Subgroups — C₆₇×#60326 #30739577

Order 17152.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3460	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2980	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2978	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2971	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2935	C₂	1	2	yes	maximal, complemented
20	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
22	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2930	C₂	1	2	yes	maximal, complemented
24	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
27	#544×C₆₇	C₄	1	1	yes	characteristic
28	#542×C₆₇	C₄	1	1	yes	characteristic
29	#542×C₆₇	C₄	1	1	yes	characteristic
30	#542×C₆₇	C₄	1	2	yes	—
31	#540×C₆₇	C₄	1	1	yes	characteristic
32	#540×C₆₇	C₄	1	1	yes	characteristic
33	#540×C₆₇	C₄	1	2	yes	—
34	#538×C₆₇	C₄	1	2	yes	—
35	#538×C₆₇	C₄	1	2	yes	—
36	#537×C₆₇	C₄	1	1	yes	characteristic
37	#535×C₆₇	C₄	1	1	yes	characteristic
38	#535×C₆₇	C₄	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	C₂²	1	1	yes	characteristic
41	#532×C₆₇	C₂²	1	2	yes	—
42	#529×C₆₇	C₂²	1	1	yes	characteristic
43	#529×C₆₇	C₂²	1	2	yes	—
44	#529×C₆₇	C₂²	1	1	yes	characteristic
45	#525×C₆₇	C₂²	1	2	yes	—
46	#525×C₆₇	C₂²	1	2	yes	—
47	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
48	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#446×C₆₇	C₂²	1	2	yes	complemented
54	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#436×C₆₇	C₂²	1	1	yes	characteristic
58	#436×C₆₇	C₂²	1	2	yes	—
59	#436×C₆₇	C₂²	1	1	yes	characteristic
60	#436×C₆₇	C₂²	1	2	yes	—
61	#436×C₆₇	C₂²	1	1	yes	characteristic
62	#436×C₆₇	C₂²	1	1	yes	characteristic
63	#436×C₆₇	C₂²	1	1	yes	characteristic
64	#436×C₆₇	C₂²	1	1	yes	characteristic
65	#436×C₆₇	C₂²	1	2	yes	—
66	#436×C₆₇	C₂²	1	2	yes	complemented
67	#436×C₆₇	C₂²	1	2	yes	complemented
68	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#436×C₆₇	C₂²	1	2	yes	complemented
70	#436×C₆₇	C₂²	1	2	yes	complemented
71	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#435×C₆₇	C₂²	1	2	yes	—
73	#435×C₆₇	C₂²	1	2	yes	—
74	#435×C₆₇	C₂²	1	1	yes	characteristic
75	#435×C₆₇	C₂²	1	2	yes	—
76	#435×C₆₇	C₂²	1	2	yes	—
77	#435×C₆₇	C₂²	1	2	yes	—
78	#435×C₆₇	C₂²	1	2	yes	—
79	#435×C₆₇	C₂²	1	1	yes	characteristic
80	#435×C₆₇	C₂²	1	2	yes	—
81	#435×C₆₇	C₂²	1	2	yes	complemented
82	#435×C₆₇	C₂²	1	2	yes	complemented
83	#435×C₆₇	C₂²	1	2	yes	complemented
84	#435×C₆₇	C₂²	1	2	yes	complemented
85	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#435×C₆₇	C₂²	1	2	yes	complemented
87	#435×C₆₇	C₂²	1	2	yes	complemented
88	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#435×C₆₇	C₂²	1	2	yes	complemented
90	#435×C₆₇	C₂²	1	2	yes	complemented
91	#435×C₆₇	C₂²	1	2	yes	complemented
92	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
93	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
94	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
95	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
96	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
97	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
99	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
100	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
101	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#433×C₆₇	C₂²	1	2	yes	complemented
103	#433×C₆₇	C₂²	1	2	yes	complemented
104	#433×C₆₇	C₂²	1	2	yes	complemented
105	#433×C₆₇	C₂²	1	2	yes	complemented
106	#432×C₆₇	C₂²	1	1	yes	characteristic
107	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#432×C₆₇	C₂²	1	2	yes	complemented
109	#432×C₆₇	C₂²	1	2	yes	complemented
110	#431×C₆₇	C₂²	1	1	yes	characteristic
111	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#424×C₆₇	C₂²	1	2	yes	complemented
115	#424×C₆₇	C₂²	1	2	yes	complemented
116	#423×C₆₇	C₂²	1	1	yes	characteristic
117	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
120	#408×C₆₇	C₂²	1	2	yes	complemented
121	#408×C₆₇	C₂²	1	2	yes	complemented
122	#408×C₆₇	C₂²	1	2	yes	complemented
123	#408×C₆₇	C₂²	1	2	yes	complemented
124	#408×C₆₇	C₂²	1	2	yes	complemented
125	#408×C₆₇	C₂²	1	2	yes	complemented
126	#407×C₆₇	C₂²	1	2	yes	—
127	#407×C₆₇	C₂²	1	2	yes	—
128	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
129	#405×C₆₇	C₂²	1	2	yes	complemented
130	#405×C₆₇	C₂²	1	2	yes	complemented
131	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
132	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
137	C₂×#41×C₆₇	C₂³	1	2	yes	—
138	C₂×#41×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	#131×C₆₇	—	4	4	no	—
142	#131×C₆₇	—	4	4	no	—
143	C₂×M₁₆×C₆₇	—	4	4	no	—
144	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
157	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
160	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
163	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
168	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
169	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
170	#127×C₆₇	C₂×C₄	1	2	yes	—
171	#126×C₆₇	C₂×C₄	1	2	yes	—
172	#126×C₆₇	C₂×C₄	1	2	yes	—
173	#126×C₆₇	C₂×C₄	1	2	yes	—
174	#126×C₆₇	C₂×C₄	1	2	yes	—
175	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
176	#125×C₆₇	C₂×C₄	1	2	yes	—
177	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
178	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
179	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
180	#124×C₆₇	C₂×C₄	1	2	yes	—
181	#124×C₆₇	C₂×C₄	1	2	yes	—
182	#124×C₆₇	C₂×C₄	1	2	yes	—
183	#124×C₆₇	C₂×C₄	1	2	yes	—
184	#124×C₆₇	C₂×C₄	1	2	yes	—
185	#123×C₆₇	C₂×C₄	1	2	yes	—
186	#123×C₆₇	C₂×C₄	1	2	yes	—
187	#123×C₆₇	C₂×C₄	1	2	yes	—
188	#123×C₆₇	C₂×C₄	1	2	yes	—
189	#123×C₆₇	C₂×C₄	1	2	yes	—
190	#123×C₆₇	C₂×C₄	1	2	yes	—
191	#123×C₆₇	C₂×C₄	1	2	yes	—
192	#123×C₆₇	C₂×C₄	1	2	yes	—
193	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
199	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
200	#121×C₆₇	C₂×C₄	1	2	yes	—
201	#121×C₆₇	C₂×C₄	1	2	yes	—
202	#121×C₆₇	C₂×C₄	1	2	yes	—
203	#121×C₆₇	C₂×C₄	1	2	yes	—
204	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
205	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
206	#121×C₆₇	C₂×C₄	1	2	yes	—
207	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
208	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
209	#121×C₆₇	C₂×C₄	1	2	yes	—
210	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
211	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
212	#121×C₆₇	C₂×C₄	1	2	yes	—
213	#121×C₆₇	C₂×C₄	1	2	yes	—
214	#121×C₆₇	C₂×C₄	1	2	yes	—
215	#121×C₆₇	C₂×C₄	1	2	yes	—
216	#121×C₆₇	C₂×C₄	1	2	yes	—
217	#120×C₆₇	C₂×C₄	1	2	yes	—
218	#120×C₆₇	C₂×C₄	1	2	yes	—
219	#120×C₆₇	C₂×C₄	1	2	yes	—
220	#120×C₆₇	C₂×C₄	1	2	yes	—
221	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
222	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
223	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
227	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
228	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
229	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
230	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
231	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
232	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
233	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₇	C₂³	1	2	yes	—
236	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
246	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
247	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
248	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
249	#117×C₆₇	C₂×C₄	1	2	yes	—
250	#117×C₆₇	C₂³	1	2	yes	—
251	#117×C₆₇	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
254	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
261	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
263	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
266	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
267	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
268	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
269	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
270	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
271	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
272	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
289	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
290	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
291	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
292	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
293	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
295	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
296	#97×C₆₇	C₂³	1	1	yes	characteristic
297	#97×C₆₇	C₂³	1	1	yes	characteristic
298	#97×C₆₇	C₂³	1	1	yes	characteristic
299	#97×C₆₇	C₂³	1	2	yes	—
300	#97×C₆₇	C₂³	1	1	yes	characteristic
301	#97×C₆₇	C₂³	1	2	yes	—
302	#97×C₆₇	C₂³	1	2	yes	—
303	#97×C₆₇	C₂³	1	2	yes	—
304	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₆₇	C₂³	1	2	yes	—
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
314	#41×C₆₇	—	4	2	no	—
315	#41×C₆₇	—	4	2	no	—
316	#41×C₆₇	—	4	2	no	—
317	#41×C₆₇	—	4	2	no	—
318	#41×C₆₇	—	4	2	no	—
319	#41×C₆₇	—	4	2	no	—
320	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
322	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
323	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
324	C₂×D₄×C₆₇	—	4	2	no	—
325	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
329	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
331	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
332	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
333	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
335	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
336	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
337	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
338	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
339	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
340	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
341	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
342	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
343	C₂²×C₄×C₆₇	—	4	2	no	—
344	C₂²×C₄×C₆₇	—	4	2	no	—
345	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
350	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
353	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
354	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
355	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
356	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
362	M₁₆×C₆₇	—	2	2	no	—
363	M₁₆×C₆₇	—	2	4	no	—
364	M₁₆×C₆₇	—	2	2	no	—
365	M₁₆×C₆₇	—	2	4	no	—
366	M₁₆×C₆₇	—	4	2	no	—
367	M₁₆×C₆₇	—	4	2	no	—
368	M₁₆×C₆₇	—	4	1	no	—
369	M₁₆×C₆₇	—	4	2	no	—
370	M₁₆×C₆₇	—	4	1	no	—
371	M₁₆×C₆₇	—	4	2	no	—
372	M₁₆×C₆₇	—	4	2	no	—
373	M₁₆×C₆₇	—	4	2	no	—
374	C₂×C₈×C₆₇	—	2	4	no	—
375	C₂×C₈×C₆₇	—	2	2	no	—
376	C₂×C₈×C₆₇	—	4	2	no	—
377	C₂×C₈×C₆₇	—	4	1	no	—
378	C₂×C₈×C₆₇	—	4	2	no	—
379	C₂×C₈×C₆₇	—	4	2	no	—
380	C₂×C₈×C₆₇	—	4	2	no	—
381	C₂×C₈×C₆₇	—	4	2	no	—
382	C₂×C₈×C₆₇	—	4	2	no	—
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
387	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
392	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
403	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
406	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
408	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
417	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
422	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
425	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
428	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
429	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
432	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
434	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
435	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
436	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
441	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
442	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
443	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
444	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
445	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
447	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
448	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
449	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₄²×C₆₇	C₂⁴	1	2	yes	—
452	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂³×C₆₇	—	4	2	no	—
455	C₂³×C₆₇	—	4	2	no	—
456	C₂³×C₆₇	—	4	2	no	—
457	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
458	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
459	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
460	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
461	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
462	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
463	Q₈×C₆₇	—	2	2	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	—	4	2	no	—
466	Q₈×C₆₇	—	4	1	no	—
467	D₄×C₆₇	—	2	2	no	—
468	D₄×C₆₇	—	2	2	no	—
469	D₄×C₆₇	—	2	2	no	—
470	D₄×C₆₇	—	4	2	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	4	2	no	—
473	D₄×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	4	2	no	—
475	D₄×C₆₇	—	4	2	no	—
476	D₄×C₆₇	—	4	2	no	—
477	D₄×C₆₇	—	4	2	no	—
478	D₄×C₆₇	—	4	2	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	4	2	no	—
481	D₄×C₆₇	—	4	1	no	—
482	D₄×C₆₇	—	4	1	no	—
483	D₄×C₆₇	—	4	1	no	—
484	D₄×C₆₇	—	4	2	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	4	2	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	4	1	no	—
504	C₂×C₄×C₆₇	—	4	1	no	—
505	C₂×C₄×C₆₇	—	4	1	no	—
506	C₂×C₄×C₆₇	—	4	2	no	—
507	C₂×C₄×C₆₇	—	4	2	no	—
508	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
509	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
511	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
514	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
515	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
518	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
519	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
520	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
522	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
523	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
525	C₈×C₆₇	—	2	1	no	—
526	C₈×C₆₇	—	2	2	no	—
527	C₈×C₆₇	—	2	1	no	—
528	C₈×C₆₇	—	2	2	no	—
529	C₈×C₆₇	—	2	2	no	—
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	1	no	—
532	C₈×C₆₇	—	2	2	no	—
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	—	2	1	no	—
535	C₈×C₆₇	—	2	1	no	—
536	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	2	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	1	no	—
542	C₂²×C₆₇	—	2	2	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	1	no	—
545	C₂²×C₆₇	—	2	1	no	—
546	C₂²×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	2	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	2	no	—
552	C₂²×C₆₇	—	2	1	no	—
553	C₂²×C₆₇	—	2	2	no	—
554	C₂²×C₆₇	—	2	2	no	—
555	C₂²×C₆₇	—	8	4	no	—
556	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
557	C₄×C₆₇	—	2	1	no	—
558	C₄×C₆₇	—	2	2	no	—
559	C₄×C₆₇	—	2	2	no	—
560	C₄×C₆₇	—	2	1	no	—
561	C₄×C₆₇	—	2	2	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	1	no	—
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	1	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	1	no	—
569	C₄×C₆₇	—	2	1	no	—
570	C₄×C₆₇	—	2	1	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	#568	1	2	yes	—
573	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₄×C₆₇	#585	1	1	yes	characteristic
575	#60326	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
576	C₂×C₆₇	—	4	1	no	—
577	C₂×C₆₇	—	4	1	no	—
578	C₂×C₆₇	—	4	2	no	—
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	4	2	no	—
581	C₂×C₆₇	—	4	1	no	—
582	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
584	C₂×C₆₇	#3573	1	1	yes	characteristic
585	#3460	C₂×C₆₇	1	1	yes	characteristic
586	#2994	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#2993	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#2992	C₂×C₆₇	1	2	yes	complemented
589	#2990	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#2989	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#2980	C₂×C₆₇	1	2	yes	complemented
593	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#2978	C₂×C₆₇	1	2	yes	complemented
595	#2976	C₂×C₆₇	1	2	yes	complemented
596	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#2971	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#2967	C₂×C₆₇	1	2	yes	complemented
600	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#2965	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#2935	C₂×C₆₇	1	2	yes	complemented
604	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#2933	C₂×C₆₇	1	2	yes	complemented
606	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2930	C₂×C₆₇	1	2	yes	complemented
608	C₆₇	#60326	1	1	yes	characteristic, direct product factor, Sylow
609	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
610	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
611	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
612	#544	C₄×C₆₇	1	1	yes	characteristic
613	#542	C₄×C₆₇	1	1	yes	characteristic
614	#542	C₄×C₆₇	1	1	yes	characteristic
615	#542	C₄×C₆₇	1	2	yes	—
616	#540	C₄×C₆₇	1	1	yes	characteristic
617	#540	C₄×C₆₇	1	1	yes	characteristic
618	#540	C₄×C₆₇	1	2	yes	—
619	#538	C₄×C₆₇	1	2	yes	—
620	#538	C₄×C₆₇	1	2	yes	—
621	#537	C₄×C₆₇	1	1	yes	characteristic
622	#535	C₄×C₆₇	1	1	yes	characteristic
623	#535	C₄×C₆₇	1	1	yes	characteristic
624	#532	C₂²×C₆₇	1	1	yes	characteristic
625	#532	C₂²×C₆₇	1	1	yes	characteristic
626	#532	C₂²×C₆₇	1	2	yes	—
627	#529	C₂²×C₆₇	1	1	yes	characteristic
628	#529	C₂²×C₆₇	1	2	yes	—
629	#529	C₂²×C₆₇	1	1	yes	characteristic
630	#525	C₂²×C₆₇	1	2	yes	—
631	#525	C₂²×C₆₇	1	2	yes	—
632	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
633	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
634	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
635	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	#446	C₂²×C₆₇	1	2	yes	complemented
639	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
642	#436	C₂²×C₆₇	1	1	yes	characteristic
643	#436	C₂²×C₆₇	1	2	yes	—
644	#436	C₂²×C₆₇	1	1	yes	characteristic
645	#436	C₂²×C₆₇	1	2	yes	—
646	#436	C₂²×C₆₇	1	1	yes	characteristic
647	#436	C₂²×C₆₇	1	1	yes	characteristic
648	#436	C₂²×C₆₇	1	1	yes	characteristic
649	#436	C₂²×C₆₇	1	1	yes	characteristic
650	#436	C₂²×C₆₇	1	2	yes	—
651	#436	C₂²×C₆₇	1	2	yes	complemented
652	#436	C₂²×C₆₇	1	2	yes	complemented
653	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#436	C₂²×C₆₇	1	2	yes	complemented
655	#436	C₂²×C₆₇	1	2	yes	complemented
656	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#435	C₂²×C₆₇	1	2	yes	—
658	#435	C₂²×C₆₇	1	2	yes	—
659	#435	C₂²×C₆₇	1	1	yes	characteristic
660	#435	C₂²×C₆₇	1	2	yes	—
661	#435	C₂²×C₆₇	1	2	yes	—
662	#435	C₂²×C₆₇	1	2	yes	—
663	#435	C₂²×C₆₇	1	2	yes	—
664	#435	C₂²×C₆₇	1	1	yes	characteristic
665	#435	C₂²×C₆₇	1	2	yes	—
666	#435	C₂²×C₆₇	1	2	yes	complemented
667	#435	C₂²×C₆₇	1	2	yes	complemented
668	#435	C₂²×C₆₇	1	2	yes	complemented
669	#435	C₂²×C₆₇	1	2	yes	complemented
670	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
671	#435	C₂²×C₆₇	1	2	yes	complemented
672	#435	C₂²×C₆₇	1	2	yes	complemented
673	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	#435	C₂²×C₆₇	1	2	yes	complemented
675	#435	C₂²×C₆₇	1	2	yes	complemented
676	#435	C₂²×C₆₇	1	2	yes	complemented
677	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
678	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
679	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
680	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
681	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
682	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
684	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
685	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
686	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#433	C₂²×C₆₇	1	2	yes	complemented
688	#433	C₂²×C₆₇	1	2	yes	complemented
689	#433	C₂²×C₆₇	1	2	yes	complemented
690	#433	C₂²×C₆₇	1	2	yes	complemented
691	#432	C₂²×C₆₇	1	1	yes	characteristic
692	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#432	C₂²×C₆₇	1	2	yes	complemented
694	#432	C₂²×C₆₇	1	2	yes	complemented
695	#431	C₂²×C₆₇	1	1	yes	characteristic
696	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#424	C₂²×C₆₇	1	2	yes	complemented
700	#424	C₂²×C₆₇	1	2	yes	complemented
701	#423	C₂²×C₆₇	1	1	yes	characteristic
702	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
705	#408	C₂²×C₆₇	1	2	yes	complemented
706	#408	C₂²×C₆₇	1	2	yes	complemented
707	#408	C₂²×C₆₇	1	2	yes	complemented
708	#408	C₂²×C₆₇	1	2	yes	complemented
709	#408	C₂²×C₆₇	1	2	yes	complemented
710	#408	C₂²×C₆₇	1	2	yes	complemented
711	#407	C₂²×C₆₇	1	2	yes	—
712	#407	C₂²×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
714	#405	C₂²×C₆₇	1	2	yes	complemented
715	#405	C₂²×C₆₇	1	2	yes	complemented
716	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
717	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
719	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
721	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
722	C₂×#41	C₂³×C₆₇	1	2	yes	—
723	C₂×#41	C₂³×C₆₇	1	2	yes	—
724	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
726	#131	—	4	4	no	—
727	#131	—	4	4	no	—
728	C₂×M₁₆	—	4	4	no	—
729	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
731	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
733	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
734	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
735	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
736	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
740	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
741	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
742	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
743	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
744	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
745	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
746	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
747	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
748	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
750	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
751	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
752	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
753	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
754	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
755	#127	C₂×C₄×C₆₇	1	2	yes	—
756	#126	C₂×C₄×C₆₇	1	2	yes	—
757	#126	C₂×C₄×C₆₇	1	2	yes	—
758	#126	C₂×C₄×C₆₇	1	2	yes	—
759	#126	C₂×C₄×C₆₇	1	2	yes	—
760	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
761	#125	C₂×C₄×C₆₇	1	2	yes	—
762	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
763	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
764	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
765	#124	C₂×C₄×C₆₇	1	2	yes	—
766	#124	C₂×C₄×C₆₇	1	2	yes	—
767	#124	C₂×C₄×C₆₇	1	2	yes	—
768	#124	C₂×C₄×C₆₇	1	2	yes	—
769	#124	C₂×C₄×C₆₇	1	2	yes	—
770	#123	C₂×C₄×C₆₇	1	2	yes	—
771	#123	C₂×C₄×C₆₇	1	2	yes	—
772	#123	C₂×C₄×C₆₇	1	2	yes	—
773	#123	C₂×C₄×C₆₇	1	2	yes	—
774	#123	C₂×C₄×C₆₇	1	2	yes	—
775	#123	C₂×C₄×C₆₇	1	2	yes	—
776	#123	C₂×C₄×C₆₇	1	2	yes	—
777	#123	C₂×C₄×C₆₇	1	2	yes	—
778	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
779	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
780	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
781	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
782	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
785	#121	C₂×C₄×C₆₇	1	2	yes	—
786	#121	C₂×C₄×C₆₇	1	2	yes	—
787	#121	C₂×C₄×C₆₇	1	2	yes	—
788	#121	C₂×C₄×C₆₇	1	2	yes	—
789	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
790	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
791	#121	C₂×C₄×C₆₇	1	2	yes	—
792	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
793	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
794	#121	C₂×C₄×C₆₇	1	2	yes	—
795	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
796	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
797	#121	C₂×C₄×C₆₇	1	2	yes	—
798	#121	C₂×C₄×C₆₇	1	2	yes	—
799	#121	C₂×C₄×C₆₇	1	2	yes	—
800	#121	C₂×C₄×C₆₇	1	2	yes	—
801	#121	C₂×C₄×C₆₇	1	2	yes	—
802	#120	C₂×C₄×C₆₇	1	2	yes	—
803	#120	C₂×C₄×C₆₇	1	2	yes	—
804	#120	C₂×C₄×C₆₇	1	2	yes	—
805	#120	C₂×C₄×C₆₇	1	2	yes	—
806	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
807	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
810	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
811	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
812	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
813	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
814	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
815	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
816	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
817	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₆₇	1	2	yes	—
821	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₆₇	1	2	yes	—
824	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₆₇	1	2	yes	—
827	C₄×D₄	C₂³×C₆₇	1	2	yes	—
828	C₄×D₄	C₂³×C₆₇	1	2	yes	—
829	C₄×D₄	C₂³×C₆₇	1	2	yes	—
830	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
831	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
832	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
833	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
834	#117	C₂×C₄×C₆₇	1	2	yes	—
835	#117	C₂³×C₆₇	1	2	yes	—
836	#117	C₂³×C₆₇	1	2	yes	—
837	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
839	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
842	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
843	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
846	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
848	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
849	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
850	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
855	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
865	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
881	#97	C₂³×C₆₇	1	1	yes	characteristic
882	#97	C₂³×C₆₇	1	1	yes	characteristic
883	#97	C₂³×C₆₇	1	1	yes	characteristic
884	#97	C₂³×C₆₇	1	2	yes	—
885	#97	C₂³×C₆₇	1	1	yes	characteristic
886	#97	C₂³×C₆₇	1	2	yes	—
887	#97	C₂³×C₆₇	1	2	yes	—
888	#97	C₂³×C₆₇	1	2	yes	—
889	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₆₇	1	2	yes	—
895	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₆₇	1	2	yes	—
897	C₄×C₈	C₂³×C₆₇	1	2	yes	—
898	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
906	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
907	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
908	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
911	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
912	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
913	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
914	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
915	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
916	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
917	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
918	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
919	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
920	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
921	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
922	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
923	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
924	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
925	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
926	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
927	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
931	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
932	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
933	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
935	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
937	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
938	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
939	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
940	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	4	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	4	no	—
951	M₁₆	—	4	2	no	—
952	M₁₆	—	4	2	no	—
953	M₁₆	—	4	2	no	—
954	M₁₆	—	4	2	no	—
955	M₁₆	—	4	1	no	—
956	M₁₆	—	4	2	no	—
957	M₁₆	—	4	1	no	—
958	M₁₆	—	4	2	no	—
959	C₂×C₈	—	2	4	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	—	4	2	no	—
963	C₂×C₈	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	—	4	2	no	—
967	C₂×C₈	—	4	1	no	—
968	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
972	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
977	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
978	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
979	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
981	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
986	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
993	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
994	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
995	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
996	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
997	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
998	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1000	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1001	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1002	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1003	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1004	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1005	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1006	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1007	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1008	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1009	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1010	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1011	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1012	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1013	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1014	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1015	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1016	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1018	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1019	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1020	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1021	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1022	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1023	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1024	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1026	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1027	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1028	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1029	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1030	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1031	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1032	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1033	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1034	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₆₇	1	2	yes	—
1037	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₂³	—	4	2	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1043	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1044	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1045	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1046	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1047	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	4	1	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	4	2	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	1	no	—
1057	D₄	—	4	1	no	—
1058	D₄	—	4	1	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1094	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1095	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1096	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1097	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1098	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1099	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1100	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1101	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1102	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1103	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1104	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1105	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1106	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1107	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1108	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1109	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	2	no	—
1114	C₈	—	2	2	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	8	4	no	—
1141	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1142	C₄	—	2	1	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	1	no	—
1157	C₄	#568×C₆₇	1	2	yes	—
1158	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1159	C₄	#585×C₆₇	1	1	yes	characteristic
1160	C₂	—	4	1	no	—
1161	C₂	—	4	2	no	—
1162	C₂	—	4	2	no	—
1163	C₂	—	4	1	no	—
1164	C₂	—	4	1	no	—
1165	C₂	—	4	2	no	—
1166	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1167	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
1168	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3460	C₂
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
2. C₆₇×#2994	C₂	semidirect
3. C₆₇×#2993	C₂	semidirect
4. C₆₇×#2992	C₂	semidirect
5. C₆₇×#2990	C₂	semidirect
6. C₆₇×#2989	C₂	semidirect
7. C₆₇×#2981	C₂	semidirect
8. C₆₇×#2980	C₂	semidirect
9. C₆₇×#2979	C₂	semidirect
10. C₆₇×#2978	C₂	semidirect
11. C₆₇×#2976	C₂	semidirect
12. C₆₇×#2974	C₂	semidirect
13. C₆₇×#2971	C₂	semidirect
14. C₆₇×#2969	C₂	semidirect
15. C₆₇×#2967	C₂	semidirect
16. C₆₇×#2966	C₂	semidirect
17. C₆₇×#2965	C₂	semidirect
18. C₆₇×#2935	C₂	semidirect
19. C₆₇×#2935	C₂	semidirect
20. D₄×M₁₆×C₆₇	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2931	C₂	semidirect
23. C₆₇×#2930	C₂	semidirect
24. C₂×#131×C₆₇	C₂²	semidirect
25. C₂×#131×C₆₇	C₂²	semidirect
50. #446×C₆₇	C₂²	semidirect
51. #446×C₆₇	C₂²	semidirect
52. #446×C₆₇	C₂²	semidirect
53. #446×C₆₇	C₂²	semidirect
54. #446×C₆₇	C₂²	semidirect
55. C₈×Q₈×C₆₇	C₂²	semidirect
56. C₈×Q₈×C₆₇	C₂²	semidirect
66. #436×C₆₇	C₂²	semidirect
67. #436×C₆₇	C₂²	semidirect
68. #436×C₆₇	C₂²	semidirect
69. #436×C₆₇	C₂²	semidirect
70. #436×C₆₇	C₂²	semidirect
71. #436×C₆₇	C₂²	semidirect
81. #435×C₆₇	C₂²	semidirect
82. #435×C₆₇	C₂²	semidirect
83. #435×C₆₇	C₂²	semidirect
84. #435×C₆₇	C₂²	semidirect
85. #435×C₆₇	C₂²	semidirect
86. #435×C₆₇	C₂²	semidirect
87. #435×C₆₇	C₂²	semidirect
88. #435×C₆₇	C₂²	semidirect
89. #435×C₆₇	C₂²	semidirect
90. #435×C₆₇	C₂²	semidirect
91. #435×C₆₇	C₂²	semidirect
96. C₈×D₄×C₆₇	C₂²	semidirect
97. C₈×D₄×C₆₇	C₂²	semidirect
98. C₈×D₄×C₆₇	C₂²	semidirect
99. C₈×D₄×C₆₇	C₂²	semidirect
100. C₈×D₄×C₆₇	C₂²	semidirect
101. C₈×D₄×C₆₇	C₂²	semidirect
102. #433×C₆₇	C₂²	semidirect
103. #433×C₆₇	C₂²	semidirect
104. #433×C₆₇	C₂²	semidirect
105. #433×C₆₇	C₂²	semidirect
107. #432×C₆₇	C₂²	semidirect
108. #432×C₆₇	C₂²	semidirect
109. #432×C₆₇	C₂²	semidirect
111. #431×C₆₇	C₂²	semidirect
112. #431×C₆₇	C₂²	semidirect
113. #431×C₆₇	C₂²	semidirect
114. #424×C₆₇	C₂²	semidirect
115. #424×C₆₇	C₂²	semidirect
117. #423×C₆₇	C₂²	semidirect
118. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
119. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
120. #408×C₆₇	C₂²	semidirect
121. #408×C₆₇	C₂²	semidirect
122. #408×C₆₇	C₂²	semidirect
123. #408×C₆₇	C₂²	semidirect
124. #408×C₆₇	C₂²	semidirect
125. #408×C₆₇	C₂²	semidirect
129. #405×C₆₇	C₂²	semidirect
130. #405×C₆₇	C₂²	semidirect
132. C₄×M₁₆×C₆₇	C₂²	semidirect
133. C₄×M₁₆×C₆₇	C₂²	semidirect
134. C₂×C₄×C₈×C₆₇	C₂²	semidirect
575. #60326	C₆₇	direct (N × H)
586. #2994	C₂×C₆₇	semidirect
587. #2993	C₂×C₆₇	semidirect
588. #2992	C₂×C₆₇	semidirect
589. #2990	C₂×C₆₇	semidirect
590. #2989	C₂×C₆₇	semidirect
591. #2981	C₂×C₆₇	semidirect
592. #2980	C₂×C₆₇	semidirect
593. #2979	C₂×C₆₇	semidirect
594. #2978	C₂×C₆₇	semidirect
595. #2976	C₂×C₆₇	semidirect
596. #2974	C₂×C₆₇	semidirect
597. #2971	C₂×C₆₇	semidirect
598. #2969	C₂×C₆₇	semidirect
599. #2967	C₂×C₆₇	semidirect
600. #2966	C₂×C₆₇	semidirect
601. #2965	C₂×C₆₇	semidirect
602. #2935	C₂×C₆₇	semidirect
603. #2935	C₂×C₆₇	semidirect
604. D₄×M₁₆	C₂×C₆₇	semidirect
605. #2933	C₂×C₆₇	semidirect
606. #2931	C₂×C₆₇	semidirect
607. #2930	C₂×C₆₇	semidirect
608. C₆₇	#60326	direct (N × H)
609. C₂×#131	C₂²×C₆₇	semidirect
610. C₂×#131	C₂²×C₆₇	semidirect
635. #446	C₂²×C₆₇	semidirect
636. #446	C₂²×C₆₇	semidirect
637. #446	C₂²×C₆₇	semidirect
638. #446	C₂²×C₆₇	semidirect
639. #446	C₂²×C₆₇	semidirect
640. C₈×Q₈	C₂²×C₆₇	semidirect
641. C₈×Q₈	C₂²×C₆₇	semidirect
651. #436	C₂²×C₆₇	semidirect
652. #436	C₂²×C₆₇	semidirect
653. #436	C₂²×C₆₇	semidirect
654. #436	C₂²×C₆₇	semidirect
655. #436	C₂²×C₆₇	semidirect
656. #436	C₂²×C₆₇	semidirect
666. #435	C₂²×C₆₇	semidirect
667. #435	C₂²×C₆₇	semidirect
668. #435	C₂²×C₆₇	semidirect
669. #435	C₂²×C₆₇	semidirect
670. #435	C₂²×C₆₇	semidirect
671. #435	C₂²×C₆₇	semidirect
672. #435	C₂²×C₆₇	semidirect
673. #435	C₂²×C₆₇	semidirect
674. #435	C₂²×C₆₇	semidirect
675. #435	C₂²×C₆₇	semidirect
676. #435	C₂²×C₆₇	semidirect
681. C₈×D₄	C₂²×C₆₇	semidirect
682. C₈×D₄	C₂²×C₆₇	semidirect
683. C₈×D₄	C₂²×C₆₇	semidirect
684. C₈×D₄	C₂²×C₆₇	semidirect
685. C₈×D₄	C₂²×C₆₇	semidirect
686. C₈×D₄	C₂²×C₆₇	semidirect
687. #433	C₂²×C₆₇	semidirect
688. #433	C₂²×C₆₇	semidirect
689. #433	C₂²×C₆₇	semidirect
690. #433	C₂²×C₆₇	semidirect
692. #432	C₂²×C₆₇	semidirect
693. #432	C₂²×C₆₇	semidirect
694. #432	C₂²×C₆₇	semidirect
696. #431	C₂²×C₆₇	semidirect
697. #431	C₂²×C₆₇	semidirect
698. #431	C₂²×C₆₇	semidirect
699. #424	C₂²×C₆₇	semidirect
700. #424	C₂²×C₆₇	semidirect
702. #423	C₂²×C₆₇	semidirect
703. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
704. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
705. #408	C₂²×C₆₇	semidirect
706. #408	C₂²×C₆₇	semidirect
707. #408	C₂²×C₆₇	semidirect
708. #408	C₂²×C₆₇	semidirect
709. #408	C₂²×C₆₇	semidirect
710. #408	C₂²×C₆₇	semidirect
714. #405	C₂²×C₆₇	semidirect
715. #405	C₂²×C₆₇	semidirect
717. C₄×M₁₆	C₂²×C₆₇	semidirect
718. C₄×M₁₆	C₂²×C₆₇	semidirect
719. C₂×C₄×C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3460	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2990	2
C₆₇×#2989	2
C₆₇×#2981	2
C₆₇×#2980	2
C₆₇×#2979	2
C₆₇×#2978	2
C₆₇×#2976	2
C₆₇×#2974	2
C₆₇×#2971	2
C₆₇×#2969	2
C₆₇×#2967	2
C₆₇×#2966	2
C₆₇×#2965	2
C₆₇×#2935	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2931	2
C₆₇×#2930	2
#60326	67

Subgroups — C67×#60326 #30739577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60326 #30739577