Subgroups — #3508×D₆₇ #31764182

Order 17152.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574086	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574085	C₂	1	1	yes	maximal, characteristic, complemented
3	#22574084	C₂	1	2	yes	maximal, complemented
4	#22574083	C₂	1	1	yes	maximal, characteristic, complemented
5	#22574082	C₂	1	4	yes	maximal, complemented
6	#22574081	C₂	1	4	yes	maximal, complemented
7	#22574080	C₂	1	2	yes	maximal, complemented
8	#22574079	C₂	1	4	yes	maximal, complemented
9	#22574078	C₂	1	4	yes	maximal, complemented
10	#22574077	C₂	1	8	yes	maximal, complemented
11	#559×D₆₇	C₂	1	4	yes	maximal, complemented
12	#550×D₆₇	C₂	1	4	yes	maximal, complemented
13	#546×D₆₇	C₂	1	8	yes	maximal, complemented
14	#540×D₆₇	C₂	1	4	yes	maximal, complemented
15	#535×D₆₇	C₂	1	2	yes	maximal, complemented
16	#533×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#532×D₆₇	C₂	1	4	yes	maximal, complemented
18	C₂×#127×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#518×D₆₇	C₂	1	2	yes	maximal, complemented
20	C₄×#41×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#41×D₆₇	C₂²	1	1	yes	characteristic
23	C₂×#41×D₆₇	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₆₇	C₂²	1	2	yes	—
25	C₂²×D₄×D₆₇	C₂²	1	4	yes	—
26	#16864132	C₂²	1	4	yes	complemented
27	#16864131	C₂²	1	4	yes	complemented
28	#16864131	C₂²	1	4	yes	complemented
29	#16864130	C₂²	1	16	yes	complemented
30	#16864129	C₂²	1	8	yes	complemented
31	#16864129	C₂²	1	8	yes	complemented
32	#16864128	C₂²	1	8	yes	complemented
33	#16864128	C₂²	1	8	yes	complemented
34	#16864068	C₂²	1	4	yes	complemented
35	#16864067	C₂²	1	8	yes	complemented
36	#16864067	C₂²	1	4	yes	complemented
37	#16864066	C₂²	1	4	yes	complemented
38	#16864066	C₂²	1	8	yes	complemented
39	#16864065	C₂²	1	8	yes	complemented
40	#16864064	C₂²	1	16	yes	complemented
41	#16864064	C₂²	1	8	yes	complemented
42	#16864043	C₂²	1	8	yes	complemented
43	#16864042	C₂²	1	8	yes	complemented
44	#16864041	C₂²	1	8	yes	complemented
45	#16864040	C₂²	1	8	yes	complemented
46	#16864039	C₂²	1	8	yes	complemented
47	#16864038	C₂²	1	16	yes	complemented
48	#16864037	C₂²	1	8	yes	complemented
49	#16864036	C₂²	1	16	yes	complemented
50	#16864035	C₂²	1	16	yes	complemented
51	#16864034	C₂²	1	8	yes	complemented
52	#16864033	C₂²	1	16	yes	complemented
53	#16864002	C₂²	1	4	yes	complemented
54	#16864001	C₂²	1	4	yes	complemented
55	#16864000	C₂²	1	4	yes	complemented
56	#16863999	C₂²	1	8	yes	complemented
57	#16863998	C₂²	1	16	yes	complemented
58	#16863997	C₂²	1	8	yes	complemented
59	#16863996	C₂²	1	16	yes	complemented
60	#16863965	C₂²	1	2	yes	complemented
61	#16863964	C₂²	1	4	yes	complemented
62	#16863963	C₂²	1	2	yes	complemented
63	#16863962	C₂²	1	8	yes	complemented
64	#16863961	C₂²	1	8	yes	complemented
65	#16863960	C₂²	1	2	yes	complemented
66	#16863959	C₂²	1	4	yes	complemented
67	#16863953	C₂²	1	1	yes	characteristic, complemented
68	#16863952	C₂²	1	2	yes	complemented
69	#16863951	C₂²	1	2	yes	complemented
70	#16863950	C₂²	1	4	yes	complemented
71	#16863949	C₂²	1	2	yes	complemented
72	#16863948	C₂²	1	4	yes	complemented
73	#16863947	C₂²	1	4	yes	complemented
74	#16863946	C₂²	1	4	yes	complemented
75	#16863945	C₂²	1	8	yes	complemented
76	#16863944	C₂²	1	4	yes	complemented
77	#16863943	C₂²	1	8	yes	complemented
78	#16863943	C₂²	1	8	yes	complemented
79	#16863942	C₂²	1	8	yes	complemented
80	#16863941	C₂²	1	8	yes	complemented
81	#16863941	C₂²	1	8	yes	complemented
82	C₄⋊Q₈×D₆₇	C₂²	1	2	yes	complemented
83	C₂×#14524040	C₂²	1	1	yes	characteristic, complemented
84	C₂×#14524039	C₂²	1	2	yes	complemented
85	C₂×#14524039	C₂²	1	4	yes	complemented
86	#127×D₆₇	C₂²	1	4	yes	—
87	#127×D₆₇	C₂²	1	2	yes	—
88	#127×D₆₇	C₂²	1	2	yes	—
89	#127×D₆₇	C₂²	1	2	yes	complemented
90	#127×D₆₇	C₂²	1	4	yes	complemented
91	#127×D₆₇	C₂²	1	2	yes	complemented
92	#127×D₆₇	C₂²	1	4	yes	complemented
93	#125×D₆₇	C₂²	1	2	yes	complemented
94	#124×D₆₇	C₂²	1	8	yes	complemented
95	#124×D₆₇	C₂²	1	4	yes	complemented
96	#123×D₆₇	C₂²	1	16	yes	complemented
97	C₂²⋊Q₈×D₆₇	C₂²	1	4	yes	—
98	#121×D₆₇	C₂²	1	8	yes	complemented
99	#121×D₆₇	C₂²	1	16	yes	complemented
100	#121×D₆₇	C₂²	1	8	yes	complemented
101	#120×D₆₇	C₂²	1	8	yes	—
102	#16863871	C₂²	1	2	yes	complemented
103	#16863870	C₂²	1	2	yes	complemented
104	#16863870	C₂²	1	2	yes	complemented
105	#16863869	C₂²	1	8	yes	complemented
106	#16863868	C₂²	1	8	yes	complemented
107	#16863868	C₂²	1	8	yes	complemented
108	#41×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₄×#11761629	C₂²	1	2	yes	complemented
110	C₄×#11761628	C₂²	1	1	yes	characteristic, complemented
111	C₄×#11761628	C₂²	1	2	yes	complemented
112	#16863864	C₂²	1	1	yes	characteristic, complemented
113	#16863864	C₂²	1	2	yes	complemented
114	C₄×#11761627	C₂²	1	4	yes	complemented
115	C₄×#11761627	C₂²	1	2	yes	complemented
116	C₄×Q₈×D₆₇	C₂²	1	2	yes	complemented
117	C₄×Q₈×D₆₇	C₂²	1	4	yes	complemented
118	C₄×D₄×D₆₇	C₂²	1	4	yes	—
119	C₄×D₄×D₆₇	C₂²	1	2	yes	complemented
120	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
121	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
122	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
123	#117×D₆₇	C₂²	1	1	yes	characteristic
124	#117×D₆₇	C₂²	1	2	yes	—
125	#117×D₆₇	C₂²	1	2	yes	complemented
126	C₂×C₂²⋊C₄×D₆₇	C₂²	1	8	yes	—
127	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
128	C₂×C₄²×D₆₇	C₂²	1	2	yes	complemented
129	#559×C₆₇	C₂²	1	4	yes	complemented
130	#550×C₆₇	C₂²	1	4	yes	complemented
131	#546×C₆₇	C₂²	1	8	yes	complemented
132	#540×C₆₇	C₂²	1	4	yes	complemented
133	#535×C₆₇	C₂²	1	2	yes	complemented
134	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#532×C₆₇	C₂²	1	4	yes	complemented
136	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	#518×C₆₇	C₂²	1	2	yes	complemented
138	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂⁴×D₆₇	C₂³	1	4	yes	—
140	C₂×#11761629	C₂³	1	1	yes	characteristic
141	C₂×#11761629	C₂³	1	8	yes	complemented
142	C₂×#11761628	C₂³	1	2	yes	—
143	C₂×#11761628	C₂³	1	1	yes	characteristic
144	C₂×#11761628	C₂³	1	16	yes	complemented
145	C₂×#11761628	C₂³	1	8	yes	complemented
146	C₂×#11761627	C₂³	1	1	yes	characteristic
147	C₂×#11761627	C₂³	1	2	yes	—
148	C₂×#11761627	C₂³	1	16	yes	complemented
149	C₂×#11761627	C₂³	1	8	yes	complemented
150	#41×D₆₇	—	2	8	no	—
151	#41×D₆₇	—	4	32	no	—
152	C₂×Q₈×D₆₇	C₂³	1	1	yes	characteristic
153	C₂×Q₈×D₆₇	C₂³	1	4	yes	—
154	C₂²×D₂₆₈	C₂³	1	2	yes	—
155	C₂²×D₂₆₈	C₂³	1	4	yes	—
156	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
157	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	—
158	C₂×D₄×D₆₇	—	2	16	no	—
159	C₂×D₄×D₆₇	—	4	16	no	—
160	C₂×D₄×D₆₇	C₂³	1	2	yes	—
161	C₂×D₄×D₆₇	C₂³	1	4	yes	—
162	C₂×D₄×D₆₇	C₂³	1	4	yes	—
163	C₂×D₄×D₆₇	C₂³	1	1	yes	characteristic
164	C₂×D₄×D₆₇	C₂³	1	8	yes	—
165	C₂×D₄×D₆₇	C₂³	1	4	yes	—
166	C₂×D₄×D₆₇	C₂³	1	4	yes	—
167	C₂×D₄×D₆₇	C₂³	1	8	yes	—
168	C₂×D₄×D₆₇	C₂³	1	8	yes	—
169	C₂×D₄×D₆₇	C₂³	1	16	yes	—
170	C₂×D₄×D₆₇	C₂³	1	8	yes	—
171	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
172	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
173	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
174	C₂²×C₄×D₆₇	C₂³	1	16	yes	—
175	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
176	#14524043	C₂³	1	2	yes	complemented
177	#14524042	C₂³	1	4	yes	complemented
178	#14524042	C₂³	1	4	yes	complemented
179	#14524041	C₂³	1	4	yes	complemented
180	#14524040	C₂³	1	2	yes	—
181	#14524040	C₂³	1	4	yes	—
182	#14524040	C₂³	1	2	yes	—
183	#14524040	C₂³	1	4	yes	complemented
184	#14524039	C₂³	1	8	yes	—
185	#14524039	C₂³	1	8	yes	—
186	#14524039	C₂³	1	8	yes	—
187	#14524039	C₂³	1	4	yes	—
188	#14524039	C₂³	1	8	yes	—
189	#14524039	C₂³	1	8	yes	—
190	#14524039	C₂³	1	4	yes	—
191	#14524039	C₂³	1	16	yes	complemented
192	#14524039	C₂³	1	4	yes	complemented
193	#14524039	C₂³	1	4	yes	complemented
194	#14524035	C₂³	1	2	yes	complemented
195	#14524034	C₂³	1	4	yes	complemented
196	#14524033	C₂³	1	8	yes	complemented
197	#14524032	C₂³	1	8	yes	complemented
198	#14524032	C₂³	1	4	yes	complemented
199	#14524031	C₂³	1	8	yes	complemented
200	#14524031	C₂³	1	4	yes	complemented
201	#14524030	C₂³	1	8	yes	complemented
202	#14524030	C₂³	1	4	yes	complemented
203	#14524029	C₂³	1	16	yes	complemented
204	#14524029	C₂³	1	16	yes	complemented
205	#14524029	C₂³	1	16	yes	complemented
206	#14524028	C₂³	1	16	yes	complemented
207	#14524028	C₂³	1	16	yes	complemented
208	#14524027	C₂³	1	16	yes	complemented
209	#14524026	C₂³	1	16	yes	complemented
210	#14524025	C₂³	1	16	yes	complemented
211	#14524025	C₂³	1	16	yes	complemented
212	#14524024	C₂³	1	16	yes	complemented
213	#14524023	C₂³	1	4	yes	—
214	#14524022	C₂³	1	4	yes	—
215	#14524021	C₂³	1	8	yes	—
216	#14524020	C₂³	1	8	yes	—
217	#14524019	C₂³	1	4	yes	—
218	#14524018	C₂³	1	16	yes	complemented
219	#14524018	C₂³	1	8	yes	complemented
220	#14524018	C₂³	1	8	yes	complemented
221	#14524017	C₂³	1	8	yes	complemented
222	#14524017	C₂³	1	8	yes	complemented
223	#14524017	C₂³	1	16	yes	complemented
224	#14524016	C₂³	1	16	yes	complemented
225	#14524016	C₂³	1	16	yes	complemented
226	#14524016	C₂³	1	16	yes	complemented
227	#14524016	C₂³	1	16	yes	complemented
228	#14524015	C₂³	1	16	yes	complemented
229	#14524015	C₂³	1	16	yes	complemented
230	#14524015	C₂³	1	16	yes	complemented
231	#14524015	C₂³	1	16	yes	complemented
232	#14524014	C₂³	1	8	yes	complemented
233	#14524014	C₂³	1	16	yes	complemented
234	#14524014	C₂³	1	8	yes	complemented
235	#14524013	C₂³	1	8	yes	—
236	#14524013	C₂³	1	16	yes	—
237	#14524012	C₂³	1	8	yes	—
238	#14524011	C₂³	1	8	yes	—
239	#14524011	C₂³	1	16	yes	—
240	Q₈×Dic₆₇	C₂³	1	4	yes	complemented
241	Q₈×Dic₆₇	C₂³	1	2	yes	complemented
242	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
243	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
244	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
245	C₄×Dic₁₃₄	C₂³	1	2	yes	complemented
246	#14524008	C₂³	1	4	yes	complemented
247	#14524008	C₂³	1	8	yes	complemented
248	#14524008	C₂³	1	2	yes	complemented
249	#14524008	C₂³	1	4	yes	complemented
250	C₄×D₂₆₈	C₂³	1	4	yes	—
251	C₄×D₂₆₈	C₂³	1	8	yes	complemented
252	C₄×D₂₆₈	C₂³	1	8	yes	complemented
253	C₄×D₂₆₈	C₂³	1	2	yes	complemented
254	C₄×D₂₆₈	C₂³	1	8	yes	complemented
255	D₄×Dic₆₇	C₂³	1	4	yes	—
256	D₄×Dic₆₇	C₂³	1	8	yes	complemented
257	D₄×Dic₆₇	C₂³	1	8	yes	complemented
258	D₄×Dic₆₇	C₂³	1	2	yes	complemented
259	D₄×Dic₆₇	C₂³	1	8	yes	complemented
260	#14524005	C₂³	1	4	yes	—
261	#14524005	C₂³	1	8	yes	complemented
262	#14524005	C₂³	1	8	yes	complemented
263	#14524005	C₂³	1	2	yes	complemented
264	#14524005	C₂³	1	8	yes	complemented
265	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	—
266	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	—
267	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
268	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
269	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
270	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
271	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	—
272	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	—
273	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
274	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
275	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
276	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
277	#14524002	C₂³	1	1	yes	characteristic
278	#14524002	C₂³	1	2	yes	—
279	#14524002	C₂³	1	2	yes	complemented
280	#14524001	C₂³	1	2	yes	—
281	#14524001	C₂³	1	4	yes	—
282	#14524001	C₂³	1	4	yes	complemented
283	#14524000	C₂³	1	2	yes	—
284	#14524000	C₂³	1	4	yes	—
285	#14524000	C₂³	1	2	yes	complemented
286	#14524000	C₂³	1	2	yes	complemented
287	#14523999	C₂³	1	2	yes	—
288	#14523999	C₂³	1	4	yes	—
289	#14523999	C₂³	1	4	yes	complemented
290	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
291	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
292	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
293	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
294	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
295	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	—
296	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
297	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
298	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
299	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
300	C₂²⋊C₄×D₆₇	C₂³	1	2	yes	—
301	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
302	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
303	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
304	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
305	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
306	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₆₇	C₂³	1	4	yes	complemented
308	C₂×C₄×Dic₆₇	C₂³	1	2	yes	complemented
309	C₄²×D₆₇	C₂³	1	1	yes	characteristic
310	C₄²×D₆₇	C₂³	1	1	yes	characteristic
311	C₄²×D₆₇	C₂³	1	2	yes	—
312	C₄²×D₆₇	C₂³	1	2	yes	—
313	C₄²×D₆₇	C₂³	1	1	yes	characteristic
314	C₄²×D₆₇	C₂³	1	1	yes	characteristic
315	C₄²×D₆₇	C₂³	1	2	yes	—
316	C₄²×D₆₇	C₂³	1	4	yes	—
317	C₄²×D₆₇	C₂³	1	4	yes	—
318	C₄²×D₆₇	C₂³	1	4	yes	complemented
319	C₄²×D₆₇	C₂³	1	2	yes	complemented
320	C₄²×D₆₇	C₂³	1	2	yes	complemented
321	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
322	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
323	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
324	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
325	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
326	#127×C₆₇	C₂³	1	2	yes	—
327	#127×C₆₇	C₂³	1	4	yes	—
328	#127×C₆₇	C₂³	1	2	yes	—
329	#127×C₆₇	C₂³	1	4	yes	complemented
330	#125×C₆₇	C₂³	1	2	yes	complemented
331	#124×C₆₇	C₂³	1	8	yes	complemented
332	#124×C₆₇	C₂³	1	4	yes	complemented
333	#123×C₆₇	C₂³	1	16	yes	complemented
334	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
335	#121×C₆₇	C₂³	1	16	yes	complemented
336	#121×C₆₇	C₂³	1	8	yes	complemented
337	#121×C₆₇	C₂³	1	8	yes	complemented
338	#120×C₆₇	C₂³	1	8	yes	—
339	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
340	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
341	C₄×D₄×C₆₇	C₂³	1	4	yes	—
342	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
343	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
344	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
345	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
346	#117×C₆₇	C₂³	1	1	yes	characteristic
347	#117×C₆₇	C₂³	1	2	yes	—
348	#117×C₆₇	C₂³	1	2	yes	complemented
349	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
350	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₆₇	C₂³	1	2	yes	complemented
352	C₂³×D₆₇	—	2	16	no	—
353	C₂³×D₆₇	—	4	16	no	—
354	C₂³×D₆₇	C₂⁴	1	8	yes	—
355	C₂³×D₆₇	C₂⁴	1	2	yes	—
356	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
357	C₂³×D₆₇	C₂⁴	1	4	yes	—
358	C₂³×D₆₇	C₂⁴	1	8	yes	—
359	#11761629	—	2	4	no	—
360	#11761629	—	4	16	no	—
361	#11761628	—	2	4	no	—
362	#11761628	—	2	8	no	—
363	#11761628	—	4	32	no	—
364	#11761628	—	4	16	no	—
365	#11761627	—	2	8	no	—
366	#11761627	—	2	4	no	—
367	#11761627	—	4	16	no	—
368	#11761627	—	4	32	no	—
369	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
370	C₂×Dic₁₃₄	C₂⁴	1	1	yes	characteristic
371	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
372	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
373	Q₈×D₆₇	—	2	4	no	—
374	Q₈×D₆₇	—	2	16	no	—
375	C₂×D₂₆₈	—	2	8	no	—
376	C₂×D₂₆₈	—	4	8	no	—
377	C₂×D₂₆₈	C₂⁴	1	2	yes	—
378	C₂×D₂₆₈	C₂⁴	1	4	yes	—
379	C₂×D₂₆₈	C₂⁴	1	4	yes	—
380	C₂×D₂₆₈	C₂⁴	1	1	yes	characteristic
381	C₂×D₂₆₈	C₂⁴	1	8	yes	—
382	C₂×D₂₆₈	C₂⁴	1	16	yes	—
383	C₂×D₂₆₈	C₂⁴	1	8	yes	—
384	C₂×C₂²⋊D₆₇	—	2	16	no	—
385	C₂×C₂²⋊D₆₇	—	4	16	no	—
386	C₂×C₂²⋊D₆₇	C₂⁴	1	2	yes	—
387	C₂×C₂²⋊D₆₇	C₂⁴	1	2	yes	—
388	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
389	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
390	C₂×C₂²⋊D₆₇	C₂⁴	1	2	yes	—
391	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
392	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
393	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
394	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
395	D₄×D₆₇	—	2	8	no	—
396	D₄×D₆₇	—	2	16	no	—
397	D₄×D₆₇	—	2	16	no	—
398	D₄×D₆₇	—	2	4	no	—
399	D₄×D₆₇	—	2	16	no	—
400	D₄×D₆₇	—	2	16	no	—
401	D₄×D₆₇	—	2	32	no	—
402	D₄×D₆₇	—	4	16	no	—
403	D₄×D₆₇	—	4	16	no	—
404	D₄×D₆₇	—	4	16	no	—
405	D₄×D₆₇	—	4	32	no	—
406	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
407	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
408	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
409	C₂²×Dic₆₇	C₂⁴	1	16	yes	—
410	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×D₆₇	—	2	8	no	—
412	C₂×C₄×D₆₇	—	2	8	no	—
413	C₂×C₄×D₆₇	—	2	16	no	—
414	C₂×C₄×D₆₇	—	4	32	no	—
415	C₂×C₄×D₆₇	#41	1	8	yes	complemented
416	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
417	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
418	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
419	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
420	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
421	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
422	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
423	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
424	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
425	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
426	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
427	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
428	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
431	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
432	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
433	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
434	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
435	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
436	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
437	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
438	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
439	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
440	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
441	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
442	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
443	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
444	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
445	C₂²⋊Dic₆₇	C₂⁴	1	2	yes	—
446	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
447	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
448	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
449	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
450	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
451	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
452	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
453	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
454	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
455	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
456	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
457	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
458	C₄×Dic₆₇	C₂⁴	1	2	yes	—
459	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
460	C₄×Dic₆₇	C₂⁴	1	2	yes	—
461	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
462	C₄×Dic₆₇	C₂⁴	1	2	yes	—
463	C₄×Dic₆₇	C₂⁴	1	2	yes	—
464	C₄×Dic₆₇	C₂⁴	1	2	yes	—
465	C₄×Dic₆₇	C₂⁴	1	4	yes	—
466	C₄×Dic₆₇	C₂⁴	1	2	yes	—
467	C₄×Dic₆₇	C₂⁴	1	4	yes	—
468	C₄×Dic₆₇	C₂⁴	1	4	yes	—
469	C₄×Dic₆₇	C₂⁴	1	4	yes	—
470	C₄×Dic₆₇	C₂⁴	1	8	yes	—
471	C₄×Dic₆₇	C₂⁴	1	4	yes	—
472	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
473	#41×C₆₇	—	2	4	no	—
474	#41×C₆₇	—	4	16	no	—
475	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
476	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
477	C₂×D₄×C₆₇	—	2	8	no	—
478	C₂×D₄×C₆₇	—	4	8	no	—
479	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
480	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
481	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
482	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
483	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
484	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
485	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
486	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
487	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
488	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
489	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
490	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
492	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
493	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
494	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
495	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₆₇	C₂⁴	1	2	yes	—
497	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
498	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
499	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
500	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
501	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₄²×C₆₇	C₂⁴	1	2	yes	—
504	C₄²×C₆₇	C₂⁴	1	2	yes	—
505	C₄²×C₆₇	C₂⁴	1	4	yes	—
506	C₄²×C₆₇	C₂⁴	1	4	yes	—
507	C₂³×C₆₇	—	2	8	no	—
508	C₂³×C₆₇	—	4	8	no	—
509	C₂³×C₆₇	C₂⁵	1	8	yes	—
510	C₂³×C₆₇	C₂⁵	1	2	yes	—
511	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
512	C₂²×D₆₇	—	2	4	no	—
513	C₂²×D₆₇	—	2	8	no	—
514	C₂²×D₆₇	—	2	4	no	—
515	C₂²×D₆₇	—	2	16	no	—
516	C₂²×D₆₇	—	2	8	no	—
517	C₂²×D₆₇	—	2	32	no	—
518	C₂²×D₆₇	—	2	16	no	—
519	C₂²×D₆₇	—	4	16	no	—
520	C₂²×D₆₇	—	4	8	no	—
521	C₂²×D₆₇	—	8	32	no	—
522	C₂²×D₆₇	C₂×#41	1	4	yes	—
523	C₂²×D₆₇	C₂⁵	1	8	yes	—
524	C₂²×D₆₇	C₂⁵	1	2	yes	—
525	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
526	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
527	Q₈×C₆₇	—	2	2	no	—
528	Q₈×C₆₇	—	2	8	no	—
529	D₄×C₆₇	—	2	4	no	—
530	D₄×C₆₇	—	2	8	no	—
531	D₄×C₆₇	—	2	8	no	—
532	D₄×C₆₇	—	2	2	no	—
533	D₄×C₆₇	—	2	16	no	—
534	D₄×C₆₇	—	4	8	no	—
535	D₄×C₆₇	—	4	16	no	—
536	C₂×C₄×C₆₇	—	2	4	no	—
537	C₂×C₄×C₆₇	—	2	4	no	—
538	C₂×C₄×C₆₇	—	2	8	no	—
539	C₂×C₄×C₆₇	—	4	16	no	—
540	C₂×C₄×C₆₇	C₂×#41	1	4	yes	complemented
541	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
542	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
543	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
544	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
545	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
546	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
547	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
548	C₂²⋊D₆₇	—	2	4	no	—
549	C₂²⋊D₆₇	—	2	4	no	—
550	C₂²⋊D₆₇	—	2	16	no	—
551	C₂²⋊D₆₇	—	2	16	no	—
552	C₂²⋊D₆₇	—	2	4	no	—
553	C₂²⋊D₆₇	—	2	32	no	—
554	C₂²⋊D₆₇	—	4	16	no	—
555	C₂²⋊D₆₇	—	4	16	no	—
556	C₂²⋊D₆₇	—	4	16	no	—
557	C₂×Dic₆₇	—	2	4	no	—
558	C₂×Dic₆₇	—	2	4	no	—
559	C₂×Dic₆₇	—	2	8	no	—
560	C₂×Dic₆₇	—	4	16	no	—
561	C₂×Dic₆₇	C₂×#41	1	4	yes	complemented
562	C₂×Dic₆₇	C₂⁵	1	2	yes	—
563	C₂×Dic₆₇	C₂⁵	1	4	yes	—
564	C₂×Dic₆₇	C₂⁵	1	2	yes	—
565	C₂×Dic₆₇	C₂⁵	1	8	yes	—
566	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
567	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
568	C₂×Dic₆₇	C₂⁵	1	2	yes	—
569	D₂₆₈	—	2	4	no	—
570	D₂₆₈	—	2	8	no	—
571	D₂₆₈	—	2	8	no	—
572	D₂₆₈	—	2	2	no	—
573	D₂₆₈	—	2	16	no	—
574	D₂₆₈	—	4	8	no	—
575	D₂₆₈	—	4	16	no	—
576	C₄×D₆₇	—	2	4	no	—
577	C₄×D₆₇	—	2	8	no	—
578	C₄×D₆₇	—	2	4	no	—
579	C₄×D₆₇	—	2	16	no	—
580	C₄×D₆₇	—	2	4	no	—
581	C₄×D₆₇	—	2	4	no	—
582	C₄×D₆₇	—	2	8	no	—
583	C₄×D₆₇	—	2	4	no	—
584	C₄×D₆₇	—	2	4	no	—
585	C₄×D₆₇	—	2	8	no	—
586	C₄×D₆₇	—	4	16	no	—
587	C₄×D₆₇	—	4	16	no	—
588	C₄×D₆₇	C₂×#41	1	4	yes	—
589	C₄×D₆₇	C₂×#41	1	4	yes	—
590	C₄×D₆₇	C₂×#41	1	4	yes	complemented
591	C₄×D₆₇	C₂×#41	1	4	yes	complemented
592	C₄×D₆₇	H(5,𝔽₂)	1	8	yes	—
593	Dic₁₃₄	—	2	2	no	—
594	Dic₁₃₄	—	2	8	no	—
595	Dic₁₃₄	—	2	4	no	—
596	Dic₁₃₄	—	2	16	no	—
597	C₂²×C₆₇	—	2	2	no	—
598	C₂²×C₆₇	—	2	2	no	—
599	C₂²×C₆₇	—	2	8	no	—
600	C₂²×C₆₇	—	2	4	no	—
601	C₂²×C₆₇	—	2	16	no	—
602	C₂²×C₆₇	—	8	8	no	—
603	C₂²×C₆₇	C₂²×#41	1	2	yes	—
604	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
605	C₂×D₆₇	—	2	2	no	—
606	C₂×D₆₇	—	2	8	no	—
607	C₂×D₆₇	—	2	2	no	—
608	C₂×D₆₇	—	2	8	no	—
609	C₂×D₆₇	—	2	4	no	—
610	C₂×D₆₇	—	2	16	no	—
611	C₂×D₆₇	—	4	8	no	—
612	C₂×D₆₇	—	4	32	no	—
613	C₂×D₆₇	—	8	16	no	—
614	C₂×D₆₇	—	8	8	no	—
615	C₂×D₆₇	C₂²×#41	1	2	yes	—
616	C₂×D₆₇	C₂²×#41	1	2	yes	—
617	C₂×D₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
618	C₄×C₆₇	—	2	2	no	—
619	C₄×C₆₇	—	2	8	no	—
620	C₄×C₆₇	—	2	4	no	—
621	C₄×C₆₇	—	2	2	no	—
622	C₄×C₆₇	C₂²×#41	1	2	yes	—
623	C₄×C₆₇	C₂²×#41	1	2	yes	—
624	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
625	Dic₆₇	—	2	2	no	—
626	Dic₆₇	—	2	8	no	—
627	Dic₆₇	—	2	4	no	—
628	Dic₆₇	—	2	2	no	—
629	Dic₆₇	C₂²×#41	1	2	yes	—
630	Dic₆₇	C₂²×#41	1	2	yes	—
631	Dic₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
632	C₂×#3508	—	67	1	no	maximal, Sylow
633	C₂×C₆₇	—	2	2	no	—
634	C₂×C₆₇	—	4	8	no	—
635	C₂×C₆₇	—	4	2	no	—
636	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
637	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	2	yes	—
638	D₆₇	—	2	2	no	—
639	D₆₇	—	4	2	no	—
640	D₆₇	—	4	8	no	—
641	D₆₇	#3508	1	4	yes	direct product factor
642	#3508	—	67	4	no	—
643	#3508	—	67	4	no	—
644	#3508	—	67	8	no	—
645	#3508	—	67	4	no	—
646	#3508	—	67	2	no	—
647	#3508	—	67	1	no	—
648	#3508	—	67	4	no	—
649	#3508	—	67	1	no	—
650	#3508	—	67	2	no	—
651	#3508	—	67	1	no	—
652	#3508	D₆₇	1	1	yes	characteristic, direct product factor
653	C₂×#559	—	67	4	no	—
654	C₂×#550	—	67	4	no	—
655	C₂×#546	—	67	8	no	—
656	C₂×#540	—	67	4	no	—
657	C₂×#535	—	67	2	no	—
658	C₂×#533	—	67	1	no	—
659	C₂×#532	—	67	4	no	—
660	C₂²×#127	—	67	1	no	—
661	C₂×#518	—	67	2	no	—
662	C₂×C₄×#41	—	67	1	no	—
663	C₆₇	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
664	C₂²×#41	—	67	8	no	—
665	C₂²×#41	—	67	1	no	—
666	C₂³×D₄	—	67	4	no	—
667	C₂³×D₄	—	67	2	no	—
668	#559	—	67	4	no	—
669	#559	—	67	8	no	—
670	#559	—	67	8	no	—
671	#559	—	67	16	no	—
672	#559	—	67	4	no	—
673	#559	—	67	4	no	—
674	#559	—	67	8	no	—
675	#559	—	67	8	no	—
676	#559	C₂×D₆₇	1	4	yes	complemented
677	#550	—	67	8	no	—
678	#550	—	67	4	no	—
679	#550	—	67	8	no	—
680	#550	—	67	8	no	—
681	#550	—	67	16	no	—
682	#550	—	67	4	no	—
683	#550	—	67	8	no	—
684	#550	—	67	4	no	—
685	#550	C₂×D₆₇	1	4	yes	complemented
686	#546	—	67	8	no	—
687	#546	—	67	8	no	—
688	#546	—	67	8	no	—
689	#546	—	67	16	no	—
690	#546	—	67	8	no	—
691	#546	—	67	16	no	—
692	#546	—	67	8	no	—
693	#546	—	67	16	no	—
694	#546	—	67	8	no	—
695	#546	—	67	8	no	—
696	#546	—	67	16	no	—
697	#546	C₂×D₆₇	1	8	yes	complemented
698	#540	—	67	4	no	—
699	#540	—	67	4	no	—
700	#540	—	67	16	no	—
701	#540	—	67	16	no	—
702	#540	—	67	8	no	—
703	#540	—	67	8	no	—
704	#540	—	67	4	no	—
705	#540	C₂×D₆₇	1	4	yes	complemented
706	#535	—	67	2	no	—
707	#535	—	67	2	no	—
708	#535	—	67	4	no	—
709	#535	—	67	4	no	—
710	#535	—	67	8	no	—
711	#535	—	67	8	no	—
712	#535	—	67	2	no	—
713	#535	C₂×D₆₇	1	2	yes	complemented
714	#533	—	67	2	no	—
715	#533	—	67	2	no	—
716	#533	—	67	4	no	—
717	#533	—	67	4	no	—
718	#533	—	67	2	no	—
719	#533	—	67	1	no	—
720	#533	C₂×D₆₇	1	1	yes	characteristic, complemented
721	#532	—	67	8	no	—
722	#532	—	67	4	no	—
723	#532	—	67	4	no	—
724	#532	—	67	8	no	—
725	#532	—	67	8	no	—
726	#532	—	67	8	no	—
727	#532	—	67	8	no	—
728	#532	—	67	8	no	—
729	#532	—	67	4	no	—
730	#532	C₂×D₆₇	1	4	yes	complemented
731	C₂×C₄⋊Q₈	—	67	2	no	—
732	C₂×#127	—	67	2	no	—
733	C₂×#127	—	67	4	no	—
734	C₂×#127	—	67	2	no	—
735	C₂×#127	—	67	2	no	—
736	C₂×#127	—	67	4	no	—
737	C₂×#127	—	67	4	no	—
738	C₂×#127	—	67	2	no	—
739	C₂×#127	—	67	2	no	—
740	C₂×#127	—	67	4	no	—
741	C₂×#127	—	67	1	no	—
742	C₂×#127	C₂×D₆₇	1	1	yes	characteristic, complemented
743	C₂×#125	—	67	2	no	—
744	C₂×#124	—	67	8	no	—
745	C₂×#124	—	67	4	no	—
746	C₂×#123	—	67	16	no	—
747	C₂×C₂²⋊Q₈	—	67	4	no	—
748	C₂×#121	—	67	8	no	—
749	C₂×#121	—	67	8	no	—
750	C₂×#121	—	67	16	no	—
751	C₂×#120	—	67	8	no	—
752	#518	—	67	2	no	—
753	#518	—	67	8	no	—
754	#518	—	67	8	no	—
755	#518	—	67	2	no	—
756	#518	—	67	2	no	—
757	#518	—	67	8	no	—
758	#518	C₂×D₆₇	1	2	yes	complemented
759	C₄×#41	—	67	1	no	—
760	C₄×#41	—	67	2	no	—
761	C₄×#41	—	67	4	no	—
762	C₄×#41	—	67	2	no	—
763	C₄×#41	—	67	1	no	—
764	C₄×#41	—	67	2	no	—
765	C₄×#41	—	67	1	no	—
766	C₄×#41	—	67	2	no	—
767	C₄×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
768	C₂×C₄×Q₈	—	67	2	no	—
769	C₂×C₄×Q₈	—	67	4	no	—
770	C₂×C₄×D₄	—	67	4	no	—
771	C₂×C₄×D₄	—	67	2	no	—
772	C₂×C₄×D₄	—	67	8	no	—
773	C₂×C₄×D₄	—	67	8	no	—
774	C₂×C₄×D₄	—	67	8	no	—
775	C₂×#117	—	67	1	no	—
776	C₂×#117	—	67	2	no	—
777	C₂×#117	—	67	2	no	—
778	C₂²×C₂²⋊C₄	—	67	8	no	—
779	C₂²×C₄²	—	67	1	no	—
780	C₂²×C₄²	—	67	2	no	—
781	C₂⁵	—	67	4	no	—
782	C₂×#41	—	268	32	no	—
783	C₂×#41	—	67	8	no	—
784	C₂×#41	—	67	1	no	—
785	C₂×#41	—	67	8	no	—
786	C₂×#41	—	67	16	no	—
787	C₂×#41	—	67	2	no	—
788	C₂×#41	—	67	1	no	—
789	C₂×#41	—	67	8	no	—
790	C₂×#41	—	67	16	no	—
791	C₂×#41	—	67	2	no	—
792	C₂×#41	—	67	1	no	—
793	C₂×#41	—	134	8	no	—
794	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
795	C₂×#41	C₂²×D₆₇	1	8	yes	complemented
796	C₂²×Q₈	—	67	1	no	—
797	C₂²×Q₈	—	67	4	no	—
798	C₂²×D₄	—	268	16	no	—
799	C₂²×D₄	—	67	8	no	—
800	C₂²×D₄	—	67	16	no	—
801	C₂²×D₄	—	67	8	no	—
802	C₂²×D₄	—	67	8	no	—
803	C₂²×D₄	—	67	8	no	—
804	C₂²×D₄	—	67	4	no	—
805	C₂²×D₄	—	67	2	no	—
806	C₂²×D₄	—	67	4	no	—
807	C₂²×D₄	—	67	4	no	—
808	C₂²×D₄	—	67	1	no	—
809	C₂²×D₄	—	67	8	no	—
810	C₂²×D₄	—	67	4	no	—
811	C₂²×D₄	—	67	4	no	—
812	C₂²×D₄	—	67	4	no	—
813	C₂²×D₄	—	67	2	no	—
814	C₂²×D₄	—	134	16	no	—
815	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
816	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
817	C₂³×C₄	—	67	16	no	—
818	C₂³×C₄	—	67	1	no	—
819	C₂³×C₄	—	67	2	no	—
820	C₂³×C₄	—	67	4	no	—
821	C₂³×C₄	—	67	2	no	—
822	C₄⋊Q₈	—	67	4	no	—
823	C₄⋊Q₈	—	67	4	no	—
824	C₄⋊Q₈	—	67	4	no	—
825	C₄⋊Q₈	—	67	2	no	—
826	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	complemented
827	#127	—	67	8	no	—
828	#127	—	67	4	no	—
829	#127	—	67	4	no	—
830	#127	—	67	8	no	—
831	#127	—	67	8	no	—
832	#127	—	67	8	no	—
833	#127	—	67	8	no	—
834	#127	—	67	4	no	—
835	#127	—	67	4	no	—
836	#127	—	67	16	no	—
837	#127	—	67	2	no	—
838	#127	—	67	2	no	—
839	#127	—	67	4	no	—
840	#127	—	67	4	no	—
841	#127	C₂²×D₆₇	1	2	yes	—
842	#127	C₂²×D₆₇	1	2	yes	—
843	#127	C₂²×D₆₇	1	4	yes	—
844	#127	C₂²×D₆₇	1	4	yes	complemented
845	#125	—	67	8	no	—
846	#125	—	67	4	no	—
847	#125	—	67	2	no	—
848	#125	C₂²×D₆₇	1	2	yes	complemented
849	#124	—	67	8	no	—
850	#124	—	67	4	no	—
851	#124	—	67	8	no	—
852	#124	—	67	4	no	—
853	#124	—	67	16	no	—
854	#124	—	67	16	no	—
855	#124	—	67	16	no	—
856	#124	—	67	8	no	—
857	#124	—	67	4	no	—
858	#124	C₂²×D₆₇	1	8	yes	complemented
859	#124	C₂²×D₆₇	1	4	yes	complemented
860	#123	—	67	16	no	—
861	#123	—	67	16	no	—
862	#123	—	67	16	no	—
863	#123	—	67	16	no	—
864	#123	—	67	16	no	—
865	#123	—	67	16	no	—
866	#123	—	67	16	no	—
867	#123	C₂²×D₆₇	1	16	yes	complemented
868	C₂²⋊Q₈	—	67	4	no	—
869	C₂²⋊Q₈	—	67	4	no	—
870	C₂²⋊Q₈	—	67	8	no	—
871	C₂²⋊Q₈	—	67	4	no	—
872	C₂²⋊Q₈	—	67	8	no	—
873	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	—
874	#121	—	67	8	no	—
875	#121	—	67	16	no	—
876	#121	—	67	8	no	—
877	#121	—	67	16	no	—
878	#121	—	67	16	no	—
879	#121	—	67	16	no	—
880	#121	—	67	16	no	—
881	#121	—	67	8	no	—
882	#121	—	67	8	no	—
883	#121	—	67	16	no	—
884	#121	—	67	8	no	—
885	#121	—	67	8	no	—
886	#121	—	67	16	no	—
887	#121	—	67	16	no	—
888	#121	—	67	16	no	—
889	#121	—	67	16	no	—
890	#121	—	67	16	no	—
891	#121	C₂²×D₆₇	1	8	yes	complemented
892	#121	C₂²×D₆₇	1	8	yes	complemented
893	#121	C₂²×D₆₇	1	16	yes	complemented
894	#120	—	67	8	no	—
895	#120	—	67	8	no	—
896	#120	—	67	16	no	—
897	#120	—	67	16	no	—
898	#120	—	67	8	no	—
899	#120	C₂²×D₆₇	1	8	yes	—
900	C₄×Q₈	—	67	2	no	—
901	C₄×Q₈	—	67	4	no	—
902	C₄×Q₈	—	67	4	no	—
903	C₄×Q₈	—	67	2	no	—
904	C₄×Q₈	—	67	8	no	—
905	C₄×Q₈	—	67	4	no	—
906	C₄×Q₈	—	67	2	no	—
907	C₄×Q₈	—	67	4	no	—
908	C₄×Q₈	—	67	8	no	—
909	C₄×Q₈	—	67	4	no	—
910	C₄×Q₈	C₂²×D₆₇	1	2	yes	complemented
911	C₄×Q₈	C₂²×D₆₇	1	4	yes	complemented
912	C₄×D₄	—	67	4	no	—
913	C₄×D₄	—	67	2	no	—
914	C₄×D₄	—	67	8	no	—
915	C₄×D₄	—	67	8	no	—
916	C₄×D₄	—	67	8	no	—
917	C₄×D₄	—	67	4	no	—
918	C₄×D₄	—	67	4	no	—
919	C₄×D₄	—	67	4	no	—
920	C₄×D₄	—	67	16	no	—
921	C₄×D₄	—	67	16	no	—
922	C₄×D₄	—	67	16	no	—
923	C₄×D₄	—	67	4	no	—
924	C₄×D₄	—	67	2	no	—
925	C₄×D₄	—	67	8	no	—
926	C₄×D₄	—	67	8	no	—
927	C₄×D₄	—	67	8	no	—
928	C₄×D₄	—	67	4	no	—
929	C₄×D₄	—	67	4	no	—
930	C₄×D₄	—	67	4	no	—
931	C₄×D₄	—	67	16	no	—
932	C₄×D₄	—	67	16	no	—
933	C₄×D₄	—	67	16	no	—
934	C₄×D₄	—	67	4	no	—
935	C₄×D₄	—	67	2	no	—
936	C₄×D₄	—	67	8	no	—
937	C₄×D₄	—	67	8	no	—
938	C₄×D₄	—	67	8	no	—
939	C₄×D₄	C₂²×D₆₇	1	4	yes	—
940	C₄×D₄	C₂²×D₆₇	1	2	yes	complemented
941	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
942	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
943	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
944	#117	—	67	1	no	—
945	#117	—	67	2	no	—
946	#117	—	67	2	no	—
947	#117	—	67	2	no	—
948	#117	—	67	4	no	—
949	#117	—	67	4	no	—
950	#117	—	67	2	no	—
951	#117	—	67	4	no	—
952	#117	—	67	4	no	—
953	#117	—	67	2	no	—
954	#117	—	67	2	no	—
955	#117	—	67	2	no	—
956	#117	—	67	4	no	—
957	#117	C₂²×D₆₇	1	1	yes	characteristic
958	#117	C₂²×D₆₇	1	2	yes	—
959	#117	C₂²×D₆₇	1	2	yes	complemented
960	C₂×C₄⋊C₄	—	67	2	no	—
961	C₂×C₄⋊C₄	—	67	4	no	—
962	C₂×C₄⋊C₄	—	67	4	no	—
963	C₂×C₄⋊C₄	—	67	4	no	—
964	C₂×C₄⋊C₄	—	67	8	no	—
965	C₂×C₂²⋊C₄	—	67	8	no	—
966	C₂×C₂²⋊C₄	—	67	16	no	—
967	C₂×C₂²⋊C₄	—	67	2	no	—
968	C₂×C₂²⋊C₄	—	67	4	no	—
969	C₂×C₂²⋊C₄	—	67	16	no	—
970	C₂×C₂²⋊C₄	—	67	8	no	—
971	C₂×C₂²⋊C₄	—	67	8	no	—
972	C₂×C₂²⋊C₄	—	67	16	no	—
973	C₂×C₂²⋊C₄	—	67	4	no	—
974	C₂×C₂²⋊C₄	—	67	16	no	—
975	C₂×C₂²⋊C₄	C₂²×D₆₇	1	8	yes	—
976	C₂×C₄²	—	67	2	no	—
977	C₂×C₄²	—	67	1	no	—
978	C₂×C₄²	—	67	4	no	—
979	C₂×C₄²	—	67	2	no	—
980	C₂×C₄²	—	67	2	no	—
981	C₂×C₄²	—	67	1	no	—
982	C₂×C₄²	—	67	4	no	—
983	C₂×C₄²	—	67	4	no	—
984	C₂×C₄²	—	67	2	no	—
985	C₂×C₄²	—	67	2	no	—
986	C₂×C₄²	—	67	1	no	—
987	C₂×C₄²	—	67	1	no	—
988	C₂×C₄²	—	67	4	no	—
989	C₂×C₄²	—	67	2	no	—
990	C₂×C₄²	—	67	2	no	—
991	C₂×C₄²	—	67	1	no	—
992	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
993	C₂×C₄²	C₂²×D₆₇	1	2	yes	complemented
994	C₂⁴	—	268	16	no	—
995	C₂⁴	—	67	8	no	—
996	C₂⁴	—	67	4	no	—
997	C₂⁴	—	67	1	no	—
998	C₂⁴	—	67	8	no	—
999	C₂⁴	—	67	2	no	—
1000	C₂⁴	—	134	16	no	—
1001	C₂⁴	C₂³×D₆₇	1	4	yes	—
1002	#41	—	2	4	no	—
1003	#41	—	4	16	no	—
1004	#41	—	268	16	no	—
1005	#41	—	268	32	no	—
1006	#41	—	268	16	no	—
1007	#41	—	268	32	no	—
1008	#41	—	268	16	no	—
1009	#41	—	134	8	no	—
1010	#41	—	134	8	no	—
1011	#41	—	134	4	no	—
1012	#41	—	134	4	no	—
1013	#41	—	134	4	no	—
1014	C₂×Q₈	—	67	2	no	—
1015	C₂×Q₈	—	67	1	no	—
1016	C₂×Q₈	—	67	8	no	—
1017	C₂×Q₈	—	67	4	no	—
1018	C₂×Q₈	—	134	16	no	—
1019	C₂×Q₈	—	134	4	no	—
1020	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
1021	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1022	C₂×D₄	—	2	8	no	—
1023	C₂×D₄	—	4	8	no	—
1024	C₂×D₄	—	268	8	no	—
1025	C₂×D₄	—	268	16	no	—
1026	C₂×D₄	—	268	16	no	—
1027	C₂×D₄	—	268	32	no	—
1028	C₂×D₄	—	268	16	no	—
1029	C₂×D₄	—	268	16	no	—
1030	C₂×D₄	—	67	16	no	—
1031	C₂×D₄	—	67	16	no	—
1032	C₂×D₄	—	67	16	no	—
1033	C₂×D₄	—	67	2	no	—
1034	C₂×D₄	—	67	2	no	—
1035	C₂×D₄	—	67	8	no	—
1036	C₂×D₄	—	67	8	no	—
1037	C₂×D₄	—	67	2	no	—
1038	C₂×D₄	—	67	16	no	—
1039	C₂×D₄	—	67	16	no	—
1040	C₂×D₄	—	67	8	no	—
1041	C₂×D₄	—	67	2	no	—
1042	C₂×D₄	—	67	4	no	—
1043	C₂×D₄	—	67	4	no	—
1044	C₂×D₄	—	67	1	no	—
1045	C₂×D₄	—	67	8	no	—
1046	C₂×D₄	—	134	32	no	—
1047	C₂×D₄	—	134	16	no	—
1048	C₂×D₄	—	134	16	no	—
1049	C₂×D₄	—	134	16	no	—
1050	C₂×D₄	—	134	16	no	—
1051	C₂×D₄	—	134	4	no	—
1052	C₂×D₄	—	134	16	no	—
1053	C₂×D₄	—	134	8	no	—
1054	C₂×D₄	—	134	8	no	—
1055	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1056	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1057	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1058	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
1059	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1060	C₂×D₄	C₂³×D₆₇	1	16	yes	—
1061	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1062	C₂²×C₄	—	268	32	no	—
1063	C₂²×C₄	—	67	16	no	—
1064	C₂²×C₄	—	67	16	no	—
1065	C₂²×C₄	—	67	16	no	—
1066	C₂²×C₄	—	67	1	no	—
1067	C₂²×C₄	—	67	8	no	—
1068	C₂²×C₄	—	67	1	no	—
1069	C₂²×C₄	—	67	1	no	—
1070	C₂²×C₄	—	67	2	no	—
1071	C₂²×C₄	—	67	1	no	—
1072	C₂²×C₄	—	67	1	no	—
1073	C₂²×C₄	—	67	2	no	—
1074	C₂²×C₄	—	67	4	no	—
1075	C₂²×C₄	—	67	2	no	—
1076	C₂²×C₄	—	67	2	no	—
1077	C₂²×C₄	—	67	4	no	—
1078	C₂²×C₄	—	67	2	no	—
1079	C₂²×C₄	—	67	2	no	—
1080	C₂²×C₄	—	67	2	no	—
1081	C₂²×C₄	—	67	4	no	—
1082	C₂²×C₄	—	67	4	no	—
1083	C₂²×C₄	—	67	2	no	—
1084	C₂²×C₄	—	67	2	no	—
1085	C₂²×C₄	—	67	8	no	—
1086	C₂²×C₄	—	134	8	no	—
1087	C₂²×C₄	—	134	16	no	—
1088	C₂²×C₄	—	134	8	no	—
1089	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1090	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1091	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1092	C₂²×C₄	C₂³×D₆₇	1	16	yes	—
1093	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1094	C₄⋊C₄	—	67	4	no	—
1095	C₄⋊C₄	—	67	2	no	—
1096	C₄⋊C₄	—	67	8	no	—
1097	C₄⋊C₄	—	67	4	no	—
1098	C₄⋊C₄	—	67	4	no	—
1099	C₄⋊C₄	—	67	4	no	—
1100	C₄⋊C₄	—	67	4	no	—
1101	C₄⋊C₄	—	67	8	no	—
1102	C₄⋊C₄	—	67	4	no	—
1103	C₄⋊C₄	—	67	8	no	—
1104	C₄⋊C₄	—	67	8	no	—
1105	C₄⋊C₄	—	67	8	no	—
1106	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
1107	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1108	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1109	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1110	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1111	C₂²⋊C₄	—	67	2	no	—
1112	C₂²⋊C₄	—	67	4	no	—
1113	C₂²⋊C₄	—	67	16	no	—
1114	C₂²⋊C₄	—	67	4	no	—
1115	C₂²⋊C₄	—	67	16	no	—
1116	C₂²⋊C₄	—	67	4	no	—
1117	C₂²⋊C₄	—	67	8	no	—
1118	C₂²⋊C₄	—	67	16	no	—
1119	C₂²⋊C₄	—	67	16	no	—
1120	C₂²⋊C₄	—	67	4	no	—
1121	C₂²⋊C₄	—	67	4	no	—
1122	C₂²⋊C₄	—	67	16	no	—
1123	C₂²⋊C₄	—	67	16	no	—
1124	C₂²⋊C₄	C₂³×D₆₇	1	2	yes	—
1125	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1126	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
1127	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1128	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
1129	C₄²	—	67	2	no	—
1130	C₄²	—	67	1	no	—
1131	C₄²	—	67	4	no	—
1132	C₄²	—	67	2	no	—
1133	C₄²	—	67	2	no	—
1134	C₄²	—	67	1	no	—
1135	C₄²	—	67	4	no	—
1136	C₄²	—	67	4	no	—
1137	C₄²	—	67	4	no	—
1138	C₄²	—	67	2	no	—
1139	C₄²	—	67	2	no	—
1140	C₄²	—	67	2	no	—
1141	C₄²	—	67	8	no	—
1142	C₄²	—	67	4	no	—
1143	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1144	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1145	C₄²	C₂³×D₆₇	1	2	yes	—
1146	C₄²	C₂³×D₆₇	1	2	yes	—
1147	C₄²	C₂³×D₆₇	1	4	yes	—
1148	C₄²	C₂³×D₆₇	1	4	yes	—
1149	C₂³	—	2	8	no	—
1150	C₂³	—	4	8	no	—
1151	C₂³	—	268	8	no	—
1152	C₂³	—	268	16	no	—
1153	C₂³	—	536	32	no	—
1154	C₂³	—	67	1	no	—
1155	C₂³	—	67	4	no	—
1156	C₂³	—	67	1	no	—
1157	C₂³	—	67	8	no	—
1158	C₂³	—	67	2	no	—
1159	C₂³	—	134	32	no	—
1160	C₂³	—	134	8	no	—
1161	C₂³	—	134	4	no	—
1162	C₂³	—	134	16	no	—
1163	C₂³	—	134	16	no	—
1164	C₂³	—	134	4	no	—
1165	C₂³	—	134	8	no	—
1166	C₂³	C₂⁴×D₆₇	1	8	yes	—
1167	C₂³	C₂⁴×D₆₇	1	2	yes	—
1168	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	8	no	—
1171	Q₈	—	134	16	no	—
1172	Q₈	—	134	4	no	—
1173	Q₈	—	134	2	no	—
1174	Q₈	—	134	8	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	2	8	no	—
1177	D₄	—	2	8	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	16	no	—
1180	D₄	—	4	8	no	—
1181	D₄	—	4	16	no	—
1182	D₄	—	268	8	no	—
1183	D₄	—	268	16	no	—
1184	D₄	—	268	16	no	—
1185	D₄	—	268	16	no	—
1186	D₄	—	268	16	no	—
1187	D₄	—	134	4	no	—
1188	D₄	—	134	32	no	—
1189	D₄	—	134	16	no	—
1190	D₄	—	134	16	no	—
1191	D₄	—	134	4	no	—
1192	D₄	—	134	4	no	—
1193	D₄	—	134	4	no	—
1194	D₄	—	134	8	no	—
1195	D₄	—	134	8	no	—
1196	D₄	—	134	2	no	—
1197	D₄	—	134	16	no	—
1198	C₂×C₄	—	2	4	no	—
1199	C₂×C₄	—	2	4	no	—
1200	C₂×C₄	—	2	8	no	—
1201	C₂×C₄	—	4	16	no	—
1202	C₂×C₄	—	268	16	no	—
1203	C₂×C₄	—	268	16	no	—
1204	C₂×C₄	—	268	16	no	—
1205	C₂×C₄	—	67	4	no	—
1206	C₂×C₄	—	67	1	no	—
1207	C₂×C₄	—	67	1	no	—
1208	C₂×C₄	—	67	2	no	—
1209	C₂×C₄	—	67	4	no	—
1210	C₂×C₄	—	67	4	no	—
1211	C₂×C₄	—	67	4	no	—
1212	C₂×C₄	—	67	4	no	—
1213	C₂×C₄	—	67	8	no	—
1214	C₂×C₄	—	67	2	no	—
1215	C₂×C₄	—	67	4	no	—
1216	C₂×C₄	—	67	2	no	—
1217	C₂×C₄	—	67	8	no	—
1218	C₂×C₄	—	134	4	no	—
1219	C₂×C₄	—	134	8	no	—
1220	C₂×C₄	—	134	4	no	—
1221	C₂×C₄	—	134	8	no	—
1222	C₂×C₄	—	134	16	no	—
1223	C₂×C₄	—	134	4	no	—
1224	C₂×C₄	—	134	4	no	—
1225	C₂×C₄	—	134	4	no	—
1226	C₂×C₄	—	134	8	no	—
1227	C₂×C₄	—	134	4	no	—
1228	C₂×C₄	—	134	4	no	—
1229	C₂×C₄	—	134	4	no	—
1230	C₂×C₄	—	134	8	no	—
1231	C₂×C₄	#41×D₆₇	1	4	yes	complemented
1232	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1233	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1234	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1235	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
1236	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1237	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1238	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1239	C₂²	—	2	2	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	8	no	—
1242	C₂²	—	2	4	no	—
1243	C₂²	—	2	16	no	—
1244	C₂²	—	8	8	no	—
1245	C₂²	—	268	32	no	—
1246	C₂²	—	268	8	no	—
1247	C₂²	—	536	8	no	—
1248	C₂²	—	536	16	no	—
1249	C₂²	—	67	2	no	—
1250	C₂²	—	67	4	no	—
1251	C₂²	—	67	2	no	—
1252	C₂²	—	134	8	no	—
1253	C₂²	—	134	2	no	—
1254	C₂²	—	134	8	no	—
1255	C₂²	—	134	16	no	—
1256	C₂²	—	134	4	no	—
1257	C₂²	—	134	2	no	—
1258	C₂²	C₂×#41×D₆₇	1	2	yes	—
1259	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1260	C₄	—	2	2	no	—
1261	C₄	—	2	4	no	—
1262	C₄	—	2	2	no	—
1263	C₄	—	2	8	no	—
1264	C₄	—	67	2	no	—
1265	C₄	—	67	2	no	—
1266	C₄	—	67	4	no	—
1267	C₄	—	134	2	no	—
1268	C₄	—	134	4	no	—
1269	C₄	—	134	8	no	—
1270	C₄	—	134	2	no	—
1271	C₄	C₂×#41×D₆₇	1	2	yes	—
1272	C₄	C₂×#41×D₆₇	1	2	yes	—
1273	C₄	H(5,𝔽₂)×D₆₇	1	4	yes	—
1274	C₂	—	2	2	no	—
1275	C₂	—	4	8	no	—
1276	C₂	—	4	2	no	—
1277	C₂	—	268	8	no	—
1278	C₂	—	268	2	no	—
1279	C₂	—	67	4	no	—
1280	C₂	—	134	2	no	—
1281	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1282	C₂	C₂×H(5,𝔽₂)×D₆₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Fitting	C₆₇×#3508	C₂
hypercenter	#3508	D₆₇
hypocenter	C₆₇	C₂×#3508
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #3508

Complements

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

N	H ≅ G/N	type
1. #22574086	C₂	semidirect
2. #22574085	C₂	semidirect
3. #22574084	C₂	semidirect
4. #22574083	C₂	semidirect
5. #22574082	C₂	semidirect
6. #22574081	C₂	semidirect
7. #22574080	C₂	semidirect
8. #22574079	C₂	semidirect
9. #22574078	C₂	semidirect
10. #22574077	C₂	semidirect
11. #559×D₆₇	C₂	semidirect
12. #550×D₆₇	C₂	semidirect
13. #546×D₆₇	C₂	semidirect
14. #540×D₆₇	C₂	semidirect
15. #535×D₆₇	C₂	semidirect
16. #533×D₆₇	C₂	semidirect
17. #532×D₆₇	C₂	semidirect
18. C₂×#127×D₆₇	C₂	semidirect
19. #518×D₆₇	C₂	semidirect
20. C₄×#41×D₆₇	C₂	semidirect
21. C₆₇×#3508	C₂	semidirect
23. C₂×#41×D₆₇	C₂²	semidirect
26. #16864132	C₂²	semidirect
27. #16864131	C₂²	semidirect
28. #16864131	C₂²	semidirect
29. #16864130	C₂²	semidirect
30. #16864129	C₂²	semidirect
31. #16864129	C₂²	semidirect
32. #16864128	C₂²	semidirect
33. #16864128	C₂²	semidirect
34. #16864068	C₂²	semidirect
35. #16864067	C₂²	semidirect
36. #16864067	C₂²	semidirect
37. #16864066	C₂²	semidirect
38. #16864066	C₂²	semidirect
39. #16864065	C₂²	semidirect
40. #16864064	C₂²	semidirect
41. #16864064	C₂²	semidirect
42. #16864043	C₂²	semidirect
43. #16864042	C₂²	semidirect
44. #16864041	C₂²	semidirect
45. #16864040	C₂²	semidirect
46. #16864039	C₂²	semidirect
47. #16864038	C₂²	semidirect
48. #16864037	C₂²	semidirect
49. #16864036	C₂²	semidirect
50. #16864035	C₂²	semidirect
51. #16864034	C₂²	semidirect
52. #16864033	C₂²	semidirect
53. #16864002	C₂²	semidirect
54. #16864001	C₂²	semidirect
55. #16864000	C₂²	semidirect
56. #16863999	C₂²	semidirect
57. #16863998	C₂²	semidirect
58. #16863997	C₂²	semidirect
59. #16863996	C₂²	semidirect
60. #16863965	C₂²	semidirect
61. #16863964	C₂²	semidirect
62. #16863963	C₂²	semidirect
63. #16863962	C₂²	semidirect
64. #16863961	C₂²	semidirect
65. #16863960	C₂²	semidirect
66. #16863959	C₂²	semidirect
67. #16863953	C₂²	semidirect
68. #16863952	C₂²	semidirect
69. #16863951	C₂²	semidirect
70. #16863950	C₂²	semidirect
71. #16863949	C₂²	semidirect
72. #16863948	C₂²	semidirect
73. #16863947	C₂²	semidirect
74. #16863946	C₂²	semidirect
75. #16863945	C₂²	semidirect
76. #16863944	C₂²	semidirect
77. #16863943	C₂²	semidirect
78. #16863943	C₂²	semidirect
79. #16863942	C₂²	semidirect
80. #16863941	C₂²	semidirect
81. #16863941	C₂²	semidirect
82. C₄⋊Q₈×D₆₇	C₂²	semidirect
83. C₂×#14524040	C₂²	semidirect
84. C₂×#14524039	C₂²	semidirect
85. C₂×#14524039	C₂²	semidirect
89. #127×D₆₇	C₂²	semidirect
90. #127×D₆₇	C₂²	semidirect
91. #127×D₆₇	C₂²	semidirect
92. #127×D₆₇	C₂²	semidirect
93. #125×D₆₇	C₂²	semidirect
94. #124×D₆₇	C₂²	semidirect
95. #124×D₆₇	C₂²	semidirect
96. #123×D₆₇	C₂²	semidirect
98. #121×D₆₇	C₂²	semidirect
99. #121×D₆₇	C₂²	semidirect
100. #121×D₆₇	C₂²	semidirect
102. #16863871	C₂²	semidirect
103. #16863870	C₂²	semidirect
104. #16863870	C₂²	semidirect
105. #16863869	C₂²	semidirect
106. #16863868	C₂²	semidirect
107. #16863868	C₂²	semidirect
108. #41×Dic₆₇	C₂²	semidirect
109. C₄×#11761629	C₂²	semidirect
110. C₄×#11761628	C₂²	semidirect
111. C₄×#11761628	C₂²	semidirect
112. #16863864	C₂²	semidirect
113. #16863864	C₂²	semidirect
114. C₄×#11761627	C₂²	semidirect
115. C₄×#11761627	C₂²	semidirect
116. C₄×Q₈×D₆₇	C₂²	semidirect
117. C₄×Q₈×D₆₇	C₂²	semidirect
119. C₄×D₄×D₆₇	C₂²	semidirect
120. C₄×D₄×D₆₇	C₂²	semidirect
121. C₄×D₄×D₆₇	C₂²	semidirect
122. C₄×D₄×D₆₇	C₂²	semidirect
125. #117×D₆₇	C₂²	semidirect
128. C₂×C₄²×D₆₇	C₂²	semidirect
129. #559×C₆₇	C₂²	semidirect
130. #550×C₆₇	C₂²	semidirect
131. #546×C₆₇	C₂²	semidirect
132. #540×C₆₇	C₂²	semidirect
133. #535×C₆₇	C₂²	semidirect
134. #533×C₆₇	C₂²	semidirect
135. #532×C₆₇	C₂²	semidirect
136. C₂×#127×C₆₇	C₂²	semidirect
137. #518×C₆₇	C₂²	semidirect
138. C₄×#41×C₆₇	C₂²	semidirect
141. C₂×#11761629	C₂³	semidirect
144. C₂×#11761628	C₂³	semidirect
145. C₂×#11761628	C₂³	semidirect
148. C₂×#11761627	C₂³	semidirect
149. C₂×#11761627	C₂³	semidirect
176. #14524043	C₂³	semidirect
177. #14524042	C₂³	semidirect
178. #14524042	C₂³	semidirect
179. #14524041	C₂³	semidirect
183. #14524040	C₂³	semidirect
191. #14524039	C₂³	semidirect
192. #14524039	C₂³	semidirect
193. #14524039	C₂³	semidirect
194. #14524035	C₂³	semidirect
195. #14524034	C₂³	semidirect
196. #14524033	C₂³	semidirect
197. #14524032	C₂³	semidirect
198. #14524032	C₂³	semidirect
199. #14524031	C₂³	semidirect
200. #14524031	C₂³	semidirect
201. #14524030	C₂³	semidirect
202. #14524030	C₂³	semidirect
203. #14524029	C₂³	semidirect
204. #14524029	C₂³	semidirect
205. #14524029	C₂³	semidirect
206. #14524028	C₂³	semidirect
207. #14524028	C₂³	semidirect
208. #14524027	C₂³	semidirect
209. #14524026	C₂³	semidirect
210. #14524025	C₂³	semidirect
211. #14524025	C₂³	semidirect
212. #14524024	C₂³	semidirect
218. #14524018	C₂³	semidirect
219. #14524018	C₂³	semidirect
220. #14524018	C₂³	semidirect
221. #14524017	C₂³	semidirect
222. #14524017	C₂³	semidirect
223. #14524017	C₂³	semidirect
224. #14524016	C₂³	semidirect
225. #14524016	C₂³	semidirect
226. #14524016	C₂³	semidirect
227. #14524016	C₂³	semidirect
228. #14524015	C₂³	semidirect
229. #14524015	C₂³	semidirect
230. #14524015	C₂³	semidirect
231. #14524015	C₂³	semidirect
232. #14524014	C₂³	semidirect
233. #14524014	C₂³	semidirect
234. #14524014	C₂³	semidirect
240. Q₈×Dic₆₇	C₂³	semidirect
241. Q₈×Dic₆₇	C₂³	semidirect
242. C₄×Dic₁₃₄	C₂³	semidirect
243. C₄×Dic₁₃₄	C₂³	semidirect
244. C₄×Dic₁₃₄	C₂³	semidirect
245. C₄×Dic₁₃₄	C₂³	semidirect
246. #14524008	C₂³	semidirect
247. #14524008	C₂³	semidirect
248. #14524008	C₂³	semidirect
249. #14524008	C₂³	semidirect
251. C₄×D₂₆₈	C₂³	semidirect
252. C₄×D₂₆₈	C₂³	semidirect
253. C₄×D₂₆₈	C₂³	semidirect
254. C₄×D₂₆₈	C₂³	semidirect
256. D₄×Dic₆₇	C₂³	semidirect
257. D₄×Dic₆₇	C₂³	semidirect
258. D₄×Dic₆₇	C₂³	semidirect
259. D₄×Dic₆₇	C₂³	semidirect
261. #14524005	C₂³	semidirect
262. #14524005	C₂³	semidirect
263. #14524005	C₂³	semidirect
264. #14524005	C₂³	semidirect
267. C₄×C₂²⋊D₆₇	C₂³	semidirect
268. C₄×C₂²⋊D₆₇	C₂³	semidirect
269. C₄×C₂²⋊D₆₇	C₂³	semidirect
270. C₄×C₂²⋊D₆₇	C₂³	semidirect
273. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
274. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
275. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
276. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
279. #14524002	C₂³	semidirect
282. #14524001	C₂³	semidirect
285. #14524000	C₂³	semidirect
286. #14524000	C₂³	semidirect
289. #14523999	C₂³	semidirect
307. C₂×C₄×Dic₆₇	C₂³	semidirect
308. C₂×C₄×Dic₆₇	C₂³	semidirect
318. C₄²×D₆₇	C₂³	semidirect
319. C₄²×D₆₇	C₂³	semidirect
320. C₄²×D₆₇	C₂³	semidirect
322. C₂×#41×C₆₇	C₂³	semidirect
325. C₄⋊Q₈×C₆₇	C₂³	semidirect
329. #127×C₆₇	C₂³	semidirect
330. #125×C₆₇	C₂³	semidirect
331. #124×C₆₇	C₂³	semidirect
332. #124×C₆₇	C₂³	semidirect
333. #123×C₆₇	C₂³	semidirect
335. #121×C₆₇	C₂³	semidirect
336. #121×C₆₇	C₂³	semidirect
337. #121×C₆₇	C₂³	semidirect
339. C₄×Q₈×C₆₇	C₂³	semidirect
340. C₄×Q₈×C₆₇	C₂³	semidirect
342. C₄×D₄×C₆₇	C₂³	semidirect
343. C₄×D₄×C₆₇	C₂³	semidirect
344. C₄×D₄×C₆₇	C₂³	semidirect
345. C₄×D₄×C₆₇	C₂³	semidirect
348. #117×C₆₇	C₂³	semidirect
351. C₂×C₄²×C₆₇	C₂³	semidirect
415. C₂×C₄×D₆₇	#41	semidirect
540. C₂×C₄×C₆₇	C₂×#41	semidirect
561. C₂×Dic₆₇	C₂×#41	semidirect
590. C₄×D₆₇	C₂×#41	semidirect
591. C₄×D₆₇	C₂×#41	semidirect
641. D₆₇	#3508	direct (N × H)
652. #3508	D₆₇	direct (N × H)
663. C₆₇	C₂×#3508	semidirect
676. #559	C₂×D₆₇	semidirect
685. #550	C₂×D₆₇	semidirect
697. #546	C₂×D₆₇	semidirect
705. #540	C₂×D₆₇	semidirect
713. #535	C₂×D₆₇	semidirect
720. #533	C₂×D₆₇	semidirect
730. #532	C₂×D₆₇	semidirect
742. C₂×#127	C₂×D₆₇	semidirect
758. #518	C₂×D₆₇	semidirect
767. C₄×#41	C₂×D₆₇	semidirect
795. C₂×#41	C₂²×D₆₇	semidirect
826. C₄⋊Q₈	C₂²×D₆₇	semidirect
844. #127	C₂²×D₆₇	semidirect
848. #125	C₂²×D₆₇	semidirect
858. #124	C₂²×D₆₇	semidirect
859. #124	C₂²×D₆₇	semidirect
867. #123	C₂²×D₆₇	semidirect
891. #121	C₂²×D₆₇	semidirect
892. #121	C₂²×D₆₇	semidirect
893. #121	C₂²×D₆₇	semidirect
910. C₄×Q₈	C₂²×D₆₇	semidirect
911. C₄×Q₈	C₂²×D₆₇	semidirect
940. C₄×D₄	C₂²×D₆₇	semidirect
941. C₄×D₄	C₂²×D₆₇	semidirect
942. C₄×D₄	C₂²×D₆₇	semidirect
943. C₄×D₄	C₂²×D₆₇	semidirect
959. #117	C₂²×D₆₇	semidirect
993. C₂×C₄²	C₂²×D₆₇	semidirect
1231. C₂×C₄	#41×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574086	2
#22574085	2
#22574084	2
#22574083	2
#22574082	2
#22574081	2
#22574080	2
#22574079	2
#22574078	2
#22574077	2
#559×D₆₇	2
#550×D₆₇	2
#546×D₆₇	2
#540×D₆₇	2
#535×D₆₇	2
#533×D₆₇	2
#532×D₆₇	2
C₂×#127×D₆₇	2
#518×D₆₇	2
C₄×#41×D₆₇	2
C₆₇×#3508	2
C₂×#3508	67

Subgroups — #3508×D67 #31764182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3508×D₆₇ #31764182