Subgroups — C₆₇×#34288 #30713539

Order 17152.

3584 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
10	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2325	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
19	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
21	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#385×C₆₇	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
27	#546×C₆₇	C₄	1	16	yes	complemented
28	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#123×C₆₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#121×C₆₇	C₂²	1	2	yes	—
33	C₂×#120×C₆₇	C₂²	1	2	yes	—
34	#520×C₆₇	—	2	8	no	—
35	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₆₇	—	2	8	no	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
50	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
51	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
54	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
55	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
56	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
58	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
59	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
60	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
61	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
62	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#390×C₆₇	C₂²	1	1	yes	characteristic
65	#390×C₆₇	C₂²	1	1	yes	characteristic
66	#390×C₆₇	C₂²	1	2	yes	complemented
67	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#389×C₆₇	C₂²	1	2	yes	complemented
69	#389×C₆₇	C₂²	1	2	yes	complemented
70	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#388×C₆₇	C₂²	1	2	yes	complemented
74	#388×C₆₇	C₂²	1	2	yes	complemented
75	#388×C₆₇	C₂²	1	2	yes	complemented
76	#388×C₆₇	C₂²	1	2	yes	complemented
77	#388×C₆₇	C₂²	1	2	yes	complemented
78	#388×C₆₇	C₂²	1	2	yes	complemented
79	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#387×C₆₇	C₂²	1	2	yes	complemented
82	#387×C₆₇	C₂²	1	2	yes	complemented
83	#386×C₆₇	C₂²	1	1	yes	characteristic
84	#386×C₆₇	C₂²	1	1	yes	characteristic
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	complemented
88	#386×C₆₇	C₂²	1	2	yes	complemented
89	#386×C₆₇	C₂²	1	2	yes	complemented
90	#386×C₆₇	C₂²	1	2	yes	complemented
91	#385×C₆₇	C₂²	1	1	yes	characteristic
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	1	yes	characteristic
96	#385×C₆₇	C₂²	1	2	yes	complemented
97	#385×C₆₇	C₂²	1	2	yes	complemented
98	#385×C₆₇	C₂²	1	2	yes	complemented
99	#385×C₆₇	C₂²	1	2	yes	complemented
100	#385×C₆₇	C₂²	1	2	yes	complemented
101	#385×C₆₇	C₂²	1	2	yes	complemented
102	#385×C₆₇	C₂²	1	2	yes	complemented
103	#385×C₆₇	C₂²	1	2	yes	complemented
104	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#381×C₆₇	C₂²	1	2	yes	complemented
106	#380×C₆₇	C₂²	1	1	yes	characteristic
107	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#380×C₆₇	C₂²	1	2	yes	complemented
109	#379×C₆₇	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
123	#376×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
125	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
126	C₂⁵×C₆₇	C₂³	1	2	yes	—
127	C₂×#41×C₆₇	—	2	4	no	—
128	C₂×#41×C₆₇	—	2	4	no	—
129	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₆₇	—	2	4	no	—
132	C₂²×D₄×C₆₇	—	2	4	no	—
133	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	—	2	8	no	—
141	C₂³×C₄×C₆₇	—	4	4	no	—
142	C₂³×C₄×C₆₇	—	4	4	no	—
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
152	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
153	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
154	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
155	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
156	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
157	#124×C₆₇	C₂×C₄	1	8	yes	complemented
158	#123×C₆₇	C₂×C₄	1	16	yes	complemented
159	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
160	#121×C₆₇	C₂×C₄	1	8	yes	complemented
161	#121×C₆₇	C₂×C₄	1	16	yes	complemented
162	#120×C₆₇	C₂×C₄	1	16	yes	complemented
163	C₄×Q₈×C₆₇	—	2	4	no	—
164	C₄×Q₈×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	4	no	—
167	C₄×D₄×C₆₇	—	2	4	no	—
168	C₄×D₄×C₆₇	—	2	8	no	—
169	C₄×D₄×C₆₇	—	2	8	no	—
170	C₄×D₄×C₆₇	—	2	4	no	—
171	C₄×D₄×C₆₇	—	2	8	no	—
172	C₄×D₄×C₆₇	—	2	8	no	—
173	C₄×D₄×C₆₇	—	2	4	no	—
174	C₄×D₄×C₆₇	—	4	4	no	—
175	C₄×D₄×C₆₇	—	4	4	no	—
176	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
177	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
178	C₄×D₄×C₆₇	D₄	1	8	yes	complemented
179	#117×C₆₇	—	2	8	no	—
180	#117×C₆₇	—	2	4	no	—
181	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
182	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
183	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
184	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
205	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
206	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	—	2	4	no	—
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
238	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
239	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
241	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
242	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
243	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	#95×C₆₇	C₂³	1	1	yes	characteristic
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	#95×C₆₇	C₂³	1	2	yes	—
251	#95×C₆₇	C₂³	1	2	yes	—
252	#95×C₆₇	C₂³	1	2	yes	—
253	#95×C₆₇	C₂³	1	1	yes	characteristic
254	#95×C₆₇	C₂³	1	1	yes	characteristic
255	#95×C₆₇	C₂³	1	1	yes	characteristic
256	#95×C₆₇	C₂³	1	2	yes	—
257	#95×C₆₇	C₂³	1	2	yes	—
258	#95×C₆₇	C₂³	1	2	yes	—
259	#95×C₆₇	C₂³	1	2	yes	—
260	#95×C₆₇	C₂³	1	1	yes	characteristic
261	#95×C₆₇	C₂³	1	1	yes	characteristic
262	#95×C₆₇	C₂³	1	1	yes	characteristic
263	#95×C₆₇	C₂³	1	1	yes	characteristic
264	#95×C₆₇	C₂³	1	2	yes	—
265	#95×C₆₇	C₂³	1	1	yes	characteristic
266	C₂⁴×C₆₇	—	2	4	no	—
267	C₂⁴×C₆₇	—	2	4	no	—
268	C₂⁴×C₆₇	—	2	4	no	—
269	C₂⁴×C₆₇	—	2	4	no	—
270	C₂⁴×C₆₇	—	4	2	no	—
271	C₂⁴×C₆₇	—	4	2	no	—
272	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
273	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
274	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
276	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
277	#41×C₆₇	—	2	32	no	—
278	C₂×Q₈×C₆₇	—	2	2	no	—
279	C₂×Q₈×C₆₇	—	2	2	no	—
280	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	complemented
281	C₂×D₄×C₆₇	—	2	4	no	—
282	C₂×D₄×C₆₇	—	2	4	no	—
283	C₂×D₄×C₆₇	—	2	4	no	—
284	C₂×D₄×C₆₇	—	2	4	no	—
285	C₂×D₄×C₆₇	—	2	2	no	—
286	C₂×D₄×C₆₇	—	2	2	no	—
287	C₂×D₄×C₆₇	—	2	32	no	—
288	C₂×D₄×C₆₇	—	2	2	no	—
289	C₂×D₄×C₆₇	—	2	2	no	—
290	C₂×D₄×C₆₇	—	4	2	no	—
291	C₂×D₄×C₆₇	—	4	2	no	—
292	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
293	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
294	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
295	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
296	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	complemented
297	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	complemented
298	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
299	C₂×D₄×C₆₇	#41	1	4	yes	—
300	C₂²×C₄×C₆₇	—	2	4	no	—
301	C₂²×C₄×C₆₇	—	2	4	no	—
302	C₂²×C₄×C₆₇	—	2	2	no	—
303	C₂²×C₄×C₆₇	—	2	2	no	—
304	C₂²×C₄×C₆₇	—	2	2	no	—
305	C₂²×C₄×C₆₇	—	2	2	no	—
306	C₂²×C₄×C₆₇	—	2	2	no	—
307	C₂²×C₄×C₆₇	—	2	2	no	—
308	C₂²×C₄×C₆₇	—	2	2	no	—
309	C₂²×C₄×C₆₇	—	2	4	no	—
310	C₂²×C₄×C₆₇	—	2	4	no	—
311	C₂²×C₄×C₆₇	—	2	2	no	—
312	C₂²×C₄×C₆₇	—	2	4	no	—
313	C₂²×C₄×C₆₇	—	2	4	no	—
314	C₂²×C₄×C₆₇	—	2	2	no	—
315	C₂²×C₄×C₆₇	—	2	4	no	—
316	C₂²×C₄×C₆₇	—	2	4	no	—
317	C₂²×C₄×C₆₇	—	2	4	no	—
318	C₂²×C₄×C₆₇	—	2	4	no	—
319	C₂²×C₄×C₆₇	—	2	4	no	—
320	C₂²×C₄×C₆₇	—	2	4	no	—
321	C₂²×C₄×C₆₇	—	4	2	no	—
322	C₂²×C₄×C₆₇	—	4	2	no	—
323	C₂²×C₄×C₆₇	—	4	2	no	—
324	C₂²×C₄×C₆₇	—	4	2	no	—
325	C₂²×C₄×C₆₇	—	4	2	no	—
326	C₂²×C₄×C₆₇	—	4	2	no	—
327	C₂²×C₄×C₆₇	—	4	2	no	—
328	C₂²×C₄×C₆₇	—	4	2	no	—
329	C₂²×C₄×C₆₇	—	4	1	no	—
330	C₂²×C₄×C₆₇	—	4	2	no	—
331	C₂²×C₄×C₆₇	—	4	2	no	—
332	C₂²×C₄×C₆₇	—	4	2	no	—
333	C₂²×C₄×C₆₇	—	4	2	no	—
334	C₂²×C₄×C₆₇	—	4	2	no	—
335	C₂²×C₄×C₆₇	—	4	2	no	—
336	C₂²×C₄×C₆₇	—	4	2	no	—
337	C₂²×C₄×C₆₇	—	4	32	no	—
338	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
339	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
340	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
341	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
342	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
343	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
361	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	4	no	—
364	C₄⋊C₄×C₆₇	—	2	4	no	—
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	—	2	4	no	—
367	C₄⋊C₄×C₆₇	—	2	4	no	—
368	C₄⋊C₄×C₆₇	—	2	2	no	—
369	C₄⋊C₄×C₆₇	—	2	2	no	—
370	C₄⋊C₄×C₆₇	—	2	2	no	—
371	C₄⋊C₄×C₆₇	—	2	2	no	—
372	C₄⋊C₄×C₆₇	—	2	4	no	—
373	C₄⋊C₄×C₆₇	—	4	2	no	—
374	C₄⋊C₄×C₆₇	—	4	2	no	—
375	C₄⋊C₄×C₆₇	—	4	1	no	—
376	C₄⋊C₄×C₆₇	—	4	2	no	—
377	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
378	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
379	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
380	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
381	C₂²⋊C₄×C₆₇	—	2	4	no	—
382	C₂²⋊C₄×C₆₇	—	2	4	no	—
383	C₂²⋊C₄×C₆₇	—	2	4	no	—
384	C₂²⋊C₄×C₆₇	—	2	2	no	—
385	C₂²⋊C₄×C₆₇	—	2	4	no	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	4	no	—
388	C₂²⋊C₄×C₆₇	—	2	4	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	—	2	2	no	—
391	C₂²⋊C₄×C₆₇	—	2	2	no	—
392	C₂²⋊C₄×C₆₇	—	4	2	no	—
393	C₂²⋊C₄×C₆₇	—	4	2	no	—
394	C₂²⋊C₄×C₆₇	—	4	2	no	—
395	C₂²⋊C₄×C₆₇	—	4	1	no	—
396	C₂²⋊C₄×C₆₇	—	4	2	no	—
397	C₂²⋊C₄×C₆₇	—	4	2	no	—
398	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
399	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
400	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
401	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
402	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
403	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
404	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
405	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
406	C₄²×C₆₇	—	2	2	no	—
407	C₄²×C₆₇	—	2	2	no	—
408	C₄²×C₆₇	—	2	2	no	—
409	C₄²×C₆₇	—	2	4	no	—
410	C₄²×C₆₇	—	2	4	no	—
411	C₄²×C₆₇	—	2	2	no	—
412	C₄²×C₆₇	—	2	2	no	—
413	C₄²×C₆₇	—	4	2	no	—
414	C₄²×C₆₇	—	4	2	no	—
415	C₄²×C₆₇	—	4	2	no	—
416	C₄²×C₆₇	C₂²×C₄	1	4	yes	complemented
417	C₄²×C₆₇	C₂×D₄	1	4	yes	—
418	C₂³×C₆₇	—	2	1	no	—
419	C₂³×C₆₇	—	2	1	no	—
420	C₂³×C₆₇	—	2	2	no	—
421	C₂³×C₆₇	—	2	1	no	—
422	C₂³×C₆₇	—	2	2	no	—
423	C₂³×C₆₇	—	2	2	no	—
424	C₂³×C₆₇	—	2	2	no	—
425	C₂³×C₆₇	—	2	1	no	—
426	C₂³×C₆₇	—	2	16	no	—
427	C₂³×C₆₇	—	2	16	no	—
428	C₂³×C₆₇	—	2	1	no	—
429	C₂³×C₆₇	—	2	2	no	—
430	C₂³×C₆₇	—	2	1	no	—
431	C₂³×C₆₇	—	2	2	no	—
432	C₂³×C₆₇	—	2	1	no	—
433	C₂³×C₆₇	—	2	1	no	—
434	C₂³×C₆₇	—	2	2	no	—
435	C₂³×C₆₇	—	2	2	no	—
436	C₂³×C₆₇	—	2	1	no	—
437	C₂³×C₆₇	—	2	2	no	—
438	C₂³×C₆₇	—	2	1	no	—
439	C₂³×C₆₇	—	2	2	no	—
440	C₂³×C₆₇	—	4	8	no	—
441	C₂³×C₆₇	—	4	8	no	—
442	C₂³×C₆₇	—	4	8	no	—
443	C₂³×C₆₇	—	4	8	no	—
444	C₂³×C₆₇	—	4	8	no	—
445	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
446	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
447	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
448	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
449	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
450	C₂³×C₆₇	C₂×#41	1	4	yes	—
451	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
452	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
453	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
454	Q₈×C₆₇	—	2	8	no	—
455	D₄×C₆₇	—	2	16	no	—
456	D₄×C₆₇	—	2	16	no	—
457	D₄×C₆₇	—	2	8	no	—
458	D₄×C₆₇	—	2	8	no	—
459	D₄×C₆₇	—	4	8	no	—
460	D₄×C₆₇	C₄×D₄	1	16	yes	complemented
461	C₂×C₄×C₆₇	—	2	8	no	—
462	C₂×C₄×C₆₇	—	2	16	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	2	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	2	2	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	2	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	8	no	—
484	C₂×C₄×C₆₇	—	2	8	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	1	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	1	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	2	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	2	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	4	8	no	—
510	C₂×C₄×C₆₇	—	4	8	no	—
511	C₂×C₄×C₆₇	—	4	8	no	—
512	C₂×C₄×C₆₇	—	4	4	no	—
513	C₂×C₄×C₆₇	—	4	8	no	—
514	C₂×C₄×C₆₇	—	4	8	no	—
515	C₂×C₄×C₆₇	—	4	8	no	—
516	C₂×C₄×C₆₇	—	8	4	no	—
517	C₂×C₄×C₆₇	—	8	4	no	—
518	C₂×C₄×C₆₇	—	8	4	no	—
519	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
520	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
521	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
522	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
523	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
524	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
525	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
529	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
531	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
532	C₂²×C₆₇	—	2	2	no	—
533	C₂²×C₆₇	—	2	4	no	—
534	C₂²×C₆₇	—	2	4	no	—
535	C₂²×C₆₇	—	2	2	no	—
536	C₂²×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	2	4	no	—
538	C₂²×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	4	no	—
540	C₂²×C₆₇	—	2	4	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	2	no	—
543	C₂²×C₆₇	—	2	4	no	—
544	C₂²×C₆₇	—	2	2	no	—
545	C₂²×C₆₇	—	2	4	no	—
546	C₂²×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	4	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	4	no	—
550	C₂²×C₆₇	—	4	32	no	—
551	C₂²×C₆₇	—	4	2	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	4	1	no	—
556	C₂²×C₆₇	—	4	2	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	2	no	—
559	C₂²×C₆₇	C₂×C₄×D₄	1	8	yes	—
560	C₂²×C₆₇	#520	1	4	yes	complemented
561	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
562	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
563	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
564	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
565	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
567	C₂²×C₆₇	#585	1	1	yes	characteristic
568	C₄×C₆₇	—	2	2	no	—
569	C₄×C₆₇	—	2	2	no	—
570	C₄×C₆₇	—	2	4	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	4	no	—
574	C₄×C₆₇	—	2	2	no	—
575	C₄×C₆₇	—	2	2	no	—
576	C₄×C₆₇	—	2	4	no	—
577	C₄×C₆₇	—	2	2	no	—
578	C₄×C₆₇	—	4	2	no	—
579	C₄×C₆₇	—	4	1	no	—
580	C₄×C₆₇	—	4	2	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	2	no	—
584	C₄×C₆₇	—	4	1	no	—
585	C₄×C₆₇	—	4	1	no	—
586	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
587	#34288	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
588	C₂×C₆₇	—	2	4	no	—
589	C₂×C₆₇	—	2	8	no	—
590	C₂×C₆₇	—	4	2	no	—
591	C₂×C₆₇	—	4	4	no	—
592	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
593	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
594	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂×C₆₇	#3484	1	1	yes	characteristic
596	C₂×C₆₇	#3489	1	1	yes	characteristic
597	C₂×C₆₇	#3513	1	1	yes	characteristic
598	C₂×C₆₇	#3520	1	1	yes	characteristic
599	C₂×#546	C₂×C₆₇	1	1	yes	characteristic
600	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
601	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#2361	C₂×C₆₇	1	2	yes	complemented
604	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#2360	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2359	C₂×C₆₇	1	2	yes	complemented
607	#2358	C₂×C₆₇	1	2	yes	complemented
608	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
609	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#2342	C₂×C₆₇	1	2	yes	complemented
611	#2339	C₂×C₆₇	1	1	yes	characteristic, complemented
612	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#2326	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#2325	C₂×C₆₇	1	2	yes	complemented
615	#2324	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#2322	C₂×C₆₇	1	2	yes	complemented
617	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
618	C₄×#120	C₂×C₆₇	1	2	yes	complemented
619	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
620	C₂×#385	C₂×C₆₇	1	2	yes	complemented
621	#2275	C₂×C₆₇	1	1	yes	characteristic, complemented
622	C₆₇	#34288	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
624	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
625	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
626	#546	C₄×C₆₇	1	16	yes	complemented
627	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
628	C₂×#123	C₂²×C₆₇	1	2	yes	—
629	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
630	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
631	C₂×#121	C₂²×C₆₇	1	2	yes	—
632	C₂×#120	C₂²×C₆₇	1	2	yes	—
633	#520	—	2	8	no	—
634	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	C₂×C₄×D₄	—	2	8	no	—
637	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
638	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
639	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
640	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
641	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
642	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
643	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
645	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
647	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
648	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
649	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
650	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
651	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
653	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
654	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
655	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
657	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
658	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
659	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
660	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
661	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#390	C₂²×C₆₇	1	1	yes	characteristic
664	#390	C₂²×C₆₇	1	1	yes	characteristic
665	#390	C₂²×C₆₇	1	2	yes	complemented
666	#389	C₂²×C₆₇	1	2	yes	complemented
667	#389	C₂²×C₆₇	1	2	yes	complemented
668	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
669	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#388	C₂²×C₆₇	1	2	yes	complemented
671	#388	C₂²×C₆₇	1	2	yes	complemented
672	#388	C₂²×C₆₇	1	2	yes	complemented
673	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	#388	C₂²×C₆₇	1	2	yes	complemented
675	#388	C₂²×C₆₇	1	2	yes	complemented
676	#388	C₂²×C₆₇	1	2	yes	complemented
677	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
679	#387	C₂²×C₆₇	1	2	yes	complemented
680	#387	C₂²×C₆₇	1	2	yes	complemented
681	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	#386	C₂²×C₆₇	1	2	yes	—
683	#386	C₂²×C₆₇	1	2	yes	—
684	#386	C₂²×C₆₇	1	1	yes	characteristic
685	#386	C₂²×C₆₇	1	1	yes	characteristic
686	#386	C₂²×C₆₇	1	2	yes	complemented
687	#386	C₂²×C₆₇	1	2	yes	complemented
688	#386	C₂²×C₆₇	1	2	yes	complemented
689	#386	C₂²×C₆₇	1	2	yes	complemented
690	#385	C₂²×C₆₇	1	1	yes	characteristic
691	#385	C₂²×C₆₇	1	2	yes	—
692	#385	C₂²×C₆₇	1	2	yes	—
693	#385	C₂²×C₆₇	1	1	yes	characteristic
694	#385	C₂²×C₆₇	1	2	yes	—
695	#385	C₂²×C₆₇	1	2	yes	complemented
696	#385	C₂²×C₆₇	1	2	yes	complemented
697	#385	C₂²×C₆₇	1	2	yes	complemented
698	#385	C₂²×C₆₇	1	2	yes	complemented
699	#385	C₂²×C₆₇	1	2	yes	complemented
700	#385	C₂²×C₆₇	1	2	yes	complemented
701	#385	C₂²×C₆₇	1	2	yes	complemented
702	#385	C₂²×C₆₇	1	2	yes	complemented
703	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#381	C₂²×C₆₇	1	2	yes	complemented
705	#380	C₂²×C₆₇	1	1	yes	characteristic
706	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#380	C₂²×C₆₇	1	2	yes	complemented
708	#379	C₂²×C₆₇	1	2	yes	—
709	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
713	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
715	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
716	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
717	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
718	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
720	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
721	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
722	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
723	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
724	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
725	C₂⁵	C₂³×C₆₇	1	2	yes	—
726	C₂×#41	—	2	4	no	—
727	C₂×#41	—	2	4	no	—
728	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
729	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
730	C₂²×D₄	—	2	4	no	—
731	C₂²×D₄	—	2	4	no	—
732	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
733	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
735	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
736	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
737	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
738	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂³×C₄	—	2	8	no	—
740	C₂³×C₄	—	4	4	no	—
741	C₂³×C₄	—	4	4	no	—
742	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
743	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
745	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
746	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
747	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
748	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
749	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
750	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
751	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
752	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
753	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
754	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
755	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
756	#124	C₂×C₄×C₆₇	1	8	yes	complemented
757	#123	C₂×C₄×C₆₇	1	16	yes	complemented
758	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
759	#121	C₂×C₄×C₆₇	1	8	yes	complemented
760	#121	C₂×C₄×C₆₇	1	16	yes	complemented
761	#120	C₂×C₄×C₆₇	1	16	yes	complemented
762	C₄×Q₈	—	2	4	no	—
763	C₄×Q₈	—	2	4	no	—
764	C₄×D₄	—	2	4	no	—
765	C₄×D₄	—	2	4	no	—
766	C₄×D₄	—	2	4	no	—
767	C₄×D₄	—	2	8	no	—
768	C₄×D₄	—	2	8	no	—
769	C₄×D₄	—	2	4	no	—
770	C₄×D₄	—	2	8	no	—
771	C₄×D₄	—	2	8	no	—
772	C₄×D₄	—	2	4	no	—
773	C₄×D₄	—	4	4	no	—
774	C₄×D₄	—	4	4	no	—
775	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
776	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
777	C₄×D₄	D₄×C₆₇	1	8	yes	complemented
778	#117	—	2	8	no	—
779	#117	—	2	4	no	—
780	C₂×C₄⋊C₄	—	2	8	no	—
781	C₂×C₄⋊C₄	—	2	4	no	—
782	C₂×C₄⋊C₄	—	2	4	no	—
783	C₂×C₄⋊C₄	—	4	4	no	—
784	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
786	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
791	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
796	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
797	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
802	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	—	2	8	no	—
804	C₂×C₂²⋊C₄	—	4	4	no	—
805	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
806	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
813	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
814	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
823	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
831	C₂×C₄²	—	2	4	no	—
832	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
833	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
834	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
835	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
836	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
837	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
840	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
841	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
842	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
843	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
844	#95	C₂³×C₆₇	1	1	yes	characteristic
845	#95	C₂³×C₆₇	1	1	yes	characteristic
846	#95	C₂³×C₆₇	1	2	yes	—
847	#95	C₂³×C₆₇	1	2	yes	—
848	#95	C₂³×C₆₇	1	2	yes	—
849	#95	C₂³×C₆₇	1	2	yes	—
850	#95	C₂³×C₆₇	1	2	yes	—
851	#95	C₂³×C₆₇	1	2	yes	—
852	#95	C₂³×C₆₇	1	1	yes	characteristic
853	#95	C₂³×C₆₇	1	1	yes	characteristic
854	#95	C₂³×C₆₇	1	1	yes	characteristic
855	#95	C₂³×C₆₇	1	2	yes	—
856	#95	C₂³×C₆₇	1	2	yes	—
857	#95	C₂³×C₆₇	1	2	yes	—
858	#95	C₂³×C₆₇	1	2	yes	—
859	#95	C₂³×C₆₇	1	1	yes	characteristic
860	#95	C₂³×C₆₇	1	1	yes	characteristic
861	#95	C₂³×C₆₇	1	1	yes	characteristic
862	#95	C₂³×C₆₇	1	1	yes	characteristic
863	#95	C₂³×C₆₇	1	2	yes	—
864	#95	C₂³×C₆₇	1	1	yes	characteristic
865	C₂⁴	—	2	4	no	—
866	C₂⁴	—	2	4	no	—
867	C₂⁴	—	2	4	no	—
868	C₂⁴	—	2	4	no	—
869	C₂⁴	—	4	2	no	—
870	C₂⁴	—	4	2	no	—
871	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
872	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
873	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
874	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
875	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
876	#41	—	2	32	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	complemented
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	—	2	4	no	—
883	C₂×D₄	—	2	4	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	32	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	4	2	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
892	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
893	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
894	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
895	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	complemented
896	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	complemented
897	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
898	C₂×D₄	#41×C₆₇	1	4	yes	—
899	C₂²×C₄	—	2	4	no	—
900	C₂²×C₄	—	2	4	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	4	no	—
909	C₂²×C₄	—	2	4	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	4	no	—
912	C₂²×C₄	—	2	4	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	4	no	—
915	C₂²×C₄	—	2	4	no	—
916	C₂²×C₄	—	2	4	no	—
917	C₂²×C₄	—	2	4	no	—
918	C₂²×C₄	—	2	4	no	—
919	C₂²×C₄	—	2	4	no	—
920	C₂²×C₄	—	4	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	—	4	2	no	—
925	C₂²×C₄	—	4	2	no	—
926	C₂²×C₄	—	4	2	no	—
927	C₂²×C₄	—	4	2	no	—
928	C₂²×C₄	—	4	1	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	—	4	2	no	—
935	C₂²×C₄	—	4	2	no	—
936	C₂²×C₄	—	4	32	no	—
937	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
938	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
939	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
940	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
941	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
942	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
950	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
959	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	4	no	—
963	C₄⋊C₄	—	2	4	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	4	no	—
966	C₄⋊C₄	—	2	4	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	4	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	2	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	4	1	no	—
976	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
977	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
978	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
979	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	4	no	—
987	C₂²⋊C₄	—	2	4	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	1	no	—
997	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
998	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
999	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1000	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1001	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1002	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
1003	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1004	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	4	no	—
1009	C₄²	—	2	4	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	4	2	no	—
1013	C₄²	—	4	2	no	—
1014	C₄²	—	4	2	no	—
1015	C₄²	C₂²×C₄×C₆₇	1	4	yes	complemented
1016	C₄²	C₂×D₄×C₆₇	1	4	yes	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	16	no	—
1026	C₂³	—	2	16	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	4	8	no	—
1040	C₂³	—	4	8	no	—
1041	C₂³	—	4	8	no	—
1042	C₂³	—	4	8	no	—
1043	C₂³	—	4	8	no	—
1044	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
1045	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1046	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
1047	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1048	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
1049	C₂³	C₂×#41×C₆₇	1	4	yes	—
1050	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
1051	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
1052	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1053	Q₈	—	2	8	no	—
1054	D₄	—	2	16	no	—
1055	D₄	—	2	16	no	—
1056	D₄	—	2	8	no	—
1057	D₄	—	2	8	no	—
1058	D₄	—	4	8	no	—
1059	D₄	C₄×D₄×C₆₇	1	16	yes	complemented
1060	C₂×C₄	—	2	8	no	—
1061	C₂×C₄	—	2	16	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	8	no	—
1083	C₂×C₄	—	2	8	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	4	8	no	—
1109	C₂×C₄	—	4	8	no	—
1110	C₂×C₄	—	4	8	no	—
1111	C₂×C₄	—	4	8	no	—
1112	C₂×C₄	—	4	8	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	4	8	no	—
1115	C₂×C₄	—	8	4	no	—
1116	C₂×C₄	—	8	4	no	—
1117	C₂×C₄	—	8	4	no	—
1118	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1119	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1120	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1121	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1122	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1123	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1124	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1128	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1129	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1130	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	4	no	—
1133	C₂²	—	2	4	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	4	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	4	no	—
1139	C₂²	—	2	4	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	4	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	4	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	4	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	4	no	—
1149	C₂²	—	4	32	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	C₂×C₄×D₄×C₆₇	1	8	yes	—
1159	C₂²	#520×C₆₇	1	4	yes	complemented
1160	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1161	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1162	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1163	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1164	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1165	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1166	C₂²	#585×C₆₇	1	1	yes	characteristic
1167	C₄	—	2	2	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	2	4	no	—
1170	C₄	—	2	2	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	4	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	4	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	1	no	—
1185	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
1186	C₂	—	2	4	no	—
1187	C₂	—	2	8	no	—
1188	C₂	—	4	4	no	—
1189	C₂	—	4	2	no	—
1190	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
1191	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
1192	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1193	C₂	C₆₇×#3484	1	1	yes	characteristic
1194	C₂	C₆₇×#3489	1	1	yes	characteristic
1195	C₂	C₆₇×#3513	1	1	yes	characteristic
1196	C₂	C₆₇×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#546×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#520×C₆₇	C₂	semidirect
3. C₂²×C₄×D₄×C₆₇	C₂	semidirect
4. C₆₇×#2367	C₂	semidirect
5. C₆₇×#2361	C₂	semidirect
6. C₆₇×#2361	C₂	semidirect
7. C₆₇×#2360	C₂	semidirect
8. C₆₇×#2359	C₂	semidirect
9. C₆₇×#2358	C₂	semidirect
10. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
11. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
12. C₆₇×#2342	C₂	semidirect
13. C₆₇×#2339	C₂	semidirect
14. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
15. C₆₇×#2326	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₆₇×#2324	C₂	semidirect
18. C₆₇×#2322	C₂	semidirect
19. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
20. C₄×#120×C₆₇	C₂	semidirect
21. C₆₇×#2290	C₂	semidirect
22. C₂×#385×C₆₇	C₂	semidirect
23. C₆₇×#2275	C₂	semidirect
27. #546×C₆₇	C₄	semidirect
35. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
36. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
49. C₂×C₄×D₄×C₆₇	C₂²	semidirect
50. C₂×C₄×D₄×C₆₇	C₂²	semidirect
51. C₂×C₄×D₄×C₆₇	C₂²	semidirect
52. C₂×#117×C₆₇	C₂²	semidirect
53. C₂×#117×C₆₇	C₂²	semidirect
55. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
56. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
57. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
62. #391×C₆₇	C₂²	semidirect
63. #391×C₆₇	C₂²	semidirect
66. #390×C₆₇	C₂²	semidirect
67. #389×C₆₇	C₂²	semidirect
68. #389×C₆₇	C₂²	semidirect
69. #389×C₆₇	C₂²	semidirect
70. #389×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #388×C₆₇	C₂²	semidirect
73. #388×C₆₇	C₂²	semidirect
74. #388×C₆₇	C₂²	semidirect
75. #388×C₆₇	C₂²	semidirect
76. #388×C₆₇	C₂²	semidirect
77. #388×C₆₇	C₂²	semidirect
78. #388×C₆₇	C₂²	semidirect
79. #387×C₆₇	C₂²	semidirect
80. #387×C₆₇	C₂²	semidirect
81. #387×C₆₇	C₂²	semidirect
82. #387×C₆₇	C₂²	semidirect
87. #386×C₆₇	C₂²	semidirect
88. #386×C₆₇	C₂²	semidirect
89. #386×C₆₇	C₂²	semidirect
90. #386×C₆₇	C₂²	semidirect
96. #385×C₆₇	C₂²	semidirect
97. #385×C₆₇	C₂²	semidirect
98. #385×C₆₇	C₂²	semidirect
99. #385×C₆₇	C₂²	semidirect
100. #385×C₆₇	C₂²	semidirect
101. #385×C₆₇	C₂²	semidirect
102. #385×C₆₇	C₂²	semidirect
103. #385×C₆₇	C₂²	semidirect
104. #384×C₆₇	C₂²	semidirect
105. #381×C₆₇	C₂²	semidirect
107. #380×C₆₇	C₂²	semidirect
108. #380×C₆₇	C₂²	semidirect
110. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
111. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
112. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
113. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
114. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
123. #376×C₆₇	C₂²	semidirect
124. C₂×#95×C₆₇	C₂²	semidirect
125. C₂×#95×C₆₇	C₂²	semidirect
129. C₂×#41×C₆₇	C₂×C₄	semidirect
133. C₂²×D₄×C₆₇	C₂×C₄	semidirect
157. #124×C₆₇	C₂×C₄	semidirect
158. #123×C₆₇	C₂×C₄	semidirect
159. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
160. #121×C₆₇	C₂×C₄	semidirect
161. #121×C₆₇	C₂×C₄	semidirect
162. #120×C₆₇	C₂×C₄	semidirect
176. C₄×D₄×C₆₇	C₂×C₄	semidirect
177. C₄×D₄×C₆₇	C₂×C₄	semidirect
178. C₄×D₄×C₆₇	D₄	semidirect
206. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
280. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
296. C₂×D₄×C₆₇	C₂²×C₄	semidirect
297. C₂×D₄×C₆₇	C₂²×C₄	semidirect
339. C₂²×C₄×C₆₇	C₂²×C₄	semidirect
340. C₂²×C₄×C₆₇	C₂²×C₄	semidirect
341. C₂²×C₄×C₆₇	C₂²×C₄	semidirect
377. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
378. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
379. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
400. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
401. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
402. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
403. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
404. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
416. C₄²×C₆₇	C₂²×C₄	semidirect
460. D₄×C₆₇	C₄×D₄	semidirect
560. C₂²×C₆₇	#520	semidirect
587. #34288	C₆₇	direct (N × H)
600. C₂×#520	C₂×C₆₇	semidirect
601. C₂²×C₄×D₄	C₂×C₆₇	semidirect
602. #2367	C₂×C₆₇	semidirect
603. #2361	C₂×C₆₇	semidirect
604. #2361	C₂×C₆₇	semidirect
605. #2360	C₂×C₆₇	semidirect
606. #2359	C₂×C₆₇	semidirect
607. #2358	C₂×C₆₇	semidirect
608. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
609. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
610. #2342	C₂×C₆₇	semidirect
611. #2339	C₂×C₆₇	semidirect
612. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
613. #2326	C₂×C₆₇	semidirect
614. #2325	C₂×C₆₇	semidirect
615. #2324	C₂×C₆₇	semidirect
616. #2322	C₂×C₆₇	semidirect
617. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
618. C₄×#120	C₂×C₆₇	semidirect
619. #2290	C₂×C₆₇	semidirect
620. C₂×#385	C₂×C₆₇	semidirect
621. #2275	C₂×C₆₇	semidirect
622. C₆₇	#34288	direct (N × H)
626. #546	C₄×C₆₇	semidirect
634. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
635. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
648. C₂×C₄×D₄	C₂²×C₆₇	semidirect
649. C₂×C₄×D₄	C₂²×C₆₇	semidirect
650. C₂×C₄×D₄	C₂²×C₆₇	semidirect
651. C₂×#117	C₂²×C₆₇	semidirect
652. C₂×#117	C₂²×C₆₇	semidirect
654. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
655. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
656. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
661. #391	C₂²×C₆₇	semidirect
662. #391	C₂²×C₆₇	semidirect
665. #390	C₂²×C₆₇	semidirect
666. #389	C₂²×C₆₇	semidirect
667. #389	C₂²×C₆₇	semidirect
668. #389	C₂²×C₆₇	semidirect
669. #389	C₂²×C₆₇	semidirect
670. #388	C₂²×C₆₇	semidirect
671. #388	C₂²×C₆₇	semidirect
672. #388	C₂²×C₆₇	semidirect
673. #388	C₂²×C₆₇	semidirect
674. #388	C₂²×C₆₇	semidirect
675. #388	C₂²×C₆₇	semidirect
676. #388	C₂²×C₆₇	semidirect
677. #388	C₂²×C₆₇	semidirect
678. #387	C₂²×C₆₇	semidirect
679. #387	C₂²×C₆₇	semidirect
680. #387	C₂²×C₆₇	semidirect
681. #387	C₂²×C₆₇	semidirect
686. #386	C₂²×C₆₇	semidirect
687. #386	C₂²×C₆₇	semidirect
688. #386	C₂²×C₆₇	semidirect
689. #386	C₂²×C₆₇	semidirect
695. #385	C₂²×C₆₇	semidirect
696. #385	C₂²×C₆₇	semidirect
697. #385	C₂²×C₆₇	semidirect
698. #385	C₂²×C₆₇	semidirect
699. #385	C₂²×C₆₇	semidirect
700. #385	C₂²×C₆₇	semidirect
701. #385	C₂²×C₆₇	semidirect
702. #385	C₂²×C₆₇	semidirect
703. #384	C₂²×C₆₇	semidirect
704. #381	C₂²×C₆₇	semidirect
706. #380	C₂²×C₆₇	semidirect
707. #380	C₂²×C₆₇	semidirect
709. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
710. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
711. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
712. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
713. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
717. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
718. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
719. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
720. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
721. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
722. #376	C₂²×C₆₇	semidirect
723. C₂×#95	C₂²×C₆₇	semidirect
724. C₂×#95	C₂²×C₆₇	semidirect
728. C₂×#41	C₂×C₄×C₆₇	semidirect
732. C₂²×D₄	C₂×C₄×C₆₇	semidirect
756. #124	C₂×C₄×C₆₇	semidirect
757. #123	C₂×C₄×C₆₇	semidirect
758. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
759. #121	C₂×C₄×C₆₇	semidirect
760. #121	C₂×C₄×C₆₇	semidirect
761. #120	C₂×C₄×C₆₇	semidirect
775. C₄×D₄	C₂×C₄×C₆₇	semidirect
776. C₄×D₄	C₂×C₄×C₆₇	semidirect
777. C₄×D₄	D₄×C₆₇	semidirect
805. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
879. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
895. C₂×D₄	C₂²×C₄×C₆₇	semidirect
896. C₂×D₄	C₂²×C₄×C₆₇	semidirect
938. C₂²×C₄	C₂²×C₄×C₆₇	semidirect
939. C₂²×C₄	C₂²×C₄×C₆₇	semidirect
940. C₂²×C₄	C₂²×C₄×C₆₇	semidirect
976. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
977. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
978. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
999. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1000. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1001. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1002. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1003. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1015. C₄²	C₂²×C₄×C₆₇	semidirect
1059. D₄	C₄×D₄×C₆₇	semidirect
1159. C₂²	#520×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₆₇	2
C₂×#520×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2367	2
C₆₇×#2361	2
C₆₇×#2360	2
C₆₇×#2359	2
C₆₇×#2358	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2342	2
C₆₇×#2339	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2326	2
C₆₇×#2325	2
C₆₇×#2324	2
C₆₇×#2322	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#120×C₆₇	2
C₆₇×#2290	2
C₂×#385×C₆₇	2
C₆₇×#2275	2
#34288	67

Subgroups — C67×#34288 #30713539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34288 #30713539