Subgroups — #3485×D₆₇ #31763867

Order 17152.

11686 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573854	C₂	1	1	yes	maximal, characteristic, complemented
4	#22573853	C₂	1	1	yes	maximal, characteristic, complemented
5	#22573852	C₂	1	2	yes	maximal, complemented
6	#22573851	C₂	1	2	yes	maximal, complemented
7	#22573850	C₂	1	4	yes	maximal, complemented
8	#22573849	C₂	1	1	yes	maximal, characteristic, complemented
9	#22573848	C₂	1	8	yes	maximal, complemented
10	#22573847	C₂	1	4	yes	maximal, complemented
11	#22573846	C₂	1	8	yes	maximal, complemented
12	#547×D₆₇	C₂	1	8	yes	maximal, complemented
13	#546×D₆₇	C₂	1	8	yes	maximal, complemented
14	#536×D₆₇	C₂	1	2	yes	maximal, complemented
15	#534×D₆₇	C₂	1	4	yes	maximal, complemented
16	#525×D₆₇	C₂	1	2	yes	maximal, complemented
17	C₂×#123×D₆₇	C₂	1	4	yes	maximal, complemented
18	#518×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14524089	C₂²	1	2	yes	complemented
21	C₂×#14524089	C₂²	1	4	yes	complemented
22	C₂×#14524088	C₂²	1	4	yes	complemented
23	C₂×#14524088	C₂²	1	1	yes	characteristic, complemented
24	C₂×#14524088	C₂²	1	4	yes	complemented
25	H(5,𝔽₂)×D₆₇	—	2	16	no	—
26	C₂²×#11761629	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#11761628	C₂²	1	2	yes	complemented
28	C₂²×#11761628	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#11761627	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11761627	C₂²	1	2	yes	complemented
31	C₂×#41×D₆₇	—	2	16	no	—
32	C₂×#41×D₆₇	C₂²	1	2	yes	—
33	C₂×#41×D₆₇	C₂²	1	8	yes	complemented
34	C₂×#41×D₆₇	C₂²	1	4	yes	complemented
35	C₂×#41×D₆₇	C₂²	1	8	yes	complemented
36	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₄×D₆₇	C₂²	1	4	yes	—
38	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
39	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
40	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
41	C₂³×C₄×D₆₇	C₂²	1	2	yes	complemented
42	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
43	#16864051	C₂²	1	8	yes	complemented
44	#16864050	C₂²	1	8	yes	complemented
45	#16864049	C₂²	1	8	yes	complemented
46	#16864048	C₂²	1	8	yes	complemented
47	#16864048	C₂²	1	8	yes	complemented
48	#16864047	C₂²	1	16	yes	complemented
49	#16864046	C₂²	1	16	yes	complemented
50	#16864045	C₂²	1	8	yes	complemented
51	#16864045	C₂²	1	8	yes	complemented
52	#16864044	C₂²	1	16	yes	complemented
53	#16864044	C₂²	1	16	yes	complemented
54	#16864043	C₂²	1	8	yes	complemented
55	#16864042	C₂²	1	8	yes	complemented
56	#16864041	C₂²	1	8	yes	complemented
57	#16864040	C₂²	1	8	yes	complemented
58	#16864039	C₂²	1	8	yes	complemented
59	#16864038	C₂²	1	16	yes	complemented
60	#16864037	C₂²	1	8	yes	complemented
61	#16864036	C₂²	1	16	yes	complemented
62	#16864035	C₂²	1	16	yes	complemented
63	#16864034	C₂²	1	8	yes	complemented
64	#16864033	C₂²	1	16	yes	complemented
65	#16863972	C₂²	1	2	yes	complemented
66	#16863971	C₂²	1	4	yes	complemented
67	#16863970	C₂²	1	2	yes	complemented
68	#16863969	C₂²	1	8	yes	complemented
69	#16863968	C₂²	1	8	yes	complemented
70	#16863967	C₂²	1	2	yes	complemented
71	#16863966	C₂²	1	4	yes	complemented
72	#16863958	C₂²	1	4	yes	complemented
73	#16863957	C₂²	1	8	yes	complemented
74	#16863957	C₂²	1	8	yes	complemented
75	#16863956	C₂²	1	8	yes	complemented
76	#16863956	C₂²	1	8	yes	complemented
77	#16863955	C₂²	1	4	yes	complemented
78	#16863955	C₂²	1	4	yes	complemented
79	#16863954	C₂²	1	16	yes	complemented
80	C₄⋊Q₈×D₆₇	C₂²	1	4	yes	complemented
81	#124×D₆₇	C₂²	1	4	yes	complemented
82	#16863909	C₂²	1	4	yes	complemented
83	#16863908	C₂²	1	2	yes	complemented
84	#16863907	C₂²	1	2	yes	complemented
85	#16863906	C₂²	1	4	yes	complemented
86	#16863905	C₂²	1	8	yes	complemented
87	#16863904	C₂²	1	4	yes	complemented
88	#16863903	C₂²	1	2	yes	complemented
89	#16863902	C₂²	1	4	yes	complemented
90	C₂×#14524028	C₂²	1	8	yes	complemented
91	C₂×#14524027	C₂²	1	4	yes	complemented
92	C₂×#14524026	C₂²	1	4	yes	complemented
93	C₂×#14524025	C₂²	1	8	yes	complemented
94	C₂×#14524024	C₂²	1	4	yes	complemented
95	#123×D₆₇	C₂²	1	16	yes	complemented
96	#123×D₆₇	C₂²	1	8	yes	complemented
97	#123×D₆₇	C₂²	1	4	yes	complemented
98	#123×D₆₇	C₂²	1	8	yes	complemented
99	#123×D₆₇	C₂²	1	16	yes	complemented
100	#123×D₆₇	C₂²	1	8	yes	complemented
101	#123×D₆₇	C₂²	1	8	yes	complemented
102	C₂²⋊Q₈×D₆₇	C₂²	1	8	yes	complemented
103	C₂²⋊Q₈×D₆₇	C₂²	1	4	yes	complemented
104	#121×D₆₇	C₂²	1	4	yes	complemented
105	#121×D₆₇	C₂²	1	16	yes	complemented
106	#120×D₆₇	C₂²	1	8	yes	complemented
107	#120×D₆₇	C₂²	1	4	yes	complemented
108	#16863871	C₂²	1	1	yes	characteristic, complemented
109	#16863870	C₂²	1	2	yes	complemented
110	#16863869	C₂²	1	4	yes	complemented
111	#16863868	C₂²	1	8	yes	complemented
112	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
113	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
114	#117×D₆₇	C₂²	1	2	yes	complemented
115	C₂×C₄⋊C₄×D₆₇	C₂²	1	8	yes	complemented
116	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
117	C₂×C₂²⋊C₄×D₆₇	C₂²	1	8	yes	complemented
118	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#547×C₆₇	C₂²	1	8	yes	complemented
121	#546×C₆₇	C₂²	1	8	yes	complemented
122	#536×C₆₇	C₂²	1	2	yes	complemented
123	#534×C₆₇	C₂²	1	4	yes	complemented
124	#525×C₆₇	C₂²	1	2	yes	complemented
125	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
126	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₆₇	C₂³	1	4	yes	—
128	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
129	C₂⁴×D₆₇	C₂³	1	2	yes	—
130	#14524089	—	2	16	no	—
131	#14524089	—	2	32	no	—
132	#14524088	—	2	32	no	—
133	#14524088	—	2	32	no	—
134	#14524088	—	2	8	no	—
135	C₂×#11761629	—	2	8	no	—
136	C₂×#11761629	C₂³	1	2	yes	—
137	C₂×#11761629	C₂³	1	8	yes	complemented
138	C₂×#11761629	C₂³	1	4	yes	complemented
139	C₂×#11761628	—	2	8	no	—
140	C₂×#11761628	—	2	16	no	—
141	C₂×#11761628	C₂³	1	4	yes	—
142	C₂×#11761628	C₂³	1	2	yes	—
143	C₂×#11761628	C₂³	1	16	yes	complemented
144	C₂×#11761628	C₂³	1	8	yes	complemented
145	C₂×#11761628	C₂³	1	8	yes	complemented
146	C₂×#11761628	C₂³	1	4	yes	complemented
147	C₂×#11761627	—	2	16	no	—
148	C₂×#11761627	—	2	8	no	—
149	C₂×#11761627	C₂³	1	4	yes	—
150	C₂×#11761627	C₂³	1	2	yes	—
151	C₂×#11761627	C₂³	1	16	yes	complemented
152	C₂×#11761627	C₂³	1	8	yes	complemented
153	C₂×#11761627	C₂³	1	8	yes	complemented
154	C₂×#11761627	C₂³	1	4	yes	complemented
155	#41×D₆₇	—	2	64	no	—
156	#41×D₆₇	—	2	32	no	—
157	#41×D₆₇	—	2	64	no	—
158	#41×D₆₇	—	2	16	no	—
159	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic, complemented
160	C₂²×Dic₁₃₄	C₂³	1	2	yes	complemented
161	C₂×Q₈×D₆₇	—	2	8	no	—
162	C₂×Q₈×D₆₇	C₂³	1	4	yes	—
163	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
164	C₂×Q₈×D₆₇	C₂³	1	4	yes	complemented
165	C₂²×D₂₆₈	C₂³	1	4	yes	—
166	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
167	C₂²×D₂₆₈	C₂³	1	4	yes	complemented
168	C₂²×D₂₆₈	C₂³	1	2	yes	complemented
169	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
170	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
171	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
172	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
173	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	complemented
174	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	complemented
175	C₂×D₄×D₆₇	—	2	32	no	—
176	C₂×D₄×D₆₇	—	2	16	no	—
177	C₂×D₄×D₆₇	—	2	32	no	—
178	C₂×D₄×D₆₇	D₄	1	16	yes	complemented
179	C₂×D₄×D₆₇	C₂³	1	8	yes	—
180	C₂×D₄×D₆₇	C₂³	1	4	yes	—
181	C₂×D₄×D₆₇	C₂³	1	8	yes	—
182	C₂×D₄×D₆₇	C₂³	1	2	yes	—
183	C₂×D₄×D₆₇	C₂³	1	8	yes	—
184	C₂×D₄×D₆₇	C₂³	1	8	yes	—
185	C₂×D₄×D₆₇	C₂³	1	8	yes	—
186	C₂×D₄×D₆₇	C₂³	1	4	yes	—
187	C₂×D₄×D₆₇	C₂³	1	4	yes	—
188	C₂×D₄×D₆₇	C₂³	1	4	yes	complemented
189	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
190	C₂×D₄×D₆₇	C₂³	1	4	yes	complemented
191	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
192	C₂³×Dic₆₇	C₂³	1	2	yes	complemented
193	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic, complemented
194	C₂²×C₄×D₆₇	—	2	16	no	—
195	C₂²×C₄×D₆₇	—	2	8	no	—
196	C₂²×C₄×D₆₇	C₂³	1	8	yes	—
197	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
198	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
199	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
200	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
202	C₂²×C₄×D₆₇	C₂³	1	8	yes	—
203	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₆₇	C₂³	1	2	yes	complemented
205	C₂²×C₄×D₆₇	C₂³	1	2	yes	complemented
206	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
207	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic, complemented
208	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic, complemented
209	C₂²×C₄×D₆₇	C₂³	1	4	yes	complemented
210	#14524043	C₂³	1	4	yes	complemented
211	#14524042	C₂³	1	16	yes	complemented
212	#14524041	C₂³	1	4	yes	complemented
213	#14524041	C₂³	1	4	yes	complemented
214	#14524032	C₂³	1	4	yes	complemented
215	#14524031	C₂³	1	4	yes	complemented
216	#14524030	C₂³	1	4	yes	complemented
217	#14524029	C₂³	1	16	yes	complemented
218	#14524028	C₂³	1	16	yes	complemented
219	#14524028	C₂³	1	16	yes	complemented
220	#14524028	C₂³	1	16	yes	complemented
221	#14524028	C₂³	1	8	yes	complemented
222	#14524028	C₂³	1	16	yes	complemented
223	#14524027	C₂³	1	16	yes	complemented
224	#14524027	C₂³	1	8	yes	complemented
225	#14524027	C₂³	1	4	yes	complemented
226	#14524027	C₂³	1	8	yes	complemented
227	#14524026	C₂³	1	16	yes	complemented
228	#14524026	C₂³	1	8	yes	complemented
229	#14524026	C₂³	1	4	yes	complemented
230	#14524026	C₂³	1	8	yes	complemented
231	#14524025	C₂³	1	16	yes	complemented
232	#14524025	C₂³	1	16	yes	complemented
233	#14524025	C₂³	1	16	yes	complemented
234	#14524025	C₂³	1	8	yes	complemented
235	#14524025	C₂³	1	16	yes	complemented
236	#14524024	C₂³	1	16	yes	complemented
237	#14524024	C₂³	1	8	yes	complemented
238	#14524024	C₂³	1	4	yes	complemented
239	#14524024	C₂³	1	8	yes	complemented
240	#14524023	C₂³	1	8	yes	complemented
241	#14524023	C₂³	1	4	yes	complemented
242	#14524022	C₂³	1	8	yes	complemented
243	#14524022	C₂³	1	4	yes	complemented
244	#14524021	C₂³	1	16	yes	complemented
245	#14524021	C₂³	1	8	yes	complemented
246	#14524020	C₂³	1	16	yes	complemented
247	#14524020	C₂³	1	8	yes	complemented
248	#14524019	C₂³	1	8	yes	complemented
249	#14524019	C₂³	1	4	yes	complemented
250	#14524018	C₂³	1	4	yes	complemented
251	#14524018	C₂³	1	16	yes	complemented
252	#14524017	C₂³	1	4	yes	complemented
253	#14524017	C₂³	1	16	yes	complemented
254	#14524016	C₂³	1	16	yes	complemented
255	#14524016	C₂³	1	8	yes	complemented
256	#14524016	C₂³	1	16	yes	complemented
257	#14524015	C₂³	1	8	yes	complemented
258	#14524015	C₂³	1	16	yes	complemented
259	#14524015	C₂³	1	16	yes	complemented
260	#14524014	C₂³	1	16	yes	complemented
261	#14524014	C₂³	1	4	yes	complemented
262	#14524013	C₂³	1	16	yes	complemented
263	#14524013	C₂³	1	8	yes	complemented
264	#14524013	C₂³	1	4	yes	complemented
265	#14524013	C₂³	1	8	yes	complemented
266	#14524012	C₂³	1	8	yes	complemented
267	#14524012	C₂³	1	4	yes	complemented
268	#14524011	C₂³	1	16	yes	complemented
269	#14524011	C₂³	1	8	yes	complemented
270	#14524011	C₂³	1	4	yes	complemented
271	#14524011	C₂³	1	8	yes	complemented
272	C₄×D₂₆₈	C₂³	1	8	yes	complemented
273	C₄×D₂₆₈	C₂³	1	8	yes	complemented
274	D₄×Dic₆₇	C₂³	1	8	yes	complemented
275	D₄×Dic₆₇	C₂³	1	8	yes	complemented
276	#14524005	C₂³	1	8	yes	complemented
277	#14524005	C₂³	1	8	yes	complemented
278	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
279	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
280	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
281	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
282	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
283	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
284	#14524002	C₂³	1	2	yes	complemented
285	#14524001	C₂³	1	4	yes	complemented
286	#14524000	C₂³	1	4	yes	complemented
287	#14523999	C₂³	1	4	yes	complemented
288	C₂×C₄⋊Dic₆₇	C₂³	1	8	yes	complemented
289	C₂×Dic₆₇⋊C₄	C₂³	1	8	yes	complemented
290	C₂×Dic₆₇⋊C₄	C₂³	1	8	yes	complemented
291	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
292	C₄⋊C₄×D₆₇	C₂³	1	16	yes	—
293	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
294	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
295	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
296	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	complemented
297	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	complemented
298	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
299	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
300	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
301	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
302	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
303	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
304	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
305	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
306	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
307	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
308	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
309	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
310	C₄²×D₆₇	C₂³	1	4	yes	—
311	H(5,𝔽₂)×C₆₇	—	2	8	no	—
312	C₂×#41×C₆₇	—	2	8	no	—
313	C₂×#41×C₆₇	C₂³	1	2	yes	—
314	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
315	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
316	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
317	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
318	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
320	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
321	C₂³×C₄×C₆₇	C₂³	1	2	yes	complemented
322	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
323	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
324	#124×C₆₇	C₂³	1	4	yes	complemented
325	#123×C₆₇	C₂³	1	16	yes	complemented
326	#123×C₆₇	C₂³	1	8	yes	complemented
327	#123×C₆₇	C₂³	1	4	yes	complemented
328	#123×C₆₇	C₂³	1	8	yes	complemented
329	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
330	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
331	#121×C₆₇	C₂³	1	16	yes	complemented
332	#121×C₆₇	C₂³	1	4	yes	complemented
333	#120×C₆₇	C₂³	1	8	yes	complemented
334	#120×C₆₇	C₂³	1	4	yes	complemented
335	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
336	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
337	#117×C₆₇	C₂³	1	2	yes	complemented
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
340	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
341	C₂³×D₆₇	—	2	4	no	—
342	C₂³×D₆₇	—	2	16	no	—
343	C₂³×D₆₇	—	4	8	no	—
344	C₂³×D₆₇	—	4	4	no	—
345	C₂³×D₆₇	—	4	16	no	—
346	C₂³×D₆₇	C₂×D₄	1	16	yes	—
347	C₂³×D₆₇	C₂⁴	1	4	yes	—
348	C₂³×D₆₇	C₂⁴	1	2	yes	—
349	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
350	C₂³×D₆₇	C₂⁴	1	4	yes	—
351	C₂³×D₆₇	C₂⁴	1	8	yes	—
352	C₂³×D₆₇	C₂⁴	1	4	yes	—
353	C₂³×D₆₇	C₂⁴	1	2	yes	—
354	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
355	C₂³×D₆₇	C₂⁴	1	2	yes	—
356	C₂³×D₆₇	C₂⁴	1	4	yes	—
357	#11761629	—	2	32	no	—
358	#11761629	—	2	16	no	—
359	#11761629	—	2	8	no	—
360	#11761628	—	2	8	no	—
361	#11761628	—	2	64	no	—
362	#11761628	—	2	32	no	—
363	#11761628	—	2	32	no	—
364	#11761628	—	2	16	no	—
365	#11761628	—	2	16	no	—
366	#11761627	—	2	32	no	—
367	#11761627	—	2	16	no	—
368	#11761627	—	2	64	no	—
369	#11761627	—	2	32	no	—
370	#11761627	—	2	16	no	—
371	#11761627	—	2	8	no	—
372	C₂×Dic₁₃₄	—	2	4	no	—
373	C₂×Dic₁₃₄	—	2	8	no	—
374	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
375	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
376	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
377	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
378	Q₈×D₆₇	—	2	16	no	—
379	Q₈×D₆₇	—	2	16	no	—
380	Q₈×D₆₇	—	2	8	no	—
381	C₂×D₂₆₈	—	2	16	no	—
382	C₂×D₂₆₈	—	2	8	no	—
383	C₂×D₂₆₈	—	2	16	no	—
384	C₂×D₂₆₈	C₂×D₄	1	8	yes	complemented
385	C₂×D₂₆₈	C₂⁴	1	8	yes	—
386	C₂×D₂₆₈	C₂⁴	1	4	yes	—
387	C₂×D₂₆₈	C₂⁴	1	8	yes	—
388	C₂×D₂₆₈	C₂⁴	1	2	yes	—
389	C₂×D₂₆₈	C₂⁴	1	8	yes	—
390	C₂×D₂₆₈	C₂⁴	1	4	yes	—
391	C₂×C₂²⋊D₆₇	—	2	16	no	—
392	C₂×C₂²⋊D₆₇	—	2	8	no	—
393	C₂×C₂²⋊D₆₇	—	2	16	no	—
394	C₂×C₂²⋊D₆₇	—	2	8	no	—
395	C₂×C₂²⋊D₆₇	—	2	32	no	—
396	C₂×C₂²⋊D₆₇	C₂×D₄	1	16	yes	complemented
397	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
398	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
399	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
400	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
401	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
402	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
403	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
404	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
405	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
406	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
407	D₄×D₆₇	—	2	16	no	—
408	D₄×D₆₇	—	2	32	no	—
409	D₄×D₆₇	—	2	32	no	—
410	D₄×D₆₇	—	2	32	no	—
411	D₄×D₆₇	—	2	32	no	—
412	D₄×D₆₇	—	2	32	no	—
413	D₄×D₆₇	—	2	16	no	—
414	D₄×D₆₇	—	2	32	no	—
415	D₄×D₆₇	—	2	16	no	—
416	D₄×D₆₇	—	2	8	no	—
417	D₄×D₆₇	—	4	16	no	—
418	D₄×D₆₇	C₂×D₄	1	32	yes	—
419	D₄×D₆₇	C₂×D₄	1	32	yes	complemented
420	C₂²×Dic₆₇	—	2	8	no	—
421	C₂²×Dic₆₇	—	2	4	no	—
422	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
423	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
424	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
425	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
426	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
428	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
429	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×D₆₇	—	2	4	no	—
431	C₂×C₄×D₆₇	—	2	8	no	—
432	C₂×C₄×D₆₇	—	2	32	no	—
433	C₂×C₄×D₆₇	—	2	32	no	—
434	C₂×C₄×D₆₇	—	2	8	no	—
435	C₂×C₄×D₆₇	—	2	8	no	—
436	C₂×C₄×D₆₇	—	2	16	no	—
437	C₂×C₄×D₆₇	—	2	4	no	—
438	C₂×C₄×D₆₇	—	2	4	no	—
439	C₂×C₄×D₆₇	—	2	16	no	—
440	C₂×C₄×D₆₇	—	2	16	no	—
441	C₂×C₄×D₆₇	—	2	16	no	—
442	C₂×C₄×D₆₇	—	4	16	no	—
443	C₂×C₄×D₆₇	C₂×D₄	1	8	yes	—
444	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
445	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
446	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
447	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
448	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
449	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
450	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
451	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
452	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
453	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
454	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
455	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
456	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
457	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
458	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
459	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
460	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
461	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
462	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
463	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
464	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
465	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
466	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
467	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
468	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
469	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
470	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
471	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
472	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
473	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
474	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
475	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
476	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
477	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
478	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
479	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
480	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
481	C₄×Dic₆₇	C₂⁴	1	8	yes	—
482	C₄×Dic₆₇	C₂⁴	1	4	yes	—
483	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
484	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
485	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
486	#41×C₆₇	—	2	32	no	—
487	#41×C₆₇	—	2	16	no	—
488	#41×C₆₇	—	2	8	no	—
489	C₂×Q₈×C₆₇	—	2	4	no	—
490	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
491	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
492	C₂×D₄×C₆₇	—	2	16	no	—
493	C₂×D₄×C₆₇	—	2	8	no	—
494	C₂×D₄×C₆₇	—	2	16	no	—
495	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	complemented
496	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
497	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
498	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
499	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
500	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
501	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
502	C₂²×C₄×C₆₇	—	2	8	no	—
503	C₂²×C₄×C₆₇	—	2	4	no	—
504	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
505	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
506	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
507	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
508	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
510	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
511	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
512	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
513	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
514	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
515	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
516	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
517	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
518	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
519	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
520	C₄²×C₆₇	C₂⁴	1	4	yes	—
521	C₂³×C₆₇	—	2	2	no	—
522	C₂³×C₆₇	—	2	8	no	—
523	C₂³×C₆₇	—	4	4	no	—
524	C₂³×C₆₇	—	4	2	no	—
525	C₂³×C₆₇	—	4	8	no	—
526	C₂³×C₆₇	C₂²×D₄	1	8	yes	—
527	C₂³×C₆₇	C₂⁵	1	4	yes	—
528	C₂³×C₆₇	C₂⁵	1	2	yes	—
529	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
530	C₂³×C₆₇	C₂⁵	1	4	yes	—
531	C₂²×D₆₇	—	2	16	no	—
532	C₂²×D₆₇	—	2	4	no	—
533	C₂²×D₆₇	—	2	2	no	—
534	C₂²×D₆₇	—	2	8	no	—
535	C₂²×D₆₇	—	2	4	no	—
536	C₂²×D₆₇	—	2	4	no	—
537	C₂²×D₆₇	—	2	8	no	—
538	C₂²×D₆₇	—	2	8	no	—
539	C₂²×D₆₇	—	2	16	no	—
540	C₂²×D₆₇	—	2	16	no	—
541	C₂²×D₆₇	—	4	32	no	—
542	C₂²×D₆₇	—	4	4	no	—
543	C₂²×D₆₇	—	4	8	no	—
544	C₂²×D₆₇	—	4	4	no	—
545	C₂²×D₆₇	—	4	2	no	—
546	C₂²×D₆₇	—	4	16	no	—
547	C₂²×D₆₇	—	4	8	no	—
548	C₂²×D₆₇	—	4	16	no	—
549	C₂²×D₆₇	—	8	32	no	—
550	C₂²×D₆₇	C₂²×D₄	1	4	yes	—
551	C₂²×D₆₇	C₂²×D₄	1	16	yes	—
552	C₂²×D₆₇	C₂²×D₄	1	16	yes	—
553	C₂²×D₆₇	C₂²×D₄	1	8	yes	—
554	C₂²×D₆₇	C₂⁵	1	4	yes	—
555	C₂²×D₆₇	C₂⁵	1	2	yes	—
556	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
557	C₂²×D₆₇	C₂⁵	1	4	yes	—
558	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
559	Q₈×C₆₇	—	2	8	no	—
560	Q₈×C₆₇	—	2	4	no	—
561	D₄×C₆₇	—	2	8	no	—
562	D₄×C₆₇	—	2	16	no	—
563	D₄×C₆₇	—	2	16	no	—
564	D₄×C₆₇	—	2	4	no	—
565	D₄×C₆₇	—	4	8	no	—
566	D₄×C₆₇	C₂²×D₄	1	16	yes	—
567	C₂×C₄×C₆₇	—	2	2	no	—
568	C₂×C₄×C₆₇	—	2	4	no	—
569	C₂×C₄×C₆₇	—	2	16	no	—
570	C₂×C₄×C₆₇	—	2	8	no	—
571	C₂×C₄×C₆₇	—	2	8	no	—
572	C₂×C₄×C₆₇	—	2	8	no	—
573	C₂×C₄×C₆₇	—	4	8	no	—
574	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
575	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
576	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
577	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
578	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
579	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
580	C₂²⋊D₆₇	—	2	8	no	—
581	C₂²⋊D₆₇	—	2	16	no	—
582	C₂²⋊D₆₇	—	2	16	no	—
583	C₂²⋊D₆₇	—	2	8	no	—
584	C₂²⋊D₆₇	—	2	16	no	—
585	C₂²⋊D₆₇	—	2	16	no	—
586	C₂²⋊D₆₇	—	2	8	no	—
587	C₂²⋊D₆₇	—	4	8	no	—
588	C₂²⋊D₆₇	—	4	8	no	—
589	C₂²⋊D₆₇	C₂²×D₄	1	32	yes	—
590	C₂×Dic₆₇	—	2	2	no	—
591	C₂×Dic₆₇	—	2	4	no	—
592	C₂×Dic₆₇	—	2	16	no	—
593	C₂×Dic₆₇	—	2	8	no	—
594	C₂×Dic₆₇	—	2	8	no	—
595	C₂×Dic₆₇	—	2	8	no	—
596	C₂×Dic₆₇	—	4	8	no	—
597	C₂×Dic₆₇	C₂²×D₄	1	4	yes	—
598	C₂×Dic₆₇	C₂⁵	1	8	yes	—
599	C₂×Dic₆₇	C₂⁵	1	2	yes	—
600	C₂×Dic₆₇	C₂⁵	1	4	yes	—
601	C₂×Dic₆₇	C₂⁵	1	4	yes	—
602	C₂×Dic₆₇	C₂⁵	1	2	yes	—
603	D₂₆₈	—	2	8	no	—
604	D₂₆₈	—	2	16	no	—
605	D₂₆₈	—	2	16	no	—
606	D₂₆₈	—	2	4	no	—
607	D₂₆₈	—	4	8	no	—
608	D₂₆₈	C₂²×D₄	1	16	yes	—
609	C₄×D₆₇	—	2	4	no	—
610	C₄×D₆₇	—	2	4	no	—
611	C₄×D₆₇	—	2	8	no	—
612	C₄×D₆₇	—	2	8	no	—
613	C₄×D₆₇	—	2	8	no	—
614	C₄×D₆₇	—	2	16	no	—
615	C₄×D₆₇	—	2	16	no	—
616	C₄×D₆₇	—	2	16	no	—
617	C₄×D₆₇	—	2	16	no	—
618	C₄×D₆₇	—	2	8	no	—
619	C₄×D₆₇	—	2	8	no	—
620	C₄×D₆₇	—	2	8	no	—
621	C₄×D₆₇	—	2	8	no	—
622	C₄×D₆₇	—	4	16	no	—
623	C₄×D₆₇	C₂²×D₄	1	8	yes	—
624	C₄×D₆₇	C₂²×D₄	1	8	yes	—
625	Dic₁₃₄	—	2	8	no	—
626	Dic₁₃₄	—	2	4	no	—
627	Dic₁₃₄	—	2	16	no	—
628	Dic₁₃₄	—	2	8	no	—
629	C₂²×C₆₇	—	2	8	no	—
630	C₂²×C₆₇	—	2	2	no	—
631	C₂²×C₆₇	—	2	2	no	—
632	C₂²×C₆₇	—	2	4	no	—
633	C₂²×C₆₇	—	2	4	no	—
634	C₂²×C₆₇	—	2	8	no	—
635	C₂²×C₆₇	—	4	8	no	—
636	C₂²×C₆₇	—	4	4	no	—
637	C₂²×C₆₇	—	8	8	no	—
638	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
639	C₂²×C₆₇	C₂³×D₄	1	8	yes	—
640	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
641	C₂×D₆₇	—	2	8	no	—
642	C₂×D₆₇	—	2	2	no	—
643	C₂×D₆₇	—	2	8	no	—
644	C₂×D₆₇	—	2	32	no	—
645	C₂×D₆₇	—	2	2	no	—
646	C₂×D₆₇	—	2	4	no	—
647	C₂×D₆₇	—	2	4	no	—
648	C₂×D₆₇	—	2	8	no	—
649	C₂×D₆₇	—	4	16	no	—
650	C₂×D₆₇	—	4	8	no	—
651	C₂×D₆₇	—	4	8	no	—
652	C₂×D₆₇	—	4	4	no	—
653	C₂×D₆₇	—	4	8	no	—
654	C₂×D₆₇	—	4	16	no	—
655	C₂×D₆₇	—	8	16	no	—
656	C₂×D₆₇	—	8	8	no	—
657	C₂×D₆₇	C₂³×D₄	1	2	yes	—
658	C₂×D₆₇	C₂³×D₄	1	8	yes	—
659	C₂×D₆₇	C₂³×D₄	1	2	yes	—
660	C₂×D₆₇	#585	1	4	yes	—
661	C₄×C₆₇	—	2	4	no	—
662	C₄×C₆₇	—	2	4	no	—
663	C₄×C₆₇	—	2	2	no	—
664	C₄×C₆₇	—	2	8	no	—
665	C₄×C₆₇	C₂³×D₄	1	4	yes	—
666	Dic₆₇	—	2	4	no	—
667	Dic₆₇	—	2	4	no	—
668	Dic₆₇	—	2	2	no	—
669	Dic₆₇	—	2	8	no	—
670	Dic₆₇	C₂³×D₄	1	4	yes	—
671	C₂×#3485	—	67	1	no	maximal, Sylow
672	C₂×C₆₇	—	2	2	no	—
673	C₂×C₆₇	—	2	8	no	—
674	C₂×C₆₇	—	4	2	no	—
675	C₂×C₆₇	—	4	4	no	—
676	C₂×C₆₇	C₂⁴×D₄	1	1	yes	characteristic
677	C₂×C₆₇	C₂×#585	1	2	yes	—
678	D₆₇	—	2	2	no	—
679	D₆₇	—	2	8	no	—
680	D₆₇	—	4	2	no	—
681	D₆₇	—	4	4	no	—
682	D₆₇	#3485	1	4	yes	direct product factor
683	C₂²×H(5,𝔽₂)	—	67	1	no	—
684	C₂³×#41	—	67	1	no	—
685	#3485	—	67	1	no	—
686	#3485	—	67	1	no	—
687	#3485	—	67	8	no	—
688	#3485	—	67	8	no	—
689	#3485	—	67	2	no	—
690	#3485	—	67	4	no	—
691	#3485	—	67	2	no	—
692	#3485	—	67	4	no	—
693	#3485	—	67	1	no	—
694	#3485	D₆₇	1	1	yes	characteristic, direct product factor
695	C₂×#547	—	67	8	no	—
696	C₂×#546	—	67	8	no	—
697	C₂×#536	—	67	2	no	—
698	C₂×#534	—	67	4	no	—
699	C₂×#525	—	67	2	no	—
700	C₂²×#123	—	67	4	no	—
701	C₂×#518	—	67	1	no	—
702	C₆₇	C₂×#3485	1	1	yes	characteristic, complemented, Sylow
703	C₂×H(5,𝔽₂)	—	67	2	no	—
704	C₂×H(5,𝔽₂)	—	67	4	no	—
705	C₂×H(5,𝔽₂)	—	67	4	no	—
706	C₂×H(5,𝔽₂)	—	67	1	no	—
707	C₂×H(5,𝔽₂)	—	67	4	no	—
708	C₂×H(5,𝔽₂)	—	134	16	no	—
709	C₂×H(5,𝔽₂)	C₂×D₆₇	1	1	yes	characteristic, complemented
710	C₂²×#41	—	67	2	no	—
711	C₂²×#41	—	67	8	no	—
712	C₂²×#41	—	67	8	no	—
713	C₂²×#41	—	67	4	no	—
714	C₂²×#41	—	67	1	no	—
715	C₂²×#41	—	67	1	no	—
716	C₂²×#41	—	67	2	no	—
717	C₂²×#41	—	67	1	no	—
718	C₂²×#41	—	67	2	no	—
719	C₂²×#41	—	134	16	no	—
720	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
721	C₂³×Q₈	—	67	1	no	—
722	C₂³×D₄	—	67	1	no	—
723	C₂³×D₄	—	67	4	no	—
724	C₂³×D₄	—	67	2	no	—
725	C₂³×D₄	—	67	4	no	—
726	C₂⁴×C₄	—	67	2	no	—
727	C₂⁴×C₄	—	67	1	no	—
728	#547	—	67	8	no	—
729	#547	—	67	8	no	—
730	#547	—	67	8	no	—
731	#547	—	67	16	no	—
732	#547	—	67	16	no	—
733	#547	—	67	8	no	—
734	#547	—	67	8	no	—
735	#547	—	67	16	no	—
736	#547	—	67	8	no	—
737	#547	—	67	8	no	—
738	#547	—	67	16	no	—
739	#547	C₂×D₆₇	1	8	yes	complemented
740	#546	—	67	8	no	—
741	#546	—	67	8	no	—
742	#546	—	67	8	no	—
743	#546	—	67	16	no	—
744	#546	—	67	8	no	—
745	#546	—	67	16	no	—
746	#546	—	67	8	no	—
747	#546	—	67	16	no	—
748	#546	—	67	8	no	—
749	#546	—	67	8	no	—
750	#546	—	67	16	no	—
751	#546	C₂×D₆₇	1	8	yes	complemented
752	#536	—	67	2	no	—
753	#536	—	67	2	no	—
754	#536	—	67	4	no	—
755	#536	—	67	4	no	—
756	#536	—	67	8	no	—
757	#536	—	67	8	no	—
758	#536	—	67	2	no	—
759	#536	C₂×D₆₇	1	2	yes	complemented
760	#534	—	67	4	no	—
761	#534	—	67	4	no	—
762	#534	—	67	8	no	—
763	#534	—	67	8	no	—
764	#534	—	67	16	no	—
765	#534	—	67	8	no	—
766	#534	—	67	8	no	—
767	#534	—	67	4	no	—
768	#534	C₂×D₆₇	1	4	yes	complemented
769	C₂×C₄⋊Q₈	—	67	4	no	—
770	C₂×#124	—	67	4	no	—
771	#525	—	67	2	no	—
772	#525	—	67	2	no	—
773	#525	—	67	4	no	—
774	#525	—	67	4	no	—
775	#525	—	67	4	no	—
776	#525	—	67	4	no	—
777	#525	—	67	8	no	—
778	#525	—	67	2	no	—
779	#525	C₂×D₆₇	1	2	yes	complemented
780	C₂×#123	—	67	4	no	—
781	C₂×#123	—	67	4	no	—
782	C₂×#123	—	67	4	no	—
783	C₂×#123	—	67	8	no	—
784	C₂×#123	—	67	16	no	—
785	C₂×#123	—	67	8	no	—
786	C₂×#123	—	67	8	no	—
787	C₂×#123	—	67	16	no	—
788	C₂×#123	—	67	8	no	—
789	C₂×#123	—	67	8	no	—
790	C₂×#123	—	67	8	no	—
791	C₂×#123	—	67	4	no	—
792	C₂×#123	C₂×D₆₇	1	4	yes	complemented
793	C₂×C₂²⋊Q₈	—	67	4	no	—
794	C₂×C₂²⋊Q₈	—	67	8	no	—
795	C₂×#121	—	67	4	no	—
796	C₂×#121	—	67	16	no	—
797	C₂×#120	—	67	4	no	—
798	C₂×#120	—	67	8	no	—
799	#518	—	67	1	no	—
800	#518	—	67	8	no	—
801	#518	—	67	2	no	—
802	#518	—	67	4	no	—
803	#518	C₂×D₆₇	1	1	yes	characteristic, complemented
804	C₂×C₄×D₄	—	67	8	no	—
805	C₂×C₄×D₄	—	67	8	no	—
806	C₂×#117	—	67	2	no	—
807	C₂²×C₄⋊C₄	—	67	8	no	—
808	C₂²×C₂²⋊C₄	—	67	4	no	—
809	C₂²×C₂²⋊C₄	—	67	8	no	—
810	C₂⁵	—	67	2	no	—
811	C₂⁵	—	67	4	no	—
812	C₂⁵	—	67	1	no	—
813	H(5,𝔽₂)	—	2	8	no	—
814	H(5,𝔽₂)	—	134	32	no	—
815	H(5,𝔽₂)	—	134	32	no	—
816	H(5,𝔽₂)	—	134	32	no	—
817	H(5,𝔽₂)	—	134	16	no	—
818	H(5,𝔽₂)	—	134	8	no	—
819	C₂×#41	—	2	8	no	—
820	C₂×#41	—	67	2	no	—
821	C₂×#41	—	67	8	no	—
822	C₂×#41	—	67	4	no	—
823	C₂×#41	—	67	4	no	—
824	C₂×#41	—	67	2	no	—
825	C₂×#41	—	67	8	no	—
826	C₂×#41	—	67	16	no	—
827	C₂×#41	—	67	4	no	—
828	C₂×#41	—	67	8	no	—
829	C₂×#41	—	67	4	no	—
830	C₂×#41	—	67	2	no	—
831	C₂×#41	—	67	8	no	—
832	C₂×#41	—	67	16	no	—
833	C₂×#41	—	67	4	no	—
834	C₂×#41	—	67	8	no	—
835	C₂×#41	—	134	16	no	—
836	C₂×#41	—	134	8	no	—
837	C₂×#41	—	134	16	no	—
838	C₂×#41	—	134	16	no	—
839	C₂×#41	—	134	8	no	—
840	C₂×#41	—	134	64	no	—
841	C₂×#41	—	134	64	no	—
842	C₂×#41	—	134	32	no	—
843	C₂×#41	—	134	8	no	—
844	C₂×#41	C₂²×D₆₇	1	2	yes	—
845	C₂×#41	C₂²×D₆₇	1	8	yes	complemented
846	C₂×#41	C₂²×D₆₇	1	4	yes	complemented
847	C₂²×Q₈	—	67	4	no	—
848	C₂²×Q₈	—	67	2	no	—
849	C₂²×Q₈	—	67	4	no	—
850	C₂²×Q₈	—	67	2	no	—
851	C₂²×Q₈	—	67	1	no	—
852	C₂²×Q₈	—	134	8	no	—
853	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic, complemented
854	C₂²×D₄	—	67	8	no	—
855	C₂²×D₄	—	67	2	no	—
856	C₂²×D₄	—	67	16	no	—
857	C₂²×D₄	—	67	4	no	—
858	C₂²×D₄	—	67	4	no	—
859	C₂²×D₄	—	67	4	no	—
860	C₂²×D₄	—	67	4	no	—
861	C₂²×D₄	—	67	2	no	—
862	C₂²×D₄	—	67	2	no	—
863	C₂²×D₄	—	67	8	no	—
864	C₂²×D₄	—	67	8	no	—
865	C₂²×D₄	—	67	4	no	—
866	C₂²×D₄	—	67	8	no	—
867	C₂²×D₄	—	67	2	no	—
868	C₂²×D₄	—	67	8	no	—
869	C₂²×D₄	—	67	8	no	—
870	C₂²×D₄	—	67	8	no	—
871	C₂²×D₄	—	67	8	no	—
872	C₂²×D₄	—	67	4	no	—
873	C₂²×D₄	—	67	4	no	—
874	C₂²×D₄	—	67	1	no	—
875	C₂²×D₄	—	67	4	no	—
876	C₂²×D₄	—	67	2	no	—
877	C₂²×D₄	—	67	4	no	—
878	C₂²×D₄	—	134	32	no	—
879	C₂²×D₄	—	134	16	no	—
880	C₂²×D₄	—	134	32	no	—
881	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
882	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
883	C₂²×D₄	C₂²×D₆₇	1	2	yes	complemented
884	C₂²×D₄	C₂²×D₆₇	1	4	yes	complemented
885	C₂³×C₄	—	67	8	no	—
886	C₂³×C₄	—	67	1	no	—
887	C₂³×C₄	—	67	2	no	—
888	C₂³×C₄	—	67	1	no	—
889	C₂³×C₄	—	67	8	no	—
890	C₂³×C₄	—	67	4	no	—
891	C₂³×C₄	—	67	4	no	—
892	C₂³×C₄	—	67	4	no	—
893	C₂³×C₄	—	67	1	no	—
894	C₂³×C₄	—	67	2	no	—
895	C₂³×C₄	—	67	8	no	—
896	C₂³×C₄	—	67	2	no	—
897	C₂³×C₄	—	67	2	no	—
898	C₂³×C₄	—	67	1	no	—
899	C₂³×C₄	—	67	4	no	—
900	C₂³×C₄	—	67	1	no	—
901	C₂³×C₄	—	134	8	no	—
902	C₂³×C₄	—	134	16	no	—
903	C₂³×C₄	C₂²×D₆₇	1	2	yes	complemented
904	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic, complemented
905	C₄⋊Q₈	—	67	4	no	—
906	C₄⋊Q₈	—	67	4	no	—
907	C₄⋊Q₈	—	67	16	no	—
908	C₄⋊Q₈	—	67	4	no	—
909	C₄⋊Q₈	C₂²×D₆₇	1	4	yes	complemented
910	#124	—	67	4	no	—
911	#124	—	67	4	no	—
912	#124	—	67	16	no	—
913	#124	—	67	4	no	—
914	#124	C₂²×D₆₇	1	4	yes	complemented
915	#123	—	67	4	no	—
916	#123	—	67	8	no	—
917	#123	—	67	16	no	—
918	#123	—	67	8	no	—
919	#123	—	67	4	no	—
920	#123	—	67	8	no	—
921	#123	—	67	16	no	—
922	#123	—	67	8	no	—
923	#123	—	67	8	no	—
924	#123	—	67	16	no	—
925	#123	—	67	16	no	—
926	#123	—	67	16	no	—
927	#123	—	67	16	no	—
928	#123	—	67	8	no	—
929	#123	—	67	4	no	—
930	#123	—	67	16	no	—
931	#123	—	67	8	no	—
932	#123	—	67	16	no	—
933	#123	—	67	16	no	—
934	#123	—	67	16	no	—
935	#123	—	67	16	no	—
936	#123	—	67	8	no	—
937	#123	C₂²×D₆₇	1	4	yes	complemented
938	#123	C₂²×D₆₇	1	8	yes	complemented
939	#123	C₂²×D₆₇	1	16	yes	complemented
940	#123	C₂²×D₆₇	1	8	yes	complemented
941	C₂²⋊Q₈	—	67	4	no	—
942	C₂²⋊Q₈	—	67	8	no	—
943	C₂²⋊Q₈	—	67	4	no	—
944	C₂²⋊Q₈	—	67	8	no	—
945	C₂²⋊Q₈	—	67	8	no	—
946	C₂²⋊Q₈	—	67	4	no	—
947	C₂²⋊Q₈	—	67	16	no	—
948	C₂²⋊Q₈	—	67	8	no	—
949	C₂²⋊Q₈	—	67	8	no	—
950	C₂²⋊Q₈	—	67	16	no	—
951	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	complemented
952	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
953	#121	—	67	4	no	—
954	#121	—	67	8	no	—
955	#121	—	67	16	no	—
956	#121	—	67	16	no	—
957	#121	—	67	16	no	—
958	#121	—	67	4	no	—
959	#121	—	67	16	no	—
960	#121	—	67	4	no	—
961	#121	—	67	16	no	—
962	#121	—	67	8	no	—
963	#121	—	67	16	no	—
964	#121	—	67	16	no	—
965	#121	C₂²×D₆₇	1	4	yes	complemented
966	#121	C₂²×D₆₇	1	16	yes	complemented
967	#120	—	67	4	no	—
968	#120	—	67	8	no	—
969	#120	—	67	4	no	—
970	#120	—	67	8	no	—
971	#120	—	67	8	no	—
972	#120	—	67	16	no	—
973	#120	—	67	8	no	—
974	#120	—	67	4	no	—
975	#120	—	67	16	no	—
976	#120	—	67	8	no	—
977	#120	C₂²×D₆₇	1	4	yes	complemented
978	#120	C₂²×D₆₇	1	8	yes	complemented
979	C₄×D₄	—	67	8	no	—
980	C₄×D₄	—	67	8	no	—
981	C₄×D₄	—	67	16	no	—
982	C₄×D₄	—	67	8	no	—
983	C₄×D₄	—	67	8	no	—
984	C₄×D₄	—	67	8	no	—
985	C₄×D₄	—	67	8	no	—
986	C₄×D₄	—	67	16	no	—
987	C₄×D₄	—	67	8	no	—
988	C₄×D₄	—	67	8	no	—
989	C₄×D₄	—	67	8	no	—
990	C₄×D₄	—	67	8	no	—
991	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
992	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
993	#117	—	67	2	no	—
994	#117	—	67	4	no	—
995	#117	—	67	4	no	—
996	#117	—	67	4	no	—
997	#117	C₂²×D₆₇	1	2	yes	complemented
998	C₂×C₄⋊C₄	—	67	8	no	—
999	C₂×C₄⋊C₄	—	67	8	no	—
1000	C₂×C₄⋊C₄	—	67	8	no	—
1001	C₂×C₄⋊C₄	—	67	8	no	—
1002	C₂×C₄⋊C₄	—	67	16	no	—
1003	C₂×C₄⋊C₄	—	67	16	no	—
1004	C₂×C₄⋊C₄	—	67	16	no	—
1005	C₂×C₄⋊C₄	—	67	4	no	—
1006	C₂×C₄⋊C₄	C₂²×D₆₇	1	8	yes	complemented
1007	C₂×C₂²⋊C₄	—	67	4	no	—
1008	C₂×C₂²⋊C₄	—	67	8	no	—
1009	C₂×C₂²⋊C₄	—	67	8	no	—
1010	C₂×C₂²⋊C₄	—	67	8	no	—
1011	C₂×C₂²⋊C₄	—	67	8	no	—
1012	C₂×C₂²⋊C₄	—	67	4	no	—
1013	C₂×C₂²⋊C₄	—	67	8	no	—
1014	C₂×C₂²⋊C₄	—	67	8	no	—
1015	C₂×C₂²⋊C₄	—	67	8	no	—
1016	C₂×C₂²⋊C₄	—	67	8	no	—
1017	C₂×C₂²⋊C₄	—	67	16	no	—
1018	C₂×C₂²⋊C₄	—	67	16	no	—
1019	C₂×C₂²⋊C₄	—	67	16	no	—
1020	C₂×C₂²⋊C₄	—	67	8	no	—
1021	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	complemented
1022	C₂×C₂²⋊C₄	C₂²×D₆₇	1	8	yes	complemented
1023	C₂×C₄²	—	67	4	no	—
1024	C₂⁴	—	268	4	no	—
1025	C₂⁴	—	268	8	no	—
1026	C₂⁴	—	268	16	no	—
1027	C₂⁴	—	67	16	no	—
1028	C₂⁴	—	67	4	no	—
1029	C₂⁴	—	67	2	no	—
1030	C₂⁴	—	67	8	no	—
1031	C₂⁴	—	67	4	no	—
1032	C₂⁴	—	67	2	no	—
1033	C₂⁴	—	67	1	no	—
1034	C₂⁴	—	67	1	no	—
1035	C₂⁴	—	67	4	no	—
1036	C₂⁴	—	67	4	no	—
1037	C₂⁴	—	67	2	no	—
1038	C₂⁴	—	134	4	no	—
1039	C₂⁴	—	134	16	no	—
1040	C₂⁴	C₂³×D₆₇	1	4	yes	—
1041	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1042	C₂⁴	C₂³×D₆₇	1	2	yes	—
1043	#41	—	2	32	no	—
1044	#41	—	2	16	no	—
1045	#41	—	2	8	no	—
1046	#41	—	134	16	no	—
1047	#41	—	134	64	no	—
1048	#41	—	134	32	no	—
1049	#41	—	134	32	no	—
1050	#41	—	134	16	no	—
1051	#41	—	134	16	no	—
1052	#41	—	134	8	no	—
1053	#41	—	134	8	no	—
1054	#41	—	134	64	no	—
1055	#41	—	134	32	no	—
1056	#41	—	134	32	no	—
1057	#41	—	134	16	no	—
1058	#41	—	134	32	no	—
1059	#41	—	134	16	no	—
1060	#41	—	134	8	no	—
1061	C₂×Q₈	—	2	4	no	—
1062	C₂×Q₈	—	67	8	no	—
1063	C₂×Q₈	—	67	4	no	—
1064	C₂×Q₈	—	67	4	no	—
1065	C₂×Q₈	—	67	2	no	—
1066	C₂×Q₈	—	134	8	no	—
1067	C₂×Q₈	—	134	16	no	—
1068	C₂×Q₈	—	134	16	no	—
1069	C₂×Q₈	—	134	8	no	—
1070	C₂×Q₈	—	134	4	no	—
1071	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1072	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
1073	C₂×D₄	—	2	16	no	—
1074	C₂×D₄	—	2	8	no	—
1075	C₂×D₄	—	2	16	no	—
1076	C₂×D₄	—	268	16	no	—
1077	C₂×D₄	—	67	8	no	—
1078	C₂×D₄	—	67	8	no	—
1079	C₂×D₄	—	67	16	no	—
1080	C₂×D₄	—	67	8	no	—
1081	C₂×D₄	—	67	32	no	—
1082	C₂×D₄	—	67	32	no	—
1083	C₂×D₄	—	67	8	no	—
1084	C₂×D₄	—	67	8	no	—
1085	C₂×D₄	—	67	4	no	—
1086	C₂×D₄	—	67	4	no	—
1087	C₂×D₄	—	67	8	no	—
1088	C₂×D₄	—	67	8	no	—
1089	C₂×D₄	—	67	4	no	—
1090	C₂×D₄	—	67	8	no	—
1091	C₂×D₄	—	67	8	no	—
1092	C₂×D₄	—	67	4	no	—
1093	C₂×D₄	—	67	8	no	—
1094	C₂×D₄	—	67	4	no	—
1095	C₂×D₄	—	67	8	no	—
1096	C₂×D₄	—	67	2	no	—
1097	C₂×D₄	—	134	16	no	—
1098	C₂×D₄	—	134	8	no	—
1099	C₂×D₄	—	134	16	no	—
1100	C₂×D₄	—	134	8	no	—
1101	C₂×D₄	—	134	32	no	—
1102	C₂×D₄	—	134	16	no	—
1103	C₂×D₄	—	134	16	no	—
1104	C₂×D₄	—	134	32	no	—
1105	C₂×D₄	—	134	32	no	—
1106	C₂×D₄	—	134	32	no	—
1107	C₂×D₄	—	134	32	no	—
1108	C₂×D₄	—	134	32	no	—
1109	C₂×D₄	—	134	32	no	—
1110	C₂×D₄	—	134	8	no	—
1111	C₂×D₄	—	134	16	no	—
1112	C₂×D₄	—	134	8	no	—
1113	C₂×D₄	—	134	16	no	—
1114	C₂×D₄	—	134	16	no	—
1115	C₂×D₄	D₄×D₆₇	1	8	yes	complemented
1116	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1117	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1118	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1119	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1120	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1121	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1122	C₂²×C₄	—	2	8	no	—
1123	C₂²×C₄	—	2	4	no	—
1124	C₂²×C₄	—	268	16	no	—
1125	C₂²×C₄	—	67	8	no	—
1126	C₂²×C₄	—	67	16	no	—
1127	C₂²×C₄	—	67	1	no	—
1128	C₂²×C₄	—	67	8	no	—
1129	C₂²×C₄	—	67	2	no	—
1130	C₂²×C₄	—	67	2	no	—
1131	C₂²×C₄	—	67	8	no	—
1132	C₂²×C₄	—	67	4	no	—
1133	C₂²×C₄	—	67	4	no	—
1134	C₂²×C₄	—	67	4	no	—
1135	C₂²×C₄	—	67	1	no	—
1136	C₂²×C₄	—	67	2	no	—
1137	C₂²×C₄	—	67	8	no	—
1138	C₂²×C₄	—	67	2	no	—
1139	C₂²×C₄	—	67	4	no	—
1140	C₂²×C₄	—	67	4	no	—
1141	C₂²×C₄	—	67	8	no	—
1142	C₂²×C₄	—	67	8	no	—
1143	C₂²×C₄	—	67	8	no	—
1144	C₂²×C₄	—	67	4	no	—
1145	C₂²×C₄	—	67	4	no	—
1146	C₂²×C₄	—	67	4	no	—
1147	C₂²×C₄	—	67	4	no	—
1148	C₂²×C₄	—	67	2	no	—
1149	C₂²×C₄	—	67	4	no	—
1150	C₂²×C₄	—	134	4	no	—
1151	C₂²×C₄	—	134	16	no	—
1152	C₂²×C₄	—	134	16	no	—
1153	C₂²×C₄	—	134	16	no	—
1154	C₂²×C₄	—	134	4	no	—
1155	C₂²×C₄	—	134	8	no	—
1156	C₂²×C₄	—	134	8	no	—
1157	C₂²×C₄	—	134	8	no	—
1158	C₂²×C₄	—	134	32	no	—
1159	C₂²×C₄	—	134	32	no	—
1160	C₂²×C₄	—	134	16	no	—
1161	C₂²×C₄	—	134	4	no	—
1162	C₂²×C₄	—	134	8	no	—
1163	C₂²×C₄	—	134	4	no	—
1164	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1165	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1166	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1167	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1168	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1170	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1171	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1172	C₄⋊C₄	—	67	8	no	—
1173	C₄⋊C₄	—	67	8	no	—
1174	C₄⋊C₄	—	67	8	no	—
1175	C₄⋊C₄	—	67	16	no	—
1176	C₄⋊C₄	—	67	16	no	—
1177	C₄⋊C₄	—	67	16	no	—
1178	C₄⋊C₄	—	67	8	no	—
1179	C₄⋊C₄	—	67	4	no	—
1180	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1181	C₄⋊C₄	C₂³×D₆₇	1	16	yes	—
1182	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1183	C₂²⋊C₄	—	67	4	no	—
1184	C₂²⋊C₄	—	67	8	no	—
1185	C₂²⋊C₄	—	67	8	no	—
1186	C₂²⋊C₄	—	67	16	no	—
1187	C₂²⋊C₄	—	67	8	no	—
1188	C₂²⋊C₄	—	67	8	no	—
1189	C₂²⋊C₄	—	67	8	no	—
1190	C₂²⋊C₄	—	67	8	no	—
1191	C₂²⋊C₄	—	67	16	no	—
1192	C₂²⋊C₄	—	67	16	no	—
1193	C₂²⋊C₄	—	67	16	no	—
1194	C₂²⋊C₄	—	67	8	no	—
1195	C₂²⋊C₄	—	67	8	no	—
1196	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1197	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1198	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1199	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
1200	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1201	C₄²	—	67	8	no	—
1202	C₄²	—	67	4	no	—
1203	C₄²	C₂³×D₆₇	1	4	yes	—
1204	C₂³	—	2	2	no	—
1205	C₂³	—	2	8	no	—
1206	C₂³	—	4	4	no	—
1207	C₂³	—	4	2	no	—
1208	C₂³	—	4	8	no	—
1209	C₂³	—	268	8	no	—
1210	C₂³	—	268	2	no	—
1211	C₂³	—	268	4	no	—
1212	C₂³	—	268	4	no	—
1213	C₂³	—	268	8	no	—
1214	C₂³	—	268	16	no	—
1215	C₂³	—	268	16	no	—
1216	C₂³	—	268	32	no	—
1217	C₂³	—	536	32	no	—
1218	C₂³	—	67	16	no	—
1219	C₂³	—	67	8	no	—
1220	C₂³	—	67	1	no	—
1221	C₂³	—	67	4	no	—
1222	C₂³	—	67	16	no	—
1223	C₂³	—	67	1	no	—
1224	C₂³	—	67	4	no	—
1225	C₂³	—	67	4	no	—
1226	C₂³	—	67	2	no	—
1227	C₂³	—	134	4	no	—
1228	C₂³	—	134	4	no	—
1229	C₂³	—	134	8	no	—
1230	C₂³	—	134	8	no	—
1231	C₂³	—	134	16	no	—
1232	C₂³	—	134	16	no	—
1233	C₂³	—	134	16	no	—
1234	C₂³	—	134	4	no	—
1235	C₂³	—	134	2	no	—
1236	C₂³	—	134	8	no	—
1237	C₂³	C₂×D₄×D₆₇	1	8	yes	—
1238	C₂³	C₂⁴×D₆₇	1	4	yes	—
1239	C₂³	C₂⁴×D₆₇	1	2	yes	—
1240	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1241	C₂³	C₂⁴×D₆₇	1	4	yes	—
1242	Q₈	—	2	8	no	—
1243	Q₈	—	2	4	no	—
1244	Q₈	—	134	16	no	—
1245	Q₈	—	134	8	no	—
1246	Q₈	—	134	8	no	—
1247	Q₈	—	134	4	no	—
1248	D₄	—	2	8	no	—
1249	D₄	—	2	16	no	—
1250	D₄	—	2	16	no	—
1251	D₄	—	2	4	no	—
1252	D₄	—	4	8	no	—
1253	D₄	—	268	8	no	—
1254	D₄	—	268	8	no	—
1255	D₄	—	268	8	no	—
1256	D₄	—	67	32	no	—
1257	D₄	—	67	16	no	—
1258	D₄	—	134	8	no	—
1259	D₄	—	134	16	no	—
1260	D₄	—	134	16	no	—
1261	D₄	—	134	8	no	—
1262	D₄	—	134	8	no	—
1263	D₄	—	134	16	no	—
1264	D₄	—	134	16	no	—
1265	D₄	—	134	8	no	—
1266	D₄	—	134	16	no	—
1267	D₄	—	134	16	no	—
1268	D₄	—	134	4	no	—
1269	D₄	C₂×D₄×D₆₇	1	16	yes	—
1270	C₂×C₄	—	2	2	no	—
1271	C₂×C₄	—	2	4	no	—
1272	C₂×C₄	—	2	16	no	—
1273	C₂×C₄	—	2	8	no	—
1274	C₂×C₄	—	2	8	no	—
1275	C₂×C₄	—	2	8	no	—
1276	C₂×C₄	—	4	8	no	—
1277	C₂×C₄	—	268	16	no	—
1278	C₂×C₄	—	268	8	no	—
1279	C₂×C₄	—	67	4	no	—
1280	C₂×C₄	—	67	2	no	—
1281	C₂×C₄	—	67	8	no	—
1282	C₂×C₄	—	67	8	no	—
1283	C₂×C₄	—	67	8	no	—
1284	C₂×C₄	—	67	2	no	—
1285	C₂×C₄	—	67	4	no	—
1286	C₂×C₄	—	67	4	no	—
1287	C₂×C₄	—	134	8	no	—
1288	C₂×C₄	—	134	8	no	—
1289	C₂×C₄	—	134	16	no	—
1290	C₂×C₄	—	134	4	no	—
1291	C₂×C₄	—	134	4	no	—
1292	C₂×C₄	—	134	8	no	—
1293	C₂×C₄	—	134	8	no	—
1294	C₂×C₄	—	134	8	no	—
1295	C₂×C₄	—	134	16	no	—
1296	C₂×C₄	—	134	16	no	—
1297	C₂×C₄	—	134	16	no	—
1298	C₂×C₄	—	134	8	no	—
1299	C₂×C₄	—	134	8	no	—
1300	C₂×C₄	—	134	2	no	—
1301	C₂×C₄	—	134	4	no	—
1302	C₂×C₄	—	134	16	no	—
1303	C₂×C₄	—	134	8	no	—
1304	C₂×C₄	—	134	8	no	—
1305	C₂×C₄	—	134	8	no	—
1306	C₂×C₄	C₂×D₄×D₆₇	1	4	yes	—
1307	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
1308	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1309	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1310	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1311	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1312	C₂²	—	2	8	no	—
1313	C₂²	—	2	2	no	—
1314	C₂²	—	2	2	no	—
1315	C₂²	—	2	4	no	—
1316	C₂²	—	2	4	no	—
1317	C₂²	—	2	8	no	—
1318	C₂²	—	4	8	no	—
1319	C₂²	—	4	4	no	—
1320	C₂²	—	8	8	no	—
1321	C₂²	—	268	4	no	—
1322	C₂²	—	268	8	no	—
1323	C₂²	—	268	16	no	—
1324	C₂²	—	268	8	no	—
1325	C₂²	—	268	16	no	—
1326	C₂²	—	268	8	no	—
1327	C₂²	—	536	8	no	—
1328	C₂²	—	536	16	no	—
1329	C₂²	—	67	2	no	—
1330	C₂²	—	67	4	no	—
1331	C₂²	—	67	2	no	—
1332	C₂²	—	67	8	no	—
1333	C₂²	—	134	8	no	—
1334	C₂²	—	134	32	no	—
1335	C₂²	—	134	2	no	—
1336	C₂²	—	134	4	no	—
1337	C₂²	—	134	4	no	—
1338	C₂²	—	134	8	no	—
1339	C₂²	—	134	8	no	—
1340	C₂²	—	134	2	no	—
1341	C₂²	C₂²×D₄×D₆₇	1	2	yes	—
1342	C₂²	C₂²×D₄×D₆₇	1	8	yes	—
1343	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1344	C₄	—	2	2	no	—
1345	C₄	—	2	4	no	—
1346	C₄	—	2	4	no	—
1347	C₄	—	2	8	no	—
1348	C₄	—	67	4	no	—
1349	C₄	—	134	2	no	—
1350	C₄	—	134	4	no	—
1351	C₄	—	134	4	no	—
1352	C₄	—	134	8	no	—
1353	C₄	C₂²×D₄×D₆₇	1	4	yes	—
1354	C₂	—	2	2	no	—
1355	C₂	—	2	8	no	—
1356	C₂	—	4	2	no	—
1357	C₂	—	4	4	no	—
1358	C₂	—	268	2	no	—
1359	C₂	—	268	4	no	—
1360	C₂	—	67	4	no	—
1361	C₂	—	134	2	no	—
1362	C₂	—	134	8	no	—
1363	C₂	C₂³×D₄×D₆₇	1	1	yes	characteristic
1364	C₂	#585×D₆₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Fitting	C₆₇×#3485	C₂
hypercenter	#3485	D₆₇
hypocenter	C₆₇	C₂×#3485
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #3485

Complements

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

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×D₆₇	C₂	semidirect
2. C₂²×#41×D₆₇	C₂	semidirect
3. #22573854	C₂	semidirect
4. #22573853	C₂	semidirect
5. #22573852	C₂	semidirect
6. #22573851	C₂	semidirect
7. #22573850	C₂	semidirect
8. #22573849	C₂	semidirect
9. #22573848	C₂	semidirect
10. #22573847	C₂	semidirect
11. #22573846	C₂	semidirect
12. #547×D₆₇	C₂	semidirect
13. #546×D₆₇	C₂	semidirect
14. #536×D₆₇	C₂	semidirect
15. #534×D₆₇	C₂	semidirect
16. #525×D₆₇	C₂	semidirect
17. C₂×#123×D₆₇	C₂	semidirect
18. #518×D₆₇	C₂	semidirect
19. C₆₇×#3485	C₂	semidirect
20. C₂×#14524089	C₂²	semidirect
21. C₂×#14524089	C₂²	semidirect
22. C₂×#14524088	C₂²	semidirect
23. C₂×#14524088	C₂²	semidirect
24. C₂×#14524088	C₂²	semidirect
26. C₂²×#11761629	C₂²	semidirect
27. C₂²×#11761628	C₂²	semidirect
28. C₂²×#11761628	C₂²	semidirect
29. C₂²×#11761627	C₂²	semidirect
30. C₂²×#11761627	C₂²	semidirect
33. C₂×#41×D₆₇	C₂²	semidirect
34. C₂×#41×D₆₇	C₂²	semidirect
35. C₂×#41×D₆₇	C₂²	semidirect
36. C₂²×Q₈×D₆₇	C₂²	semidirect
39. C₂²×D₄×D₆₇	C₂²	semidirect
40. C₂²×D₄×D₆₇	C₂²	semidirect
41. C₂³×C₄×D₆₇	C₂²	semidirect
42. C₂³×C₄×D₆₇	C₂²	semidirect
43. #16864051	C₂²	semidirect
44. #16864050	C₂²	semidirect
45. #16864049	C₂²	semidirect
46. #16864048	C₂²	semidirect
47. #16864048	C₂²	semidirect
48. #16864047	C₂²	semidirect
49. #16864046	C₂²	semidirect
50. #16864045	C₂²	semidirect
51. #16864045	C₂²	semidirect
52. #16864044	C₂²	semidirect
53. #16864044	C₂²	semidirect
54. #16864043	C₂²	semidirect
55. #16864042	C₂²	semidirect
56. #16864041	C₂²	semidirect
57. #16864040	C₂²	semidirect
58. #16864039	C₂²	semidirect
59. #16864038	C₂²	semidirect
60. #16864037	C₂²	semidirect
61. #16864036	C₂²	semidirect
62. #16864035	C₂²	semidirect
63. #16864034	C₂²	semidirect
64. #16864033	C₂²	semidirect
65. #16863972	C₂²	semidirect
66. #16863971	C₂²	semidirect
67. #16863970	C₂²	semidirect
68. #16863969	C₂²	semidirect
69. #16863968	C₂²	semidirect
70. #16863967	C₂²	semidirect
71. #16863966	C₂²	semidirect
72. #16863958	C₂²	semidirect
73. #16863957	C₂²	semidirect
74. #16863957	C₂²	semidirect
75. #16863956	C₂²	semidirect
76. #16863956	C₂²	semidirect
77. #16863955	C₂²	semidirect
78. #16863955	C₂²	semidirect
79. #16863954	C₂²	semidirect
80. C₄⋊Q₈×D₆₇	C₂²	semidirect
81. #124×D₆₇	C₂²	semidirect
82. #16863909	C₂²	semidirect
83. #16863908	C₂²	semidirect
84. #16863907	C₂²	semidirect
85. #16863906	C₂²	semidirect
86. #16863905	C₂²	semidirect
87. #16863904	C₂²	semidirect
88. #16863903	C₂²	semidirect
89. #16863902	C₂²	semidirect
90. C₂×#14524028	C₂²	semidirect
91. C₂×#14524027	C₂²	semidirect
92. C₂×#14524026	C₂²	semidirect
93. C₂×#14524025	C₂²	semidirect
94. C₂×#14524024	C₂²	semidirect
95. #123×D₆₇	C₂²	semidirect
96. #123×D₆₇	C₂²	semidirect
97. #123×D₆₇	C₂²	semidirect
98. #123×D₆₇	C₂²	semidirect
99. #123×D₆₇	C₂²	semidirect
100. #123×D₆₇	C₂²	semidirect
101. #123×D₆₇	C₂²	semidirect
102. C₂²⋊Q₈×D₆₇	C₂²	semidirect
103. C₂²⋊Q₈×D₆₇	C₂²	semidirect
104. #121×D₆₇	C₂²	semidirect
105. #121×D₆₇	C₂²	semidirect
106. #120×D₆₇	C₂²	semidirect
107. #120×D₆₇	C₂²	semidirect
108. #16863871	C₂²	semidirect
109. #16863870	C₂²	semidirect
110. #16863869	C₂²	semidirect
111. #16863868	C₂²	semidirect
112. C₄×D₄×D₆₇	C₂²	semidirect
113. C₄×D₄×D₆₇	C₂²	semidirect
114. #117×D₆₇	C₂²	semidirect
115. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
116. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
117. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
118. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
119. C₂²×#41×C₆₇	C₂²	semidirect
120. #547×C₆₇	C₂²	semidirect
121. #546×C₆₇	C₂²	semidirect
122. #536×C₆₇	C₂²	semidirect
123. #534×C₆₇	C₂²	semidirect
124. #525×C₆₇	C₂²	semidirect
125. C₂×#123×C₆₇	C₂²	semidirect
126. #518×C₆₇	C₂²	semidirect
137. C₂×#11761629	C₂³	semidirect
138. C₂×#11761629	C₂³	semidirect
143. C₂×#11761628	C₂³	semidirect
144. C₂×#11761628	C₂³	semidirect
145. C₂×#11761628	C₂³	semidirect
146. C₂×#11761628	C₂³	semidirect
151. C₂×#11761627	C₂³	semidirect
152. C₂×#11761627	C₂³	semidirect
153. C₂×#11761627	C₂³	semidirect
154. C₂×#11761627	C₂³	semidirect
159. C₂²×Dic₁₃₄	C₂³	semidirect
160. C₂²×Dic₁₃₄	C₂³	semidirect
164. C₂×Q₈×D₆₇	C₂³	semidirect
167. C₂²×D₂₆₈	C₂³	semidirect
168. C₂²×D₂₆₈	C₂³	semidirect
172. C₂²×C₂²⋊D₆₇	C₂³	semidirect
173. C₂²×C₂²⋊D₆₇	C₂³	semidirect
174. C₂²×C₂²⋊D₆₇	C₂³	semidirect
178. C₂×D₄×D₆₇	D₄	semidirect
188. C₂×D₄×D₆₇	C₂³	semidirect
189. C₂×D₄×D₆₇	C₂³	semidirect
190. C₂×D₄×D₆₇	C₂³	semidirect
191. C₂×D₄×D₆₇	C₂³	semidirect
192. C₂³×Dic₆₇	C₂³	semidirect
193. C₂³×Dic₆₇	C₂³	semidirect
204. C₂²×C₄×D₆₇	C₂³	semidirect
205. C₂²×C₄×D₆₇	C₂³	semidirect
206. C₂²×C₄×D₆₇	C₂³	semidirect
207. C₂²×C₄×D₆₇	C₂³	semidirect
208. C₂²×C₄×D₆₇	C₂³	semidirect
209. C₂²×C₄×D₆₇	C₂³	semidirect
210. #14524043	C₂³	semidirect
211. #14524042	C₂³	semidirect
212. #14524041	C₂³	semidirect
213. #14524041	C₂³	semidirect
214. #14524032	C₂³	semidirect
215. #14524031	C₂³	semidirect
216. #14524030	C₂³	semidirect
217. #14524029	C₂³	semidirect
218. #14524028	C₂³	semidirect
219. #14524028	C₂³	semidirect
220. #14524028	C₂³	semidirect
221. #14524028	C₂³	semidirect
222. #14524028	C₂³	semidirect
223. #14524027	C₂³	semidirect
224. #14524027	C₂³	semidirect
225. #14524027	C₂³	semidirect
226. #14524027	C₂³	semidirect
227. #14524026	C₂³	semidirect
228. #14524026	C₂³	semidirect
229. #14524026	C₂³	semidirect
230. #14524026	C₂³	semidirect
231. #14524025	C₂³	semidirect
232. #14524025	C₂³	semidirect
233. #14524025	C₂³	semidirect
234. #14524025	C₂³	semidirect
235. #14524025	C₂³	semidirect
236. #14524024	C₂³	semidirect
237. #14524024	C₂³	semidirect
238. #14524024	C₂³	semidirect
239. #14524024	C₂³	semidirect
240. #14524023	C₂³	semidirect
241. #14524023	C₂³	semidirect
242. #14524022	C₂³	semidirect
243. #14524022	C₂³	semidirect
244. #14524021	C₂³	semidirect
245. #14524021	C₂³	semidirect
246. #14524020	C₂³	semidirect
247. #14524020	C₂³	semidirect
248. #14524019	C₂³	semidirect
249. #14524019	C₂³	semidirect
250. #14524018	C₂³	semidirect
251. #14524018	C₂³	semidirect
252. #14524017	C₂³	semidirect
253. #14524017	C₂³	semidirect
254. #14524016	C₂³	semidirect
255. #14524016	C₂³	semidirect
256. #14524016	C₂³	semidirect
257. #14524015	C₂³	semidirect
258. #14524015	C₂³	semidirect
259. #14524015	C₂³	semidirect
260. #14524014	C₂³	semidirect
261. #14524014	C₂³	semidirect
262. #14524013	C₂³	semidirect
263. #14524013	C₂³	semidirect
264. #14524013	C₂³	semidirect
265. #14524013	C₂³	semidirect
266. #14524012	C₂³	semidirect
267. #14524012	C₂³	semidirect
268. #14524011	C₂³	semidirect
269. #14524011	C₂³	semidirect
270. #14524011	C₂³	semidirect
271. #14524011	C₂³	semidirect
272. C₄×D₂₆₈	C₂³	semidirect
273. C₄×D₂₆₈	C₂³	semidirect
274. D₄×Dic₆₇	C₂³	semidirect
275. D₄×Dic₆₇	C₂³	semidirect
276. #14524005	C₂³	semidirect
277. #14524005	C₂³	semidirect
278. C₄×C₂²⋊D₆₇	C₂³	semidirect
279. C₄×C₂²⋊D₆₇	C₂³	semidirect
280. C₄×C₂²⋊D₆₇	C₂³	semidirect
281. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
282. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
283. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
284. #14524002	C₂³	semidirect
285. #14524001	C₂³	semidirect
286. #14524000	C₂³	semidirect
287. #14523999	C₂³	semidirect
288. C₂×C₄⋊Dic₆₇	C₂³	semidirect
289. C₂×Dic₆₇⋊C₄	C₂³	semidirect
290. C₂×Dic₆₇⋊C₄	C₂³	semidirect
294. C₄⋊C₄×D₆₇	C₂³	semidirect
295. C₄⋊C₄×D₆₇	C₂³	semidirect
296. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
297. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
298. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
299. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
300. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
306. C₂²⋊C₄×D₆₇	C₂³	semidirect
307. C₂²⋊C₄×D₆₇	C₂³	semidirect
308. C₂²⋊C₄×D₆₇	C₂³	semidirect
309. C₂²⋊C₄×D₆₇	C₂³	semidirect
314. C₂×#41×C₆₇	C₂³	semidirect
315. C₂×#41×C₆₇	C₂³	semidirect
316. C₂²×Q₈×C₆₇	C₂³	semidirect
319. C₂²×D₄×C₆₇	C₂³	semidirect
320. C₂²×D₄×C₆₇	C₂³	semidirect
321. C₂³×C₄×C₆₇	C₂³	semidirect
322. C₂³×C₄×C₆₇	C₂³	semidirect
323. C₄⋊Q₈×C₆₇	C₂³	semidirect
324. #124×C₆₇	C₂³	semidirect
325. #123×C₆₇	C₂³	semidirect
326. #123×C₆₇	C₂³	semidirect
327. #123×C₆₇	C₂³	semidirect
328. #123×C₆₇	C₂³	semidirect
329. C₂²⋊Q₈×C₆₇	C₂³	semidirect
330. C₂²⋊Q₈×C₆₇	C₂³	semidirect
331. #121×C₆₇	C₂³	semidirect
332. #121×C₆₇	C₂³	semidirect
333. #120×C₆₇	C₂³	semidirect
334. #120×C₆₇	C₂³	semidirect
335. C₄×D₄×C₆₇	C₂³	semidirect
336. C₄×D₄×C₆₇	C₂³	semidirect
337. #117×C₆₇	C₂³	semidirect
338. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
339. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
340. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
384. C₂×D₂₆₈	C₂×D₄	semidirect
396. C₂×C₂²⋊D₆₇	C₂×D₄	semidirect
419. D₄×D₆₇	C₂×D₄	semidirect
495. C₂×D₄×C₆₇	C₂×D₄	semidirect
682. D₆₇	#3485	direct (N × H)
694. #3485	D₆₇	direct (N × H)
702. C₆₇	C₂×#3485	semidirect
709. C₂×H(5,𝔽₂)	C₂×D₆₇	semidirect
720. C₂²×#41	C₂×D₆₇	semidirect
739. #547	C₂×D₆₇	semidirect
751. #546	C₂×D₆₇	semidirect
759. #536	C₂×D₆₇	semidirect
768. #534	C₂×D₆₇	semidirect
779. #525	C₂×D₆₇	semidirect
792. C₂×#123	C₂×D₆₇	semidirect
803. #518	C₂×D₆₇	semidirect
845. C₂×#41	C₂²×D₆₇	semidirect
846. C₂×#41	C₂²×D₆₇	semidirect
853. C₂²×Q₈	C₂²×D₆₇	semidirect
883. C₂²×D₄	C₂²×D₆₇	semidirect
884. C₂²×D₄	C₂²×D₆₇	semidirect
903. C₂³×C₄	C₂²×D₆₇	semidirect
904. C₂³×C₄	C₂²×D₆₇	semidirect
909. C₄⋊Q₈	C₂²×D₆₇	semidirect
914. #124	C₂²×D₆₇	semidirect
937. #123	C₂²×D₆₇	semidirect
938. #123	C₂²×D₆₇	semidirect
939. #123	C₂²×D₆₇	semidirect
940. #123	C₂²×D₆₇	semidirect
951. C₂²⋊Q₈	C₂²×D₆₇	semidirect
952. C₂²⋊Q₈	C₂²×D₆₇	semidirect
965. #121	C₂²×D₆₇	semidirect
966. #121	C₂²×D₆₇	semidirect
977. #120	C₂²×D₆₇	semidirect
978. #120	C₂²×D₆₇	semidirect
991. C₄×D₄	C₂²×D₆₇	semidirect
992. C₄×D₄	C₂²×D₆₇	semidirect
997. #117	C₂²×D₆₇	semidirect
1006. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
1021. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1022. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1115. C₂×D₄	D₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×H(5,𝔽₂)×D₆₇	2
C₂²×#41×D₆₇	2
#22573854	2
#22573853	2
#22573852	2
#22573851	2
#22573850	2
#22573849	2
#22573848	2
#22573847	2
#22573846	2
#547×D₆₇	2
#546×D₆₇	2
#536×D₆₇	2
#534×D₆₇	2
#525×D₆₇	2
C₂×#123×D₆₇	2
#518×D₆₇	2
C₆₇×#3485	2
C₂×#3485	67

Subgroups — #3485×D67 #31763867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3485×D₆₇ #31763867