Subgroups — C₆₇×#59802 #30739053

Order 17152.

3152 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2709	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2691	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2684	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2559	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2544	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2534	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2425	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2411	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2405	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2405	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
17	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#386×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
21	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	#551×C₆₇	—	2	8	no	—
24	D₄²×C₆₇	—	2	8	no	—
25	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#123×C₆₇	C₂²	1	2	yes	—
30	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#121×C₆₇	C₂²	1	2	yes	—
35	C₂×#121×C₆₇	C₂²	1	2	yes	—
36	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#120×C₆₇	C₂²	1	2	yes	—
38	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
43	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
45	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
47	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
48	#400×C₆₇	C₂²	1	2	yes	complemented
49	#398×C₆₇	C₂²	1	2	yes	complemented
50	#397×C₆₇	C₂²	1	2	yes	complemented
51	#397×C₆₇	C₂²	1	2	yes	complemented
52	#396×C₆₇	C₂²	1	2	yes	complemented
53	#396×C₆₇	C₂²	1	2	yes	complemented
54	#394×C₆₇	C₂²	1	2	yes	complemented
55	#394×C₆₇	C₂²	1	2	yes	complemented
56	#394×C₆₇	C₂²	1	2	yes	complemented
57	#394×C₆₇	C₂²	1	2	yes	complemented
58	#394×C₆₇	C₂²	1	2	yes	complemented
59	#394×C₆₇	C₂²	1	2	yes	complemented
60	#394×C₆₇	C₂²	1	2	yes	complemented
61	#394×C₆₇	C₂²	1	2	yes	complemented
62	#394×C₆₇	C₂²	1	2	yes	complemented
63	#393×C₆₇	C₂²	1	2	yes	complemented
64	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#390×C₆₇	C₂²	1	2	yes	complemented
67	#390×C₆₇	C₂²	1	2	yes	complemented
68	#389×C₆₇	C₂²	1	2	yes	complemented
69	#388×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#388×C₆₇	C₂²	1	2	yes	complemented
73	#387×C₆₇	C₂²	1	2	yes	complemented
74	#387×C₆₇	C₂²	1	2	yes	complemented
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	complemented
79	#386×C₆₇	C₂²	1	2	yes	complemented
80	#386×C₆₇	C₂²	1	2	yes	complemented
81	#386×C₆₇	C₂²	1	2	yes	complemented
82	#386×C₆₇	C₂²	1	2	yes	complemented
83	#386×C₆₇	C₂²	1	2	yes	complemented
84	#386×C₆₇	C₂²	1	2	yes	complemented
85	#386×C₆₇	C₂²	1	2	yes	complemented
86	#386×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#386×C₆₇	C₂²	1	2	yes	complemented
88	#386×C₆₇	C₂²	1	2	yes	complemented
89	#385×C₆₇	C₂²	1	2	yes	complemented
90	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#385×C₆₇	C₂²	1	2	yes	complemented
92	#385×C₆₇	C₂²	1	2	yes	complemented
93	#385×C₆₇	C₂²	1	2	yes	complemented
94	#385×C₆₇	C₂²	1	2	yes	complemented
95	#381×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#380×C₆₇	C₂²	1	2	yes	complemented
98	#379×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#379×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#379×C₆₇	C₂²	1	2	yes	complemented
101	#379×C₆₇	C₂²	1	2	yes	complemented
102	#379×C₆₇	C₂²	1	2	yes	complemented
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
107	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
108	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
109	C₂⁵×C₆₇	C₂³	1	2	yes	—
110	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
111	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₆₇	—	2	8	no	—
114	C₂²×D₄×C₆₇	—	2	8	no	—
115	C₂²×D₄×C₆₇	—	2	8	no	—
116	C₂²×D₄×C₆₇	—	2	8	no	—
117	C₂²×D₄×C₆₇	—	4	4	no	—
118	C₂²×D₄×C₆₇	—	4	4	no	—
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	—	4	2	no	—
129	C₂³×C₄×C₆₇	—	4	4	no	—
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	#127×C₆₇	—	2	4	no	—
141	#126×C₆₇	—	2	8	no	—
142	#124×C₆₇	—	2	4	no	—
143	#124×C₆₇	—	4	2	no	—
144	#123×C₆₇	—	2	8	no	—
145	#123×C₆₇	—	2	4	no	—
146	#123×C₆₇	—	2	8	no	—
147	#123×C₆₇	—	4	4	no	—
148	C₂²⋊Q₈×C₆₇	—	2	8	no	—
149	#121×C₆₇	—	2	8	no	—
150	#121×C₆₇	—	2	8	no	—
151	#120×C₆₇	—	2	4	no	—
152	#120×C₆₇	—	2	8	no	—
153	#120×C₆₇	D₄	1	8	yes	—
154	C₄×D₄×C₆₇	—	2	8	no	—
155	C₄×D₄×C₆₇	—	2	8	no	—
156	C₄×D₄×C₆₇	—	4	2	no	—
157	C₄×D₄×C₆₇	—	4	4	no	—
158	#117×C₆₇	—	2	8	no	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
171	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
172	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
173	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	2	yes	—
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	C₂⁴×C₆₇	—	2	4	no	—
228	C₂⁴×C₆₇	—	2	4	no	—
229	C₂⁴×C₆₇	—	2	4	no	—
230	C₂⁴×C₆₇	—	2	2	no	—
231	C₂⁴×C₆₇	—	2	4	no	—
232	C₂⁴×C₆₇	—	2	4	no	—
233	C₂⁴×C₆₇	—	2	4	no	—
234	C₂⁴×C₆₇	—	2	4	no	—
235	C₂⁴×C₆₇	—	4	1	no	—
236	C₂⁴×C₆₇	—	4	1	no	—
237	C₂⁴×C₆₇	—	4	2	no	—
238	C₂⁴×C₆₇	—	4	1	no	—
239	C₂⁴×C₆₇	—	4	2	no	—
240	C₂⁴×C₆₇	—	4	2	no	—
241	C₂⁴×C₆₇	—	4	2	no	—
242	C₂⁴×C₆₇	—	4	1	no	—
243	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
244	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
245	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
248	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₆₇	—	2	2	no	—
250	C₂×Q₈×C₆₇	—	4	1	no	—
251	C₂×Q₈×C₆₇	—	4	1	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	4	no	—
264	C₂×D₄×C₆₇	—	2	4	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	2	4	no	—
267	C₂×D₄×C₆₇	—	2	4	no	—
268	C₂×D₄×C₆₇	—	4	1	no	—
269	C₂×D₄×C₆₇	—	4	2	no	—
270	C₂×D₄×C₆₇	—	4	2	no	—
271	C₂×D₄×C₆₇	—	4	2	no	—
272	C₂×D₄×C₆₇	—	4	2	no	—
273	C₂×D₄×C₆₇	—	4	1	no	—
274	C₂×D₄×C₆₇	—	4	1	no	—
275	C₂×D₄×C₆₇	—	4	1	no	—
276	C₂×D₄×C₆₇	—	4	32	no	—
277	C₂×D₄×C₆₇	—	4	32	no	—
278	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
279	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
280	C₂×D₄×C₆₇	#41	1	8	yes	—
281	C₂²×C₄×C₆₇	—	2	4	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	2	4	no	—
284	C₂²×C₄×C₆₇	—	2	4	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	2	4	no	—
287	C₂²×C₄×C₆₇	—	2	4	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	2	4	no	—
290	C₂²×C₄×C₆₇	—	2	4	no	—
291	C₂²×C₄×C₆₇	—	2	4	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	4	2	no	—
296	C₂²×C₄×C₆₇	—	4	2	no	—
297	C₂²×C₄×C₆₇	—	4	1	no	—
298	C₂²×C₄×C₆₇	—	4	2	no	—
299	C₂²×C₄×C₆₇	—	4	2	no	—
300	C₂²×C₄×C₆₇	—	4	2	no	—
301	C₂²×C₄×C₆₇	—	4	2	no	—
302	C₂²×C₄×C₆₇	—	4	2	no	—
303	C₂²×C₄×C₆₇	—	4	1	no	—
304	C₂²×C₄×C₆₇	—	4	2	no	—
305	C₂²×C₄×C₆₇	—	4	2	no	—
306	C₂²×C₄×C₆₇	—	4	1	no	—
307	C₂²×C₄×C₆₇	—	4	2	no	—
308	C₂²×C₄×C₆₇	—	4	16	no	—
309	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	4	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	2	4	no	—
327	C₄⋊C₄×C₆₇	—	2	4	no	—
328	C₄⋊C₄×C₆₇	—	2	4	no	—
329	C₄⋊C₄×C₆₇	—	2	4	no	—
330	C₄⋊C₄×C₆₇	—	4	1	no	—
331	C₄⋊C₄×C₆₇	—	4	2	no	—
332	C₄⋊C₄×C₆₇	—	4	2	no	—
333	C₄⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	4	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	4	no	—
347	C₂²⋊C₄×C₆₇	—	2	4	no	—
348	C₂²⋊C₄×C₆₇	—	2	4	no	—
349	C₂²⋊C₄×C₆₇	—	4	2	no	—
350	C₂²⋊C₄×C₆₇	—	4	2	no	—
351	C₂²⋊C₄×C₆₇	—	4	2	no	—
352	C₂²⋊C₄×C₆₇	—	4	2	no	—
353	C₂²⋊C₄×C₆₇	—	4	2	no	—
354	C₂²⋊C₄×C₆₇	—	4	2	no	—
355	C₂²⋊C₄×C₆₇	—	4	2	no	—
356	C₂²⋊C₄×C₆₇	—	4	1	no	—
357	C₂²⋊C₄×C₆₇	—	4	2	no	—
358	C₂²⋊C₄×C₆₇	—	4	2	no	—
359	C₂²⋊C₄×C₆₇	—	4	1	no	—
360	C₂²⋊C₄×C₆₇	—	4	1	no	—
361	C₂²⋊C₄×C₆₇	—	4	2	no	—
362	C₂²⋊C₄×C₆₇	—	4	2	no	—
363	C₂²⋊C₄×C₆₇	—	4	2	no	—
364	C₂²⋊C₄×C₆₇	—	4	2	no	—
365	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
366	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	2	4	no	—
369	C₄²×C₆₇	—	2	2	no	—
370	C₄²×C₆₇	—	2	2	no	—
371	C₄²×C₆₇	—	4	2	no	—
372	C₂³×C₆₇	—	2	2	no	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	2	2	no	—
375	C₂³×C₆₇	—	2	2	no	—
376	C₂³×C₆₇	—	2	16	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	2	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	1	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	2	no	—
386	C₂³×C₆₇	—	2	2	no	—
387	C₂³×C₆₇	—	2	2	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	2	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	2	no	—
392	C₂³×C₆₇	—	2	2	no	—
393	C₂³×C₆₇	—	2	2	no	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	—	2	2	no	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	4	4	no	—
399	C₂³×C₆₇	—	4	4	no	—
400	C₂³×C₆₇	—	4	4	no	—
401	C₂³×C₆₇	—	4	8	no	—
402	C₂³×C₆₇	—	4	8	no	—
403	C₂³×C₆₇	—	4	8	no	—
404	C₂³×C₆₇	—	4	8	no	—
405	C₂³×C₆₇	—	4	8	no	—
406	C₂³×C₆₇	—	4	4	no	—
407	C₂³×C₆₇	—	4	8	no	—
408	C₂³×C₆₇	—	8	4	no	—
409	C₂³×C₆₇	—	8	4	no	—
410	C₂³×C₆₇	—	8	4	no	—
411	C₂³×C₆₇	—	8	2	no	—
412	C₂³×C₆₇	—	8	4	no	—
413	C₂³×C₆₇	—	8	2	no	—
414	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
415	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
417	C₂³×C₆₇	C₂×#41	1	4	yes	—
418	C₂³×C₆₇	C₂×#41	1	4	yes	—
419	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
420	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
421	Q₈×C₆₇	—	8	2	no	—
422	D₄×C₆₇	—	2	16	no	—
423	D₄×C₆₇	—	2	16	no	—
424	D₄×C₆₇	—	4	4	no	—
425	D₄×C₆₇	—	4	8	no	—
426	D₄×C₆₇	—	4	8	no	—
427	D₄×C₆₇	—	4	8	no	—
428	D₄×C₆₇	—	4	8	no	—
429	D₄×C₆₇	—	4	8	no	—
430	D₄×C₆₇	—	8	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	4	8	no	—
466	C₂×C₄×C₆₇	—	4	8	no	—
467	C₂×C₄×C₆₇	—	4	8	no	—
468	C₂×C₄×C₆₇	—	4	4	no	—
469	C₂×C₄×C₆₇	—	4	8	no	—
470	C₂×C₄×C₆₇	—	4	4	no	—
471	C₂×C₄×C₆₇	—	4	8	no	—
472	C₂×C₄×C₆₇	—	8	2	no	—
473	C₂×C₄×C₆₇	—	8	2	no	—
474	C₂×C₄×C₆₇	—	8	4	no	—
475	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
477	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
478	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
479	C₂²×C₆₇	—	2	4	no	—
480	C₂²×C₆₇	—	2	4	no	—
481	C₂²×C₆₇	—	2	4	no	—
482	C₂²×C₆₇	—	2	4	no	—
483	C₂²×C₆₇	—	2	4	no	—
484	C₂²×C₆₇	—	2	4	no	—
485	C₂²×C₆₇	—	2	4	no	—
486	C₂²×C₆₇	—	2	4	no	—
487	C₂²×C₆₇	—	2	4	no	—
488	C₂²×C₆₇	—	2	4	no	—
489	C₂²×C₆₇	—	2	2	no	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	2	4	no	—
492	C₂²×C₆₇	—	4	16	no	—
493	C₂²×C₆₇	—	4	2	no	—
494	C₂²×C₆₇	—	4	1	no	—
495	C₂²×C₆₇	—	4	1	no	—
496	C₂²×C₆₇	—	4	2	no	—
497	C₂²×C₆₇	—	4	2	no	—
498	C₂²×C₆₇	—	4	2	no	—
499	C₂²×C₆₇	—	4	2	no	—
500	C₂²×C₆₇	—	4	1	no	—
501	C₂²×C₆₇	—	4	1	no	—
502	C₂²×C₆₇	—	4	2	no	—
503	C₂²×C₆₇	—	4	2	no	—
504	C₂²×C₆₇	—	4	2	no	—
505	C₂²×C₆₇	—	4	2	no	—
506	C₂²×C₆₇	—	4	2	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	2	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	—	8	16	no	—
511	C₂²×C₆₇	—	8	8	no	—
512	C₂²×C₆₇	#546	1	8	yes	—
513	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
514	C₂²×C₆₇	C₂²×#41	1	2	yes	—
515	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
516	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂²×C₆₇	#585	1	1	yes	characteristic
518	C₄×C₆₇	—	2	4	no	—
519	C₄×C₆₇	—	2	4	no	—
520	C₄×C₆₇	—	2	2	no	—
521	C₄×C₆₇	—	2	2	no	—
522	C₄×C₆₇	—	4	2	no	—
523	C₄×C₆₇	—	4	2	no	—
524	C₄×C₆₇	—	4	2	no	—
525	C₄×C₆₇	—	4	1	no	—
526	C₄×C₆₇	—	4	2	no	—
527	C₄×C₆₇	—	4	2	no	—
528	C₄×C₆₇	—	4	2	no	—
529	C₄×C₆₇	—	4	2	no	—
530	C₄×C₆₇	—	4	1	no	—
531	C₄×C₆₇	—	4	1	no	—
532	#59802	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
533	C₂×C₆₇	—	2	8	no	—
534	C₂×C₆₇	—	4	2	no	—
535	C₂×C₆₇	—	4	2	no	—
536	C₂×C₆₇	—	4	4	no	—
537	C₂×C₆₇	—	8	2	no	—
538	C₂×C₆₇	C₂×#546	1	2	yes	—
539	C₂×C₆₇	#3481	1	1	yes	characteristic
540	C₂×C₆₇	#3496	1	1	yes	characteristic
541	C₂×C₆₇	#3513	1	2	yes	—
542	C₂×C₆₇	#3532	1	1	yes	characteristic
543	C₂×#551	C₂×C₆₇	1	1	yes	characteristic, complemented
544	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic
545	#2709	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#2691	C₂×C₆₇	1	2	yes	complemented
547	#2684	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#2559	C₂×C₆₇	1	2	yes	complemented
549	#2544	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#2534	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#2472	C₂×C₆₇	1	2	yes	complemented
552	#2450	C₂×C₆₇	1	2	yes	complemented
553	#2444	C₂×C₆₇	1	2	yes	complemented
554	#2425	C₂×C₆₇	1	2	yes	complemented
555	#2411	C₂×C₆₇	1	2	yes	complemented
556	#2405	C₂×C₆₇	1	2	yes	complemented
557	#2405	C₂×C₆₇	1	2	yes	complemented
558	#2359	C₂×C₆₇	1	2	yes	complemented
559	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
560	C₄×#120	C₂×C₆₇	1	1	yes	characteristic, complemented
561	C₂×#386	C₂×C₆₇	1	2	yes	complemented
562	C₆₇	#59802	1	1	yes	characteristic, direct product factor, Sylow
563	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
564	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
565	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
566	#551	—	2	8	no	—
567	D₄²	—	2	8	no	—
568	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
569	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
570	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	C₂×#123	C₂²×C₆₇	1	2	yes	—
573	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
574	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
576	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
577	C₂×#121	C₂²×C₆₇	1	2	yes	—
578	C₂×#121	C₂²×C₆₇	1	2	yes	—
579	C₂×#120	C₂²×C₆₇	1	2	yes	—
580	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
581	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
582	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
583	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
584	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
585	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
587	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
588	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
589	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
590	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
591	#400	C₂²×C₆₇	1	2	yes	complemented
592	#398	C₂²×C₆₇	1	2	yes	complemented
593	#397	C₂²×C₆₇	1	2	yes	complemented
594	#397	C₂²×C₆₇	1	2	yes	complemented
595	#396	C₂²×C₆₇	1	2	yes	complemented
596	#396	C₂²×C₆₇	1	2	yes	complemented
597	#394	C₂²×C₆₇	1	2	yes	complemented
598	#394	C₂²×C₆₇	1	2	yes	complemented
599	#394	C₂²×C₆₇	1	2	yes	complemented
600	#394	C₂²×C₆₇	1	2	yes	complemented
601	#394	C₂²×C₆₇	1	2	yes	complemented
602	#394	C₂²×C₆₇	1	2	yes	complemented
603	#394	C₂²×C₆₇	1	2	yes	complemented
604	#394	C₂²×C₆₇	1	2	yes	complemented
605	#394	C₂²×C₆₇	1	2	yes	complemented
606	#393	C₂²×C₆₇	1	2	yes	complemented
607	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
608	#390	C₂²×C₆₇	1	2	yes	complemented
609	#390	C₂²×C₆₇	1	2	yes	complemented
610	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	#389	C₂²×C₆₇	1	2	yes	complemented
612	#388	C₂²×C₆₇	1	2	yes	complemented
613	#388	C₂²×C₆₇	1	2	yes	complemented
614	#388	C₂²×C₆₇	1	2	yes	complemented
615	#388	C₂²×C₆₇	1	2	yes	complemented
616	#387	C₂²×C₆₇	1	2	yes	complemented
617	#387	C₂²×C₆₇	1	2	yes	complemented
618	#386	C₂²×C₆₇	1	2	yes	—
619	#386	C₂²×C₆₇	1	2	yes	—
620	#386	C₂²×C₆₇	1	2	yes	—
621	#386	C₂²×C₆₇	1	2	yes	complemented
622	#386	C₂²×C₆₇	1	2	yes	complemented
623	#386	C₂²×C₆₇	1	2	yes	complemented
624	#386	C₂²×C₆₇	1	2	yes	complemented
625	#386	C₂²×C₆₇	1	2	yes	complemented
626	#386	C₂²×C₆₇	1	2	yes	complemented
627	#386	C₂²×C₆₇	1	2	yes	complemented
628	#386	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#386	C₂²×C₆₇	1	2	yes	complemented
630	#386	C₂²×C₆₇	1	2	yes	complemented
631	#386	C₂²×C₆₇	1	2	yes	complemented
632	#385	C₂²×C₆₇	1	2	yes	complemented
633	#385	C₂²×C₆₇	1	2	yes	complemented
634	#385	C₂²×C₆₇	1	2	yes	complemented
635	#385	C₂²×C₆₇	1	2	yes	complemented
636	#385	C₂²×C₆₇	1	2	yes	complemented
637	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	#381	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#380	C₂²×C₆₇	1	2	yes	complemented
640	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#379	C₂²×C₆₇	1	2	yes	complemented
642	#379	C₂²×C₆₇	1	2	yes	complemented
643	#379	C₂²×C₆₇	1	2	yes	complemented
644	#379	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	#379	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
648	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
649	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
651	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
652	C₂⁵	C₂³×C₆₇	1	2	yes	—
653	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
654	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
655	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
656	C₂²×D₄	—	2	8	no	—
657	C₂²×D₄	—	2	8	no	—
658	C₂²×D₄	—	2	8	no	—
659	C₂²×D₄	—	2	8	no	—
660	C₂²×D₄	—	4	4	no	—
661	C₂²×D₄	—	4	4	no	—
662	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
663	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
664	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
665	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
666	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
667	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
668	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
669	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
670	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂³×C₄	—	4	2	no	—
672	C₂³×C₄	—	4	4	no	—
673	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
674	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
675	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
676	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
677	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
678	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
681	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
683	#127	—	2	4	no	—
684	#126	—	2	8	no	—
685	#124	—	2	4	no	—
686	#124	—	4	2	no	—
687	#123	—	2	8	no	—
688	#123	—	2	4	no	—
689	#123	—	2	8	no	—
690	#123	—	4	4	no	—
691	C₂²⋊Q₈	—	2	8	no	—
692	#121	—	2	8	no	—
693	#121	—	2	8	no	—
694	#120	—	2	4	no	—
695	#120	—	2	8	no	—
696	#120	D₄×C₆₇	1	8	yes	—
697	C₄×D₄	—	2	8	no	—
698	C₄×D₄	—	2	8	no	—
699	C₄×D₄	—	4	2	no	—
700	C₄×D₄	—	4	4	no	—
701	#117	—	2	8	no	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₄	—	2	8	no	—
714	C₂×C₂²⋊C₄	—	4	2	no	—
715	C₂×C₂²⋊C₄	—	4	4	no	—
716	C₂×C₂²⋊C₄	—	4	4	no	—
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
752	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
755	#95	C₂³×C₆₇	1	2	yes	—
756	#95	C₂³×C₆₇	1	2	yes	—
757	#95	C₂³×C₆₇	1	2	yes	—
758	#95	C₂³×C₆₇	1	2	yes	—
759	#95	C₂³×C₆₇	1	2	yes	—
760	#95	C₂³×C₆₇	1	2	yes	—
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	2	yes	—
763	#95	C₂³×C₆₇	1	2	yes	—
764	#95	C₂³×C₆₇	1	2	yes	—
765	#95	C₂³×C₆₇	1	2	yes	—
766	#95	C₂³×C₆₇	1	2	yes	—
767	#95	C₂³×C₆₇	1	2	yes	—
768	#95	C₂³×C₆₇	1	2	yes	—
769	#95	C₂³×C₆₇	1	2	yes	—
770	C₂⁴	—	2	4	no	—
771	C₂⁴	—	2	4	no	—
772	C₂⁴	—	2	4	no	—
773	C₂⁴	—	2	2	no	—
774	C₂⁴	—	2	4	no	—
775	C₂⁴	—	2	4	no	—
776	C₂⁴	—	2	4	no	—
777	C₂⁴	—	2	4	no	—
778	C₂⁴	—	4	1	no	—
779	C₂⁴	—	4	1	no	—
780	C₂⁴	—	4	2	no	—
781	C₂⁴	—	4	1	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	1	no	—
786	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
787	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
788	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
789	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
790	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
791	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	4	1	no	—
794	C₂×Q₈	—	4	1	no	—
795	C₂×D₄	—	2	4	no	—
796	C₂×D₄	—	2	4	no	—
797	C₂×D₄	—	2	4	no	—
798	C₂×D₄	—	2	4	no	—
799	C₂×D₄	—	2	4	no	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	4	1	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	1	no	—
817	C₂×D₄	—	4	1	no	—
818	C₂×D₄	—	4	1	no	—
819	C₂×D₄	—	4	32	no	—
820	C₂×D₄	—	4	32	no	—
821	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
822	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
823	C₂×D₄	#41×C₆₇	1	8	yes	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	4	no	—
826	C₂²×C₄	—	2	4	no	—
827	C₂²×C₄	—	2	4	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	2	4	no	—
830	C₂²×C₄	—	2	4	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	4	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	2	4	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	1	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	16	no	—
852	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	4	no	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	4	no	—
873	C₄⋊C₄	—	4	1	no	—
874	C₄⋊C₄	—	4	2	no	—
875	C₄⋊C₄	—	4	2	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	2	4	no	—
881	C₂²⋊C₄	—	2	4	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	4	2	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	2	no	—
899	C₂²⋊C₄	—	4	1	no	—
900	C₂²⋊C₄	—	4	1	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	—	4	1	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
909	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	4	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	4	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	16	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	4	4	no	—
942	C₂³	—	4	4	no	—
943	C₂³	—	4	4	no	—
944	C₂³	—	4	8	no	—
945	C₂³	—	4	8	no	—
946	C₂³	—	4	8	no	—
947	C₂³	—	4	8	no	—
948	C₂³	—	4	8	no	—
949	C₂³	—	4	4	no	—
950	C₂³	—	4	8	no	—
951	C₂³	—	8	4	no	—
952	C₂³	—	8	4	no	—
953	C₂³	—	8	4	no	—
954	C₂³	—	8	2	no	—
955	C₂³	—	8	4	no	—
956	C₂³	—	8	2	no	—
957	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
958	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
959	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
960	C₂³	C₂×#41×C₆₇	1	4	yes	—
961	C₂³	C₂×#41×C₆₇	1	4	yes	—
962	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
963	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
964	Q₈	—	8	2	no	—
965	D₄	—	2	16	no	—
966	D₄	—	2	16	no	—
967	D₄	—	4	4	no	—
968	D₄	—	4	8	no	—
969	D₄	—	4	8	no	—
970	D₄	—	4	8	no	—
971	D₄	—	4	8	no	—
972	D₄	—	4	8	no	—
973	D₄	—	8	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	4	8	no	—
1009	C₂×C₄	—	4	8	no	—
1010	C₂×C₄	—	4	8	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	8	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	8	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	4	no	—
1018	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1020	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1021	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	4	no	—
1024	C₂²	—	2	4	no	—
1025	C₂²	—	2	4	no	—
1026	C₂²	—	2	4	no	—
1027	C₂²	—	2	4	no	—
1028	C₂²	—	2	4	no	—
1029	C₂²	—	2	4	no	—
1030	C₂²	—	2	4	no	—
1031	C₂²	—	2	4	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	4	16	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	8	16	no	—
1054	C₂²	—	8	8	no	—
1055	C₂²	#546×C₆₇	1	8	yes	—
1056	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1057	C₂²	C₂²×#41×C₆₇	1	2	yes	—
1058	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1059	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1060	C₂²	#585×C₆₇	1	1	yes	characteristic
1061	C₄	—	2	2	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	2	no	—
1075	C₂	—	2	8	no	—
1076	C₂	—	4	2	no	—
1077	C₂	—	4	4	no	—
1078	C₂	—	4	2	no	—
1079	C₂	—	8	2	no	—
1080	C₂	C₂×#546×C₆₇	1	2	yes	—
1081	C₂	C₆₇×#3481	1	1	yes	characteristic
1082	C₂	C₆₇×#3496	1	1	yes	characteristic
1083	C₂	C₆₇×#3513	1	2	yes	—
1084	C₂	C₆₇×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×D₄²×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#551×C₆₇	C₂	semidirect
3. C₆₇×#2709	C₂	semidirect
4. C₆₇×#2691	C₂	semidirect
5. C₆₇×#2684	C₂	semidirect
6. C₆₇×#2559	C₂	semidirect
7. C₆₇×#2544	C₂	semidirect
8. C₆₇×#2534	C₂	semidirect
9. C₆₇×#2472	C₂	semidirect
10. C₆₇×#2450	C₂	semidirect
11. C₆₇×#2444	C₂	semidirect
12. C₆₇×#2425	C₂	semidirect
13. C₆₇×#2411	C₂	semidirect
14. C₆₇×#2405	C₂	semidirect
15. C₆₇×#2405	C₂	semidirect
16. C₆₇×#2359	C₂	semidirect
17. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₂×#386×C₆₇	C₂	semidirect
22. C₂⁴×C₄×C₆₇	C₂²	semidirect
26. C₂×#126×C₆₇	C₂²	semidirect
27. C₂×#124×C₆₇	C₂²	semidirect
28. C₂×#124×C₆₇	C₂²	semidirect
30. C₂×#123×C₆₇	C₂²	semidirect
31. C₂×#123×C₆₇	C₂²	semidirect
32. C₂×#123×C₆₇	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
40. C₂×C₄×D₄×C₆₇	C₂²	semidirect
41. C₂×C₄×D₄×C₆₇	C₂²	semidirect
42. C₂×C₄×D₄×C₆₇	C₂²	semidirect
43. C₂×#117×C₆₇	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
45. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
46. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
47. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
48. #400×C₆₇	C₂²	semidirect
49. #398×C₆₇	C₂²	semidirect
50. #397×C₆₇	C₂²	semidirect
51. #397×C₆₇	C₂²	semidirect
52. #396×C₆₇	C₂²	semidirect
53. #396×C₆₇	C₂²	semidirect
54. #394×C₆₇	C₂²	semidirect
55. #394×C₆₇	C₂²	semidirect
56. #394×C₆₇	C₂²	semidirect
57. #394×C₆₇	C₂²	semidirect
58. #394×C₆₇	C₂²	semidirect
59. #394×C₆₇	C₂²	semidirect
60. #394×C₆₇	C₂²	semidirect
61. #394×C₆₇	C₂²	semidirect
62. #394×C₆₇	C₂²	semidirect
63. #393×C₆₇	C₂²	semidirect
64. #391×C₆₇	C₂²	semidirect
65. #390×C₆₇	C₂²	semidirect
66. #390×C₆₇	C₂²	semidirect
67. #390×C₆₇	C₂²	semidirect
68. #389×C₆₇	C₂²	semidirect
69. #388×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #388×C₆₇	C₂²	semidirect
73. #387×C₆₇	C₂²	semidirect
74. #387×C₆₇	C₂²	semidirect
78. #386×C₆₇	C₂²	semidirect
79. #386×C₆₇	C₂²	semidirect
80. #386×C₆₇	C₂²	semidirect
81. #386×C₆₇	C₂²	semidirect
82. #386×C₆₇	C₂²	semidirect
83. #386×C₆₇	C₂²	semidirect
84. #386×C₆₇	C₂²	semidirect
85. #386×C₆₇	C₂²	semidirect
86. #386×C₆₇	C₂²	semidirect
87. #386×C₆₇	C₂²	semidirect
88. #386×C₆₇	C₂²	semidirect
89. #385×C₆₇	C₂²	semidirect
90. #385×C₆₇	C₂²	semidirect
91. #385×C₆₇	C₂²	semidirect
92. #385×C₆₇	C₂²	semidirect
93. #385×C₆₇	C₂²	semidirect
94. #385×C₆₇	C₂²	semidirect
95. #381×C₆₇	C₂²	semidirect
96. #380×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
98. #379×C₆₇	C₂²	semidirect
99. #379×C₆₇	C₂²	semidirect
100. #379×C₆₇	C₂²	semidirect
101. #379×C₆₇	C₂²	semidirect
102. #379×C₆₇	C₂²	semidirect
103. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
107. C₂×#95×C₆₇	C₂²	semidirect
108. C₂×#95×C₆₇	C₂²	semidirect
532. #59802	C₆₇	direct (N × H)
543. C₂×#551	C₂×C₆₇	semidirect
545. #2709	C₂×C₆₇	semidirect
546. #2691	C₂×C₆₇	semidirect
547. #2684	C₂×C₆₇	semidirect
548. #2559	C₂×C₆₇	semidirect
549. #2544	C₂×C₆₇	semidirect
550. #2534	C₂×C₆₇	semidirect
551. #2472	C₂×C₆₇	semidirect
552. #2450	C₂×C₆₇	semidirect
553. #2444	C₂×C₆₇	semidirect
554. #2425	C₂×C₆₇	semidirect
555. #2411	C₂×C₆₇	semidirect
556. #2405	C₂×C₆₇	semidirect
557. #2405	C₂×C₆₇	semidirect
558. #2359	C₂×C₆₇	semidirect
559. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
560. C₄×#120	C₂×C₆₇	semidirect
561. C₂×#386	C₂×C₆₇	semidirect
562. C₆₇	#59802	direct (N × H)
565. C₂⁴×C₄	C₂²×C₆₇	semidirect
569. C₂×#126	C₂²×C₆₇	semidirect
570. C₂×#124	C₂²×C₆₇	semidirect
571. C₂×#124	C₂²×C₆₇	semidirect
573. C₂×#123	C₂²×C₆₇	semidirect
574. C₂×#123	C₂²×C₆₇	semidirect
575. C₂×#123	C₂²×C₆₇	semidirect
576. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
583. C₂×C₄×D₄	C₂²×C₆₇	semidirect
584. C₂×C₄×D₄	C₂²×C₆₇	semidirect
585. C₂×C₄×D₄	C₂²×C₆₇	semidirect
586. C₂×#117	C₂²×C₆₇	semidirect
587. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
588. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
589. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
590. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
591. #400	C₂²×C₆₇	semidirect
592. #398	C₂²×C₆₇	semidirect
593. #397	C₂²×C₆₇	semidirect
594. #397	C₂²×C₆₇	semidirect
595. #396	C₂²×C₆₇	semidirect
596. #396	C₂²×C₆₇	semidirect
597. #394	C₂²×C₆₇	semidirect
598. #394	C₂²×C₆₇	semidirect
599. #394	C₂²×C₆₇	semidirect
600. #394	C₂²×C₆₇	semidirect
601. #394	C₂²×C₆₇	semidirect
602. #394	C₂²×C₆₇	semidirect
603. #394	C₂²×C₆₇	semidirect
604. #394	C₂²×C₆₇	semidirect
605. #394	C₂²×C₆₇	semidirect
606. #393	C₂²×C₆₇	semidirect
607. #391	C₂²×C₆₇	semidirect
608. #390	C₂²×C₆₇	semidirect
609. #390	C₂²×C₆₇	semidirect
610. #390	C₂²×C₆₇	semidirect
611. #389	C₂²×C₆₇	semidirect
612. #388	C₂²×C₆₇	semidirect
613. #388	C₂²×C₆₇	semidirect
614. #388	C₂²×C₆₇	semidirect
615. #388	C₂²×C₆₇	semidirect
616. #387	C₂²×C₆₇	semidirect
617. #387	C₂²×C₆₇	semidirect
621. #386	C₂²×C₆₇	semidirect
622. #386	C₂²×C₆₇	semidirect
623. #386	C₂²×C₆₇	semidirect
624. #386	C₂²×C₆₇	semidirect
625. #386	C₂²×C₆₇	semidirect
626. #386	C₂²×C₆₇	semidirect
627. #386	C₂²×C₆₇	semidirect
628. #386	C₂²×C₆₇	semidirect
629. #386	C₂²×C₆₇	semidirect
630. #386	C₂²×C₆₇	semidirect
631. #386	C₂²×C₆₇	semidirect
632. #385	C₂²×C₆₇	semidirect
633. #385	C₂²×C₆₇	semidirect
634. #385	C₂²×C₆₇	semidirect
635. #385	C₂²×C₆₇	semidirect
636. #385	C₂²×C₆₇	semidirect
637. #385	C₂²×C₆₇	semidirect
638. #381	C₂²×C₆₇	semidirect
639. #380	C₂²×C₆₇	semidirect
640. #380	C₂²×C₆₇	semidirect
641. #379	C₂²×C₆₇	semidirect
642. #379	C₂²×C₆₇	semidirect
643. #379	C₂²×C₆₇	semidirect
644. #379	C₂²×C₆₇	semidirect
645. #379	C₂²×C₆₇	semidirect
646. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
647. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
648. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
649. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
650. C₂×#95	C₂²×C₆₇	semidirect
651. C₂×#95	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551×C₆₇	2
C₂×D₄²×C₆₇	2
C₆₇×#2709	2
C₆₇×#2691	2
C₆₇×#2684	2
C₆₇×#2559	2
C₆₇×#2544	2
C₆₇×#2534	2
C₆₇×#2472	2
C₆₇×#2450	2
C₆₇×#2444	2
C₆₇×#2425	2
C₆₇×#2411	2
C₆₇×#2405	2
C₆₇×#2359	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×#120×C₆₇	2
C₂×#386×C₆₇	2
#59802	67

Subgroups — C67×#59802 #30739053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59802 #30739053