	268	4	no	—
1090	C₂×D₄	—	67	8	no	—
1091	C₂×D₄	—	67	8	no	—
1092	C₂×D₄	—	67	8	no	—
1093	C₂×D₄	—	67	4	no	—
1094	C₂×D₄	—	67	8	no	—
1095	C₂×D₄	—	67	4	no	—
1096	C₂×D₄	—	67	8	no	—
1097	C₂×D₄	—	67	4	no	—
1098	C₂×D₄	—	67	4	no	—
1099	C₂×D₄	—	67	8	no	—
1100	C₂×D₄	—	67	4	no	—
1101	C₂×D₄	—	67	4	no	—
1102	C₂×D₄	—	67	8	no	—
1103	C₂×D₄	—	67	4	no	—
1104	C₂×D₄	—	67	8	no	—
1105	C₂×D₄	—	67	4	no	—
1106	C₂×D₄	—	134	4	no	—
1107	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1108	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1109	C₂²×C₄	—	2	4	no	—
1110	C₂²×C₄	—	4	4	no	—
1111	C₂²×C₄	—	268	2	no	—
1112	C₂²×C₄	—	268	2	no	—
1113	C₂²×C₄	—	268	4	no	—
1114	C₂²×C₄	—	268	4	no	—
1115	C₂²×C₄	—	268	4	no	—
1116	C₂²×C₄	—	268	16	no	—
1117	C₂²×C₄	—	268	2	no	—
1118	C₂²×C₄	—	268	4	no	—
1119	C₂²×C₄	—	67	8	no	—
1120	C₂²×C₄	—	67	4	no	—
1121	C₂²×C₄	—	67	8	no	—
1122	C₂²×C₄	—	67	8	no	—
1123	C₂²×C₄	—	67	8	no	—
1124	C₂²×C₄	—	67	4	no	—
1125	C₂²×C₄	—	67	4	no	—
1126	C₂²×C₄	—	67	2	no	—
1127	C₂²×C₄	—	67	2	no	—
1128	C₂²×C₄	—	67	1	no	—
1129	C₂²×C₄	—	67	1	no	—
1130	C₂²×C₄	—	67	1	no	—
1131	C₂²×C₄	—	67	1	no	—
1132	C₂²×C₄	—	67	2	no	—
1133	C₂²×C₄	—	67	4	no	—
1134	C₂²×C₄	—	67	4	no	—
1135	C₂²×C₄	—	67	4	no	—
1136	C₂²×C₄	—	67	4	no	—
1137	C₂²×C₄	—	134	4	no	—
1138	C₂²×C₄	—	134	4	no	—
1139	C₂²×C₄	—	134	4	no	—
1140	C₂²×C₄	—	134	4	no	—
1141	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1142	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1143	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1144	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1145	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1147	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1148	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1149	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1151	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1152	C₄⋊C₄	—	67	4	no	—
1153	C₄⋊C₄	—	67	4	no	—
1154	C₄⋊C₄	—	67	4	no	—
1155	C₄⋊C₄	—	67	4	no	—
1156	C₄⋊C₄	—	67	8	no	—
1157	C₄⋊C₄	—	67	8	no	—
1158	C₄⋊C₄	—	67	8	no	—
1159	C₄⋊C₄	—	67	4	no	—
1160	C₄⋊C₄	—	67	4	no	—
1161	C₄⋊C₄	—	67	8	no	—
1162	C₄⋊C₄	—	67	8	no	—
1163	C₄⋊C₄	—	67	8	no	—
1164	C₄⋊C₄	—	67	8	no	—
1165	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1166	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1167	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1168	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1169	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1170	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1171	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1172	C₂²⋊C₄	—	67	8	no	—
1173	C₂²⋊C₄	—	67	8	no	—
1174	C₂²⋊C₄	—	67	8	no	—
1175	C₂²⋊C₄	—	67	4	no	—
1176	C₂²⋊C₄	—	67	4	no	—
1177	C₂²⋊C₄	—	67	8	no	—
1178	C₂²⋊C₄	—	67	8	no	—
1179	C₂²⋊C₄	—	67	8	no	—
1180	C₂²⋊C₄	—	67	8	no	—
1181	C₂²⋊C₄	—	67	8	no	—
1182	C₂²⋊C₄	—	67	8	no	—
1183	C₂²⋊C₄	—	67	8	no	—
1184	C₂²⋊C₄	—	67	8	no	—
1185	C₂²⋊C₄	—	67	8	no	—
1186	C₂²⋊C₄	—	67	4	no	—
1187	C₂²⋊C₄	—	67	4	no	—
1188	C₂²⋊C₄	—	67	4	no	—
1189	C₂²⋊C₄	—	67	4	no	—
1190	C₂²⋊C₄	—	67	8	no	—
1191	C₂²⋊C₄	—	67	8	no	—
1192	C₂²⋊C₄	—	67	8	no	—
1193	C₂²⋊C₄	—	67	8	no	—
1194	C₂²⋊C₄	—	67	4	no	—
1195	C₂²⋊C₄	—	67	4	no	—
1196	C₂²⋊C₄	—	67	8	no	—
1197	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1198	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1199	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1200	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1201	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1202	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1203	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1204	C₄²	—	67	8	no	—
1205	C₄²	—	67	8	no	—
1206	C₄²	—	67	8	no	—
1207	C₄²	—	67	8	no	—
1208	C₄²	—	67	8	no	—
1209	C₄²	C₂³×D₆₇	1	4	yes	—
1210	C₄²	C₂³×D₆₇	1	4	yes	—
1211	C₄²	C₂³×D₆₇	1	8	yes	—
1212	C₂³	—	2	2	no	—
1213	C₂³	—	2	4	no	—
1214	C₂³	—	2	4	no	—
1215	C₂³	—	2	2	no	—
1216	C₂³	—	2	2	no	—
1217	C₂³	—	2	4	no	—
1218	C₂³	—	268	4	no	—
1219	C₂³	—	268	4	no	—
1220	C₂³	—	268	4	no	—
1221	C₂³	—	268	8	no	—
1222	C₂³	—	268	8	no	—
1223	C₂³	—	268	8	no	—
1224	C₂³	—	268	16	no	—
1225	C₂³	—	536	16	no	—
1226	C₂³	—	67	2	no	—
1227	C₂³	—	67	2	no	—
1228	C₂³	—	67	2	no	—
1229	C₂³	—	67	4	no	—
1230	C₂³	—	67	2	no	—
1231	C₂³	—	134	2	no	—
1232	C₂³	—	134	2	no	—
1233	C₂³	—	134	2	no	—
1234	C₂³	—	134	4	no	—
1235	C₂³	—	134	2	no	—
1236	C₂³	—	134	2	no	—
1237	C₂³	—	134	2	no	—
1238	C₂³	—	134	2	no	—
1239	C₂³	—	134	4	no	—
1240	C₂³	—	134	2	no	—
1241	C₂³	—	134	4	no	—
1242	C₂³	—	134	2	no	—
1243	C₂³	—	134	2	no	—
1244	C₂³	—	134	2	no	—
1245	C₂³	—	134	2	no	—
1246	C₂³	C₂⁴×D₆₇	1	2	yes	—
1247	C₂³	C₂⁴×D₆₇	1	4	yes	—
1248	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1249	Q₈	—	2	8	no	—
1250	Q₈	—	4	8	no	—
1251	Q₈	—	268	8	no	—
1252	Q₈	—	268	4	no	—
1253	Q₈	—	268	8	no	—
1254	Q₈	—	134	8	no	—
1255	D₄	—	2	8	no	—
1256	D₄	—	4	8	no	—
1257	D₄	—	268	4	no	—
1258	D₄	—	268	8	no	—
1259	D₄	—	268	4	no	—
1260	D₄	—	268	8	no	—
1261	D₄	—	268	8	no	—
1262	D₄	—	268	4	no	—
1263	D₄	—	268	4	no	—
1264	D₄	—	268	4	no	—
1265	D₄	—	268	8	no	—
1266	D₄	—	268	8	no	—
1267	D₄	—	268	4	no	—
1268	D₄	—	268	4	no	—
1269	D₄	—	268	8	no	—
1270	D₄	—	268	8	no	—
1271	D₄	—	268	8	no	—
1272	D₄	—	134	8	no	—
1273	C₂×C₄	—	2	2	no	—
1274	C₂×C₄	—	2	4	no	—
1275	C₂×C₄	—	2	2	no	—
1276	C₂×C₄	—	2	4	no	—
1277	C₂×C₄	—	2	4	no	—
1278	C₂×C₄	—	2	2	no	—
1279	C₂×C₄	—	2	2	no	—
1280	C₂×C₄	—	2	2	no	—
1281	C₂×C₄	—	2	8	no	—
1282	C₂×C₄	—	4	8	no	—
1283	C₂×C₄	—	268	4	no	—
1284	C₂×C₄	—	268	4	no	—
1285	C₂×C₄	—	268	8	no	—
1286	C₂×C₄	—	268	8	no	—
1287	C₂×C₄	—	268	8	no	—
1288	C₂×C₄	—	268	4	no	—
1289	C₂×C₄	—	268	8	no	—
1290	C₂×C₄	—	67	4	no	—
1291	C₂×C₄	—	67	4	no	—
1292	C₂×C₄	—	67	2	no	—
1293	C₂×C₄	—	67	2	no	—
1294	C₂×C₄	—	67	2	no	—
1295	C₂×C₄	—	67	2	no	—
1296	C₂×C₄	—	67	4	no	—
1297	C₂×C₄	—	134	2	no	—
1298	C₂×C₄	—	134	2	no	—
1299	C₂×C₄	—	134	4	no	—
1300	C₂×C₄	—	134	2	no	—
1301	C₂×C₄	—	134	2	no	—
1302	C₂×C₄	—	134	4	no	—
1303	C₂×C₄	—	134	4	no	—
1304	C₂×C₄	—	134	8	no	—
1305	C₂×C₄	—	134	8	no	—
1306	C₂×C₄	—	134	8	no	—
1307	C₂×C₄	—	134	8	no	—
1308	C₂×C₄	#14524089	1	4	yes	—
1309	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1310	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1311	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1312	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1313	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1314	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1315	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1316	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1317	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	4	no	—
1320	C₂²	—	2	4	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	2	4	no	—
1324	C₂²	—	4	4	no	—
1325	C₂²	—	4	8	no	—
1326	C₂²	—	268	16	no	—
1327	C₂²	—	268	4	no	—
1328	C₂²	—	268	4	no	—
1329	C₂²	—	268	4	no	—
1330	C₂²	—	268	8	no	—
1331	C₂²	—	268	4	no	—
1332	C₂²	—	536	16	no	—
1333	C₂²	—	134	2	no	—
1334	C₂²	—	134	2	no	—
1335	C₂²	—	134	2	no	—
1336	C₂²	—	134	4	no	—
1337	C₂²	—	134	2	no	—
1338	C₂²	—	134	2	no	—
1339	C₂²	—	134	2	no	—
1340	C₂²	—	134	2	no	—
1341	C₂²	—	134	4	no	—
1342	C₂²	—	134	2	no	—
1343	C₂²	—	134	4	no	—
1344	C₂²	—	134	2	no	—
1345	C₂²	—	134	2	no	—
1346	C₂²	—	134	2	no	—
1347	C₂²	—	134	2	no	—
1348	C₂²	C₂×#14524089	1	2	yes	—
1349	C₂²	#16864231	1	2	yes	—
1350	C₂²	#16864233	1	2	yes	—
1351	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1352	C₄	—	2	2	no	—
1353	C₄	—	2	4	no	—
1354	C₄	—	2	2	no	—
1355	C₄	—	2	4	no	—
1356	C₄	—	2	4	no	—
1357	C₄	—	2	2	no	—
1358	C₄	—	2	2	no	—
1359	C₄	—	2	2	no	—
1360	C₄	—	134	2	no	—
1361	C₄	—	134	2	no	—
1362	C₄	—	134	4	no	—
1363	C₄	—	134	2	no	—
1364	C₄	—	134	2	no	—
1365	C₄	—	134	4	no	—
1366	C₄	—	134	4	no	—
1367	C₄	C₂×#14524089	1	4	yes	—
1368	C₂	—	4	2	no	—
1369	C₂	—	4	4	no	—
1370	C₂	—	268	2	no	—
1371	C₂	—	268	2	no	—
1372	C₂	—	268	2	no	—
1373	C₂	—	268	4	no	—
1374	C₂	—	268	2	no	—
1375	C₂	#22574481	1	4	yes	direct product factor
1376	C₂	C₂²×#14524089	1	1	yes	characteristic
1377	C₂	C₂×#16864231	1	1	yes	characteristic
1378	C₂	C₂×#16864233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#542×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#542	D₆₇
hypocenter	C₆₇	C₂×#3540
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #22574481	C₂	direct (N × H)
2. C₂×#16864138	C₂	semidirect
3. C₂×#16864136	C₂	semidirect
4. C₂×#16864128	C₂	semidirect
5. C₂×#16864120	C₂	semidirect
6. C₂×#16864119	C₂	semidirect
7. C₂×#16864112	C₂	semidirect
8. C₂×#16864111	C₂	semidirect
9. C₂×#16864069	C₂	semidirect
10. C₂×#16864058	C₂	semidirect
11. C₂×#16864054	C₂	semidirect
12. C₂×#16864041	C₂	semidirect
13. C₂×#16864039	C₂	semidirect
14. C₂×#16864019	C₂	semidirect
15. C₂×#16864017	C₂	semidirect
16. C₂×#16864012	C₂	semidirect
17. C₂×#16863986	C₂	semidirect
18. C₂×#16863985	C₂	semidirect
19. C₂×#16863969	C₂	semidirect
20. C₂×#16863962	C₂	semidirect
21. C₂×#16863909	C₂	semidirect
22. C₂×#16863908	C₂	semidirect
23. C₂×#16863906	C₂	semidirect
24. C₂×#542×C₆₇	C₂	semidirect
28. C₂²×Q₈×D₆₇	C₂²	semidirect
29. C₂²×D₄×D₆₇	C₂²	semidirect
30. C₂³×C₄×D₆₇	C₂²	semidirect
31. #16864138	C₂²	semidirect
32. #16864136	C₂²	semidirect
33. #16864128	C₂²	semidirect
34. #16864120	C₂²	semidirect
35. #16864119	C₂²	semidirect
36. #16864112	C₂²	semidirect
37. #16864111	C₂²	semidirect
38. #16864069	C₂²	semidirect
39. #16864058	C₂²	semidirect
40. #16864054	C₂²	semidirect
41. #16864041	C₂²	semidirect
42. #16864039	C₂²	semidirect
43. #16864019	C₂²	semidirect
44. #16864017	C₂²	semidirect
45. #16864012	C₂²	semidirect
46. #16863986	C₂²	semidirect
47. #16863985	C₂²	semidirect
48. #16863969	C₂²	semidirect
49. #16863962	C₂²	semidirect
50. C₂×#14524043	C₂²	semidirect
51. C₂×#14524042	C₂²	semidirect
53. C₂×#14524038	C₂²	semidirect
54. C₂×#14524038	C₂²	semidirect
55. C₂×#14524038	C₂²	semidirect
56. C₂×#14524038	C₂²	semidirect
57. C₂×#14524038	C₂²	semidirect
59. C₂×#14524032	C₂²	semidirect
60. C₂×#14524032	C₂²	semidirect
62. C₂×#14524031	C₂²	semidirect
63. C₂×#14524031	C₂²	semidirect
65. C₂×#14524029	C₂²	semidirect
66. C₂×#14524029	C₂²	semidirect
67. C₂×#14524029	C₂²	semidirect
68. C₂×#14524029	C₂²	semidirect
69. C₂×#14524029	C₂²	semidirect
70. #16863909	C₂²	semidirect
71. #16863908	C₂²	semidirect
72. #16863906	C₂²	semidirect
73. C₂×#14524028	C₂²	semidirect
74. C₂×#14524028	C₂²	semidirect
76. C₂×#14524027	C₂²	semidirect
77. C₂×#14524027	C₂²	semidirect
78. C₂×#14524025	C₂²	semidirect
79. C₂×#14524025	C₂²	semidirect
80. C₂×#14524025	C₂²	semidirect
81. C₂×#14524025	C₂²	semidirect
82. C₂×#14524023	C₂²	semidirect
83. C₂×#14524023	C₂²	semidirect
84. C₂×#14524023	C₂²	semidirect
85. C₂×#14524023	C₂²	semidirect
86. C₂×#14524023	C₂²	semidirect
87. C₂×#14524022	C₂²	semidirect
88. C₂×#14524021	C₂²	semidirect
89. C₂×#14524020	C₂²	semidirect
90. C₂×#14524019	C₂²	semidirect
91. C₂×#14524019	C₂²	semidirect
95. C₂×#14524018	C₂²	semidirect
96. C₂×#14524018	C₂²	semidirect
97. C₂×#14524018	C₂²	semidirect
100. C₂×#14524017	C₂²	semidirect
102. C₂×#14524016	C₂²	semidirect
104. C₂×#14524014	C₂²	semidirect
108. C₂×#14524013	C₂²	semidirect
109. C₂×#14524013	C₂²	semidirect
110. C₂×#14524013	C₂²	semidirect
112. C₂×#14524011	C₂²	semidirect
113. C₂×Q₈×Dic₆₇	C₂²	semidirect
114. C₂×C₄×Dic₁₃₄	C₂²	semidirect
115. C₂×C₄×Dic₁₃₄	C₂²	semidirect
118. C₂×C₄×D₂₆₈	C₂²	semidirect
119. C₂×C₄×D₂₆₈	C₂²	semidirect
120. C₂×C₄×D₂₆₈	C₂²	semidirect
121. C₂×C₄×D₂₆₈	C₂²	semidirect
122. C₂×D₄×Dic₆₇	C₂²	semidirect
123. C₂×#14524005	C₂²	semidirect
124. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
125. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
126. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
127. C₂×#14524002	C₂²	semidirect
128. C₂×#14524001	C₂²	semidirect
129. C₂×#14524001	C₂²	semidirect
130. C₂×#14524001	C₂²	semidirect
131. C₂×#14524001	C₂²	semidirect
132. C₂×#14524001	C₂²	semidirect
133. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
134. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
135. #542×C₆₇	C₂²	semidirect
136. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
137. C₂×#126×C₆₇	C₂²	semidirect
138. C₂×#124×C₆₇	C₂²	semidirect
139. C₂×#124×C₆₇	C₂²	semidirect
140. C₂×#123×C₆₇	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
144. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
145. C₂×C₄×D₄×C₆₇	C₂²	semidirect
146. C₂×#117×C₆₇	C₂²	semidirect
160. C₂×Q₈×D₆₇	C₂³	semidirect
178. C₂×D₄×D₆₇	C₂³	semidirect
191. C₂²×C₄×D₆₇	C₂³	semidirect
192. #14524043	C₂³	semidirect
193. #14524042	C₂³	semidirect
195. #14524038	C₂³	semidirect
196. #14524038	C₂³	semidirect
197. #14524038	C₂³	semidirect
198. #14524038	C₂³	semidirect
199. #14524038	C₂³	semidirect
201. #14524032	C₂³	semidirect
202. #14524032	C₂³	semidirect
204. #14524031	C₂³	semidirect
205. #14524031	C₂³	semidirect
207. #14524029	C₂³	semidirect
208. #14524029	C₂³	semidirect
209. #14524029	C₂³	semidirect
210. #14524029	C₂³	semidirect
211. #14524029	C₂³	semidirect
212. #14524028	C₂³	semidirect
213. #14524028	C₂³	semidirect
215. #14524027	C₂³	semidirect
216. #14524027	C₂³	semidirect
217. #14524025	C₂³	semidirect
218. #14524025	C₂³	semidirect
219. #14524025	C₂³	semidirect
220. #14524025	C₂³	semidirect
221. #14524023	C₂³	semidirect
222. #14524023	C₂³	semidirect
223. #14524023	C₂³	semidirect
224. #14524023	C₂³	semidirect
225. #14524023	C₂³	semidirect
226. #14524022	C₂³	semidirect
227. #14524021	C₂³	semidirect
228. #14524020	C₂³	semidirect
229. #14524019	C₂³	semidirect
230. #14524019	C₂³	semidirect
234. #14524018	C₂³	semidirect
235. #14524018	C₂³	semidirect
236. #14524018	C₂³	semidirect
239. #14524017	C₂³	semidirect
241. #14524016	C₂³	semidirect
243. #14524014	C₂³	semidirect
247. #14524013	C₂³	semidirect
248. #14524013	C₂³	semidirect
249. #14524013	C₂³	semidirect
251. #14524011	C₂³	semidirect
252. Q₈×Dic₆₇	C₂³	semidirect
253. C₄×Dic₁₃₄	C₂³	semidirect
254. C₄×Dic₁₃₄	C₂³	semidirect
257. C₄×D₂₆₈	C₂³	semidirect
258. C₄×D₂₆₈	C₂³	semidirect
259. C₄×D₂₆₈	C₂³	semidirect
260. C₄×D₂₆₈	C₂³	semidirect
261. D₄×Dic₆₇	C₂³	semidirect
262. #14524005	C₂³	semidirect
263. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
264. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
265. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
266. #14524002	C₂³	semidirect
267. #14524001	C₂³	semidirect
268. #14524001	C₂³	semidirect
269. #14524001	C₂³	semidirect
270. #14524001	C₂³	semidirect
271. #14524001	C₂³	semidirect
310. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
311. C₂²⋊C₄×D₆₇	C₂³	semidirect
323. C₄⋊Q₈×C₆₇	C₂³	semidirect
324. #126×C₆₇	C₂³	semidirect
325. #124×C₆₇	C₂³	semidirect
326. #124×C₆₇	C₂³	semidirect
327. #123×C₆₇	C₂³	semidirect
328. C₂²⋊Q₈×C₆₇	C₂³	semidirect
329. C₂²⋊Q₈×C₆₇	C₂³	semidirect
331. C₄×Q₈×C₆₇	C₂³	semidirect
332. C₄×D₄×C₆₇	C₂³	semidirect
333. #117×C₆₇	C₂³	semidirect
681. C₂×C₆₇	#3540	semidirect
706. C₂×#542	D₆₇	semidirect
714. C₆₇	C₂×#3540	semidirect
736. #542	C₂×D₆₇	semidirect
743. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
750. C₂×#126	C₂×D₆₇	semidirect
763. C₂×#124	C₂×D₆₇	semidirect
764. C₂×#124	C₂×D₆₇	semidirect
777. C₂×#123	C₂×D₆₇	semidirect
788. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
789. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
815. C₂×C₄×Q₈	C₂×D₆₇	semidirect
827. C₂×C₄×D₄	C₂×D₆₇	semidirect
834. C₂×#117	C₂×D₆₇	semidirect
890. C₄⋊Q₈	C₂²×D₆₇	semidirect
897. #126	C₂²×D₆₇	semidirect
910. #124	C₂²×D₆₇	semidirect
911. #124	C₂²×D₆₇	semidirect
921. #123	C₂²×D₆₇	semidirect
932. C₂²⋊Q₈	C₂²×D₆₇	semidirect
933. C₂²⋊Q₈	C₂²×D₆₇	semidirect
959. C₄×Q₈	C₂²×D₆₇	semidirect
971. C₄×D₄	C₂²×D₆₇	semidirect
978. #117	C₂²×D₆₇	semidirect
1375. C₂	#22574481	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574481	2
C₂×#16864138	2
C₂×#16864136	2
C₂×#16864128	2
C₂×#16864120	2
C₂×#16864119	2
C₂×#16864112	2
C₂×#16864111	2
C₂×#16864069	2
C₂×#16864058	2
C₂×#16864054	2
C₂×#16864041	2
C₂×#16864039	2
C₂×#16864019	2
C₂×#16864017	2
C₂×#16864012	2
C₂×#16863986	2
C₂×#16863985	2
C₂×#16863969	2
C₂×#16863962	2
C₂×#16863909	2
C₂×#16863908	2
C₂×#16863906	2
C₂×#542×C₆₇	2
C₂×#3540	67

Subgroups — C2×#22574481 #31763129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574481 #31763129