Subgroups — #22574499

Order 8576.

1032 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864147	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864143	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864142	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864113	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864107	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864102	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864100	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864099	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864097	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864097	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864082	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864061	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864056	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864054	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864044	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864020	C₂	1	1	yes	maximal, characteristic, complemented
17	#16864012	C₂	1	1	yes	maximal, characteristic, complemented
18	#16864012	C₂	1	1	yes	maximal, characteristic, complemented
19	#16864005	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863995	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863994	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863985	C₂	1	1	yes	maximal, characteristic, complemented
23	#16863985	C₂	1	1	yes	maximal, characteristic, complemented
24	#16863982	C₂	1	1	yes	maximal, characteristic, complemented
25	#16863980	C₂	1	1	yes	maximal, characteristic, complemented
26	#16863976	C₂	1	1	yes	maximal, characteristic, complemented
27	#16863971	C₂	1	1	yes	maximal, characteristic, complemented
28	#16863909	C₂	1	1	yes	maximal, characteristic, complemented
29	#16863904	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#563×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11761629	C₂²	1	1	yes	characteristic
33	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11761627	C₂²	1	1	yes	characteristic
35	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic
36	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
38	#14524042	C₂²	1	1	yes	characteristic, complemented
39	#14524042	C₂²	1	1	yes	characteristic, complemented
40	#14524042	C₂²	1	1	yes	characteristic, complemented
41	#14524041	C₂²	1	1	yes	characteristic, complemented
42	#14524038	C₂²	1	1	yes	characteristic
43	#14524038	C₂²	1	1	yes	characteristic
44	#14524038	C₂²	1	1	yes	characteristic
45	#14524038	C₂²	1	1	yes	characteristic, complemented
46	#14524038	C₂²	1	1	yes	characteristic, complemented
47	#14524038	C₂²	1	1	yes	characteristic, complemented
48	#14524038	C₂²	1	1	yes	characteristic, complemented
49	#14524037	C₂²	1	1	yes	characteristic
50	#14524036	C₂²	1	1	yes	characteristic
51	#14524036	C₂²	1	1	yes	characteristic
52	#14524034	C₂²	1	1	yes	characteristic, complemented
53	#14524034	C₂²	1	1	yes	characteristic, complemented
54	#14524034	C₂²	1	1	yes	characteristic, complemented
55	#14524033	C₂²	1	1	yes	characteristic, complemented
56	#14524033	C₂²	1	1	yes	characteristic, complemented
57	#14524033	C₂²	1	1	yes	characteristic, complemented
58	#14524033	C₂²	1	1	yes	characteristic, complemented
59	#14524032	C₂²	1	1	yes	characteristic
60	#14524032	C₂²	1	1	yes	characteristic, complemented
61	#14524031	C₂²	1	1	yes	characteristic
62	#14524031	C₂²	1	1	yes	characteristic
63	#14524029	C₂²	1	1	yes	characteristic
64	#14524029	C₂²	1	1	yes	characteristic
65	#14524029	C₂²	1	1	yes	characteristic
66	#14524029	C₂²	1	1	yes	characteristic
67	#14524029	C₂²	1	1	yes	characteristic, complemented
68	#14524029	C₂²	1	1	yes	characteristic, complemented
69	#14524028	C₂²	1	1	yes	characteristic
70	#14524028	C₂²	1	1	yes	characteristic
71	#14524028	C₂²	1	1	yes	characteristic
72	#14524028	C₂²	1	1	yes	characteristic
73	#14524028	C₂²	1	1	yes	characteristic
74	#14524028	C₂²	1	1	yes	characteristic, complemented
75	#14524028	C₂²	1	1	yes	characteristic, complemented
76	#14524028	C₂²	1	1	yes	characteristic, complemented
77	#14524028	C₂²	1	1	yes	characteristic, complemented
78	#14524027	C₂²	1	1	yes	characteristic
79	#14524027	C₂²	1	1	yes	characteristic, complemented
80	#14524027	C₂²	1	1	yes	characteristic, complemented
81	#14524026	C₂²	1	1	yes	characteristic
82	#14524025	C₂²	1	1	yes	characteristic
83	#14524025	C₂²	1	1	yes	characteristic
84	#14524025	C₂²	1	1	yes	characteristic
85	#14524023	C₂²	1	1	yes	characteristic
86	#14524023	C₂²	1	1	yes	characteristic
87	#14524023	C₂²	1	1	yes	characteristic, complemented
88	#14524023	C₂²	1	1	yes	characteristic, complemented
89	#14524022	C₂²	1	1	yes	characteristic
90	#14524021	C₂²	1	1	yes	characteristic
91	#14524021	C₂²	1	1	yes	characteristic
92	#14524021	C₂²	1	1	yes	characteristic
93	#14524021	C₂²	1	1	yes	characteristic
94	#14524021	C₂²	1	1	yes	characteristic
95	#14524021	C₂²	1	1	yes	characteristic
96	#14524021	C₂²	1	1	yes	characteristic, complemented
97	#14524021	C₂²	1	1	yes	characteristic, complemented
98	#14524021	C₂²	1	1	yes	characteristic, complemented
99	#14524021	C₂²	1	1	yes	characteristic, complemented
100	#14524021	C₂²	1	1	yes	characteristic, complemented
101	#14524021	C₂²	1	1	yes	characteristic, complemented
102	#14524020	C₂²	1	1	yes	characteristic
103	#14524020	C₂²	1	1	yes	characteristic
104	#14524020	C₂²	1	1	yes	characteristic, complemented
105	#14524020	C₂²	1	1	yes	characteristic, complemented
106	#14524019	C₂²	1	1	yes	characteristic
107	#14524019	C₂²	1	1	yes	characteristic
108	#14524019	C₂²	1	1	yes	characteristic
109	#14524019	C₂²	1	1	yes	characteristic, complemented
110	#14524019	C₂²	1	1	yes	characteristic, complemented
111	#14524019	C₂²	1	1	yes	characteristic, complemented
112	#14524018	C₂²	1	1	yes	characteristic
113	#14524018	C₂²	1	1	yes	characteristic
114	#14524018	C₂²	1	1	yes	characteristic
115	#14524018	C₂²	1	1	yes	characteristic
116	#14524018	C₂²	1	1	yes	characteristic
117	#14524018	C₂²	1	1	yes	characteristic, complemented
118	#14524017	C₂²	1	1	yes	characteristic
119	#14524017	C₂²	1	1	yes	characteristic
120	#14524016	C₂²	1	1	yes	characteristic
121	#14524016	C₂²	1	1	yes	characteristic
122	#14524016	C₂²	1	1	yes	characteristic
123	#14524016	C₂²	1	1	yes	characteristic
124	#14524016	C₂²	1	1	yes	characteristic
125	#14524016	C₂²	1	1	yes	characteristic
126	#14524016	C₂²	1	1	yes	characteristic
127	#14524016	C₂²	1	1	yes	characteristic, complemented
128	#14524016	C₂²	1	1	yes	characteristic, complemented
129	#14524015	C₂²	1	1	yes	characteristic
130	#14524014	C₂²	1	1	yes	characteristic
131	#14524013	C₂²	1	1	yes	characteristic
132	#14524013	C₂²	1	1	yes	characteristic
133	#14524013	C₂²	1	1	yes	characteristic
134	#14524011	C₂²	1	1	yes	characteristic
135	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
137	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
138	#14524008	C₂²	1	1	yes	characteristic, complemented
139	#14524008	C₂²	1	1	yes	characteristic, complemented
140	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
141	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
142	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
143	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
144	#14524005	C₂²	1	1	yes	characteristic
145	#14524005	C₂²	1	1	yes	characteristic
146	#14524005	C₂²	1	1	yes	characteristic
147	#14524005	C₂²	1	1	yes	characteristic
148	#14524005	C₂²	1	1	yes	characteristic
149	#14524005	C₂²	1	1	yes	characteristic
150	#14524005	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
152	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
153	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
154	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
155	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
156	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
157	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	#14524001	C₂²	1	1	yes	characteristic
160	#14524001	C₂²	1	1	yes	characteristic, complemented
161	#14524000	C₂²	1	1	yes	characteristic, complemented
162	#14524000	C₂²	1	1	yes	characteristic, complemented
163	#14523999	C₂²	1	1	yes	characteristic
164	C₂×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
166	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
167	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
168	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
169	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
173	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
174	#126×C₆₇	C₂²	1	1	yes	characteristic
175	#126×C₆₇	C₂²	1	1	yes	characteristic
176	#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
177	#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
178	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
179	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	#124×C₆₇	C₂²	1	1	yes	characteristic
181	#123×C₆₇	C₂²	1	1	yes	characteristic
182	#123×C₆₇	C₂²	1	1	yes	characteristic
183	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
184	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
185	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
186	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₆₇	C₂³	1	1	yes	characteristic
188	#11761629	—	4	2	no	—
189	#11761628	—	4	2	no	—
190	#11761627	—	4	2	no	—
191	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
192	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
193	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
194	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
195	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
196	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
197	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
198	Q₈×D₆₇	—	4	2	no	—
199	Q₈×D₆₇	—	4	2	no	—
200	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
201	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
202	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
203	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
204	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
205	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
206	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
207	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
208	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
217	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
218	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
219	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₆₇	—	4	2	no	—
221	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
248	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
268	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
269	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
274	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
304	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
305	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
306	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
307	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
308	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
309	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
310	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
311	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
312	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₄²×C₆₇	C₂³	1	1	yes	characteristic
347	C₄²×C₆₇	C₂³	1	1	yes	characteristic
348	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂²×D₆₇	—	2	2	no	—
351	C₂²×D₆₇	—	4	1	no	—
352	C₂²×D₆₇	—	4	1	no	—
353	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
354	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
356	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
358	Q₈×C₆₇	—	4	1	no	—
359	Q₈×C₆₇	—	4	1	no	—
360	Q₈×C₆₇	—	4	1	no	—
361	D₄×C₆₇	—	4	1	no	—
362	C₂×C₄×C₆₇	—	4	1	no	—
363	C₂×C₄×C₆₇	—	4	1	no	—
364	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²⋊D₆₇	—	2	2	no	—
378	C₂²⋊D₆₇	—	2	2	no	—
379	C₂²⋊D₆₇	—	4	1	no	—
380	C₂²⋊D₆₇	—	4	1	no	—
381	C₂²⋊D₆₇	—	4	1	no	—
382	C₂²⋊D₆₇	—	4	1	no	—
383	C₂²⋊D₆₇	—	4	1	no	—
384	C₂²⋊D₆₇	—	4	1	no	—
385	C₂×Dic₆₇	—	2	2	no	—
386	C₂×Dic₆₇	—	4	1	no	—
387	C₂×Dic₆₇	—	4	1	no	—
388	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
399	D₂₆₈	—	2	2	no	—
400	D₂₆₈	—	2	2	no	—
401	D₂₆₈	—	2	2	no	—
402	D₂₆₈	—	4	1	no	—
403	D₂₆₈	—	4	1	no	—
404	D₂₆₈	—	4	1	no	—
405	D₂₆₈	—	4	1	no	—
406	D₂₆₈	—	4	1	no	—
407	D₂₆₈	—	4	1	no	—
408	C₄×D₆₇	—	2	2	no	—
409	C₄×D₆₇	—	2	2	no	—
410	C₄×D₆₇	—	2	2	no	—
411	C₄×D₆₇	—	2	2	no	—
412	C₄×D₆₇	—	4	1	no	—
413	C₄×D₆₇	—	4	1	no	—
414	C₄×D₆₇	—	4	1	no	—
415	C₄×D₆₇	—	4	1	no	—
416	C₄×D₆₇	—	4	1	no	—
417	C₄×D₆₇	—	4	1	no	—
418	C₄×D₆₇	—	4	1	no	—
419	C₄×D₆₇	—	4	1	no	—
420	C₄×D₆₇	—	4	1	no	—
421	C₄×D₆₇	—	4	1	no	—
422	C₄×D₆₇	—	4	1	no	—
423	C₄×D₆₇	—	4	1	no	—
424	C₄×D₆₇	—	4	1	no	—
425	Dic₁₃₄	—	2	2	no	—
426	Dic₁₃₄	—	2	2	no	—
427	Dic₁₃₄	—	2	2	no	—
428	Dic₁₃₄	—	4	1	no	—
429	Dic₁₃₄	—	4	1	no	—
430	Dic₁₃₄	—	4	1	no	—
431	Dic₁₃₄	—	4	1	no	—
432	C₂²×C₆₇	—	2	1	no	—
433	C₂²×C₆₇	—	2	1	no	—
434	C₂²×C₆₇	—	2	1	no	—
435	C₂²×C₆₇	—	2	1	no	—
436	C₂²×C₆₇	—	2	1	no	—
437	C₂²×C₆₇	—	2	1	no	—
438	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
439	C₂×D₆₇	—	2	1	no	—
440	C₂×D₆₇	—	2	1	no	—
441	C₂×D₆₇	—	2	1	no	—
442	C₂×D₆₇	—	2	1	no	—
443	C₂×D₆₇	—	2	1	no	—
444	C₂×D₆₇	—	2	1	no	—
445	C₂×D₆₇	—	2	1	no	—
446	C₂×D₆₇	—	2	1	no	—
447	C₂×D₆₇	—	2	1	no	—
448	C₂×D₆₇	—	2	1	no	—
449	C₂×D₆₇	—	2	1	no	—
450	C₂×D₆₇	—	2	1	no	—
451	C₂×D₆₇	—	2	1	no	—
452	C₂×D₆₇	—	2	1	no	—
453	C₂×D₆₇	—	4	4	no	—
454	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
455	C₄×C₆₇	—	2	1	no	—
456	C₄×C₆₇	—	2	1	no	—
457	C₄×C₆₇	—	2	1	no	—
458	C₄×C₆₇	—	2	1	no	—
459	C₄×C₆₇	—	2	1	no	—
460	C₄×C₆₇	—	2	1	no	—
461	C₄×C₆₇	—	2	1	no	—
462	C₄×C₆₇	—	2	1	no	—
463	C₄×C₆₇	—	2	1	no	—
464	C₄×C₆₇	—	2	1	no	—
465	C₄×C₆₇	—	2	1	no	—
466	C₄×C₆₇	—	2	1	no	—
467	C₄×C₆₇	—	2	1	no	—
468	Dic₆₇	—	2	1	no	—
469	Dic₆₇	—	2	1	no	—
470	Dic₆₇	—	2	1	no	—
471	Dic₆₇	—	2	1	no	—
472	Dic₆₇	—	2	1	no	—
473	Dic₆₇	—	2	1	no	—
474	Dic₆₇	—	2	1	no	—
475	Dic₆₇	—	2	1	no	—
476	Dic₆₇	—	2	1	no	—
477	Dic₆₇	—	2	1	no	—
478	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₆₇	—	4	1	no	—
480	C₂×C₆₇	—	4	1	no	—
481	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂×C₆₇	#585	1	1	yes	characteristic
484	D₆₇	—	2	2	no	—
485	D₆₇	—	4	1	no	—
486	D₆₇	—	4	1	no	—
487	D₆₇	—	4	1	no	—
488	D₆₇	—	4	1	no	—
489	#3541	—	67	1	no	maximal, Sylow
490	C₆₇	#3541	1	1	yes	characteristic, complemented, Sylow
491	#563	—	67	1	no	—
492	#563	D₆₇	1	1	yes	characteristic, complemented
493	#562	—	67	1	no	—
494	#562	—	67	1	no	—
495	#556	—	67	1	no	—
496	#554	—	67	1	no	—
497	#554	—	67	1	no	—
498	#554	—	67	1	no	—
499	#553	—	67	1	no	—
500	#553	—	67	1	no	—
501	#553	—	67	1	no	—
502	#552	—	67	1	no	—
503	D₄×Q₈	—	67	1	no	—
504	#548	—	67	1	no	—
505	#548	—	67	1	no	—
506	#547	—	67	1	no	—
507	#542	—	67	1	no	—
508	#542	—	67	1	no	—
509	#542	—	67	1	no	—
510	#541	—	67	1	no	—
511	#539	—	67	1	no	—
512	#539	—	67	1	no	—
513	#538	—	67	1	no	—
514	#538	—	67	1	no	—
515	#538	—	67	1	no	—
516	#538	—	67	1	no	—
517	#537	—	67	1	no	—
518	#536	—	67	1	no	—
519	#525	—	67	1	no	—
520	#525	—	67	1	no	—
521	C₂×C₂²⋊Q₈	—	67	1	no	—
522	C₂×#41	—	67	1	no	—
523	C₂×#41	—	67	1	no	—
524	C₂×#41	—	67	1	no	—
525	C₂²×Q₈	—	67	1	no	—
526	C₂²×Q₈	—	67	1	no	—
527	C₂³×C₄	—	67	1	no	—
528	C₄⋊Q₈	—	67	1	no	—
529	C₄⋊Q₈	—	67	1	no	—
530	C₄⋊Q₈	—	67	1	no	—
531	C₄⋊Q₈	—	67	1	no	—
532	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
533	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
534	#126	—	67	1	no	—
535	#126	—	67	1	no	—
536	#126	—	67	1	no	—
537	#126	—	67	1	no	—
538	#126	—	67	1	no	—
539	#126	—	67	1	no	—
540	#126	—	67	1	no	—
541	#126	—	67	1	no	—
542	#126	—	67	1	no	—
543	#126	—	67	1	no	—
544	#126	C₂×D₆₇	1	1	yes	characteristic
545	#126	C₂×D₆₇	1	1	yes	characteristic
546	#126	C₂×D₆₇	1	1	yes	characteristic, complemented
547	#126	C₂×D₆₇	1	1	yes	characteristic, complemented
548	#125	—	67	1	no	—
549	#125	—	67	1	no	—
550	#125	—	67	1	no	—
551	#125	—	67	1	no	—
552	#125	—	67	1	no	—
553	#125	—	67	1	no	—
554	#125	—	67	1	no	—
555	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
556	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
557	#124	—	67	1	no	—
558	#124	—	67	1	no	—
559	#124	—	67	1	no	—
560	#124	—	67	1	no	—
561	#124	—	67	1	no	—
562	#124	—	67	1	no	—
563	#124	—	67	1	no	—
564	#124	—	67	1	no	—
565	#124	—	67	1	no	—
566	#124	—	67	1	no	—
567	#124	C₂×D₆₇	1	1	yes	characteristic
568	#123	—	67	1	no	—
569	#123	—	67	1	no	—
570	#123	—	67	1	no	—
571	#123	—	67	1	no	—
572	#123	—	67	1	no	—
573	#123	—	67	1	no	—
574	#123	—	67	1	no	—
575	#123	—	67	1	no	—
576	#123	—	67	1	no	—
577	#123	—	67	1	no	—
578	#123	—	67	1	no	—
579	#123	—	67	1	no	—
580	#123	—	67	1	no	—
581	#123	—	67	1	no	—
582	#123	—	67	1	no	—
583	#123	—	67	1	no	—
584	#123	C₂×D₆₇	1	1	yes	characteristic
585	#123	C₂×D₆₇	1	1	yes	characteristic
586	C₂²⋊Q₈	—	67	1	no	—
587	C₂²⋊Q₈	—	67	1	no	—
588	C₂²⋊Q₈	—	67	1	no	—
589	C₂²⋊Q₈	—	67	1	no	—
590	C₂²⋊Q₈	—	67	1	no	—
591	C₂²⋊Q₈	—	67	1	no	—
592	C₂²⋊Q₈	—	67	1	no	—
593	C₂²⋊Q₈	—	67	1	no	—
594	C₂²⋊Q₈	—	67	1	no	—
595	C₂²⋊Q₈	—	67	1	no	—
596	C₂²⋊Q₈	—	67	1	no	—
597	C₂²⋊Q₈	—	67	1	no	—
598	C₂²⋊Q₈	—	67	1	no	—
599	C₂²⋊Q₈	—	67	1	no	—
600	C₂²⋊Q₈	—	67	1	no	—
601	C₂²⋊Q₈	—	67	1	no	—
602	C₂²⋊Q₈	—	67	1	no	—
603	C₂²⋊Q₈	—	67	1	no	—
604	C₂²⋊Q₈	—	67	1	no	—
605	C₂²⋊Q₈	—	67	1	no	—
606	C₂²⋊Q₈	—	67	1	no	—
607	C₂²⋊Q₈	—	67	1	no	—
608	C₂²⋊Q₈	—	67	1	no	—
609	C₂²⋊Q₈	—	67	1	no	—
610	C₂²⋊Q₈	—	67	1	no	—
611	C₂²⋊Q₈	—	67	1	no	—
612	C₂²⋊Q₈	—	67	1	no	—
613	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
615	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
616	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
617	#121	—	67	1	no	—
618	#121	—	67	1	no	—
619	#121	—	67	1	no	—
620	#121	—	67	1	no	—
621	#121	—	67	1	no	—
622	#121	—	67	1	no	—
623	#121	—	67	1	no	—
624	#121	—	67	1	no	—
625	#121	—	67	1	no	—
626	#121	—	67	1	no	—
627	#121	—	67	1	no	—
628	#121	—	67	1	no	—
629	#121	—	67	1	no	—
630	#121	—	67	1	no	—
631	#121	—	67	1	no	—
632	#121	—	67	1	no	—
633	#121	—	67	1	no	—
634	#121	—	67	1	no	—
635	#121	—	67	1	no	—
636	#120	—	67	1	no	—
637	#120	—	67	1	no	—
638	#120	—	67	1	no	—
639	#120	—	67	1	no	—
640	C₄×Q₈	—	67	1	no	—
641	C₄×Q₈	—	67	1	no	—
642	C₄×Q₈	—	67	1	no	—
643	C₄×Q₈	—	67	1	no	—
644	C₄×Q₈	—	67	1	no	—
645	C₄×D₄	—	67	1	no	—
646	C₄×D₄	—	67	1	no	—
647	C₄×D₄	—	67	1	no	—
648	C₄×D₄	—	67	1	no	—
649	C₄×D₄	—	67	1	no	—
650	C₄×D₄	—	67	1	no	—
651	C₄×D₄	—	67	1	no	—
652	C₄×D₄	—	67	1	no	—
653	C₄×D₄	—	67	1	no	—
654	C₄×D₄	—	67	1	no	—
655	C₄×D₄	—	67	1	no	—
656	C₄×D₄	—	67	1	no	—
657	C₄×D₄	—	67	1	no	—
658	C₄×D₄	—	67	1	no	—
659	C₄×D₄	—	67	1	no	—
660	C₄×D₄	—	67	1	no	—
661	C₄×D₄	—	67	1	no	—
662	C₄×D₄	—	67	1	no	—
663	C₄×D₄	—	67	1	no	—
664	#117	—	67	1	no	—
665	#117	—	67	1	no	—
666	#117	—	67	1	no	—
667	#117	—	67	1	no	—
668	#117	—	67	1	no	—
669	C₂×C₄⋊C₄	—	67	1	no	—
670	C₂×C₄⋊C₄	—	67	1	no	—
671	C₂×C₄⋊C₄	—	67	1	no	—
672	C₂×C₄⋊C₄	—	67	1	no	—
673	C₂×C₄⋊C₄	—	67	1	no	—
674	C₂×C₄⋊C₄	—	67	1	no	—
675	C₂×C₂²⋊C₄	—	67	1	no	—
676	C₂×C₂²⋊C₄	—	67	1	no	—
677	C₂⁴	—	67	1	no	—
678	#41	—	268	2	no	—
679	#41	—	268	2	no	—
680	#41	—	268	2	no	—
681	C₂×Q₈	—	268	2	no	—
682	C₂×Q₈	—	268	2	no	—
683	C₂×Q₈	—	67	1	no	—
684	C₂×Q₈	—	67	1	no	—
685	C₂×Q₈	—	67	1	no	—
686	C₂×Q₈	—	67	1	no	—
687	C₂×Q₈	—	67	1	no	—
688	C₂×Q₈	—	67	1	no	—
689	C₂×Q₈	—	67	1	no	—
690	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
691	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
692	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
693	C₂×D₄	—	67	1	no	—
694	C₂×D₄	—	67	1	no	—
695	C₂×D₄	—	67	1	no	—
696	C₂×D₄	—	67	1	no	—
697	C₂×D₄	—	67	1	no	—
698	C₂×D₄	—	67	1	no	—
699	C₂×D₄	—	67	1	no	—
700	C₂×D₄	—	67	1	no	—
701	C₂×D₄	—	67	1	no	—
702	C₂×D₄	—	67	1	no	—
703	C₂×D₄	—	67	1	no	—
704	C₂×D₄	—	67	1	no	—
705	C₂×D₄	—	67	1	no	—
706	C₂×D₄	—	67	1	no	—
707	C₂×D₄	—	67	1	no	—
708	C₂×D₄	—	67	1	no	—
709	C₂×D₄	—	67	1	no	—
710	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
711	C₂²×C₄	—	268	2	no	—
712	C₂²×C₄	—	67	1	no	—
713	C₂²×C₄	—	67	1	no	—
714	C₂²×C₄	—	67	1	no	—
715	C₂²×C₄	—	67	1	no	—
716	C₂²×C₄	—	67	1	no	—
717	C₂²×C₄	—	67	1	no	—
718	C₂²×C₄	—	67	1	no	—
719	C₂²×C₄	—	67	1	no	—
720	C₂²×C₄	—	67	1	no	—
721	C₂²×C₄	—	67	1	no	—
722	C₂²×C₄	—	67	1	no	—
723	C₂²×C₄	—	67	1	no	—
724	C₂²×C₄	—	67	1	no	—
725	C₂²×C₄	—	67	1	no	—
726	C₂²×C₄	—	67	1	no	—
727	C₂²×C₄	—	67	1	no	—
728	C₂²×C₄	—	67	1	no	—
729	C₂²×C₄	—	67	1	no	—
730	C₂²×C₄	—	67	1	no	—
731	C₂²×C₄	—	67	1	no	—
732	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
733	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
734	C₄⋊C₄	—	67	1	no	—
735	C₄⋊C₄	—	67	1	no	—
736	C₄⋊C₄	—	67	1	no	—
737	C₄⋊C₄	—	67	1	no	—
738	C₄⋊C₄	—	67	1	no	—
739	C₄⋊C₄	—	67	1	no	—
740	C₄⋊C₄	—	67	1	no	—
741	C₄⋊C₄	—	67	1	no	—
742	C₄⋊C₄	—	67	1	no	—
743	C₄⋊C₄	—	67	1	no	—
744	C₄⋊C₄	—	67	1	no	—
745	C₄⋊C₄	—	67	1	no	—
746	C₄⋊C₄	—	67	1	no	—
747	C₄⋊C₄	—	67	1	no	—
748	C₄⋊C₄	—	67	1	no	—
749	C₄⋊C₄	—	67	1	no	—
750	C₄⋊C₄	—	67	1	no	—
751	C₄⋊C₄	—	67	1	no	—
752	C₄⋊C₄	—	67	1	no	—
753	C₄⋊C₄	—	67	1	no	—
754	C₄⋊C₄	—	67	1	no	—
755	C₄⋊C₄	—	67	1	no	—
756	C₄⋊C₄	—	67	1	no	—
757	C₄⋊C₄	—	67	1	no	—
758	C₄⋊C₄	—	67	1	no	—
759	C₄⋊C₄	—	67	1	no	—
760	C₄⋊C₄	—	67	1	no	—
761	C₄⋊C₄	—	67	1	no	—
762	C₄⋊C₄	—	67	1	no	—
763	C₄⋊C₄	—	67	1	no	—
764	C₄⋊C₄	—	67	1	no	—
765	C₄⋊C₄	—	67	1	no	—
766	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
782	C₂²⋊C₄	—	67	1	no	—
783	C₂²⋊C₄	—	67	1	no	—
784	C₂²⋊C₄	—	67	1	no	—
785	C₂²⋊C₄	—	67	1	no	—
786	C₂²⋊C₄	—	67	1	no	—
787	C₂²⋊C₄	—	67	1	no	—
788	C₂²⋊C₄	—	67	1	no	—
789	C₂²⋊C₄	—	67	1	no	—
790	C₂²⋊C₄	—	67	1	no	—
791	C₂²⋊C₄	—	67	1	no	—
792	C₂²⋊C₄	—	67	1	no	—
793	C₂²⋊C₄	—	67	1	no	—
794	C₂²⋊C₄	—	67	1	no	—
795	C₂²⋊C₄	—	67	1	no	—
796	C₂²⋊C₄	—	67	1	no	—
797	C₂²⋊C₄	—	67	1	no	—
798	C₂²⋊C₄	—	67	1	no	—
799	C₂²⋊C₄	—	67	1	no	—
800	C₂²⋊C₄	—	67	1	no	—
801	C₂²⋊C₄	—	67	1	no	—
802	C₂²⋊C₄	—	67	1	no	—
803	C₂²⋊C₄	—	67	1	no	—
804	C₂²⋊C₄	—	67	1	no	—
805	C₂²⋊C₄	—	67	1	no	—
806	C₂²⋊C₄	—	67	1	no	—
807	C₂²⋊C₄	—	67	1	no	—
808	C₂²⋊C₄	—	67	1	no	—
809	C₂²⋊C₄	—	67	1	no	—
810	C₂²⋊C₄	—	67	1	no	—
811	C₂²⋊C₄	—	67	1	no	—
812	C₂²⋊C₄	—	67	1	no	—
813	C₂²⋊C₄	—	67	1	no	—
814	C₂²⋊C₄	—	67	1	no	—
815	C₂²⋊C₄	—	67	1	no	—
816	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
826	C₄²	—	67	1	no	—
827	C₄²	—	67	1	no	—
828	C₄²	—	67	1	no	—
829	C₄²	—	67	1	no	—
830	C₄²	—	67	1	no	—
831	C₄²	—	67	1	no	—
832	C₄²	—	67	1	no	—
833	C₄²	—	67	1	no	—
834	C₄²	—	67	1	no	—
835	C₄²	C₂²×D₆₇	1	1	yes	characteristic
836	C₄²	C₂²×D₆₇	1	1	yes	characteristic
837	C₄²	C₂²×D₆₇	1	1	yes	characteristic
838	C₂³	—	268	1	no	—
839	C₂³	—	268	1	no	—
840	C₂³	—	67	1	no	—
841	C₂³	—	67	1	no	—
842	C₂³	—	67	1	no	—
843	C₂³	—	67	1	no	—
844	C₂³	—	67	1	no	—
845	C₂³	—	134	2	no	—
846	C₂³	C₂³×D₆₇	1	1	yes	characteristic
847	C₂³	C₂³×D₆₇	1	1	yes	characteristic
848	Q₈	—	4	1	no	—
849	Q₈	—	4	1	no	—
850	Q₈	—	4	1	no	—
851	Q₈	—	268	1	no	—
852	Q₈	—	268	1	no	—
853	Q₈	—	268	1	no	—
854	Q₈	—	268	1	no	—
855	Q₈	—	134	2	no	—
856	Q₈	—	134	2	no	—
857	Q₈	—	134	2	no	—
858	D₄	—	4	1	no	—
859	D₄	—	268	1	no	—
860	D₄	—	268	1	no	—
861	D₄	—	268	1	no	—
862	D₄	—	268	1	no	—
863	D₄	—	268	1	no	—
864	D₄	—	268	1	no	—
865	D₄	—	268	1	no	—
866	D₄	—	268	1	no	—
867	D₄	—	268	1	no	—
868	D₄	—	268	1	no	—
869	D₄	—	268	1	no	—
870	D₄	—	268	1	no	—
871	D₄	—	134	2	no	—
872	D₄	—	134	2	no	—
873	D₄	—	134	2	no	—
874	D₄	—	134	2	no	—
875	D₄	—	134	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	268	1	no	—
879	C₂×C₄	—	268	1	no	—
880	C₂×C₄	—	268	1	no	—
881	C₂×C₄	—	268	1	no	—
882	C₂×C₄	—	268	1	no	—
883	C₂×C₄	—	268	1	no	—
884	C₂×C₄	—	268	1	no	—
885	C₂×C₄	—	268	1	no	—
886	C₂×C₄	—	268	1	no	—
887	C₂×C₄	—	268	1	no	—
888	C₂×C₄	—	268	1	no	—
889	C₂×C₄	—	268	1	no	—
890	C₂×C₄	—	268	1	no	—
891	C₂×C₄	—	268	1	no	—
892	C₂×C₄	—	268	1	no	—
893	C₂×C₄	—	67	1	no	—
894	C₂×C₄	—	67	1	no	—
895	C₂×C₄	—	67	1	no	—
896	C₂×C₄	—	67	1	no	—
897	C₂×C₄	—	67	1	no	—
898	C₂×C₄	—	67	1	no	—
899	C₂×C₄	—	67	1	no	—
900	C₂×C₄	—	67	1	no	—
901	C₂×C₄	—	67	1	no	—
902	C₂×C₄	—	67	1	no	—
903	C₂×C₄	—	67	1	no	—
904	C₂×C₄	—	134	2	no	—
905	C₂×C₄	—	134	2	no	—
906	C₂×C₄	—	134	2	no	—
907	C₂×C₄	—	134	2	no	—
908	C₂×C₄	—	134	2	no	—
909	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	268	4	no	—
929	C₂²	—	67	2	no	—
930	C₂²	—	134	1	no	—
931	C₂²	—	134	1	no	—
932	C₂²	—	134	1	no	—
933	C₂²	—	134	1	no	—
934	C₂²	—	134	1	no	—
935	C₂²	—	134	1	no	—
936	C₂²	—	134	1	no	—
937	C₂²	—	134	1	no	—
938	C₂²	—	134	1	no	—
939	C₂²	—	134	1	no	—
940	C₂²	—	134	1	no	—
941	C₂²	—	134	1	no	—
942	C₂²	—	134	1	no	—
943	C₂²	—	134	1	no	—
944	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	67	2	no	—
959	C₄	—	134	1	no	—
960	C₄	—	134	1	no	—
961	C₄	—	134	1	no	—
962	C₄	—	134	1	no	—
963	C₄	—	134	1	no	—
964	C₄	—	134	1	no	—
965	C₄	—	134	1	no	—
966	C₄	—	134	1	no	—
967	C₄	—	134	1	no	—
968	C₄	—	134	1	no	—
969	C₂	—	4	1	no	—
970	C₂	—	4	1	no	—
971	C₂	—	268	1	no	—
972	C₂	—	268	1	no	—
973	C₂	—	268	1	no	—
974	C₂	—	268	1	no	—
975	C₂	—	134	2	no	—
976	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
977	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
978	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#563×C₆₇	C₂
hypercenter	#563	D₆₇
hypocenter	C₆₇	#3541
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #16864147	C₂	semidirect
2. #16864143	C₂	semidirect
3. #16864142	C₂	semidirect
4. #16864113	C₂	semidirect
5. #16864107	C₂	semidirect
6. #16864102	C₂	semidirect
7. #16864100	C₂	semidirect
8. #16864099	C₂	semidirect
9. #16864097	C₂	semidirect
10. #16864097	C₂	semidirect
11. #16864082	C₂	semidirect
12. #16864061	C₂	semidirect
13. #16864056	C₂	semidirect
14. #16864054	C₂	semidirect
15. #16864044	C₂	semidirect
16. #16864020	C₂	semidirect
17. #16864012	C₂	semidirect
18. #16864012	C₂	semidirect
19. #16864005	C₂	semidirect
20. #16863995	C₂	semidirect
21. #16863994	C₂	semidirect
22. #16863985	C₂	semidirect
23. #16863985	C₂	semidirect
24. #16863982	C₂	semidirect
25. #16863980	C₂	semidirect
26. #16863976	C₂	semidirect
27. #16863971	C₂	semidirect
28. #16863909	C₂	semidirect
29. #16863904	C₂	semidirect
30. C₂²⋊Q₈×D₆₇	C₂	semidirect
31. #563×C₆₇	C₂	semidirect
33. C₂×#11761628	C₂²	semidirect
36. C₂×Q₈×D₆₇	C₂²	semidirect
38. #14524042	C₂²	semidirect
39. #14524042	C₂²	semidirect
40. #14524042	C₂²	semidirect
41. #14524041	C₂²	semidirect
45. #14524038	C₂²	semidirect
46. #14524038	C₂²	semidirect
47. #14524038	C₂²	semidirect
48. #14524038	C₂²	semidirect
52. #14524034	C₂²	semidirect
53. #14524034	C₂²	semidirect
54. #14524034	C₂²	semidirect
55. #14524033	C₂²	semidirect
56. #14524033	C₂²	semidirect
57. #14524033	C₂²	semidirect
58. #14524033	C₂²	semidirect
60. #14524032	C₂²	semidirect
67. #14524029	C₂²	semidirect
68. #14524029	C₂²	semidirect
74. #14524028	C₂²	semidirect
75. #14524028	C₂²	semidirect
76. #14524028	C₂²	semidirect
77. #14524028	C₂²	semidirect
79. #14524027	C₂²	semidirect
80. #14524027	C₂²	semidirect
87. #14524023	C₂²	semidirect
88. #14524023	C₂²	semidirect
96. #14524021	C₂²	semidirect
97. #14524021	C₂²	semidirect
98. #14524021	C₂²	semidirect
99. #14524021	C₂²	semidirect
100. #14524021	C₂²	semidirect
101. #14524021	C₂²	semidirect
104. #14524020	C₂²	semidirect
105. #14524020	C₂²	semidirect
109. #14524019	C₂²	semidirect
110. #14524019	C₂²	semidirect
111. #14524019	C₂²	semidirect
117. #14524018	C₂²	semidirect
127. #14524016	C₂²	semidirect
128. #14524016	C₂²	semidirect
135. C₄×Dic₁₃₄	C₂²	semidirect
136. C₄×Dic₁₃₄	C₂²	semidirect
137. C₄×Dic₁₃₄	C₂²	semidirect
138. #14524008	C₂²	semidirect
139. #14524008	C₂²	semidirect
143. C₄×D₂₆₈	C₂²	semidirect
157. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
158. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
160. #14524001	C₂²	semidirect
161. #14524000	C₂²	semidirect
162. #14524000	C₂²	semidirect
164. C₂×Dic₆₇⋊C₄	C₂²	semidirect
168. C₄⋊C₄×D₆₇	C₂²	semidirect
169. C₄⋊C₄×D₆₇	C₂²	semidirect
172. C₄⋊Q₈×C₆₇	C₂²	semidirect
173. C₄⋊Q₈×C₆₇	C₂²	semidirect
176. #126×C₆₇	C₂²	semidirect
177. #126×C₆₇	C₂²	semidirect
178. #125×C₆₇	C₂²	semidirect
179. #125×C₆₇	C₂²	semidirect
185. C₂²⋊Q₈×C₆₇	C₂²	semidirect
186. C₂²⋊Q₈×C₆₇	C₂²	semidirect
490. C₆₇	#3541	semidirect
492. #563	D₆₇	semidirect
532. C₄⋊Q₈	C₂×D₆₇	semidirect
533. C₄⋊Q₈	C₂×D₆₇	semidirect
546. #126	C₂×D₆₇	semidirect
547. #126	C₂×D₆₇	semidirect
555. #125	C₂×D₆₇	semidirect
556. #125	C₂×D₆₇	semidirect
615. C₂²⋊Q₈	C₂×D₆₇	semidirect
616. C₂²⋊Q₈	C₂×D₆₇	semidirect