Subgroups — C₆₇×#62781 #30742032

Order 17152.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3521	C₂	1	8	yes	maximal, complemented
2	C₆₇×#3515	C₂	1	4	yes	maximal, complemented
3	C₆₇×#3514	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3507	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3505	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3493	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3491	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3485	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3482	C₂	1	4	yes	maximal, complemented
12	C₆₇×#3481	C₂	1	4	yes	maximal, complemented
13	C₆₇×#3475	C₂	1	8	yes	maximal, complemented
14	C₆₇×#3461	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3459	C₂	1	4	yes	maximal, complemented
16	C₆₇×#3444	C₂	1	2	yes	maximal, complemented
17	C₂×#529×C₆₇	C₂	1	4	yes	maximal, complemented
18	C₄×H(5,𝔽₂)×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	#559×C₆₇	C₂²	1	4	yes	complemented
23	#557×C₆₇	C₂²	1	4	yes	complemented
24	#556×C₆₇	C₂²	1	8	yes	complemented
25	#556×C₆₇	C₂²	1	8	yes	complemented
26	#556×C₆₇	C₂²	1	4	yes	complemented
27	#555×C₆₇	C₂²	1	8	yes	complemented
28	#554×C₆₇	C₂²	1	8	yes	complemented
29	#554×C₆₇	C₂²	1	4	yes	complemented
30	#554×C₆₇	C₂²	1	4	yes	complemented
31	#553×C₆₇	C₂²	1	16	yes	complemented
32	#553×C₆₇	C₂²	1	8	yes	complemented
33	#553×C₆₇	C₂²	1	8	yes	complemented
34	#552×C₆₇	C₂²	1	8	yes	complemented
35	#552×C₆₇	C₂²	1	16	yes	complemented
36	#552×C₆₇	C₂²	1	16	yes	complemented
37	#552×C₆₇	C₂²	1	8	yes	complemented
38	#552×C₆₇	C₂²	1	8	yes	complemented
39	#551×C₆₇	C₂²	1	16	yes	complemented
40	#551×C₆₇	C₂²	1	16	yes	complemented
41	#551×C₆₇	C₂²	1	16	yes	complemented
42	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
43	#548×C₆₇	C₂²	1	8	yes	complemented
44	#547×C₆₇	C₂²	1	8	yes	complemented
45	#547×C₆₇	C₂²	1	8	yes	complemented
46	#547×C₆₇	C₂²	1	4	yes	complemented
47	#546×C₆₇	C₂²	1	8	yes	complemented
48	#546×C₆₇	C₂²	1	8	yes	complemented
49	#546×C₆₇	C₂²	1	8	yes	complemented
50	#546×C₆₇	C₂²	1	8	yes	complemented
51	D₄²×C₆₇	C₂²	1	4	yes	complemented
52	#544×C₆₇	C₂²	1	2	yes	complemented
53	#543×C₆₇	C₂²	1	4	yes	complemented
54	#542×C₆₇	C₂²	1	8	yes	complemented
55	#541×C₆₇	C₂²	1	8	yes	complemented
56	#539×C₆₇	C₂²	1	16	yes	complemented
57	#539×C₆₇	C₂²	1	8	yes	complemented
58	#539×C₆₇	C₂²	1	8	yes	complemented
59	#538×C₆₇	C₂²	1	16	yes	complemented
60	#538×C₆₇	C₂²	1	8	yes	complemented
61	#537×C₆₇	C₂²	1	2	yes	—
62	#536×C₆₇	C₂²	1	4	yes	complemented
63	#534×C₆₇	C₂²	1	4	yes	—
64	#534×C₆₇	C₂²	1	8	yes	complemented
65	#533×C₆₇	C₂²	1	2	yes	complemented
66	#533×C₆₇	C₂²	1	2	yes	complemented
67	#533×C₆₇	C₂²	1	2	yes	complemented
68	#533×C₆₇	C₂²	1	8	yes	complemented
69	#532×C₆₇	C₂²	1	2	yes	—
70	#532×C₆₇	C₂²	1	2	yes	complemented
71	#532×C₆₇	C₂²	1	2	yes	complemented
72	#529×C₆₇	C₂²	1	8	yes	complemented
73	#529×C₆₇	C₂²	1	4	yes	complemented
74	#529×C₆₇	C₂²	1	4	yes	complemented
75	#529×C₆₇	C₂²	1	4	yes	complemented
76	#529×C₆₇	C₂²	1	8	yes	complemented
77	#529×C₆₇	C₂²	1	8	yes	complemented
78	#529×C₆₇	C₂²	1	8	yes	complemented
79	#529×C₆₇	C₂²	1	8	yes	complemented
80	#529×C₆₇	C₂²	1	8	yes	complemented
81	#529×C₆₇	C₂²	1	8	yes	complemented
82	#529×C₆₇	C₂²	1	4	yes	complemented
83	#529×C₆₇	C₂²	1	4	yes	complemented
84	#529×C₆₇	C₂²	1	4	yes	complemented
85	#529×C₆₇	C₂²	1	16	yes	complemented
86	#529×C₆₇	C₂²	1	8	yes	complemented
87	C₂×#126×C₆₇	C₂²	1	8	yes	complemented
88	C₂×#125×C₆₇	C₂²	1	4	yes	complemented
89	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
90	#525×C₆₇	C₂²	1	4	yes	complemented
91	#525×C₆₇	C₂²	1	4	yes	complemented
92	#525×C₆₇	C₂²	1	4	yes	complemented
93	#525×C₆₇	C₂²	1	16	yes	complemented
94	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
95	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
96	C₂×#121×C₆₇	C₂²	1	4	yes	—
97	#520×C₆₇	C₂²	1	8	yes	complemented
98	#520×C₆₇	C₂²	1	4	yes	complemented
99	#518×C₆₇	C₂²	1	2	yes	—
100	#518×C₆₇	C₂²	1	8	yes	complemented
101	#518×C₆₇	C₂²	1	8	yes	complemented
102	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
103	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
104	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
105	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
106	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
107	C₄×#41×C₆₇	C₂²	1	8	yes	complemented
108	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
109	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
110	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
113	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
116	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
117	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
118	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
119	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
120	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
121	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×#117×C₆₇	C₂²	1	8	yes	complemented
123	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
124	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	H(5,𝔽₂)×C₆₇	—	2	16	no	—
126	C₂×#41×C₆₇	—	2	8	no	—
127	C₂×#41×C₆₇	C₂³	1	4	yes	—
128	C₂×#41×C₆₇	C₂³	1	4	yes	—
129	C₂×#41×C₆₇	C₂³	1	4	yes	—
130	C₂×#41×C₆₇	C₂³	1	8	yes	—
131	C₂×#41×C₆₇	C₂³	1	4	yes	—
132	C₂×#41×C₆₇	C₂³	1	4	yes	—
133	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
138	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
147	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
151	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
152	#127×C₆₇	C₂³	1	2	yes	—
153	#126×C₆₇	C₂³	1	8	yes	—
154	#126×C₆₇	C₂³	1	16	yes	—
155	#126×C₆₇	C₂³	1	16	yes	—
156	#126×C₆₇	C₂³	1	16	yes	—
157	#126×C₆₇	C₂³	1	8	yes	—
158	#126×C₆₇	C₂³	1	16	yes	—
159	#126×C₆₇	C₂³	1	16	yes	—
160	#126×C₆₇	C₂³	1	16	yes	—
161	#125×C₆₇	C₂³	1	4	yes	—
162	#125×C₆₇	C₂³	1	8	yes	—
163	#125×C₆₇	C₂³	1	8	yes	—
164	#125×C₆₇	C₂³	1	8	yes	—
165	#125×C₆₇	C₂³	1	4	yes	—
166	#125×C₆₇	C₂³	1	4	yes	—
167	#125×C₆₇	C₂³	1	16	yes	—
168	#125×C₆₇	C₂³	1	8	yes	—
169	#125×C₆₇	C₂³	1	16	yes	—
170	#124×C₆₇	C₂³	1	4	yes	—
171	#124×C₆₇	C₂³	1	8	yes	—
172	#124×C₆₇	C₂³	1	8	yes	—
173	#124×C₆₇	C₂³	1	8	yes	—
174	#124×C₆₇	C₂³	1	4	yes	—
175	#124×C₆₇	C₂³	1	4	yes	—
176	#124×C₆₇	C₂³	1	8	yes	—
177	#124×C₆₇	C₂³	1	16	yes	—
178	#123×C₆₇	C₂³	1	8	yes	—
179	#123×C₆₇	C₂³	1	16	yes	—
180	#123×C₆₇	C₂³	1	16	yes	—
181	#123×C₆₇	C₂³	1	16	yes	—
182	#123×C₆₇	C₂³	1	8	yes	—
183	#123×C₆₇	C₂³	1	8	yes	—
184	#123×C₆₇	C₂³	1	16	yes	—
185	#123×C₆₇	C₂³	1	16	yes	—
186	#123×C₆₇	C₂³	1	16	yes	—
187	#123×C₆₇	C₂³	1	16	yes	—
188	#123×C₆₇	C₂³	1	16	yes	—
189	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
190	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
191	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
194	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
199	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
204	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
205	#121×C₆₇	C₂³	1	4	yes	—
206	#121×C₆₇	C₂³	1	8	yes	—
207	#121×C₆₇	C₂³	1	8	yes	—
208	#121×C₆₇	C₂³	1	8	yes	—
209	#121×C₆₇	C₂³	1	4	yes	—
210	#121×C₆₇	C₂³	1	4	yes	—
211	#121×C₆₇	C₂³	1	4	yes	—
212	#121×C₆₇	C₂³	1	4	yes	—
213	#121×C₆₇	C₂³	1	4	yes	—
214	#121×C₆₇	C₂³	1	16	yes	—
215	#121×C₆₇	C₂³	1	16	yes	—
216	#121×C₆₇	C₂³	1	16	yes	—
217	#121×C₆₇	C₂³	1	8	yes	—
218	#120×C₆₇	C₂³	1	8	yes	—
219	#120×C₆₇	C₂³	1	16	yes	—
220	#120×C₆₇	C₂³	1	16	yes	—
221	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
222	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
223	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
224	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
225	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
226	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
227	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
228	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
229	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
230	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
231	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
232	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
233	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
234	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
235	C₄×D₄×C₆₇	C₂³	1	4	yes	—
236	C₄×D₄×C₆₇	C₂³	1	4	yes	—
237	C₄×D₄×C₆₇	C₂³	1	4	yes	—
238	C₄×D₄×C₆₇	C₂³	1	4	yes	—
239	C₄×D₄×C₆₇	C₂³	1	8	yes	—
240	C₄×D₄×C₆₇	C₂³	1	16	yes	—
241	C₄×D₄×C₆₇	C₂³	1	4	yes	—
242	C₄×D₄×C₆₇	C₂³	1	4	yes	—
243	C₄×D₄×C₆₇	C₂³	1	8	yes	—
244	C₄×D₄×C₆₇	C₂³	1	8	yes	—
245	C₄×D₄×C₆₇	C₂³	1	8	yes	—
246	C₄×D₄×C₆₇	C₂³	1	8	yes	—
247	C₄×D₄×C₆₇	C₂³	1	8	yes	—
248	C₄×D₄×C₆₇	C₂³	1	16	yes	—
249	C₄×D₄×C₆₇	C₂³	1	16	yes	—
250	C₄×D₄×C₆₇	C₂³	1	16	yes	—
251	C₄×D₄×C₆₇	C₂³	1	8	yes	—
252	C₄×D₄×C₆₇	C₂³	1	8	yes	—
253	C₄×D₄×C₆₇	C₂³	1	8	yes	—
254	C₄×D₄×C₆₇	C₂³	1	8	yes	—
255	C₄×D₄×C₆₇	C₂³	1	8	yes	—
256	C₄×D₄×C₆₇	C₂³	1	8	yes	—
257	C₄×D₄×C₆₇	C₂³	1	4	yes	—
258	C₄×D₄×C₆₇	C₂³	1	16	yes	—
259	C₄×D₄×C₆₇	C₂³	1	8	yes	—
260	C₄×D₄×C₆₇	C₂³	1	8	yes	—
261	C₄×D₄×C₆₇	C₂³	1	8	yes	—
262	C₄×D₄×C₆₇	C₂³	1	8	yes	—
263	C₄×D₄×C₆₇	C₂³	1	4	yes	—
264	C₄×D₄×C₆₇	C₂³	1	4	yes	—
265	C₄×D₄×C₆₇	C₂³	1	4	yes	—
266	#117×C₆₇	C₂³	1	8	yes	—
267	#117×C₆₇	C₂³	1	8	yes	—
268	#117×C₆₇	C₂³	1	8	yes	—
269	#117×C₆₇	C₂³	1	4	yes	—
270	#117×C₆₇	C₂³	1	4	yes	—
271	#117×C₆₇	C₂³	1	16	yes	—
272	#117×C₆₇	C₂³	1	16	yes	—
273	#117×C₆₇	C₂³	1	16	yes	—
274	#117×C₆₇	C₂³	1	4	yes	—
275	#117×C₆₇	C₂³	1	8	yes	—
276	#117×C₆₇	C₂³	1	16	yes	—
277	#117×C₆₇	C₂³	1	8	yes	—
278	#117×C₆₇	C₂³	1	4	yes	—
279	#117×C₆₇	C₂³	1	4	yes	—
280	#117×C₆₇	C₂³	1	8	yes	—
281	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
284	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
287	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
292	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
295	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
296	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
297	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
298	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
299	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
300	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
303	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
304	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
308	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
309	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
310	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
311	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
312	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
313	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
314	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
315	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
316	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
317	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
318	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
319	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
321	#41×C₆₇	—	2	16	no	—
322	#41×C₆₇	—	2	16	no	—
323	#41×C₆₇	—	2	32	no	—
324	#41×C₆₇	—	2	16	no	—
325	#41×C₆₇	—	4	8	no	—
326	#41×C₆₇	—	4	8	no	—
327	C₂×Q₈×C₆₇	—	2	4	no	—
328	C₂×Q₈×C₆₇	—	4	8	no	—
329	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
330	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
331	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
332	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
333	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
334	C₂×D₄×C₆₇	—	2	8	no	—
335	C₂×D₄×C₆₇	—	2	32	no	—
336	C₂×D₄×C₆₇	—	2	32	no	—
337	C₂×D₄×C₆₇	—	4	8	no	—
338	C₂×D₄×C₆₇	#41	1	8	yes	complemented
339	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
340	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
341	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
342	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
343	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
344	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
345	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
346	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
347	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
348	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₆₇	—	2	8	no	—
350	C₂²×C₄×C₆₇	—	2	4	no	—
351	C₂²×C₄×C₆₇	—	4	4	no	—
352	C₂²×C₄×C₆₇	—	4	16	no	—
353	C₂²×C₄×C₆₇	—	4	4	no	—
354	C₂²×C₄×C₆₇	—	4	2	no	—
355	C₂²×C₄×C₆₇	—	4	2	no	—
356	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
366	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
367	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
369	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
371	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
374	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
375	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
380	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
381	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
382	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
383	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
385	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
388	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
389	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
390	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
391	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
392	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
393	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
394	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
395	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
396	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
397	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
398	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
399	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
400	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
401	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
402	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
403	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
404	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
405	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
409	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
410	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
411	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
412	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
413	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
414	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
415	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
416	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
417	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
418	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
419	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
420	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
421	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
422	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
423	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₄²×C₆₇	C₂⁴	1	4	yes	—
426	C₄²×C₆₇	C₂⁴	1	2	yes	—
427	C₄²×C₆₇	C₂⁴	1	2	yes	—
428	C₄²×C₆₇	C₂⁴	1	4	yes	—
429	C₄²×C₆₇	C₂⁴	1	4	yes	—
430	C₄²×C₆₇	C₂⁴	1	2	yes	—
431	C₄²×C₆₇	C₂⁴	1	2	yes	—
432	C₄²×C₆₇	C₂⁴	1	4	yes	—
433	C₄²×C₆₇	C₂⁴	1	2	yes	—
434	C₄²×C₆₇	C₂⁴	1	4	yes	—
435	C₄²×C₆₇	C₂⁴	1	8	yes	—
436	C₄²×C₆₇	C₂⁴	1	16	yes	—
437	C₄²×C₆₇	C₂⁴	1	8	yes	—
438	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄²×C₆₇	C₂⁴	1	2	yes	—
440	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₄²×C₆₇	C₂⁴	1	8	yes	—
442	C₄²×C₆₇	C₂⁴	1	4	yes	—
443	C₂³×C₆₇	—	2	2	no	—
444	C₂³×C₆₇	—	2	16	no	—
445	C₂³×C₆₇	—	4	2	no	—
446	C₂³×C₆₇	—	4	2	no	—
447	C₂³×C₆₇	—	4	1	no	—
448	C₂³×C₆₇	—	4	1	no	—
449	C₂³×C₆₇	—	4	8	no	—
450	C₂³×C₆₇	—	4	8	no	—
451	C₂³×C₆₇	C₂×#41	1	8	yes	—
452	C₂³×C₆₇	C₂⁵	1	8	yes	—
453	C₂³×C₆₇	C₂⁵	1	2	yes	—
454	C₂³×C₆₇	C₂⁵	1	4	yes	—
455	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
456	Q₈×C₆₇	—	2	8	no	—
457	Q₈×C₆₇	—	2	8	no	—
458	Q₈×C₆₇	—	2	8	no	—
459	Q₈×C₆₇	—	4	8	no	—
460	Q₈×C₆₇	—	4	4	no	—
461	D₄×C₆₇	—	2	32	no	—
462	D₄×C₆₇	—	2	16	no	—
463	D₄×C₆₇	—	2	16	no	—
464	D₄×C₆₇	—	2	8	no	—
465	D₄×C₆₇	—	2	8	no	—
466	D₄×C₆₇	—	4	8	no	—
467	D₄×C₆₇	—	4	8	no	—
468	D₄×C₆₇	—	4	4	no	—
469	D₄×C₆₇	—	4	8	no	—
470	D₄×C₆₇	C₂×#41	1	16	yes	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	4	no	—
473	C₂×C₄×C₆₇	—	2	8	no	—
474	C₂×C₄×C₆₇	—	2	8	no	—
475	C₂×C₄×C₆₇	—	2	16	no	—
476	C₂×C₄×C₆₇	—	2	4	no	—
477	C₂×C₄×C₆₇	—	2	4	no	—
478	C₂×C₄×C₆₇	—	2	16	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	8	no	—
481	C₂×C₄×C₆₇	—	2	2	no	—
482	C₂×C₄×C₆₇	—	2	16	no	—
483	C₂×C₄×C₆₇	—	2	8	no	—
484	C₂×C₄×C₆₇	—	2	4	no	—
485	C₂×C₄×C₆₇	—	2	4	no	—
486	C₂×C₄×C₆₇	—	4	2	no	—
487	C₂×C₄×C₆₇	—	4	4	no	—
488	C₂×C₄×C₆₇	—	4	1	no	—
489	C₂×C₄×C₆₇	—	4	2	no	—
490	C₂×C₄×C₆₇	—	4	16	no	—
491	C₂×C₄×C₆₇	—	4	4	no	—
492	C₂×C₄×C₆₇	—	4	2	no	—
493	C₂×C₄×C₆₇	—	4	8	no	—
494	C₂×C₄×C₆₇	—	4	2	no	—
495	C₂×C₄×C₆₇	—	4	1	no	—
496	C₂×C₄×C₆₇	—	4	8	no	—
497	C₂×C₄×C₆₇	—	4	8	no	—
498	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
499	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
500	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
501	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
502	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
503	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
504	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
505	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
506	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
507	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
508	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
509	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
510	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
511	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
512	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
514	C₂²×C₆₇	—	2	1	no	—
515	C₂²×C₆₇	—	2	1	no	—
516	C₂²×C₆₇	—	2	4	no	—
517	C₂²×C₆₇	—	2	4	no	—
518	C₂²×C₆₇	—	2	2	no	—
519	C₂²×C₆₇	—	2	8	no	—
520	C₂²×C₆₇	—	2	8	no	—
521	C₂²×C₆₇	—	2	2	no	—
522	C₂²×C₆₇	—	2	2	no	—
523	C₂²×C₆₇	—	2	8	no	—
524	C₂²×C₆₇	—	4	8	no	—
525	C₂²×C₆₇	—	4	4	no	—
526	C₂²×C₆₇	—	8	16	no	—
527	C₂²×C₆₇	C₂²×#41	1	8	yes	—
528	C₂²×C₆₇	C₂²×#41	1	2	yes	—
529	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
530	C₄×C₆₇	—	2	1	no	—
531	C₄×C₆₇	—	2	1	no	—
532	C₄×C₆₇	—	2	8	no	—
533	C₄×C₆₇	—	2	4	no	—
534	C₄×C₆₇	—	2	1	no	—
535	C₄×C₆₇	—	2	4	no	—
536	C₄×C₆₇	—	2	1	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	—	2	8	no	—
539	C₄×C₆₇	—	2	4	no	—
540	C₄×C₆₇	—	2	2	no	—
541	C₄×C₆₇	—	2	8	no	—
542	C₄×C₆₇	C₂²×#41	1	4	yes	—
543	C₄×C₆₇	#585	1	2	yes	—
544	C₄×C₆₇	#585	1	2	yes	—
545	#62781	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₂×C₆₇	—	2	2	no	—
547	C₂×C₆₇	—	2	8	no	—
548	C₂×C₆₇	—	4	2	no	—
549	C₂×C₆₇	—	4	8	no	—
550	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
551	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
552	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
553	#3521	C₂×C₆₇	1	8	yes	complemented
554	#3515	C₂×C₆₇	1	4	yes	complemented
555	#3514	C₂×C₆₇	1	4	yes	complemented
556	#3507	C₂×C₆₇	1	2	yes	complemented
557	#3505	C₂×C₆₇	1	4	yes	complemented
558	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
560	#3493	C₂×C₆₇	1	2	yes	complemented
561	#3491	C₂×C₆₇	1	4	yes	complemented
562	#3485	C₂×C₆₇	1	2	yes	complemented
563	#3482	C₂×C₆₇	1	4	yes	complemented
564	#3481	C₂×C₆₇	1	4	yes	complemented
565	#3475	C₂×C₆₇	1	8	yes	complemented
566	#3461	C₂×C₆₇	1	2	yes	complemented
567	#3459	C₂×C₆₇	1	4	yes	complemented
568	#3444	C₂×C₆₇	1	2	yes	complemented
569	C₂×#529	C₂×C₆₇	1	4	yes	complemented
570	C₄×H(5,𝔽₂)	C₂×C₆₇	1	2	yes	complemented
571	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
572	C₆₇	#62781	1	1	yes	characteristic, direct product factor, Sylow
573	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
574	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
575	#559	C₂²×C₆₇	1	4	yes	complemented
576	#557	C₂²×C₆₇	1	4	yes	complemented
577	#556	C₂²×C₆₇	1	8	yes	complemented
578	#556	C₂²×C₆₇	1	8	yes	complemented
579	#556	C₂²×C₆₇	1	4	yes	complemented
580	#555	C₂²×C₆₇	1	8	yes	complemented
581	#554	C₂²×C₆₇	1	8	yes	complemented
582	#554	C₂²×C₆₇	1	4	yes	complemented
583	#554	C₂²×C₆₇	1	4	yes	complemented
584	#553	C₂²×C₆₇	1	16	yes	complemented
585	#553	C₂²×C₆₇	1	8	yes	complemented
586	#553	C₂²×C₆₇	1	8	yes	complemented
587	#552	C₂²×C₆₇	1	16	yes	complemented
588	#552	C₂²×C₆₇	1	8	yes	complemented
589	#552	C₂²×C₆₇	1	8	yes	complemented
590	#552	C₂²×C₆₇	1	16	yes	complemented
591	#552	C₂²×C₆₇	1	8	yes	complemented
592	#551	C₂²×C₆₇	1	16	yes	complemented
593	#551	C₂²×C₆₇	1	16	yes	complemented
594	#551	C₂²×C₆₇	1	16	yes	complemented
595	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
596	#548	C₂²×C₆₇	1	8	yes	complemented
597	#547	C₂²×C₆₇	1	8	yes	complemented
598	#547	C₂²×C₆₇	1	8	yes	complemented
599	#547	C₂²×C₆₇	1	4	yes	complemented
600	#546	C₂²×C₆₇	1	8	yes	complemented
601	#546	C₂²×C₆₇	1	8	yes	complemented
602	#546	C₂²×C₆₇	1	8	yes	complemented
603	#546	C₂²×C₆₇	1	8	yes	complemented
604	D₄²	C₂²×C₆₇	1	4	yes	complemented
605	#544	C₂²×C₆₇	1	2	yes	complemented
606	#543	C₂²×C₆₇	1	4	yes	complemented
607	#542	C₂²×C₆₇	1	8	yes	complemented
608	#541	C₂²×C₆₇	1	8	yes	complemented
609	#539	C₂²×C₆₇	1	8	yes	complemented
610	#539	C₂²×C₆₇	1	16	yes	complemented
611	#539	C₂²×C₆₇	1	8	yes	complemented
612	#538	C₂²×C₆₇	1	8	yes	complemented
613	#538	C₂²×C₆₇	1	16	yes	complemented
614	#537	C₂²×C₆₇	1	2	yes	—
615	#536	C₂²×C₆₇	1	4	yes	complemented
616	#534	C₂²×C₆₇	1	4	yes	—
617	#534	C₂²×C₆₇	1	8	yes	complemented
618	#533	C₂²×C₆₇	1	2	yes	complemented
619	#533	C₂²×C₆₇	1	2	yes	complemented
620	#533	C₂²×C₆₇	1	2	yes	complemented
621	#533	C₂²×C₆₇	1	8	yes	complemented
622	#532	C₂²×C₆₇	1	2	yes	—
623	#532	C₂²×C₆₇	1	2	yes	complemented
624	#532	C₂²×C₆₇	1	2	yes	complemented
625	#529	C₂²×C₆₇	1	4	yes	complemented
626	#529	C₂²×C₆₇	1	8	yes	complemented
627	#529	C₂²×C₆₇	1	8	yes	complemented
628	#529	C₂²×C₆₇	1	8	yes	complemented
629	#529	C₂²×C₆₇	1	8	yes	complemented
630	#529	C₂²×C₆₇	1	8	yes	complemented
631	#529	C₂²×C₆₇	1	8	yes	complemented
632	#529	C₂²×C₆₇	1	8	yes	complemented
633	#529	C₂²×C₆₇	1	4	yes	complemented
634	#529	C₂²×C₆₇	1	4	yes	complemented
635	#529	C₂²×C₆₇	1	4	yes	complemented
636	#529	C₂²×C₆₇	1	4	yes	complemented
637	#529	C₂²×C₆₇	1	4	yes	complemented
638	#529	C₂²×C₆₇	1	16	yes	complemented
639	#529	C₂²×C₆₇	1	8	yes	complemented
640	C₂×#126	C₂²×C₆₇	1	8	yes	complemented
641	C₂×#125	C₂²×C₆₇	1	4	yes	complemented
642	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
643	#525	C₂²×C₆₇	1	4	yes	complemented
644	#525	C₂²×C₆₇	1	4	yes	complemented
645	#525	C₂²×C₆₇	1	4	yes	complemented
646	#525	C₂²×C₆₇	1	16	yes	complemented
647	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
648	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
649	C₂×#121	C₂²×C₆₇	1	4	yes	—
650	#520	C₂²×C₆₇	1	4	yes	complemented
651	#520	C₂²×C₆₇	1	8	yes	complemented
652	#518	C₂²×C₆₇	1	2	yes	—
653	#518	C₂²×C₆₇	1	8	yes	complemented
654	#518	C₂²×C₆₇	1	8	yes	complemented
655	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
656	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
657	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
658	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
659	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
660	C₄×#41	C₂²×C₆₇	1	8	yes	complemented
661	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
662	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
663	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
666	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
667	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
668	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
669	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
670	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
671	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
672	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
673	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
674	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	C₂×#117	C₂²×C₆₇	1	8	yes	complemented
676	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
677	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	H(5,𝔽₂)	—	2	16	no	—
679	C₂×#41	—	2	8	no	—
680	C₂×#41	C₂³×C₆₇	1	4	yes	—
681	C₂×#41	C₂³×C₆₇	1	4	yes	—
682	C₂×#41	C₂³×C₆₇	1	4	yes	—
683	C₂×#41	C₂³×C₆₇	1	8	yes	—
684	C₂×#41	C₂³×C₆₇	1	4	yes	—
685	C₂×#41	C₂³×C₆₇	1	4	yes	—
686	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
687	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
688	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
689	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
690	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
691	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
692	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
694	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₆₇	1	8	yes	—
696	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
697	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
698	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
704	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
705	#127	C₂³×C₆₇	1	2	yes	—
706	#126	C₂³×C₆₇	1	8	yes	—
707	#126	C₂³×C₆₇	1	16	yes	—
708	#126	C₂³×C₆₇	1	16	yes	—
709	#126	C₂³×C₆₇	1	16	yes	—
710	#126	C₂³×C₆₇	1	8	yes	—
711	#126	C₂³×C₆₇	1	16	yes	—
712	#126	C₂³×C₆₇	1	16	yes	—
713	#126	C₂³×C₆₇	1	16	yes	—
714	#125	C₂³×C₆₇	1	4	yes	—
715	#125	C₂³×C₆₇	1	8	yes	—
716	#125	C₂³×C₆₇	1	8	yes	—
717	#125	C₂³×C₆₇	1	8	yes	—
718	#125	C₂³×C₆₇	1	4	yes	—
719	#125	C₂³×C₆₇	1	4	yes	—
720	#125	C₂³×C₆₇	1	16	yes	—
721	#125	C₂³×C₆₇	1	8	yes	—
722	#125	C₂³×C₆₇	1	16	yes	—
723	#124	C₂³×C₆₇	1	4	yes	—
724	#124	C₂³×C₆₇	1	8	yes	—
725	#124	C₂³×C₆₇	1	8	yes	—
726	#124	C₂³×C₆₇	1	8	yes	—
727	#124	C₂³×C₆₇	1	4	yes	—
728	#124	C₂³×C₆₇	1	4	yes	—
729	#124	C₂³×C₆₇	1	8	yes	—
730	#124	C₂³×C₆₇	1	16	yes	—
731	#123	C₂³×C₆₇	1	8	yes	—
732	#123	C₂³×C₆₇	1	16	yes	—
733	#123	C₂³×C₆₇	1	16	yes	—
734	#123	C₂³×C₆₇	1	16	yes	—
735	#123	C₂³×C₆₇	1	8	yes	—
736	#123	C₂³×C₆₇	1	8	yes	—
737	#123	C₂³×C₆₇	1	16	yes	—
738	#123	C₂³×C₆₇	1	16	yes	—
739	#123	C₂³×C₆₇	1	16	yes	—
740	#123	C₂³×C₆₇	1	16	yes	—
741	#123	C₂³×C₆₇	1	16	yes	—
742	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
743	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
744	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
745	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
746	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
747	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
748	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
749	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
750	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
751	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
752	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
753	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
754	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
755	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
756	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
757	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
758	#121	C₂³×C₆₇	1	4	yes	—
759	#121	C₂³×C₆₇	1	8	yes	—
760	#121	C₂³×C₆₇	1	8	yes	—
761	#121	C₂³×C₆₇	1	8	yes	—
762	#121	C₂³×C₆₇	1	4	yes	—
763	#121	C₂³×C₆₇	1	4	yes	—
764	#121	C₂³×C₆₇	1	4	yes	—
765	#121	C₂³×C₆₇	1	4	yes	—
766	#121	C₂³×C₆₇	1	4	yes	—
767	#121	C₂³×C₆₇	1	16	yes	—
768	#121	C₂³×C₆₇	1	16	yes	—
769	#121	C₂³×C₆₇	1	16	yes	—
770	#121	C₂³×C₆₇	1	8	yes	—
771	#120	C₂³×C₆₇	1	8	yes	—
772	#120	C₂³×C₆₇	1	16	yes	—
773	#120	C₂³×C₆₇	1	16	yes	—
774	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
775	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
776	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
777	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
778	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
779	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
780	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
781	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
782	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
783	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
784	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
785	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
786	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
787	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
788	C₄×D₄	C₂³×C₆₇	1	4	yes	—
789	C₄×D₄	C₂³×C₆₇	1	4	yes	—
790	C₄×D₄	C₂³×C₆₇	1	4	yes	—
791	C₄×D₄	C₂³×C₆₇	1	4	yes	—
792	C₄×D₄	C₂³×C₆₇	1	8	yes	—
793	C₄×D₄	C₂³×C₆₇	1	16	yes	—
794	C₄×D₄	C₂³×C₆₇	1	4	yes	—
795	C₄×D₄	C₂³×C₆₇	1	4	yes	—
796	C₄×D₄	C₂³×C₆₇	1	8	yes	—
797	C₄×D₄	C₂³×C₆₇	1	8	yes	—
798	C₄×D₄	C₂³×C₆₇	1	8	yes	—
799	C₄×D₄	C₂³×C₆₇	1	8	yes	—
800	C₄×D₄	C₂³×C₆₇	1	8	yes	—
801	C₄×D₄	C₂³×C₆₇	1	16	yes	—
802	C₄×D₄	C₂³×C₆₇	1	16	yes	—
803	C₄×D₄	C₂³×C₆₇	1	16	yes	—
804	C₄×D₄	C₂³×C₆₇	1	8	yes	—
805	C₄×D₄	C₂³×C₆₇	1	8	yes	—
806	C₄×D₄	C₂³×C₆₇	1	8	yes	—
807	C₄×D₄	C₂³×C₆₇	1	8	yes	—
808	C₄×D₄	C₂³×C₆₇	1	8	yes	—
809	C₄×D₄	C₂³×C₆₇	1	8	yes	—
810	C₄×D₄	C₂³×C₆₇	1	4	yes	—
811	C₄×D₄	C₂³×C₆₇	1	16	yes	—
812	C₄×D₄	C₂³×C₆₇	1	8	yes	—
813	C₄×D₄	C₂³×C₆₇	1	8	yes	—
814	C₄×D₄	C₂³×C₆₇	1	8	yes	—
815	C₄×D₄	C₂³×C₆₇	1	8	yes	—
816	C₄×D₄	C₂³×C₆₇	1	4	yes	—
817	C₄×D₄	C₂³×C₆₇	1	4	yes	—
818	C₄×D₄	C₂³×C₆₇	1	4	yes	—
819	#117	C₂³×C₆₇	1	8	yes	—
820	#117	C₂³×C₆₇	1	8	yes	—
821	#117	C₂³×C₆₇	1	8	yes	—
822	#117	C₂³×C₆₇	1	4	yes	—
823	#117	C₂³×C₆₇	1	4	yes	—
824	#117	C₂³×C₆₇	1	16	yes	—
825	#117	C₂³×C₆₇	1	16	yes	—
826	#117	C₂³×C₆₇	1	16	yes	—
827	#117	C₂³×C₆₇	1	4	yes	—
828	#117	C₂³×C₆₇	1	8	yes	—
829	#117	C₂³×C₆₇	1	16	yes	—
830	#117	C₂³×C₆₇	1	8	yes	—
831	#117	C₂³×C₆₇	1	4	yes	—
832	#117	C₂³×C₆₇	1	4	yes	—
833	#117	C₂³×C₆₇	1	8	yes	—
834	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
839	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
840	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
841	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
842	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
843	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
844	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
845	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
847	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
848	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
849	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
850	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
851	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
852	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
853	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
854	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
855	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
856	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
857	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
858	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
859	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
860	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
861	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
862	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
863	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
864	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
865	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
866	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
867	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
868	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
869	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
870	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
871	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
872	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
873	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
874	#41	—	2	16	no	—
875	#41	—	2	16	no	—
876	#41	—	2	32	no	—
877	#41	—	2	16	no	—
878	#41	—	4	8	no	—
879	#41	—	4	8	no	—
880	C₂×Q₈	—	2	4	no	—
881	C₂×Q₈	—	4	8	no	—
882	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
883	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
884	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
885	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
886	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
887	C₂×D₄	—	2	8	no	—
888	C₂×D₄	—	2	32	no	—
889	C₂×D₄	—	2	32	no	—
890	C₂×D₄	—	4	8	no	—
891	C₂×D₄	#41×C₆₇	1	8	yes	complemented
892	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
893	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
894	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
895	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
896	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
897	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
898	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
899	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
900	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
901	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
902	C₂²×C₄	—	2	8	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	4	4	no	—
905	C₂²×C₄	—	4	16	no	—
906	C₂²×C₄	—	4	4	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
910	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
914	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
915	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
916	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
922	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
923	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
924	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
927	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
928	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
933	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
934	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
935	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
936	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
938	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
939	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
941	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
942	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
943	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
944	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
945	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
946	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
947	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
948	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
949	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
950	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
951	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
952	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
953	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
954	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
955	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
956	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
957	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
958	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
962	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
963	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
964	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
965	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
966	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
967	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
968	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
969	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
970	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
971	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
972	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
973	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
974	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
975	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
976	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₄²	C₂⁴×C₆₇	1	2	yes	—
978	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
979	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₄²	C₂⁴×C₆₇	1	4	yes	—
982	C₄²	C₂⁴×C₆₇	1	2	yes	—
983	C₄²	C₂⁴×C₆₇	1	2	yes	—
984	C₄²	C₂⁴×C₆₇	1	8	yes	—
985	C₄²	C₂⁴×C₆₇	1	4	yes	—
986	C₄²	C₂⁴×C₆₇	1	4	yes	—
987	C₄²	C₂⁴×C₆₇	1	4	yes	—
988	C₄²	C₂⁴×C₆₇	1	2	yes	—
989	C₄²	C₂⁴×C₆₇	1	2	yes	—
990	C₄²	C₂⁴×C₆₇	1	4	yes	—
991	C₄²	C₂⁴×C₆₇	1	2	yes	—
992	C₄²	C₂⁴×C₆₇	1	4	yes	—
993	C₄²	C₂⁴×C₆₇	1	8	yes	—
994	C₄²	C₂⁴×C₆₇	1	16	yes	—
995	C₄²	C₂⁴×C₆₇	1	8	yes	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	16	no	—
998	C₂³	—	4	2	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	1	no	—
1002	C₂³	—	4	8	no	—
1003	C₂³	—	4	8	no	—
1004	C₂³	C₂×#41×C₆₇	1	8	yes	—
1005	C₂³	C₂⁵×C₆₇	1	8	yes	—
1006	C₂³	C₂⁵×C₆₇	1	2	yes	—
1007	C₂³	C₂⁵×C₆₇	1	4	yes	—
1008	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1009	Q₈	—	2	8	no	—
1010	Q₈	—	2	8	no	—
1011	Q₈	—	2	8	no	—
1012	Q₈	—	4	8	no	—
1013	Q₈	—	4	4	no	—
1014	D₄	—	2	32	no	—
1015	D₄	—	2	16	no	—
1016	D₄	—	2	16	no	—
1017	D₄	—	2	8	no	—
1018	D₄	—	2	8	no	—
1019	D₄	—	4	8	no	—
1020	D₄	—	4	8	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	8	no	—
1023	D₄	C₂×#41×C₆₇	1	16	yes	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	4	no	—
1026	C₂×C₄	—	2	8	no	—
1027	C₂×C₄	—	2	8	no	—
1028	C₂×C₄	—	2	16	no	—
1029	C₂×C₄	—	2	4	no	—
1030	C₂×C₄	—	2	4	no	—
1031	C₂×C₄	—	2	16	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	8	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	16	no	—
1036	C₂×C₄	—	2	8	no	—
1037	C₂×C₄	—	2	4	no	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	4	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	16	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	8	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	—	4	8	no	—
1051	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1052	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1053	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1054	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1055	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1056	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1057	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1058	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1059	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1060	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1061	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1062	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1063	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1064	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1065	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1066	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	8	no	—
1073	C₂²	—	2	8	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	8	no	—
1077	C₂²	—	4	8	no	—
1078	C₂²	—	4	4	no	—
1079	C₂²	—	8	16	no	—
1080	C₂²	C₂²×#41×C₆₇	1	8	yes	—
1081	C₂²	C₂²×#41×C₆₇	1	2	yes	—
1082	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
1083	C₄	—	2	1	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	2	8	no	—
1086	C₄	—	2	4	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	4	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	8	no	—
1092	C₄	—	2	4	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	8	no	—
1095	C₄	C₂²×#41×C₆₇	1	4	yes	—
1096	C₄	#585×C₆₇	1	2	yes	—
1097	C₄	#585×C₆₇	1	2	yes	—
1098	C₂	—	2	2	no	—
1099	C₂	—	2	8	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	4	8	no	—
1102	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
1103	C₂	C₂×#585×C₆₇	1	1	yes	characteristic
1104	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
socle	C₂²×C₆₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3521	C₂	semidirect
2. C₆₇×#3515	C₂	semidirect
3. C₆₇×#3514	C₂	semidirect
4. C₆₇×#3507	C₂	semidirect
5. C₆₇×#3505	C₂	semidirect
6. C₆₇×#3501	C₂	semidirect
7. C₆₇×#3496	C₂	semidirect
8. C₆₇×#3493	C₂	semidirect
9. C₆₇×#3491	C₂	semidirect
10. C₆₇×#3485	C₂	semidirect
11. C₆₇×#3482	C₂	semidirect
12. C₆₇×#3481	C₂	semidirect
13. C₆₇×#3475	C₂	semidirect
14. C₆₇×#3461	C₂	semidirect
15. C₆₇×#3459	C₂	semidirect
16. C₆₇×#3444	C₂	semidirect
17. C₂×#529×C₆₇	C₂	semidirect
18. C₄×H(5,𝔽₂)×C₆₇	C₂	semidirect
19. C₂×C₄×#41×C₆₇	C₂	semidirect
22. #559×C₆₇	C₂²	semidirect
23. #557×C₆₇	C₂²	semidirect
24. #556×C₆₇	C₂²	semidirect
25. #556×C₆₇	C₂²	semidirect
26. #556×C₆₇	C₂²	semidirect
27. #555×C₆₇	C₂²	semidirect
28. #554×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
30. #554×C₆₇	C₂²	semidirect
31. #553×C₆₇	C₂²	semidirect
32. #553×C₆₇	C₂²	semidirect
33. #553×C₆₇	C₂²	semidirect
34. #552×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
36. #552×C₆₇	C₂²	semidirect
37. #552×C₆₇	C₂²	semidirect
38. #552×C₆₇	C₂²	semidirect
39. #551×C₆₇	C₂²	semidirect
40. #551×C₆₇	C₂²	semidirect
41. #551×C₆₇	C₂²	semidirect
42. D₄×Q₈×C₆₇	C₂²	semidirect
43. #548×C₆₇	C₂²	semidirect
44. #547×C₆₇	C₂²	semidirect
45. #547×C₆₇	C₂²	semidirect
46. #547×C₆₇	C₂²	semidirect
47. #546×C₆₇	C₂²	semidirect
48. #546×C₆₇	C₂²	semidirect
49. #546×C₆₇	C₂²	semidirect
50. #546×C₆₇	C₂²	semidirect
51. D₄²×C₆₇	C₂²	semidirect
52. #544×C₆₇	C₂²	semidirect
53. #543×C₆₇	C₂²	semidirect
54. #542×C₆₇	C₂²	semidirect
55. #541×C₆₇	C₂²	semidirect
56. #539×C₆₇	C₂²	semidirect
57. #539×C₆₇	C₂²	semidirect
58. #539×C₆₇	C₂²	semidirect
59. #538×C₆₇	C₂²	semidirect
60. #538×C₆₇	C₂²	semidirect
62. #536×C₆₇	C₂²	semidirect
64. #534×C₆₇	C₂²	semidirect
65. #533×C₆₇	C₂²	semidirect
66. #533×C₆₇	C₂²	semidirect
67. #533×C₆₇	C₂²	semidirect
68. #533×C₆₇	C₂²	semidirect
70. #532×C₆₇	C₂²	semidirect
71. #532×C₆₇	C₂²	semidirect
72. #529×C₆₇	C₂²	semidirect
73. #529×C₆₇	C₂²	semidirect
74. #529×C₆₇	C₂²	semidirect
75. #529×C₆₇	C₂²	semidirect
76. #529×C₆₇	C₂²	semidirect
77. #529×C₆₇	C₂²	semidirect
78. #529×C₆₇	C₂²	semidirect
79. #529×C₆₇	C₂²	semidirect
80. #529×C₆₇	C₂²	semidirect
81. #529×C₆₇	C₂²	semidirect
82. #529×C₆₇	C₂²	semidirect
83. #529×C₆₇	C₂²	semidirect
84. #529×C₆₇	C₂²	semidirect
85. #529×C₆₇	C₂²	semidirect
86. #529×C₆₇	C₂²	semidirect
87. C₂×#126×C₆₇	C₂²	semidirect
88. C₂×#125×C₆₇	C₂²	semidirect
89. C₂×#124×C₆₇	C₂²	semidirect
90. #525×C₆₇	C₂²	semidirect
91. #525×C₆₇	C₂²	semidirect
92. #525×C₆₇	C₂²	semidirect
93. #525×C₆₇	C₂²	semidirect
94. C₂×#123×C₆₇	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
97. #520×C₆₇	C₂²	semidirect
98. #520×C₆₇	C₂²	semidirect
100. #518×C₆₇	C₂²	semidirect
101. #518×C₆₇	C₂²	semidirect
102. C₄×#41×C₆₇	C₂²	semidirect
103. C₄×#41×C₆₇	C₂²	semidirect
104. C₄×#41×C₆₇	C₂²	semidirect
105. C₄×#41×C₆₇	C₂²	semidirect
106. C₄×#41×C₆₇	C₂²	semidirect
107. C₄×#41×C₆₇	C₂²	semidirect
108. C₄×#41×C₆₇	C₂²	semidirect
109. C₄×#41×C₆₇	C₂²	semidirect
110. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
111. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
112. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
115. C₂×C₄×D₄×C₆₇	C₂²	semidirect
116. C₂×C₄×D₄×C₆₇	C₂²	semidirect
117. C₂×C₄×D₄×C₆₇	C₂²	semidirect
118. C₂×C₄×D₄×C₆₇	C₂²	semidirect
119. C₂×C₄×D₄×C₆₇	C₂²	semidirect
120. C₂×#117×C₆₇	C₂²	semidirect
121. C₂×#117×C₆₇	C₂²	semidirect
122. C₂×#117×C₆₇	C₂²	semidirect
123. C₂²×C₄²×C₆₇	C₂²	semidirect
124. C₂²×C₄²×C₆₇	C₂²	semidirect
338. C₂×D₄×C₆₇	#41	semidirect
545. #62781	C₆₇	direct (N × H)
553. #3521	C₂×C₆₇	semidirect
554. #3515	C₂×C₆₇	semidirect
555. #3514	C₂×C₆₇	semidirect
556. #3507	C₂×C₆₇	semidirect
557. #3505	C₂×C₆₇	semidirect
558. #3501	C₂×C₆₇	semidirect
559. #3496	C₂×C₆₇	semidirect
560. #3493	C₂×C₆₇	semidirect
561. #3491	C₂×C₆₇	semidirect
562. #3485	C₂×C₆₇	semidirect
563. #3482	C₂×C₆₇	semidirect
564. #3481	C₂×C₆₇	semidirect
565. #3475	C₂×C₆₇	semidirect
566. #3461	C₂×C₆₇	semidirect
567. #3459	C₂×C₆₇	semidirect
568. #3444	C₂×C₆₇	semidirect
569. C₂×#529	C₂×C₆₇	semidirect
570. C₄×H(5,𝔽₂)	C₂×C₆₇	semidirect
571. C₂×C₄×#41	C₂×C₆₇	semidirect
572. C₆₇	#62781	direct (N × H)
575. #559	C₂²×C₆₇	semidirect
576. #557	C₂²×C₆₇	semidirect
577. #556	C₂²×C₆₇	semidirect
578. #556	C₂²×C₆₇	semidirect
579. #556	C₂²×C₆₇	semidirect
580. #555	C₂²×C₆₇	semidirect
581. #554	C₂²×C₆₇	semidirect
582. #554	C₂²×C₆₇	semidirect
583. #554	C₂²×C₆₇	semidirect
584. #553	C₂²×C₆₇	semidirect
585. #553	C₂²×C₆₇	semidirect
586. #553	C₂²×C₆₇	semidirect
587. #552	C₂²×C₆₇	semidirect
588. #552	C₂²×C₆₇	semidirect
589. #552	C₂²×C₆₇	semidirect
590. #552	C₂²×C₆₇	semidirect
591. #552	C₂²×C₆₇	semidirect
592. #551	C₂²×C₆₇	semidirect
593. #551	C₂²×C₆₇	semidirect
594. #551	C₂²×C₆₇	semidirect
595. D₄×Q₈	C₂²×C₆₇	semidirect
596. #548	C₂²×C₆₇	semidirect
597. #547	C₂²×C₆₇	semidirect
598. #547	C₂²×C₆₇	semidirect
599. #547	C₂²×C₆₇	semidirect
600. #546	C₂²×C₆₇	semidirect
601. #546	C₂²×C₆₇	semidirect
602. #546	C₂²×C₆₇	semidirect
603. #546	C₂²×C₆₇	semidirect
604. D₄²	C₂²×C₆₇	semidirect
605. #544	C₂²×C₆₇	semidirect
606. #543	C₂²×C₆₇	semidirect
607. #542	C₂²×C₆₇	semidirect
608. #541	C₂²×C₆₇	semidirect
609. #539	C₂²×C₆₇	semidirect
610. #539	C₂²×C₆₇	semidirect
611. #539	C₂²×C₆₇	semidirect
612. #538	C₂²×C₆₇	semidirect
613. #538	C₂²×C₆₇	semidirect
615. #536	C₂²×C₆₇	semidirect
617. #534	C₂²×C₆₇	semidirect
618. #533	C₂²×C₆₇	semidirect
619. #533	C₂²×C₆₇	semidirect
620. #533	C₂²×C₆₇	semidirect
621. #533	C₂²×C₆₇	semidirect
623. #532	C₂²×C₆₇	semidirect
624. #532	C₂²×C₆₇	semidirect
625. #529	C₂²×C₆₇	semidirect
626. #529	C₂²×C₆₇	semidirect
627. #529	C₂²×C₆₇	semidirect
628. #529	C₂²×C₆₇	semidirect
629. #529	C₂²×C₆₇	semidirect
630. #529	C₂²×C₆₇	semidirect
631. #529	C₂²×C₆₇	semidirect
632. #529	C₂²×C₆₇	semidirect
633. #529	C₂²×C₆₇	semidirect
634. #529	C₂²×C₆₇	semidirect
635. #529	C₂²×C₆₇	semidirect
636. #529	C₂²×C₆₇	semidirect
637. #529	C₂²×C₆₇	semidirect
638. #529	C₂²×C₆₇	semidirect
639. #529	C₂²×C₆₇	semidirect
640. C₂×#126	C₂²×C₆₇	semidirect
641. C₂×#125	C₂²×C₆₇	semidirect
642. C₂×#124	C₂²×C₆₇	semidirect
643. #525	C₂²×C₆₇	semidirect
644. #525	C₂²×C₆₇	semidirect
645. #525	C₂²×C₆₇	semidirect
646. #525	C₂²×C₆₇	semidirect
647. C₂×#123	C₂²×C₆₇	semidirect
648. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
650. #520	C₂²×C₆₇	semidirect
651. #520	C₂²×C₆₇	semidirect
653. #518	C₂²×C₆₇	semidirect
654. #518	C₂²×C₆₇	semidirect
655. C₄×#41	C₂²×C₆₇	semidirect
656. C₄×#41	C₂²×C₆₇	semidirect
657. C₄×#41	C₂²×C₆₇	semidirect
658. C₄×#41	C₂²×C₆₇	semidirect
659. C₄×#41	C₂²×C₆₇	semidirect
660. C₄×#41	C₂²×C₆₇	semidirect
661. C₄×#41	C₂²×C₆₇	semidirect
662. C₄×#41	C₂²×C₆₇	semidirect
663. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
664. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
665. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
668. C₂×C₄×D₄	C₂²×C₆₇	semidirect
669. C₂×C₄×D₄	C₂²×C₆₇	semidirect
670. C₂×C₄×D₄	C₂²×C₆₇	semidirect
671. C₂×C₄×D₄	C₂²×C₆₇	semidirect
672. C₂×C₄×D₄	C₂²×C₆₇	semidirect
673. C₂×#117	C₂²×C₆₇	semidirect
674. C₂×#117	C₂²×C₆₇	semidirect
675. C₂×#117	C₂²×C₆₇	semidirect
676. C₂²×C₄²	C₂²×C₆₇	semidirect
677. C₂²×C₄²	C₂²×C₆₇	semidirect
891. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3521	2
C₆₇×#3515	2
C₆₇×#3514	2
C₆₇×#3507	2
C₆₇×#3505	2
C₆₇×#3501	2
C₆₇×#3496	2
C₆₇×#3493	2
C₆₇×#3491	2
C₆₇×#3485	2
C₆₇×#3482	2
C₆₇×#3481	2
C₆₇×#3475	2
C₆₇×#3461	2
C₆₇×#3459	2
C₆₇×#3444	2
C₂×#529×C₆₇	2
C₄×H(5,𝔽₂)×C₆₇	2
C₂×C₄×#41×C₆₇	2
#62781	67

Subgroups — C67×#62781 #30742032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#62781 #30742032