Subgroups — C₆₇×#34290 #30713541

Order 17152.

3960 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2364	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2328	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×#2321	C₂	1	2	yes	maximal, complemented
19	C₄×#121×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×#386×C₆₇	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	complemented
28	D₄²×C₆₇	C₄	1	16	yes	complemented
29	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×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	C₂×#120×C₆₇	C₂²	1	2	yes	—
35	#518×C₆₇	—	2	8	no	—
36	C₂×C₄×D₄×C₆₇	—	2	8	no	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
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	complemented
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
52	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
53	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
54	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
58	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
59	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
60	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
61	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
62	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#390×C₆₇	C₂²	1	2	yes	complemented
65	#390×C₆₇	C₂²	1	2	yes	complemented
66	#390×C₆₇	C₂²	1	2	yes	complemented
67	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#388×C₆₇	C₂²	1	1	yes	characteristic, 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	#386×C₆₇	C₂²	1	1	yes	characteristic
83	#386×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	1	yes	characteristic
85	#386×C₆₇	C₂²	1	2	yes	complemented
86	#386×C₆₇	C₂²	1	2	yes	complemented
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	#386×C₆₇	C₂²	1	2	yes	complemented
92	#386×C₆₇	C₂²	1	2	yes	complemented
93	#386×C₆₇	C₂²	1	2	yes	complemented
94	#386×C₆₇	C₂²	1	2	yes	complemented
95	#386×C₆₇	C₂²	1	2	yes	complemented
96	#386×C₆₇	C₂²	1	2	yes	complemented
97	#386×C₆₇	C₂²	1	2	yes	complemented
98	#386×C₆₇	C₂²	1	2	yes	complemented
99	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#385×C₆₇	C₂²	1	1	yes	characteristic, 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	#385×C₆₇	C₂²	1	2	yes	complemented
105	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#380×C₆₇	C₂²	1	2	yes	complemented
109	#379×C₆₇	C₂²	1	2	yes	complemented
110	#379×C₆₇	C₂²	1	2	yes	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	1	yes	characteristic, complemented
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	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	C₂⁵×C₆₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₇	—	2	4	no	—
129	C₂²×D₄×C₆₇	—	2	4	no	—
130	C₂²×D₄×C₆₇	—	2	4	no	—
131	C₂²×D₄×C₆₇	—	2	4	no	—
132	C₂²×D₄×C₆₇	—	4	4	no	—
133	C₂²×D₄×C₆₇	—	4	4	no	—
134	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
135	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
136	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
137	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
142	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
144	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
145	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
146	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₆₇	—	2	8	no	—
148	C₂³×C₄×C₆₇	—	4	4	no	—
149	C₂³×C₄×C₆₇	—	4	4	no	—
150	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
156	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
158	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
159	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
160	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
161	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
162	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
163	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
164	#127×C₆₇	C₂×C₄	1	8	yes	complemented
165	#121×C₆₇	C₂×C₄	1	8	yes	complemented
166	#121×C₆₇	C₂×C₄	1	8	yes	complemented
167	#121×C₆₇	C₂×C₄	1	16	yes	complemented
168	#120×C₆₇	C₂×C₄	1	16	yes	complemented
169	#120×C₆₇	C₂×C₄	1	16	yes	complemented
170	C₄×D₄×C₆₇	—	2	4	no	—
171	C₄×D₄×C₆₇	—	2	4	no	—
172	C₄×D₄×C₆₇	—	2	4	no	—
173	C₄×D₄×C₆₇	—	2	8	no	—
174	C₄×D₄×C₆₇	—	2	8	no	—
175	C₄×D₄×C₆₇	—	2	4	no	—
176	C₄×D₄×C₆₇	—	2	4	no	—
177	C₄×D₄×C₆₇	—	2	8	no	—
178	C₄×D₄×C₆₇	—	2	8	no	—
179	C₄×D₄×C₆₇	—	2	4	no	—
180	C₄×D₄×C₆₇	—	2	4	no	—
181	C₄×D₄×C₆₇	—	4	4	no	—
182	C₄×D₄×C₆₇	—	4	4	no	—
183	C₄×D₄×C₆₇	—	4	4	no	—
184	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
185	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
186	C₄×D₄×C₆₇	D₄	1	8	yes	complemented
187	#117×C₆₇	—	2	4	no	—
188	#117×C₆₇	—	2	4	no	—
189	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
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	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
204	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
205	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
206	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
207	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
238	C₂×C₄²×C₆₇	—	2	4	no	—
239	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
244	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
246	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
247	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
248	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
250	#95×C₆₇	C₂³	1	1	yes	characteristic
251	#95×C₆₇	C₂³	1	1	yes	characteristic
252	#95×C₆₇	C₂³	1	2	yes	—
253	#95×C₆₇	C₂³	1	2	yes	—
254	#95×C₆₇	C₂³	1	2	yes	—
255	#95×C₆₇	C₂³	1	2	yes	—
256	#95×C₆₇	C₂³	1	2	yes	—
257	#95×C₆₇	C₂³	1	2	yes	—
258	#95×C₆₇	C₂³	1	1	yes	characteristic
259	#95×C₆₇	C₂³	1	1	yes	characteristic
260	#95×C₆₇	C₂³	1	1	yes	characteristic
261	#95×C₆₇	C₂³	1	1	yes	characteristic
262	#95×C₆₇	C₂³	1	2	yes	—
263	#95×C₆₇	C₂³	1	2	yes	—
264	#95×C₆₇	C₂³	1	2	yes	—
265	#95×C₆₇	C₂³	1	1	yes	characteristic
266	#95×C₆₇	C₂³	1	1	yes	characteristic
267	#95×C₆₇	C₂³	1	1	yes	characteristic
268	#95×C₆₇	C₂³	1	1	yes	characteristic
269	C₂⁴×C₆₇	—	2	4	no	—
270	C₂⁴×C₆₇	—	2	4	no	—
271	C₂⁴×C₆₇	—	2	4	no	—
272	C₂⁴×C₆₇	—	2	4	no	—
273	C₂⁴×C₆₇	—	2	4	no	—
274	C₂⁴×C₆₇	—	2	4	no	—
275	C₂⁴×C₆₇	—	4	2	no	—
276	C₂⁴×C₆₇	—	4	2	no	—
277	C₂⁴×C₆₇	—	4	2	no	—
278	C₂⁴×C₆₇	—	4	2	no	—
279	C₂⁴×C₆₇	—	4	2	no	—
280	C₂⁴×C₆₇	—	4	2	no	—
281	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
282	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	complemented
283	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
285	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
286	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
287	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂×D₄×C₆₇	—	2	4	no	—
289	C₂×D₄×C₆₇	—	2	4	no	—
290	C₂×D₄×C₆₇	—	2	4	no	—
291	C₂×D₄×C₆₇	—	2	4	no	—
292	C₂×D₄×C₆₇	—	2	4	no	—
293	C₂×D₄×C₆₇	—	2	4	no	—
294	C₂×D₄×C₆₇	—	2	2	no	—
295	C₂×D₄×C₆₇	—	2	2	no	—
296	C₂×D₄×C₆₇	—	2	32	no	—
297	C₂×D₄×C₆₇	—	2	32	no	—
298	C₂×D₄×C₆₇	—	2	2	no	—
299	C₂×D₄×C₆₇	—	2	2	no	—
300	C₂×D₄×C₆₇	—	2	2	no	—
301	C₂×D₄×C₆₇	—	2	2	no	—
302	C₂×D₄×C₆₇	—	4	2	no	—
303	C₂×D₄×C₆₇	—	4	2	no	—
304	C₂×D₄×C₆₇	—	4	2	no	—
305	C₂×D₄×C₆₇	—	4	2	no	—
306	C₂×D₄×C₆₇	—	4	2	no	—
307	C₂×D₄×C₆₇	—	4	2	no	—
308	C₂×D₄×C₆₇	—	4	32	no	—
309	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
310	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
311	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
312	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
313	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
314	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	complemented
315	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	complemented
316	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	complemented
317	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	complemented
318	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	complemented
319	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
320	C₂×D₄×C₆₇	#41	1	4	yes	—
321	C₂²×C₄×C₆₇	—	2	2	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	2	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	2	no	—
328	C₂²×C₄×C₆₇	—	2	4	no	—
329	C₂²×C₄×C₆₇	—	2	2	no	—
330	C₂²×C₄×C₆₇	—	2	4	no	—
331	C₂²×C₄×C₆₇	—	2	4	no	—
332	C₂²×C₄×C₆₇	—	2	4	no	—
333	C₂²×C₄×C₆₇	—	2	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	4	no	—
340	C₂²×C₄×C₆₇	—	2	4	no	—
341	C₂²×C₄×C₆₇	—	4	2	no	—
342	C₂²×C₄×C₆₇	—	4	2	no	—
343	C₂²×C₄×C₆₇	—	4	2	no	—
344	C₂²×C₄×C₆₇	—	4	2	no	—
345	C₂²×C₄×C₆₇	—	4	2	no	—
346	C₂²×C₄×C₆₇	—	4	2	no	—
347	C₂²×C₄×C₆₇	—	4	2	no	—
348	C₂²×C₄×C₆₇	—	4	1	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	2	no	—
357	C₂²×C₄×C₆₇	—	4	2	no	—
358	C₂²×C₄×C₆₇	—	4	2	no	—
359	C₂²×C₄×C₆₇	—	4	32	no	—
360	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
361	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
362	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
363	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	complemented
364	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
367	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₆₇	—	2	4	no	—
383	C₄⋊C₄×C₆₇	—	2	2	no	—
384	C₄⋊C₄×C₆₇	—	2	2	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	2	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	4	1	no	—
390	C₄⋊C₄×C₆₇	—	4	2	no	—
391	C₄⋊C₄×C₆₇	—	4	2	no	—
392	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
393	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
394	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	complemented
395	C₂²⋊C₄×C₆₇	—	2	4	no	—
396	C₂²⋊C₄×C₆₇	—	2	4	no	—
397	C₂²⋊C₄×C₆₇	—	2	4	no	—
398	C₂²⋊C₄×C₆₇	—	2	2	no	—
399	C₂²⋊C₄×C₆₇	—	2	4	no	—
400	C₂²⋊C₄×C₆₇	—	2	2	no	—
401	C₂²⋊C₄×C₆₇	—	2	2	no	—
402	C₂²⋊C₄×C₆₇	—	2	2	no	—
403	C₂²⋊C₄×C₆₇	—	2	4	no	—
404	C₂²⋊C₄×C₆₇	—	2	4	no	—
405	C₂²⋊C₄×C₆₇	—	2	4	no	—
406	C₂²⋊C₄×C₆₇	—	2	4	no	—
407	C₂²⋊C₄×C₆₇	—	2	4	no	—
408	C₂²⋊C₄×C₆₇	—	2	2	no	—
409	C₂²⋊C₄×C₆₇	—	2	4	no	—
410	C₂²⋊C₄×C₆₇	—	4	2	no	—
411	C₂²⋊C₄×C₆₇	—	4	2	no	—
412	C₂²⋊C₄×C₆₇	—	4	2	no	—
413	C₂²⋊C₄×C₆₇	—	4	2	no	—
414	C₂²⋊C₄×C₆₇	—	4	1	no	—
415	C₂²⋊C₄×C₆₇	—	4	2	no	—
416	C₂²⋊C₄×C₆₇	—	4	2	no	—
417	C₂²⋊C₄×C₆₇	—	4	2	no	—
418	C₂²⋊C₄×C₆₇	—	4	2	no	—
419	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
420	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
421	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
422	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
423	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
424	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	complemented
425	C₄²×C₆₇	—	2	2	no	—
426	C₄²×C₆₇	—	2	2	no	—
427	C₄²×C₆₇	—	2	2	no	—
428	C₄²×C₆₇	—	2	4	no	—
429	C₄²×C₆₇	—	2	2	no	—
430	C₄²×C₆₇	—	2	2	no	—
431	C₄²×C₆₇	—	4	2	no	—
432	C₄²×C₆₇	—	4	2	no	—
433	C₄²×C₆₇	—	4	2	no	—
434	C₄²×C₆₇	C₂²×C₄	1	4	yes	complemented
435	C₄²×C₆₇	C₂×D₄	1	4	yes	complemented
436	C₂³×C₆₇	—	2	1	no	—
437	C₂³×C₆₇	—	2	1	no	—
438	C₂³×C₆₇	—	2	1	no	—
439	C₂³×C₆₇	—	2	2	no	—
440	C₂³×C₆₇	—	2	2	no	—
441	C₂³×C₆₇	—	2	2	no	—
442	C₂³×C₆₇	—	2	1	no	—
443	C₂³×C₆₇	—	2	2	no	—
444	C₂³×C₆₇	—	2	16	no	—
445	C₂³×C₆₇	—	2	16	no	—
446	C₂³×C₆₇	—	2	1	no	—
447	C₂³×C₆₇	—	2	2	no	—
448	C₂³×C₆₇	—	2	2	no	—
449	C₂³×C₆₇	—	2	1	no	—
450	C₂³×C₆₇	—	2	2	no	—
451	C₂³×C₆₇	—	2	2	no	—
452	C₂³×C₆₇	—	2	1	no	—
453	C₂³×C₆₇	—	2	2	no	—
454	C₂³×C₆₇	—	2	2	no	—
455	C₂³×C₆₇	—	2	2	no	—
456	C₂³×C₆₇	—	2	2	no	—
457	C₂³×C₆₇	—	2	2	no	—
458	C₂³×C₆₇	—	2	2	no	—
459	C₂³×C₆₇	—	2	1	no	—
460	C₂³×C₆₇	—	2	1	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	2	1	no	—
463	C₂³×C₆₇	—	2	2	no	—
464	C₂³×C₆₇	—	2	16	no	—
465	C₂³×C₆₇	—	4	8	no	—
466	C₂³×C₆₇	—	4	8	no	—
467	C₂³×C₆₇	—	4	8	no	—
468	C₂³×C₆₇	—	4	8	no	—
469	C₂³×C₆₇	—	4	8	no	—
470	C₂³×C₆₇	—	4	8	no	—
471	C₂³×C₆₇	—	4	8	no	—
472	C₂³×C₆₇	—	8	4	no	—
473	C₂³×C₆₇	—	8	4	no	—
474	C₂³×C₆₇	—	8	4	no	—
475	C₂³×C₆₇	—	8	4	no	—
476	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
477	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
478	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
479	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
480	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
481	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
482	C₂³×C₆₇	C₂×#41	1	4	yes	—
483	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
484	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
485	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
486	D₄×C₆₇	—	2	16	no	—
487	D₄×C₆₇	—	2	16	no	—
488	D₄×C₆₇	—	2	8	no	—
489	D₄×C₆₇	—	2	16	no	—
490	D₄×C₆₇	—	2	8	no	—
491	D₄×C₆₇	—	2	8	no	—
492	D₄×C₆₇	—	4	8	no	—
493	D₄×C₆₇	—	4	8	no	—
494	D₄×C₆₇	—	4	8	no	—
495	D₄×C₆₇	C₄×D₄	1	16	yes	complemented
496	C₂×C₄×C₆₇	—	2	8	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	2	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	8	no	—
516	C₂×C₄×C₆₇	—	2	8	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	2	1	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	2	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	2	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	4	8	no	—
542	C₂×C₄×C₆₇	—	4	8	no	—
543	C₂×C₄×C₆₇	—	4	8	no	—
544	C₂×C₄×C₆₇	—	4	4	no	—
545	C₂×C₄×C₆₇	—	4	8	no	—
546	C₂×C₄×C₆₇	—	4	8	no	—
547	C₂×C₄×C₆₇	—	4	8	no	—
548	C₂×C₄×C₆₇	—	8	4	no	—
549	C₂×C₄×C₆₇	—	8	4	no	—
550	C₂×C₄×C₆₇	—	8	4	no	—
551	C₂×C₄×C₆₇	—	8	4	no	—
552	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
553	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
554	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
555	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
556	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
557	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
558	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
561	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
563	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
564	C₂²×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	4	no	—
566	C₂²×C₆₇	—	2	2	no	—
567	C₂²×C₆₇	—	2	4	no	—
568	C₂²×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	4	no	—
570	C₂²×C₆₇	—	2	2	no	—
571	C₂²×C₆₇	—	2	4	no	—
572	C₂²×C₆₇	—	2	2	no	—
573	C₂²×C₆₇	—	2	4	no	—
574	C₂²×C₆₇	—	2	4	no	—
575	C₂²×C₆₇	—	2	2	no	—
576	C₂²×C₆₇	—	2	2	no	—
577	C₂²×C₆₇	—	2	4	no	—
578	C₂²×C₆₇	—	2	4	no	—
579	C₂²×C₆₇	—	2	2	no	—
580	C₂²×C₆₇	—	2	4	no	—
581	C₂²×C₆₇	—	2	4	no	—
582	C₂²×C₆₇	—	2	4	no	—
583	C₂²×C₆₇	—	2	4	no	—
584	C₂²×C₆₇	—	2	2	no	—
585	C₂²×C₆₇	—	4	32	no	—
586	C₂²×C₆₇	—	4	2	no	—
587	C₂²×C₆₇	—	4	2	no	—
588	C₂²×C₆₇	—	4	1	no	—
589	C₂²×C₆₇	—	4	2	no	—
590	C₂²×C₆₇	—	4	2	no	—
591	C₂²×C₆₇	—	4	1	no	—
592	C₂²×C₆₇	—	4	2	no	—
593	C₂²×C₆₇	—	4	2	no	—
594	C₂²×C₆₇	—	4	1	no	—
595	C₂²×C₆₇	—	4	2	no	—
596	C₂²×C₆₇	—	4	2	no	—
597	C₂²×C₆₇	—	4	1	no	—
598	C₂²×C₆₇	—	8	16	no	—
599	C₂²×C₆₇	C₂×C₄×D₄	1	8	yes	—
600	C₂²×C₆₇	#518	1	4	yes	complemented
601	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
602	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
603	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
604	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
605	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂²×C₆₇	#585	1	1	yes	characteristic
608	C₄×C₆₇	—	2	2	no	—
609	C₄×C₆₇	—	2	2	no	—
610	C₄×C₆₇	—	2	2	no	—
611	C₄×C₆₇	—	2	4	no	—
612	C₄×C₆₇	—	2	2	no	—
613	C₄×C₆₇	—	2	2	no	—
614	C₄×C₆₇	—	2	2	no	—
615	C₄×C₆₇	—	2	4	no	—
616	C₄×C₆₇	—	2	2	no	—
617	C₄×C₆₇	—	4	2	no	—
618	C₄×C₆₇	—	4	1	no	—
619	C₄×C₆₇	—	4	1	no	—
620	C₄×C₆₇	—	4	1	no	—
621	C₄×C₆₇	—	4	2	no	—
622	C₄×C₆₇	—	4	1	no	—
623	C₄×C₆₇	—	4	2	no	—
624	C₄×C₆₇	—	4	1	no	—
625	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
626	#34290	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
627	C₂×C₆₇	—	2	4	no	—
628	C₂×C₆₇	—	2	8	no	—
629	C₂×C₆₇	—	4	4	no	—
630	C₂×C₆₇	—	4	4	no	—
631	C₂×C₆₇	—	4	2	no	—
632	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
633	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
634	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂×C₆₇	#3484	1	1	yes	characteristic
636	C₂×C₆₇	#3488	1	1	yes	characteristic
637	C₂×C₆₇	#3513	1	1	yes	characteristic
638	C₂×C₆₇	#3519	1	1	yes	characteristic
639	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic
640	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
641	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
642	#2366	C₂×C₆₇	1	1	yes	characteristic, complemented
643	#2364	C₂×C₆₇	1	2	yes	complemented
644	#2363	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
646	#2358	C₂×C₆₇	1	2	yes	complemented
647	#2358	C₂×C₆₇	1	2	yes	complemented
648	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
649	#2349	C₂×C₆₇	1	1	yes	characteristic, complemented
650	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
651	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
652	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
653	#2328	C₂×C₆₇	1	1	yes	characteristic, complemented
654	#2325	C₂×C₆₇	1	2	yes	complemented
655	#2324	C₂×C₆₇	1	1	yes	characteristic, complemented
656	#2321	C₂×C₆₇	1	2	yes	complemented
657	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
658	C₄×#120	C₂×C₆₇	1	2	yes	complemented
659	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
660	C₂×#386	C₂×C₆₇	1	2	yes	complemented
661	#2275	C₂×C₆₇	1	1	yes	characteristic, complemented
662	C₆₇	#34290	1	1	yes	characteristic, direct product factor, Sylow
663	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
664	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
665	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
666	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	complemented
667	D₄²	C₄×C₆₇	1	16	yes	complemented
668	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
669	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
670	C₂×#121	C₂²×C₆₇	1	2	yes	—
671	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
672	C₂×#120	C₂²×C₆₇	1	2	yes	—
673	C₂×#120	C₂²×C₆₇	1	2	yes	—
674	#518	—	2	8	no	—
675	C₂×C₄×D₄	—	2	8	no	—
676	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
677	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
678	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
679	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
680	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
681	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
682	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
683	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
685	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
687	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
688	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
691	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
692	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
693	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
697	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
698	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
699	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
700	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
701	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#390	C₂²×C₆₇	1	2	yes	complemented
703	#390	C₂²×C₆₇	1	2	yes	complemented
704	#390	C₂²×C₆₇	1	2	yes	complemented
705	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
706	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	#388	C₂²×C₆₇	1	2	yes	complemented
713	#388	C₂²×C₆₇	1	2	yes	complemented
714	#388	C₂²×C₆₇	1	2	yes	complemented
715	#388	C₂²×C₆₇	1	2	yes	complemented
716	#388	C₂²×C₆₇	1	2	yes	complemented
717	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	#387	C₂²×C₆₇	1	2	yes	complemented
720	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
721	#386	C₂²×C₆₇	1	1	yes	characteristic
722	#386	C₂²×C₆₇	1	2	yes	—
723	#386	C₂²×C₆₇	1	1	yes	characteristic
724	#386	C₂²×C₆₇	1	2	yes	complemented
725	#386	C₂²×C₆₇	1	2	yes	complemented
726	#386	C₂²×C₆₇	1	2	yes	complemented
727	#386	C₂²×C₆₇	1	2	yes	complemented
728	#386	C₂²×C₆₇	1	2	yes	complemented
729	#386	C₂²×C₆₇	1	2	yes	complemented
730	#386	C₂²×C₆₇	1	2	yes	complemented
731	#386	C₂²×C₆₇	1	2	yes	complemented
732	#386	C₂²×C₆₇	1	2	yes	complemented
733	#386	C₂²×C₆₇	1	2	yes	complemented
734	#386	C₂²×C₆₇	1	2	yes	complemented
735	#386	C₂²×C₆₇	1	2	yes	complemented
736	#386	C₂²×C₆₇	1	2	yes	complemented
737	#386	C₂²×C₆₇	1	2	yes	complemented
738	#385	C₂²×C₆₇	1	2	yes	complemented
739	#385	C₂²×C₆₇	1	2	yes	complemented
740	#385	C₂²×C₆₇	1	2	yes	complemented
741	#385	C₂²×C₆₇	1	2	yes	complemented
742	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
743	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
744	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
745	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	#380	C₂²×C₆₇	1	2	yes	complemented
747	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	#379	C₂²×C₆₇	1	2	yes	complemented
749	#379	C₂²×C₆₇	1	2	yes	complemented
750	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
751	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
752	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
753	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
755	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
756	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
757	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
758	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
759	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
760	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
761	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
762	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
764	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
765	C₂⁵	C₂³×C₆₇	1	2	yes	—
766	C₂⁵	C₂³×C₆₇	1	2	yes	—
767	C₂²×D₄	—	2	4	no	—
768	C₂²×D₄	—	2	4	no	—
769	C₂²×D₄	—	2	4	no	—
770	C₂²×D₄	—	2	4	no	—
771	C₂²×D₄	—	4	4	no	—
772	C₂²×D₄	—	4	4	no	—
773	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
774	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
775	C₂²×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
776	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
777	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
778	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
779	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
780	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
781	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
782	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
783	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
784	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
785	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
786	C₂³×C₄	—	2	8	no	—
787	C₂³×C₄	—	4	4	no	—
788	C₂³×C₄	—	4	4	no	—
789	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
790	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
791	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
792	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
793	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
794	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
795	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
796	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
797	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
798	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
799	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
800	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
801	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
802	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
803	#127	C₂×C₄×C₆₇	1	8	yes	complemented
804	#121	C₂×C₄×C₆₇	1	8	yes	complemented
805	#121	C₂×C₄×C₆₇	1	8	yes	complemented
806	#121	C₂×C₄×C₆₇	1	16	yes	complemented
807	#120	C₂×C₄×C₆₇	1	16	yes	complemented
808	#120	C₂×C₄×C₆₇	1	16	yes	complemented
809	C₄×D₄	—	2	4	no	—
810	C₄×D₄	—	2	4	no	—
811	C₄×D₄	—	2	4	no	—
812	C₄×D₄	—	2	8	no	—
813	C₄×D₄	—	2	8	no	—
814	C₄×D₄	—	2	4	no	—
815	C₄×D₄	—	2	4	no	—
816	C₄×D₄	—	2	8	no	—
817	C₄×D₄	—	2	8	no	—
818	C₄×D₄	—	2	4	no	—
819	C₄×D₄	—	2	4	no	—
820	C₄×D₄	—	4	4	no	—
821	C₄×D₄	—	4	4	no	—
822	C₄×D₄	—	4	4	no	—
823	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
824	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
825	C₄×D₄	D₄×C₆₇	1	8	yes	complemented
826	#117	—	2	4	no	—
827	#117	—	2	4	no	—
828	C₂×C₄⋊C₄	—	2	4	no	—
829	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
832	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
842	C₂×C₂²⋊C₄	—	2	8	no	—
843	C₂×C₂²⋊C₄	—	2	8	no	—
844	C₂×C₂²⋊C₄	—	2	8	no	—
845	C₂×C₂²⋊C₄	—	4	4	no	—
846	C₂×C₂²⋊C₄	—	4	4	no	—
847	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
848	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
849	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
851	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
852	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
853	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
854	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
855	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
856	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
857	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
858	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
859	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
860	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
861	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
862	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
863	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
864	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
865	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
866	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
867	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
868	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
869	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
871	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
872	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
873	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
875	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
876	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
877	C₂×C₄²	—	2	4	no	—
878	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
879	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
880	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
881	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
882	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
883	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
884	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
885	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
886	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
887	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
888	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
889	#95	C₂³×C₆₇	1	1	yes	characteristic
890	#95	C₂³×C₆₇	1	1	yes	characteristic
891	#95	C₂³×C₆₇	1	2	yes	—
892	#95	C₂³×C₆₇	1	2	yes	—
893	#95	C₂³×C₆₇	1	2	yes	—
894	#95	C₂³×C₆₇	1	2	yes	—
895	#95	C₂³×C₆₇	1	2	yes	—
896	#95	C₂³×C₆₇	1	2	yes	—
897	#95	C₂³×C₆₇	1	1	yes	characteristic
898	#95	C₂³×C₆₇	1	1	yes	characteristic
899	#95	C₂³×C₆₇	1	1	yes	characteristic
900	#95	C₂³×C₆₇	1	1	yes	characteristic
901	#95	C₂³×C₆₇	1	2	yes	—
902	#95	C₂³×C₆₇	1	2	yes	—
903	#95	C₂³×C₆₇	1	2	yes	—
904	#95	C₂³×C₆₇	1	1	yes	characteristic
905	#95	C₂³×C₆₇	1	1	yes	characteristic
906	#95	C₂³×C₆₇	1	1	yes	characteristic
907	#95	C₂³×C₆₇	1	1	yes	characteristic
908	C₂⁴	—	2	4	no	—
909	C₂⁴	—	2	4	no	—
910	C₂⁴	—	2	4	no	—
911	C₂⁴	—	2	4	no	—
912	C₂⁴	—	2	4	no	—
913	C₂⁴	—	2	4	no	—
914	C₂⁴	—	4	2	no	—
915	C₂⁴	—	4	2	no	—
916	C₂⁴	—	4	2	no	—
917	C₂⁴	—	4	2	no	—
918	C₂⁴	—	4	2	no	—
919	C₂⁴	—	4	2	no	—
920	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
921	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	complemented
922	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
923	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
924	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
925	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
926	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂×D₄	—	2	4	no	—
928	C₂×D₄	—	2	4	no	—
929	C₂×D₄	—	2	4	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	4	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	32	no	—
936	C₂×D₄	—	2	32	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	4	2	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	4	2	no	—
946	C₂×D₄	—	4	2	no	—
947	C₂×D₄	—	4	32	no	—
948	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
949	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
950	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
951	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
952	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
953	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	complemented
954	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	complemented
955	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	complemented
956	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	complemented
957	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	complemented
958	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
959	C₂×D₄	#41×C₆₇	1	4	yes	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	4	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	4	no	—
970	C₂²×C₄	—	2	4	no	—
971	C₂²×C₄	—	2	4	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	4	no	—
974	C₂²×C₄	—	2	4	no	—
975	C₂²×C₄	—	2	4	no	—
976	C₂²×C₄	—	2	4	no	—
977	C₂²×C₄	—	2	4	no	—
978	C₂²×C₄	—	2	4	no	—
979	C₂²×C₄	—	2	4	no	—
980	C₂²×C₄	—	4	2	no	—
981	C₂²×C₄	—	4	2	no	—
982	C₂²×C₄	—	4	2	no	—
983	C₂²×C₄	—	4	2	no	—
984	C₂²×C₄	—	4	2	no	—
985	C₂²×C₄	—	4	2	no	—
986	C₂²×C₄	—	4	2	no	—
987	C₂²×C₄	—	4	2	no	—
988	C₂²×C₄	—	4	2	no	—
989	C₂²×C₄	—	4	1	no	—
990	C₂²×C₄	—	4	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	2	no	—
997	C₂²×C₄	—	4	2	no	—
998	C₂²×C₄	—	4	32	no	—
999	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
1000	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
1001	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1002	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	complemented
1003	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1008	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1009	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1019	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1021	C₄⋊C₄	—	2	4	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	4	2	no	—
1029	C₄⋊C₄	—	4	2	no	—
1030	C₄⋊C₄	—	4	1	no	—
1031	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
1032	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
1033	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	complemented
1034	C₂²⋊C₄	—	2	4	no	—
1035	C₂²⋊C₄	—	2	4	no	—
1036	C₂²⋊C₄	—	2	4	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	4	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	4	no	—
1043	C₂²⋊C₄	—	2	4	no	—
1044	C₂²⋊C₄	—	2	4	no	—
1045	C₂²⋊C₄	—	2	4	no	—
1046	C₂²⋊C₄	—	2	4	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	4	no	—
1049	C₂²⋊C₄	—	4	2	no	—
1050	C₂²⋊C₄	—	4	2	no	—
1051	C₂²⋊C₄	—	4	2	no	—
1052	C₂²⋊C₄	—	4	2	no	—
1053	C₂²⋊C₄	—	4	2	no	—
1054	C₂²⋊C₄	—	4	2	no	—
1055	C₂²⋊C₄	—	4	2	no	—
1056	C₂²⋊C₄	—	4	1	no	—
1057	C₂²⋊C₄	—	4	2	no	—
1058	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
1059	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
1060	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1061	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1062	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
1063	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	complemented
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	2	no	—
1067	C₄²	—	2	4	no	—
1068	C₄²	—	2	2	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	4	2	no	—
1071	C₄²	—	4	2	no	—
1072	C₄²	—	4	2	no	—
1073	C₄²	C₂²×C₄×C₆₇	1	4	yes	complemented
1074	C₄²	C₂×D₄×C₆₇	1	4	yes	complemented
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	2	no	—
1081	C₂³	—	2	1	no	—
1082	C₂³	—	2	2	no	—
1083	C₂³	—	2	16	no	—
1084	C₂³	—	2	16	no	—
1085	C₂³	—	2	1	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	2	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	2	2	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	2	1	no	—
1099	C₂³	—	2	1	no	—
1100	C₂³	—	2	2	no	—
1101	C₂³	—	2	1	no	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	16	no	—
1104	C₂³	—	4	8	no	—
1105	C₂³	—	4	8	no	—
1106	C₂³	—	4	8	no	—
1107	C₂³	—	4	8	no	—
1108	C₂³	—	4	8	no	—
1109	C₂³	—	4	8	no	—
1110	C₂³	—	4	8	no	—
1111	C₂³	—	8	4	no	—
1112	C₂³	—	8	4	no	—
1113	C₂³	—	8	4	no	—
1114	C₂³	—	8	4	no	—
1115	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1116	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
1117	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
1118	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
1119	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1120	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
1121	C₂³	C₂×#41×C₆₇	1	4	yes	—
1122	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
1123	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
1124	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1125	D₄	—	2	16	no	—
1126	D₄	—	2	16	no	—
1127	D₄	—	2	8	no	—
1128	D₄	—	2	16	no	—
1129	D₄	—	2	8	no	—
1130	D₄	—	2	8	no	—
1131	D₄	—	4	8	no	—
1132	D₄	—	4	8	no	—
1133	D₄	—	4	8	no	—
1134	D₄	C₄×D₄×C₆₇	1	16	yes	complemented
1135	C₂×C₄	—	2	8	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	8	no	—
1155	C₂×C₄	—	2	8	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	4	8	no	—
1181	C₂×C₄	—	4	8	no	—
1182	C₂×C₄	—	4	8	no	—
1183	C₂×C₄	—	4	8	no	—
1184	C₂×C₄	—	4	8	no	—
1185	C₂×C₄	—	4	4	no	—
1186	C₂×C₄	—	4	8	no	—
1187	C₂×C₄	—	8	4	no	—
1188	C₂×C₄	—	8	4	no	—
1189	C₂×C₄	—	8	4	no	—
1190	C₂×C₄	—	8	4	no	—
1191	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1192	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1193	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1194	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1195	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1196	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1197	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1198	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1199	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1200	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1201	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1202	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	4	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	4	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	4	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	4	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	4	no	—
1213	C₂²	—	2	4	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	2	no	—
1216	C₂²	—	2	4	no	—
1217	C₂²	—	2	4	no	—
1218	C₂²	—	2	2	no	—
1219	C₂²	—	2	4	no	—
1220	C₂²	—	2	4	no	—
1221	C₂²	—	2	4	no	—
1222	C₂²	—	2	4	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	4	32	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	2	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	8	16	no	—
1238	C₂²	C₂×C₄×D₄×C₆₇	1	8	yes	—
1239	C₂²	#518×C₆₇	1	4	yes	complemented
1240	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1241	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1242	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1243	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1244	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1245	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1246	C₂²	#585×C₆₇	1	1	yes	characteristic
1247	C₄	—	2	2	no	—
1248	C₄	—	2	2	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	2	4	no	—
1251	C₄	—	2	2	no	—
1252	C₄	—	2	2	no	—
1253	C₄	—	2	2	no	—
1254	C₄	—	2	4	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	4	2	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	2	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	2	no	—
1264	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
1265	C₂	—	2	4	no	—
1266	C₂	—	2	8	no	—
1267	C₂	—	4	4	no	—
1268	C₂	—	4	2	no	—
1269	C₂	—	4	4	no	—
1270	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
1271	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
1272	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1273	C₂	C₆₇×#3484	1	1	yes	characteristic
1274	C₂	C₆₇×#3488	1	1	yes	characteristic
1275	C₂	C₆₇×#3513	1	1	yes	characteristic
1276	C₂	C₆₇×#3519	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×D₄²×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×#518×C₆₇	C₂	semidirect
3. C₂²×C₄×D₄×C₆₇	C₂	semidirect
4. C₆₇×#2366	C₂	semidirect
5. C₆₇×#2364	C₂	semidirect
6. C₆₇×#2363	C₂	semidirect
7. C₆₇×#2361	C₂	semidirect
8. C₆₇×#2358	C₂	semidirect
9. C₆₇×#2358	C₂	semidirect
10. C₆₇×#2352	C₂	semidirect
11. C₆₇×#2349	C₂	semidirect
12. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
13. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
14. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
15. C₆₇×#2328	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₆₇×#2324	C₂	semidirect
18. C₆₇×#2321	C₂	semidirect
19. C₄×#121×C₆₇	C₂	semidirect
20. C₄×#120×C₆₇	C₂	semidirect
21. C₆₇×#2290	C₂	semidirect
22. C₂×#386×C₆₇	C₂	semidirect
23. C₆₇×#2275	C₂	semidirect
27. C₂⁴×C₄×C₆₇	C₂²	semidirect
28. D₄²×C₆₇	C₄	semidirect
43. C₂×C₄×D₄×C₆₇	C₂²	semidirect
44. C₂×C₄×D₄×C₆₇	C₂²	semidirect
45. C₂×C₄×D₄×C₆₇	C₂²	semidirect
46. C₂×C₄×D₄×C₆₇	C₂²	semidirect
47. C₂×C₄×D₄×C₆₇	C₂²	semidirect
48. C₂×C₄×D₄×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×C₄×D₄×C₆₇	C₂²	semidirect
53. C₂×C₄×D₄×C₆₇	C₂²	semidirect
54. C₂×#117×C₆₇	C₂²	semidirect
55. C₂×#117×C₆₇	C₂²	semidirect
56. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
57. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
58. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
59. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
60. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
61. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
62. C₂²×C₄²×C₆₇	C₂²	semidirect
63. #390×C₆₇	C₂²	semidirect
64. #390×C₆₇	C₂²	semidirect
65. #390×C₆₇	C₂²	semidirect
66. #390×C₆₇	C₂²	semidirect
67. #390×C₆₇	C₂²	semidirect
68. #390×C₆₇	C₂²	semidirect
69. #390×C₆₇	C₂²	semidirect
70. #389×C₆₇	C₂²	semidirect
71. #389×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
85. #386×C₆₇	C₂²	semidirect
86. #386×C₆₇	C₂²	semidirect
87. #386×C₆₇	C₂²	semidirect
88. #386×C₆₇	C₂²	semidirect
89. #386×C₆₇	C₂²	semidirect
90. #386×C₆₇	C₂²	semidirect
91. #386×C₆₇	C₂²	semidirect
92. #386×C₆₇	C₂²	semidirect
93. #386×C₆₇	C₂²	semidirect
94. #386×C₆₇	C₂²	semidirect
95. #386×C₆₇	C₂²	semidirect
96. #386×C₆₇	C₂²	semidirect
97. #386×C₆₇	C₂²	semidirect
98. #386×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. #385×C₆₇	C₂²	semidirect
105. #382×C₆₇	C₂²	semidirect
106. #380×C₆₇	C₂²	semidirect
107. #380×C₆₇	C₂²	semidirect
108. #380×C₆₇	C₂²	semidirect
109. #379×C₆₇	C₂²	semidirect
110. #379×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
115. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
116. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
117. C₄×C₂²⋊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
134. C₂²×D₄×C₆₇	C₂×C₄	semidirect
135. C₂²×D₄×C₆₇	C₂×C₄	semidirect
136. C₂²×D₄×C₆₇	C₂×C₄	semidirect
164. #127×C₆₇	C₂×C₄	semidirect
165. #121×C₆₇	C₂×C₄	semidirect
166. #121×C₆₇	C₂×C₄	semidirect
167. #121×C₆₇	C₂×C₄	semidirect
168. #120×C₆₇	C₂×C₄	semidirect
169. #120×C₆₇	C₂×C₄	semidirect
184. C₄×D₄×C₆₇	C₂×C₄	semidirect
185. C₄×D₄×C₆₇	C₂×C₄	semidirect
186. C₄×D₄×C₆₇	D₄	semidirect
282. C₂⁴×C₆₇	C₂²×C₄	semidirect
314. C₂×D₄×C₆₇	C₂²×C₄	semidirect
315. C₂×D₄×C₆₇	C₂²×C₄	semidirect
316. C₂×D₄×C₆₇	C₂²×C₄	semidirect
317. C₂×D₄×C₆₇	C₂²×C₄	semidirect
318. C₂×D₄×C₆₇	C₂²×C₄	semidirect
361. C₂²×C₄×C₆₇	C₂²×C₄	semidirect
362. C₂²×C₄×C₆₇	C₂²×C₄	semidirect
363. C₂²×C₄×C₆₇	C₂×D₄	semidirect
392. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
393. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
394. C₄⋊C₄×C₆₇	C₂×D₄	semidirect
420. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
421. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
422. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
423. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
424. C₂²⋊C₄×C₆₇	C₂×D₄	semidirect
434. C₄²×C₆₇	C₂²×C₄	semidirect
435. C₄²×C₆₇	C₂×D₄	semidirect
495. D₄×C₆₇	C₄×D₄	semidirect
600. C₂²×C₆₇	#518	semidirect
626. #34290	C₆₇	direct (N × H)
640. C₂×#518	C₂×C₆₇	semidirect
641. C₂²×C₄×D₄	C₂×C₆₇	semidirect
642. #2366	C₂×C₆₇	semidirect
643. #2364	C₂×C₆₇	semidirect
644. #2363	C₂×C₆₇	semidirect
645. #2361	C₂×C₆₇	semidirect
646. #2358	C₂×C₆₇	semidirect
647. #2358	C₂×C₆₇	semidirect
648. #2352	C₂×C₆₇	semidirect
649. #2349	C₂×C₆₇	semidirect
650. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
651. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
652. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
653. #2328	C₂×C₆₇	semidirect
654. #2325	C₂×C₆₇	semidirect
655. #2324	C₂×C₆₇	semidirect
656. #2321	C₂×C₆₇	semidirect
657. C₄×#121	C₂×C₆₇	semidirect
658. C₄×#120	C₂×C₆₇	semidirect
659. #2290	C₂×C₆₇	semidirect
660. C₂×#386	C₂×C₆₇	semidirect
661. #2275	C₂×C₆₇	semidirect
662. C₆₇	#34290	direct (N × H)
666. C₂⁴×C₄	C₂²×C₆₇	semidirect
667. D₄²	C₄×C₆₇	semidirect
682. C₂×C₄×D₄	C₂²×C₆₇	semidirect
683. C₂×C₄×D₄	C₂²×C₆₇	semidirect
684. C₂×C₄×D₄	C₂²×C₆₇	semidirect
685. C₂×C₄×D₄	C₂²×C₆₇	semidirect
686. C₂×C₄×D₄	C₂²×C₆₇	semidirect
687. C₂×C₄×D₄	C₂²×C₆₇	semidirect
688. C₂×C₄×D₄	C₂²×C₆₇	semidirect
689. C₂×C₄×D₄	C₂²×C₆₇	semidirect
690. C₂×C₄×D₄	C₂²×C₆₇	semidirect
691. C₂×C₄×D₄	C₂²×C₆₇	semidirect
692. C₂×C₄×D₄	C₂²×C₆₇	semidirect
693. C₂×#117	C₂²×C₆₇	semidirect
694. C₂×#117	C₂²×C₆₇	semidirect
695. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
696. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
697. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
698. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
699. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
700. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
701. C₂²×C₄²	C₂²×C₆₇	semidirect
702. #390	C₂²×C₆₇	semidirect
703. #390	C₂²×C₆₇	semidirect
704. #390	C₂²×C₆₇	semidirect
705. #390	C₂²×C₆₇	semidirect
706. #390	C₂²×C₆₇	semidirect
707. #390	C₂²×C₆₇	semidirect
708. #390	C₂²×C₆₇	semidirect
709. #389	C₂²×C₆₇	semidirect
710. #389	C₂²×C₆₇	semidirect
711. #388	C₂²×C₆₇	semidirect
712. #388	C₂²×C₆₇	semidirect
713. #388	C₂²×C₆₇	semidirect
714. #388	C₂²×C₆₇	semidirect
715. #388	C₂²×C₆₇	semidirect
716. #388	C₂²×C₆₇	semidirect
717. #388	C₂²×C₆₇	semidirect
718. #387	C₂²×C₆₇	semidirect
719. #387	C₂²×C₆₇	semidirect
720. #387	C₂²×C₆₇	semidirect
724. #386	C₂²×C₆₇	semidirect
725. #386	C₂²×C₆₇	semidirect
726. #386	C₂²×C₆₇	semidirect
727. #386	C₂²×C₆₇	semidirect
728. #386	C₂²×C₆₇	semidirect
729. #386	C₂²×C₆₇	semidirect
730. #386	C₂²×C₆₇	semidirect
731. #386	C₂²×C₆₇	semidirect
732. #386	C₂²×C₆₇	semidirect
733. #386	C₂²×C₆₇	semidirect
734. #386	C₂²×C₆₇	semidirect
735. #386	C₂²×C₆₇	semidirect
736. #386	C₂²×C₆₇	semidirect
737. #386	C₂²×C₆₇	semidirect
738. #385	C₂²×C₆₇	semidirect
739. #385	C₂²×C₆₇	semidirect
740. #385	C₂²×C₆₇	semidirect
741. #385	C₂²×C₆₇	semidirect
742. #385	C₂²×C₆₇	semidirect
743. #385	C₂²×C₆₇	semidirect
744. #382	C₂²×C₆₇	semidirect
745. #380	C₂²×C₆₇	semidirect
746. #380	C₂²×C₆₇	semidirect
747. #380	C₂²×C₆₇	semidirect
748. #379	C₂²×C₆₇	semidirect
749. #379	C₂²×C₆₇	semidirect
750. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
751. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
752. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
753. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
754. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
755. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
756. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
757. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
758. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
759. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
760. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
761. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
762. #376	C₂²×C₆₇	semidirect
763. C₂×#95	C₂²×C₆₇	semidirect
764. C₂×#95	C₂²×C₆₇	semidirect
773. C₂²×D₄	C₂×C₄×C₆₇	semidirect
774. C₂²×D₄	C₂×C₄×C₆₇	semidirect
775. C₂²×D₄	C₂×C₄×C₆₇	semidirect
803. #127	C₂×C₄×C₆₇	semidirect
804. #121	C₂×C₄×C₆₇	semidirect
805. #121	C₂×C₄×C₆₇	semidirect
806. #121	C₂×C₄×C₆₇	semidirect
807. #120	C₂×C₄×C₆₇	semidirect
808. #120	C₂×C₄×C₆₇	semidirect
823. C₄×D₄	C₂×C₄×C₆₇	semidirect
824. C₄×D₄	C₂×C₄×C₆₇	semidirect
825. C₄×D₄	D₄×C₆₇	semidirect
921. C₂⁴	C₂²×C₄×C₆₇	semidirect
953. C₂×D₄	C₂²×C₄×C₆₇	semidirect
954. C₂×D₄	C₂²×C₄×C₆₇	semidirect
955. C₂×D₄	C₂²×C₄×C₆₇	semidirect
956. C₂×D₄	C₂²×C₄×C₆₇	semidirect
957. C₂×D₄	C₂²×C₄×C₆₇	semidirect
1000. C₂²×C₄	C₂²×C₄×C₆₇	semidirect
1001. C₂²×C₄	C₂²×C₄×C₆₇	semidirect
1002. C₂²×C₄	C₂×D₄×C₆₇	semidirect
1031. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
1032. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
1033. C₄⋊C₄	C₂×D₄×C₆₇	semidirect
1059. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1060. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1061. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1062. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
1063. C₂²⋊C₄	C₂×D₄×C₆₇	semidirect
1073. C₄²	C₂²×C₄×C₆₇	semidirect
1074. C₄²	C₂×D₄×C₆₇	semidirect
1134. D₄	C₄×D₄×C₆₇	semidirect
1239. C₂²	#518×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₆₇	2
C₂×#518×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2366	2
C₆₇×#2364	2
C₆₇×#2363	2
C₆₇×#2361	2
C₆₇×#2358	2
C₆₇×#2352	2
C₆₇×#2349	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2328	2
C₆₇×#2325	2
C₆₇×#2324	2
C₆₇×#2321	2
C₄×#121×C₆₇	2
C₄×#120×C₆₇	2
C₆₇×#2290	2
C₂×#386×C₆₇	2
C₆₇×#2275	2
#34290	67

Subgroups — C67×#34290 #30713541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34290 #30713541