Subgroups — #22574516

Order 8576.

1160 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864144	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864141	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864136	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864134	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864109	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864095	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864078	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864074	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864070	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864064	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864044	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864042	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864038	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864035	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864035	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864030	C₂	1	1	yes	maximal, characteristic, complemented
17	#16864014	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863998	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863996	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863979	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863978	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863973	C₂	1	1	yes	maximal, characteristic, complemented
23	#16863962	C₂	1	1	yes	maximal, characteristic, complemented
24	#16863959	C₂	1	1	yes	maximal, characteristic, complemented
25	#16863959	C₂	1	1	yes	maximal, characteristic, complemented
26	#16863957	C₂	1	1	yes	maximal, characteristic, complemented
27	#16863954	C₂	1	1	yes	maximal, characteristic, complemented
28	#16863905	C₂	1	1	yes	maximal, characteristic, complemented
29	#16863904	C₂	1	1	yes	maximal, characteristic, complemented
30	#121×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#540×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11761627	C₂²	1	1	yes	characteristic, complemented
35	C₂×#11761627	C₂²	1	1	yes	characteristic, complemented
36	C₂×#11761627	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
40	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
44	#14524042	C₂²	1	1	yes	characteristic, complemented
45	#14524039	C₂²	1	1	yes	characteristic, complemented
46	#14524039	C₂²	1	1	yes	characteristic, complemented
47	#14524039	C₂²	1	1	yes	characteristic, complemented
48	#14524039	C₂²	1	1	yes	characteristic, complemented
49	#14524038	C₂²	1	1	yes	characteristic, complemented
50	#14524038	C₂²	1	1	yes	characteristic, complemented
51	#14524038	C₂²	1	1	yes	characteristic, complemented
52	#14524037	C₂²	1	1	yes	characteristic, complemented
53	#14524036	C₂²	1	1	yes	characteristic, complemented
54	#14524036	C₂²	1	1	yes	characteristic, complemented
55	#14524033	C₂²	1	1	yes	characteristic, complemented
56	#14524033	C₂²	1	1	yes	characteristic, complemented
57	#14524031	C₂²	1	1	yes	characteristic, complemented
58	#14524031	C₂²	1	1	yes	characteristic, complemented
59	#14524031	C₂²	1	1	yes	characteristic, complemented
60	#14524030	C₂²	1	1	yes	characteristic, complemented
61	#14524030	C₂²	1	1	yes	characteristic, complemented
62	#14524029	C₂²	1	1	yes	characteristic, complemented
63	#14524029	C₂²	1	1	yes	characteristic, complemented
64	#14524029	C₂²	1	1	yes	characteristic, complemented
65	#14524029	C₂²	1	1	yes	characteristic, complemented
66	#14524028	C₂²	1	1	yes	characteristic
67	#14524028	C₂²	1	1	yes	characteristic
68	#14524028	C₂²	1	1	yes	characteristic, complemented
69	#14524028	C₂²	1	1	yes	characteristic, complemented
70	#14524028	C₂²	1	1	yes	characteristic, complemented
71	#14524028	C₂²	1	1	yes	characteristic, complemented
72	#14524028	C₂²	1	1	yes	characteristic, complemented
73	#14524028	C₂²	1	1	yes	characteristic, complemented
74	#14524027	C₂²	1	1	yes	characteristic, complemented
75	#14524026	C₂²	1	1	yes	characteristic, complemented
76	#14524026	C₂²	1	1	yes	characteristic, complemented
77	#14524026	C₂²	1	1	yes	characteristic, complemented
78	#14524025	C₂²	1	1	yes	characteristic, complemented
79	#14524025	C₂²	1	1	yes	characteristic, complemented
80	#14524025	C₂²	1	1	yes	characteristic, complemented
81	#14524025	C₂²	1	1	yes	characteristic, complemented
82	#14524024	C₂²	1	1	yes	characteristic, complemented
83	#14524024	C₂²	1	1	yes	characteristic, complemented
84	#14524022	C₂²	1	1	yes	characteristic, complemented
85	#14524021	C₂²	1	1	yes	characteristic, complemented
86	#14524021	C₂²	1	1	yes	characteristic, complemented
87	#14524021	C₂²	1	1	yes	characteristic, complemented
88	#14524021	C₂²	1	1	yes	characteristic, complemented
89	#14524021	C₂²	1	1	yes	characteristic, complemented
90	#14524021	C₂²	1	1	yes	characteristic, complemented
91	#14524021	C₂²	1	1	yes	characteristic, complemented
92	#14524020	C₂²	1	1	yes	characteristic, complemented
93	#14524020	C₂²	1	1	yes	characteristic, complemented
94	#14524020	C₂²	1	1	yes	characteristic, complemented
95	#14524018	C₂²	1	1	yes	characteristic, complemented
96	#14524018	C₂²	1	1	yes	characteristic, complemented
97	#14524018	C₂²	1	1	yes	characteristic, complemented
98	#14524018	C₂²	1	1	yes	characteristic, complemented
99	#14524018	C₂²	1	1	yes	characteristic, complemented
100	#14524017	C₂²	1	1	yes	characteristic, complemented
101	#14524017	C₂²	1	1	yes	characteristic, complemented
102	#14524017	C₂²	1	1	yes	characteristic, complemented
103	#14524017	C₂²	1	1	yes	characteristic, complemented
104	#14524016	C₂²	1	1	yes	characteristic
105	#14524016	C₂²	1	1	yes	characteristic
106	#14524016	C₂²	1	1	yes	characteristic
107	#14524016	C₂²	1	1	yes	characteristic, complemented
108	#14524016	C₂²	1	1	yes	characteristic, complemented
109	#14524016	C₂²	1	1	yes	characteristic, complemented
110	#14524016	C₂²	1	1	yes	characteristic, complemented
111	#14524016	C₂²	1	1	yes	characteristic, complemented
112	#14524016	C₂²	1	1	yes	characteristic, complemented
113	#14524016	C₂²	1	1	yes	characteristic, complemented
114	#14524015	C₂²	1	1	yes	characteristic
115	#14524015	C₂²	1	1	yes	characteristic, complemented
116	#14524015	C₂²	1	1	yes	characteristic, complemented
117	#14524015	C₂²	1	1	yes	characteristic, complemented
118	#14524015	C₂²	1	1	yes	characteristic, complemented
119	#14524015	C₂²	1	1	yes	characteristic, complemented
120	#14524015	C₂²	1	1	yes	characteristic, complemented
121	#14524015	C₂²	1	1	yes	characteristic, complemented
122	#14524015	C₂²	1	1	yes	characteristic, complemented
123	#14524015	C₂²	1	1	yes	characteristic, complemented
124	#14524015	C₂²	1	1	yes	characteristic, complemented
125	#14524015	C₂²	1	1	yes	characteristic, complemented
126	#14524014	C₂²	1	1	yes	characteristic, complemented
127	#14524014	C₂²	1	1	yes	characteristic, complemented
128	#14524013	C₂²	1	1	yes	characteristic
129	#14524013	C₂²	1	1	yes	characteristic
130	#14524013	C₂²	1	1	yes	characteristic, complemented
131	#14524013	C₂²	1	1	yes	characteristic, complemented
132	#14524013	C₂²	1	1	yes	characteristic, complemented
133	#14524013	C₂²	1	1	yes	characteristic, complemented
134	#14524011	C₂²	1	1	yes	characteristic
135	#14524011	C₂²	1	1	yes	characteristic, complemented
136	#14524011	C₂²	1	1	yes	characteristic, complemented
137	#14524011	C₂²	1	1	yes	characteristic, complemented
138	#14524011	C₂²	1	1	yes	characteristic, complemented
139	#14524011	C₂²	1	1	yes	characteristic, complemented
140	#14524011	C₂²	1	1	yes	characteristic, complemented
141	#14524011	C₂²	1	1	yes	characteristic, complemented
142	#14524011	C₂²	1	1	yes	characteristic, complemented
143	#14524011	C₂²	1	1	yes	characteristic, complemented
144	#14524008	C₂²	1	1	yes	characteristic, complemented
145	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
146	#14524005	C₂²	1	1	yes	characteristic
147	#14524005	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
152	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	#14524001	C₂²	1	1	yes	characteristic, complemented
159	#14524001	C₂²	1	1	yes	characteristic, complemented
160	#14524000	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, complemented
164	C₂×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
166	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
172	#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
173	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
174	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
175	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
176	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
177	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
178	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
179	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
181	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
182	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
183	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
186	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₆₇	C₂³	1	1	yes	characteristic
188	C₂³×D₆₇	C₂³	1	1	yes	characteristic
189	C₂³×D₆₇	C₂³	1	1	yes	characteristic
190	C₂³×D₆₇	C₂³	1	1	yes	characteristic
191	C₂³×D₆₇	C₂³	1	1	yes	characteristic
192	#11761628	—	4	2	no	—
193	#11761628	—	4	2	no	—
194	#11761627	—	4	2	no	—
195	#11761627	—	4	2	no	—
196	#11761627	—	4	2	no	—
197	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
198	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
199	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
200	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
201	C₂×D₂₆₈	—	4	2	no	—
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×D₂₆₈	C₂³	1	1	yes	characteristic
210	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
211	C₂×D₂₆₈	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	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
232	D₄×D₆₇	—	4	2	no	—
233	D₄×D₆₇	—	4	2	no	—
234	D₄×D₆₇	—	4	2	no	—
235	D₄×D₆₇	—	4	2	no	—
236	D₄×D₆₇	—	4	2	no	—
237	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
238	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
239	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
240	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
241	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₆₇	—	4	2	no	—
243	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
255	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
256	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
257	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
258	C₄⋊Dic₆₇	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	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
271	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
272	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
273	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
274	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₆₇	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	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
313	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
314	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
315	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
316	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
317	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
318	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
319	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₄⋊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	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
350	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
351	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
352	C₄²×C₆₇	C₂³	1	1	yes	characteristic
353	C₄²×C₆₇	C₂³	1	1	yes	characteristic
354	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²×D₆₇	—	2	2	no	—
360	C₂²×D₆₇	—	2	2	no	—
361	C₂²×D₆₇	—	2	2	no	—
362	C₂²×D₆₇	—	4	1	no	—
363	C₂²×D₆₇	—	4	1	no	—
364	C₂²×D₆₇	—	4	1	no	—
365	C₂²×D₆₇	—	4	1	no	—
366	C₂²×D₆₇	—	4	1	no	—
367	C₂²×D₆₇	—	4	1	no	—
368	C₂²×D₆₇	—	4	1	no	—
369	C₂²×D₆₇	—	4	1	no	—
370	C₂²×D₆₇	—	4	1	no	—
371	C₂²×D₆₇	—	4	1	no	—
372	C₂²×D₆₇	—	4	1	no	—
373	C₂²×D₆₇	—	4	1	no	—
374	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
375	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
378	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
380	D₄×C₆₇	—	4	1	no	—
381	D₄×C₆₇	—	4	1	no	—
382	D₄×C₆₇	—	4	1	no	—
383	D₄×C₆₇	—	4	1	no	—
384	D₄×C₆₇	—	4	1	no	—
385	D₄×C₆₇	—	4	1	no	—
386	D₄×C₆₇	—	4	1	no	—
387	D₄×C₆₇	—	4	1	no	—
388	D₄×C₆₇	—	4	1	no	—
389	D₄×C₆₇	—	4	1	no	—
390	C₂×C₄×C₆₇	—	4	1	no	—
391	C₂×C₄×C₆₇	—	4	1	no	—
392	C₂×C₄×C₆₇	—	4	1	no	—
393	C₂×C₄×C₆₇	—	4	1	no	—
394	C₂×C₄×C₆₇	—	4	1	no	—
395	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²⋊D₆₇	—	2	2	no	—
406	C₂²⋊D₆₇	—	2	2	no	—
407	C₂²⋊D₆₇	—	2	2	no	—
408	C₂²⋊D₆₇	—	2	2	no	—
409	C₂²⋊D₆₇	—	2	2	no	—
410	C₂²⋊D₆₇	—	4	1	no	—
411	C₂²⋊D₆₇	—	4	1	no	—
412	C₂²⋊D₆₇	—	4	1	no	—
413	C₂²⋊D₆₇	—	4	1	no	—
414	C₂²⋊D₆₇	—	4	1	no	—
415	C₂²⋊D₆₇	—	4	1	no	—
416	C₂²⋊D₆₇	—	4	1	no	—
417	C₂²⋊D₆₇	—	4	1	no	—
418	C₂²⋊D₆₇	—	4	1	no	—
419	C₂²⋊D₆₇	—	4	1	no	—
420	C₂²⋊D₆₇	—	4	1	no	—
421	C₂²⋊D₆₇	—	4	1	no	—
422	C₂²⋊D₆₇	—	4	1	no	—
423	C₂²⋊D₆₇	—	4	1	no	—
424	C₂²⋊D₆₇	—	4	1	no	—
425	C₂×Dic₆₇	—	2	2	no	—
426	C₂×Dic₆₇	—	2	2	no	—
427	C₂×Dic₆₇	—	4	1	no	—
428	C₂×Dic₆₇	—	4	1	no	—
429	C₂×Dic₆₇	—	4	1	no	—
430	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
440	D₂₆₈	—	2	2	no	—
441	D₂₆₈	—	2	2	no	—
442	D₂₆₈	—	4	1	no	—
443	D₂₆₈	—	4	1	no	—
444	D₂₆₈	—	4	1	no	—
445	D₂₆₈	—	4	1	no	—
446	D₂₆₈	—	4	1	no	—
447	D₂₆₈	—	4	1	no	—
448	D₂₆₈	—	4	1	no	—
449	D₂₆₈	—	4	1	no	—
450	C₄×D₆₇	—	2	2	no	—
451	C₄×D₆₇	—	2	2	no	—
452	C₄×D₆₇	—	2	2	no	—
453	C₄×D₆₇	—	2	2	no	—
454	C₄×D₆₇	—	2	2	no	—
455	C₄×D₆₇	—	4	1	no	—
456	C₄×D₆₇	—	4	1	no	—
457	C₄×D₆₇	—	4	1	no	—
458	C₄×D₆₇	—	4	1	no	—
459	C₄×D₆₇	—	4	1	no	—
460	C₄×D₆₇	—	4	1	no	—
461	C₄×D₆₇	—	4	1	no	—
462	Dic₁₃₄	—	2	2	no	—
463	Dic₁₃₄	—	4	1	no	—
464	Dic₁₃₄	—	4	1	no	—
465	Dic₁₃₄	—	4	1	no	—
466	C₂²×C₆₇	—	2	1	no	—
467	C₂²×C₆₇	—	2	1	no	—
468	C₂²×C₆₇	—	2	1	no	—
469	C₂²×C₆₇	—	2	1	no	—
470	C₂²×C₆₇	—	2	1	no	—
471	C₂²×C₆₇	—	2	1	no	—
472	C₂²×C₆₇	—	2	1	no	—
473	C₂²×C₆₇	—	2	1	no	—
474	C₂²×C₆₇	—	2	1	no	—
475	C₂²×C₆₇	—	2	1	no	—
476	C₂²×C₆₇	—	2	1	no	—
477	C₂²×C₆₇	—	2	1	no	—
478	C₂²×C₆₇	—	2	1	no	—
479	C₂²×C₆₇	—	2	1	no	—
480	C₂²×C₆₇	—	2	1	no	—
481	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
482	C₂×D₆₇	—	2	1	no	—
483	C₂×D₆₇	—	2	1	no	—
484	C₂×D₆₇	—	2	1	no	—
485	C₂×D₆₇	—	2	1	no	—
486	C₂×D₆₇	—	2	1	no	—
487	C₂×D₆₇	—	2	1	no	—
488	C₂×D₆₇	—	2	1	no	—
489	C₂×D₆₇	—	2	1	no	—
490	C₂×D₆₇	—	2	1	no	—
491	C₂×D₆₇	—	2	1	no	—
492	C₂×D₆₇	—	2	1	no	—
493	C₂×D₆₇	—	2	1	no	—
494	C₂×D₆₇	—	2	1	no	—
495	C₂×D₆₇	—	2	1	no	—
496	C₂×D₆₇	—	2	1	no	—
497	C₂×D₆₇	—	2	1	no	—
498	C₂×D₆₇	—	2	1	no	—
499	C₂×D₆₇	—	4	4	no	—
500	C₂×D₆₇	—	8	2	no	—
501	C₂×D₆₇	—	8	2	no	—
502	C₂×D₆₇	—	8	2	no	—
503	C₂×D₆₇	—	8	2	no	—
504	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
505	C₄×C₆₇	—	2	1	no	—
506	C₄×C₆₇	—	2	1	no	—
507	C₄×C₆₇	—	2	1	no	—
508	C₄×C₆₇	—	2	1	no	—
509	C₄×C₆₇	—	2	1	no	—
510	C₄×C₆₇	—	2	1	no	—
511	C₄×C₆₇	—	2	1	no	—
512	C₄×C₆₇	—	2	1	no	—
513	C₄×C₆₇	—	2	1	no	—
514	C₄×C₆₇	—	2	1	no	—
515	Dic₆₇	—	2	1	no	—
516	Dic₆₇	—	2	1	no	—
517	Dic₆₇	—	2	1	no	—
518	Dic₆₇	—	2	1	no	—
519	Dic₆₇	—	2	1	no	—
520	Dic₆₇	—	2	1	no	—
521	Dic₆₇	—	2	1	no	—
522	Dic₆₇	—	2	1	no	—
523	Dic₆₇	—	2	1	no	—
524	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₆₇	—	4	1	no	—
526	C₂×C₆₇	—	4	1	no	—
527	C₂×C₆₇	—	4	1	no	—
528	C₂×C₆₇	—	4	1	no	—
529	C₂×C₆₇	—	4	1	no	—
530	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₆₇	#585	1	1	yes	characteristic
533	D₆₇	—	2	2	no	—
534	D₆₇	—	4	1	no	—
535	D₆₇	—	4	1	no	—
536	D₆₇	—	4	1	no	—
537	D₆₇	—	4	1	no	—
538	D₆₇	—	4	1	no	—
539	#3542	—	67	1	no	maximal, Sylow
540	C₆₇	#3542	1	1	yes	characteristic, complemented, Sylow
541	#562	—	67	1	no	—
542	#562	—	67	1	no	—
543	#560	—	67	1	no	—
544	#560	—	67	1	no	—
545	#555	—	67	1	no	—
546	#553	—	67	1	no	—
547	#552	—	67	1	no	—
548	#551	—	67	1	no	—
549	#551	—	67	1	no	—
550	#550	—	67	1	no	—
551	#547	—	67	1	no	—
552	#546	—	67	1	no	—
553	#546	—	67	1	no	—
554	#546	—	67	1	no	—
555	#546	—	67	1	no	—
556	D₄²	—	67	1	no	—
557	#542	—	67	1	no	—
558	#540	—	67	1	no	—
559	#540	—	67	1	no	—
560	#540	D₆₇	1	1	yes	characteristic, complemented
561	#538	—	67	1	no	—
562	#538	—	67	1	no	—
563	#537	—	67	1	no	—
564	#535	—	67	1	no	—
565	#535	—	67	1	no	—
566	#535	—	67	1	no	—
567	#534	—	67	1	no	—
568	#534	—	67	1	no	—
569	#525	—	67	1	no	—
570	#525	—	67	1	no	—
571	C₂×#121	—	67	1	no	—
572	C₂×#41	—	67	1	no	—
573	C₂×#41	—	67	1	no	—
574	C₂×#41	—	67	1	no	—
575	C₂×#41	—	67	1	no	—
576	C₂×#41	—	67	1	no	—
577	C₂²×D₄	—	67	1	no	—
578	C₂²×D₄	—	67	1	no	—
579	C₂²×D₄	—	67	1	no	—
580	C₂²×D₄	—	67	1	no	—
581	C₂²×D₄	—	67	1	no	—
582	C₂²×D₄	—	67	1	no	—
583	C₂³×C₄	—	67	1	no	—
584	C₄⋊Q₈	—	67	1	no	—
585	#127	—	67	1	no	—
586	#127	—	67	1	no	—
587	#127	—	67	1	no	—
588	#127	—	67	1	no	—
589	#127	C₂×D₆₇	1	1	yes	characteristic, complemented
590	#126	—	67	1	no	—
591	#126	—	67	1	no	—
592	#126	—	67	1	no	—
593	#126	—	67	1	no	—
594	#126	—	67	1	no	—
595	#126	—	67	1	no	—
596	#125	—	67	1	no	—
597	#125	—	67	1	no	—
598	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
599	#124	—	67	1	no	—
600	#124	—	67	1	no	—
601	#124	—	67	1	no	—
602	#124	—	67	1	no	—
603	#124	—	67	1	no	—
604	#124	—	67	1	no	—
605	#124	—	67	1	no	—
606	#124	—	67	1	no	—
607	#124	—	67	1	no	—
608	#123	—	67	1	no	—
609	#123	—	67	1	no	—
610	#123	—	67	1	no	—
611	#123	—	67	1	no	—
612	#123	—	67	1	no	—
613	#123	—	67	1	no	—
614	#123	—	67	1	no	—
615	#123	—	67	1	no	—
616	#123	—	67	1	no	—
617	#123	—	67	1	no	—
618	#123	—	67	1	no	—
619	#123	—	67	1	no	—
620	#123	—	67	1	no	—
621	#123	—	67	1	no	—
622	#123	—	67	1	no	—
623	#123	—	67	1	no	—
624	#123	—	67	1	no	—
625	#123	—	67	1	no	—
626	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
627	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
628	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
629	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
630	C₂²⋊Q₈	—	67	1	no	—
631	C₂²⋊Q₈	—	67	1	no	—
632	C₂²⋊Q₈	—	67	1	no	—
633	C₂²⋊Q₈	—	67	1	no	—
634	C₂²⋊Q₈	—	67	1	no	—
635	C₂²⋊Q₈	—	67	1	no	—
636	C₂²⋊Q₈	—	67	1	no	—
637	C₂²⋊Q₈	—	67	1	no	—
638	C₂²⋊Q₈	—	67	1	no	—
639	C₂²⋊Q₈	—	67	1	no	—
640	C₂²⋊Q₈	—	67	1	no	—
641	#121	—	67	1	no	—
642	#121	—	67	1	no	—
643	#121	—	67	1	no	—
644	#121	—	67	1	no	—
645	#121	—	67	1	no	—
646	#121	—	67	1	no	—
647	#121	—	67	1	no	—
648	#121	—	67	1	no	—
649	#121	—	67	1	no	—
650	#121	—	67	1	no	—
651	#121	—	67	1	no	—
652	#121	—	67	1	no	—
653	#121	—	67	1	no	—
654	#121	—	67	1	no	—
655	#121	—	67	1	no	—
656	#121	—	67	1	no	—
657	#121	—	67	1	no	—
658	#121	—	67	1	no	—
659	#121	—	67	1	no	—
660	#121	—	67	1	no	—
661	#121	—	67	1	no	—
662	#121	—	67	1	no	—
663	#121	—	67	1	no	—
664	#121	—	67	1	no	—
665	#121	—	67	1	no	—
666	#121	—	67	1	no	—
667	#121	—	67	1	no	—
668	#121	—	67	1	no	—
669	#121	—	67	1	no	—
670	#121	—	67	1	no	—
671	#121	—	67	1	no	—
672	#121	—	67	1	no	—
673	#121	—	67	1	no	—
674	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
675	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
676	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
677	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
678	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
679	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
680	#120	—	67	1	no	—
681	#120	—	67	1	no	—
682	#120	—	67	1	no	—
683	#120	—	67	1	no	—
684	#120	—	67	1	no	—
685	#120	—	67	1	no	—
686	#120	—	67	1	no	—
687	#120	—	67	1	no	—
688	#120	—	67	1	no	—
689	#120	—	67	1	no	—
690	#120	—	67	1	no	—
691	#120	—	67	1	no	—
692	#120	—	67	1	no	—
693	#120	—	67	1	no	—
694	#120	—	67	1	no	—
695	#120	—	67	1	no	—
696	C₄×Q₈	—	67	1	no	—
697	C₄×D₄	—	67	1	no	—
698	C₄×D₄	—	67	1	no	—
699	C₄×D₄	—	67	1	no	—
700	C₄×D₄	—	67	1	no	—
701	C₄×D₄	—	67	1	no	—
702	C₄×D₄	—	67	1	no	—
703	C₄×D₄	—	67	1	no	—
704	C₄×D₄	—	67	1	no	—
705	C₄×D₄	—	67	1	no	—
706	C₄×D₄	—	67	1	no	—
707	C₄×D₄	—	67	1	no	—
708	C₄×D₄	—	67	1	no	—
709	C₄×D₄	—	67	1	no	—
710	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
711	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
712	#117	—	67	1	no	—
713	#117	—	67	1	no	—
714	#117	—	67	1	no	—
715	#117	—	67	1	no	—
716	#117	—	67	1	no	—
717	#117	—	67	1	no	—
718	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
719	C₂×C₄⋊C₄	—	67	1	no	—
720	C₂×C₄⋊C₄	—	67	1	no	—
721	C₂×C₂²⋊C₄	—	67	1	no	—
722	C₂×C₂²⋊C₄	—	67	1	no	—
723	C₂×C₂²⋊C₄	—	67	1	no	—
724	C₂×C₂²⋊C₄	—	67	1	no	—
725	C₂×C₂²⋊C₄	—	67	1	no	—
726	C₂×C₂²⋊C₄	—	67	1	no	—
727	C₂⁴	—	67	1	no	—
728	C₂⁴	—	67	1	no	—
729	C₂⁴	—	67	1	no	—
730	C₂⁴	—	67	1	no	—
731	C₂⁴	—	67	1	no	—
732	#41	—	268	2	no	—
733	#41	—	268	2	no	—
734	#41	—	268	2	no	—
735	#41	—	268	2	no	—
736	#41	—	268	2	no	—
737	C₂×Q₈	—	67	1	no	—
738	C₂×Q₈	—	67	1	no	—
739	C₂×Q₈	—	67	1	no	—
740	C₂×Q₈	—	67	1	no	—
741	C₂×D₄	—	268	2	no	—
742	C₂×D₄	—	268	2	no	—
743	C₂×D₄	—	268	2	no	—
744	C₂×D₄	—	268	2	no	—
745	C₂×D₄	—	268	2	no	—
746	C₂×D₄	—	268	2	no	—
747	C₂×D₄	—	67	1	no	—
748	C₂×D₄	—	67	1	no	—
749	C₂×D₄	—	67	1	no	—
750	C₂×D₄	—	67	1	no	—
751	C₂×D₄	—	67	1	no	—
752	C₂×D₄	—	67	1	no	—
753	C₂×D₄	—	67	1	no	—
754	C₂×D₄	—	67	1	no	—
755	C₂×D₄	—	67	1	no	—
756	C₂×D₄	—	67	1	no	—
757	C₂×D₄	—	67	1	no	—
758	C₂×D₄	—	67	1	no	—
759	C₂×D₄	—	67	1	no	—
760	C₂×D₄	—	67	1	no	—
761	C₂×D₄	—	67	1	no	—
762	C₂×D₄	—	67	1	no	—
763	C₂×D₄	—	67	1	no	—
764	C₂×D₄	—	67	1	no	—
765	C₂×D₄	—	67	1	no	—
766	C₂×D₄	—	67	1	no	—
767	C₂×D₄	—	67	1	no	—
768	C₂×D₄	—	67	1	no	—
769	C₂×D₄	—	67	1	no	—
770	C₂×D₄	—	67	1	no	—
771	C₂×D₄	—	67	1	no	—
772	C₂×D₄	—	67	1	no	—
773	C₂×D₄	—	67	1	no	—
774	C₂×D₄	—	67	1	no	—
775	C₂×D₄	—	67	1	no	—
776	C₂×D₄	—	67	1	no	—
777	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
778	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
779	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
780	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
781	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
782	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
783	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
784	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
785	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
786	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
787	C₂²×C₄	—	268	2	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	C₂²×D₆₇	1	1	yes	characteristic
806	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
807	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
808	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
809	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
810	C₄⋊C₄	—	67	1	no	—
811	C₄⋊C₄	—	67	1	no	—
812	C₄⋊C₄	—	67	1	no	—
813	C₄⋊C₄	—	67	1	no	—
814	C₄⋊C₄	—	67	1	no	—
815	C₄⋊C₄	—	67	1	no	—
816	C₄⋊C₄	—	67	1	no	—
817	C₄⋊C₄	—	67	1	no	—
818	C₄⋊C₄	—	67	1	no	—
819	C₄⋊C₄	—	67	1	no	—
820	C₄⋊C₄	—	67	1	no	—
821	C₄⋊C₄	—	67	1	no	—
822	C₄⋊C₄	—	67	1	no	—
823	C₄⋊C₄	—	67	1	no	—
824	C₄⋊C₄	—	67	1	no	—
825	C₄⋊C₄	—	67	1	no	—
826	C₄⋊C₄	—	67	1	no	—
827	C₄⋊C₄	—	67	1	no	—
828	C₄⋊C₄	—	67	1	no	—
829	C₄⋊C₄	—	67	1	no	—
830	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
831	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
832	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
833	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
834	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
835	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
838	C₂²⋊C₄	—	67	1	no	—
839	C₂²⋊C₄	—	67	1	no	—
840	C₂²⋊C₄	—	67	1	no	—
841	C₂²⋊C₄	—	67	1	no	—
842	C₂²⋊C₄	—	67	1	no	—
843	C₂²⋊C₄	—	67	1	no	—
844	C₂²⋊C₄	—	67	1	no	—
845	C₂²⋊C₄	—	67	1	no	—
846	C₂²⋊C₄	—	67	1	no	—
847	C₂²⋊C₄	—	67	1	no	—
848	C₂²⋊C₄	—	67	1	no	—
849	C₂²⋊C₄	—	67	1	no	—
850	C₂²⋊C₄	—	67	1	no	—
851	C₂²⋊C₄	—	67	1	no	—
852	C₂²⋊C₄	—	67	1	no	—
853	C₂²⋊C₄	—	67	1	no	—
854	C₂²⋊C₄	—	67	1	no	—
855	C₂²⋊C₄	—	67	1	no	—
856	C₂²⋊C₄	—	67	1	no	—
857	C₂²⋊C₄	—	67	1	no	—
858	C₂²⋊C₄	—	67	1	no	—
859	C₂²⋊C₄	—	67	1	no	—
860	C₂²⋊C₄	—	67	1	no	—
861	C₂²⋊C₄	—	67	1	no	—
862	C₂²⋊C₄	—	67	1	no	—
863	C₂²⋊C₄	—	67	1	no	—
864	C₂²⋊C₄	—	67	1	no	—
865	C₂²⋊C₄	—	67	1	no	—
866	C₂²⋊C₄	—	67	1	no	—
867	C₂²⋊C₄	—	67	1	no	—
868	C₂²⋊C₄	—	67	1	no	—
869	C₂²⋊C₄	—	67	1	no	—
870	C₂²⋊C₄	—	67	1	no	—
871	C₂²⋊C₄	—	67	1	no	—
872	C₂²⋊C₄	—	67	1	no	—
873	C₂²⋊C₄	—	67	1	no	—
874	C₂²⋊C₄	—	67	1	no	—
875	C₂²⋊C₄	—	67	1	no	—
876	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
877	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
878	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
880	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
881	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
882	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
883	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
886	C₄²	—	67	1	no	—
887	C₄²	—	67	1	no	—
888	C₄²	—	67	1	no	—
889	C₄²	—	67	1	no	—
890	C₄²	—	67	1	no	—
891	C₄²	—	67	1	no	—
892	C₄²	C₂²×D₆₇	1	1	yes	characteristic
893	C₄²	C₂²×D₆₇	1	1	yes	characteristic
894	C₂³	—	268	1	no	—
895	C₂³	—	268	1	no	—
896	C₂³	—	268	1	no	—
897	C₂³	—	268	1	no	—
898	C₂³	—	268	1	no	—
899	C₂³	—	268	1	no	—
900	C₂³	—	268	1	no	—
901	C₂³	—	268	1	no	—
902	C₂³	—	268	1	no	—
903	C₂³	—	268	1	no	—
904	C₂³	—	268	1	no	—
905	C₂³	—	268	1	no	—
906	C₂³	—	67	1	no	—
907	C₂³	—	67	1	no	—
908	C₂³	—	67	1	no	—
909	C₂³	—	67	1	no	—
910	C₂³	—	67	1	no	—
911	C₂³	—	67	1	no	—
912	C₂³	—	134	2	no	—
913	C₂³	—	134	2	no	—
914	C₂³	—	134	2	no	—
915	C₂³	C₂³×D₆₇	1	1	yes	characteristic
916	C₂³	C₂³×D₆₇	1	1	yes	characteristic
917	C₂³	C₂³×D₆₇	1	1	yes	characteristic
918	C₂³	C₂³×D₆₇	1	1	yes	characteristic
919	C₂³	C₂³×D₆₇	1	1	yes	characteristic
920	Q₈	—	268	1	no	—
921	Q₈	—	268	1	no	—
922	Q₈	—	268	1	no	—
923	Q₈	—	134	2	no	—
924	D₄	—	4	1	no	—
925	D₄	—	4	1	no	—
926	D₄	—	4	1	no	—
927	D₄	—	4	1	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	268	1	no	—
935	D₄	—	268	1	no	—
936	D₄	—	268	1	no	—
937	D₄	—	268	1	no	—
938	D₄	—	268	1	no	—
939	D₄	—	268	1	no	—
940	D₄	—	268	1	no	—
941	D₄	—	268	1	no	—
942	D₄	—	268	1	no	—
943	D₄	—	268	1	no	—
944	D₄	—	268	1	no	—
945	D₄	—	268	1	no	—
946	D₄	—	268	1	no	—
947	D₄	—	268	1	no	—
948	D₄	—	268	1	no	—
949	D₄	—	268	1	no	—
950	D₄	—	268	1	no	—
951	D₄	—	268	1	no	—
952	D₄	—	268	1	no	—
953	D₄	—	268	1	no	—
954	D₄	—	268	1	no	—
955	D₄	—	268	1	no	—
956	D₄	—	268	1	no	—
957	D₄	—	134	2	no	—
958	D₄	—	134	2	no	—
959	D₄	—	134	2	no	—
960	D₄	—	134	2	no	—
961	D₄	—	134	2	no	—
962	D₄	—	134	2	no	—
963	D₄	—	134	2	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	268	1	no	—
970	C₂×C₄	—	268	1	no	—
971	C₂×C₄	—	268	1	no	—
972	C₂×C₄	—	268	1	no	—
973	C₂×C₄	—	268	1	no	—
974	C₂×C₄	—	268	1	no	—
975	C₂×C₄	—	268	1	no	—
976	C₂×C₄	—	268	1	no	—
977	C₂×C₄	—	268	1	no	—
978	C₂×C₄	—	268	1	no	—
979	C₂×C₄	—	67	1	no	—
980	C₂×C₄	—	67	1	no	—
981	C₂×C₄	—	67	1	no	—
982	C₂×C₄	—	67	1	no	—
983	C₂×C₄	—	67	1	no	—
984	C₂×C₄	—	67	1	no	—
985	C₂×C₄	—	67	1	no	—
986	C₂×C₄	—	67	1	no	—
987	C₂×C₄	—	67	1	no	—
988	C₂×C₄	—	67	1	no	—
989	C₂×C₄	—	134	2	no	—
990	C₂×C₄	—	134	2	no	—
991	C₂×C₄	—	134	2	no	—
992	C₂×C₄	—	134	2	no	—
993	C₂×C₄	—	134	2	no	—
994	C₂×C₄	—	134	2	no	—
995	C₂×C₄	—	134	2	no	—
996	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
997	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
998	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	2	1	no	—
1021	C₂²	—	268	4	no	—
1022	C₂²	—	536	2	no	—
1023	C₂²	—	536	2	no	—
1024	C₂²	—	536	2	no	—
1025	C₂²	—	536	2	no	—
1026	C₂²	—	67	2	no	—
1027	C₂²	—	134	1	no	—
1028	C₂²	—	134	1	no	—
1029	C₂²	—	134	1	no	—
1030	C₂²	—	134	1	no	—
1031	C₂²	—	134	1	no	—
1032	C₂²	—	134	1	no	—
1033	C₂²	—	134	1	no	—
1034	C₂²	—	134	1	no	—
1035	C₂²	—	134	1	no	—
1036	C₂²	—	134	1	no	—
1037	C₂²	—	134	1	no	—
1038	C₂²	—	134	1	no	—
1039	C₂²	—	134	1	no	—
1040	C₂²	—	134	1	no	—
1041	C₂²	—	134	1	no	—
1042	C₂²	—	134	1	no	—
1043	C₂²	—	134	1	no	—
1044	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
1045	C₄	—	2	1	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	67	2	no	—
1056	C₄	—	134	1	no	—
1057	C₄	—	134	1	no	—
1058	C₄	—	134	1	no	—
1059	C₄	—	134	1	no	—
1060	C₄	—	134	1	no	—
1061	C₄	—	134	1	no	—
1062	C₄	—	134	1	no	—
1063	C₄	—	134	1	no	—
1064	C₄	—	134	1	no	—
1065	C₂	—	4	1	no	—
1066	C₂	—	4	1	no	—
1067	C₂	—	4	1	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	268	1	no	—
1071	C₂	—	268	1	no	—
1072	C₂	—	268	1	no	—
1073	C₂	—	268	1	no	—
1074	C₂	—	268	1	no	—
1075	C₂	—	134	2	no	—
1076	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1077	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1078	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#540×C₆₇	C₂
hypercenter	#540	D₆₇
hypocenter	C₆₇	#3542
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #16864144	C₂	semidirect
2. #16864141	C₂	semidirect
3. #16864136	C₂	semidirect
4. #16864134	C₂	semidirect
5. #16864109	C₂	semidirect
6. #16864095	C₂	semidirect
7. #16864078	C₂	semidirect
8. #16864074	C₂	semidirect
9. #16864070	C₂	semidirect
10. #16864064	C₂	semidirect
11. #16864044	C₂	semidirect
12. #16864042	C₂	semidirect
13. #16864038	C₂	semidirect
14. #16864035	C₂	semidirect
15. #16864035	C₂	semidirect
16. #16864030	C₂	semidirect
17. #16864014	C₂	semidirect
18. #16863998	C₂	semidirect
19. #16863996	C₂	semidirect
20. #16863979	C₂	semidirect
21. #16863978	C₂	semidirect
22. #16863973	C₂	semidirect
23. #16863962	C₂	semidirect
24. #16863959	C₂	semidirect
25. #16863959	C₂	semidirect
26. #16863957	C₂	semidirect
27. #16863954	C₂	semidirect
28. #16863905	C₂	semidirect
29. #16863904	C₂	semidirect
30. #121×D₆₇	C₂	semidirect
31. #540×C₆₇	C₂	semidirect
32. C₂×#11761628	C₂²	semidirect
33. C₂×#11761628	C₂²	semidirect
34. C₂×#11761627	C₂²	semidirect
35. C₂×#11761627	C₂²	semidirect
36. C₂×#11761627	C₂²	semidirect
40. C₂×D₄×D₆₇	C₂²	semidirect
41. C₂×D₄×D₆₇	C₂²	semidirect
42. C₂×D₄×D₆₇	C₂²	semidirect
43. C₂²×C₄×D₆₇	C₂²	semidirect
44. #14524042	C₂²	semidirect
45. #14524039	C₂²	semidirect
46. #14524039	C₂²	semidirect
47. #14524039	C₂²	semidirect
48. #14524039	C₂²	semidirect
49. #14524038	C₂²	semidirect
50. #14524038	C₂²	semidirect
51. #14524038	C₂²	semidirect
52. #14524037	C₂²	semidirect
53. #14524036	C₂²	semidirect
54. #14524036	C₂²	semidirect
55. #14524033	C₂²	semidirect
56. #14524033	C₂²	semidirect
57. #14524031	C₂²	semidirect
58. #14524031	C₂²	semidirect
59. #14524031	C₂²	semidirect
60. #14524030	C₂²	semidirect
61. #14524030	C₂²	semidirect
62. #14524029	C₂²	semidirect
63. #14524029	C₂²	semidirect
64. #14524029	C₂²	semidirect
65. #14524029	C₂²	semidirect
68. #14524028	C₂²	semidirect
69. #14524028	C₂²	semidirect
70. #14524028	C₂²	semidirect
71. #14524028	C₂²	semidirect
72. #14524028	C₂²	semidirect
73. #14524028	C₂²	semidirect
74. #14524027	C₂²	semidirect
75. #14524026	C₂²	semidirect
76. #14524026	C₂²	semidirect
77. #14524026	C₂²	semidirect
78. #14524025	C₂²	semidirect
79. #14524025	C₂²	semidirect
80. #14524025	C₂²	semidirect
81. #14524025	C₂²	semidirect
82. #14524024	C₂²	semidirect
83. #14524024	C₂²	semidirect
84. #14524022	C₂²	semidirect
85. #14524021	C₂²	semidirect
86. #14524021	C₂²	semidirect
87. #14524021	C₂²	semidirect
88. #14524021	C₂²	semidirect
89. #14524021	C₂²	semidirect
90. #14524021	C₂²	semidirect
91. #14524021	C₂²	semidirect
92. #14524020	C₂²	semidirect
93. #14524020	C₂²	semidirect
94. #14524020	C₂²	semidirect
95. #14524018	C₂²	semidirect
96. #14524018	C₂²	semidirect
97. #14524018	C₂²	semidirect
98. #14524018	C₂²	semidirect
99. #14524018	C₂²	semidirect
100. #14524017	C₂²	semidirect
101. #14524017	C₂²	semidirect
102. #14524017	C₂²	semidirect
103. #14524017	C₂²	semidirect
107. #14524016	C₂²	semidirect
108. #14524016	C₂²	semidirect
109. #14524016	C₂²	semidirect
110. #14524016	C₂²	semidirect
111. #14524016	C₂²	semidirect
112. #14524016	C₂²	semidirect
113. #14524016	C₂²	semidirect
115. #14524015	C₂²	semidirect
116. #14524015	C₂²	semidirect
117. #14524015	C₂²	semidirect
118. #14524015	C₂²	semidirect
119. #14524015	C₂²	semidirect
120. #14524015	C₂²	semidirect
121. #14524015	C₂²	semidirect
122. #14524015	C₂²	semidirect
123. #14524015	C₂²	semidirect
124. #14524015	C₂²	semidirect
125. #14524015	C₂²	semidirect
126. #14524014	C₂²	semidirect
127. #14524014	C₂²	semidirect
130. #14524013	C₂²	semidirect
131. #14524013	C₂²	semidirect
132. #14524013	C₂²	semidirect
133. #14524013	C₂²	semidirect
135. #14524011	C₂²	semidirect
136. #14524011	C₂²	semidirect
137. #14524011	C₂²	semidirect
138. #14524011	C₂²	semidirect
139. #14524011	C₂²	semidirect
140. #14524011	C₂²	semidirect
141. #14524011	C₂²	semidirect
142. #14524011	C₂²	semidirect
143. #14524011	C₂²	semidirect
144. #14524008	C₂²	semidirect
145. C₄×D₂₆₈	C₂²	semidirect
147. #14524005	C₂²	semidirect
148. C₄×C₂²⋊D₆₇	C₂²	semidirect
149. C₄×C₂²⋊D₆₇	C₂²	semidirect
150. C₄×C₂²⋊D₆₇	C₂²	semidirect
151. C₄×C₂²⋊D₆₇	C₂²	semidirect
152. C₄×C₂²⋊D₆₇	C₂²	semidirect
153. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
154. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
155. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
156. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
157. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
158. #14524001	C₂²	semidirect
159. #14524001	C₂²	semidirect
160. #14524000	C₂²	semidirect
161. #14524000	C₂²	semidirect
162. #14524000	C₂²	semidirect
163. #14523999	C₂²	semidirect
164. C₂×Dic₆₇⋊C₄	C₂²	semidirect
165. C₄⋊C₄×D₆₇	C₂²	semidirect
166. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
167. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
168. C₂²⋊C₄×D₆₇	C₂²	semidirect
169. C₂²⋊C₄×D₆₇	C₂²	semidirect
170. C₂²⋊C₄×D₆₇	C₂²	semidirect
171. C₂²⋊C₄×D₆₇	C₂²	semidirect
172. #127×C₆₇	C₂²	semidirect
173. #125×C₆₇	C₂²	semidirect
174. #123×C₆₇	C₂²	semidirect
175. #123×C₆₇	C₂²	semidirect
176. #123×C₆₇	C₂²	semidirect
177. #123×C₆₇	C₂²	semidirect
178. #121×C₆₇	C₂²	semidirect
179. #121×C₆₇	C₂²	semidirect
180. #121×C₆₇	C₂²	semidirect
181. #121×C₆₇	C₂²	semidirect
182. #121×C₆₇	C₂²	semidirect
183. #121×C₆₇	C₂²	semidirect
184. C₄×D₄×C₆₇	C₂²	semidirect
185. C₄×D₄×C₆₇	C₂²	semidirect
186. #117×C₆₇	C₂²	semidirect
540. C₆₇	#3542	semidirect
560. #540	D₆₇	semidirect
589. #127	C₂×D₆₇	semidirect
598. #125	C₂×D₆₇	semidirect
626. #123	C₂×D₆₇	semidirect
627. #123	C₂×D₆₇	semidirect
628. #123	C₂×D₆₇	semidirect
629. #123	C₂×D₆₇	semidirect
674. #121	C₂×D₆₇	semidirect
675. #121	C₂×D₆₇	semidirect
676. #121	C₂×D₆₇	semidirect
677. #121	C₂×D₆₇	semidirect
678. #121	C₂×D₆₇	semidirect
679. #121	C₂×D₆₇	semidirect
710. C₄×D₄	C₂×D₆₇	semidirect
711. C₄×D₄	C₂×D₆₇	semidirect
718. #117	C₂×D₆₇	semidirect