Subgroups — C₆₇×#34437 #30713688

Order 17152.

2810 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2376	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2375	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2374	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2364	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
8	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2312	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
21	#534×C₆₇	C₄	1	16	yes	complemented
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×#120×C₆₇	C₂²	1	2	yes	—
28	C₂×#120×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
42	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#390×C₆₇	C₂²	1	2	yes	—
44	#390×C₆₇	C₂²	1	2	yes	—
45	#390×C₆₇	C₂²	1	2	yes	—
46	#390×C₆₇	C₂²	1	2	yes	—
47	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#390×C₆₇	C₂²	1	2	yes	complemented
50	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#389×C₆₇	C₂²	1	2	yes	complemented
53	#388×C₆₇	C₂²	1	2	yes	complemented
54	#388×C₆₇	C₂²	1	2	yes	complemented
55	#388×C₆₇	C₂²	1	2	yes	complemented
56	#388×C₆₇	C₂²	1	2	yes	complemented
57	#388×C₆₇	C₂²	1	2	yes	complemented
58	#388×C₆₇	C₂²	1	2	yes	complemented
59	#388×C₆₇	C₂²	1	2	yes	complemented
60	#388×C₆₇	C₂²	1	2	yes	complemented
61	#388×C₆₇	C₂²	1	2	yes	complemented
62	#388×C₆₇	C₂²	1	2	yes	complemented
63	#388×C₆₇	C₂²	1	2	yes	complemented
64	#388×C₆₇	C₂²	1	2	yes	complemented
65	#388×C₆₇	C₂²	1	2	yes	complemented
66	#388×C₆₇	C₂²	1	2	yes	complemented
67	#388×C₆₇	C₂²	1	2	yes	complemented
68	#388×C₆₇	C₂²	1	2	yes	complemented
69	#387×C₆₇	C₂²	1	2	yes	complemented
70	#387×C₆₇	C₂²	1	2	yes	complemented
71	#387×C₆₇	C₂²	1	2	yes	complemented
72	#387×C₆₇	C₂²	1	2	yes	complemented
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	2	yes	—
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	complemented
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	#385×C₆₇	C₂²	1	2	yes	complemented
86	#385×C₆₇	C₂²	1	2	yes	complemented
87	#385×C₆₇	C₂²	1	2	yes	complemented
88	#385×C₆₇	C₂²	1	2	yes	complemented
89	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#380×C₆₇	C₂²	1	2	yes	complemented
92	#380×C₆₇	C₂²	1	2	yes	complemented
93	#379×C₆₇	C₂²	1	2	yes	—
94	#379×C₆₇	C₂²	1	2	yes	complemented
95	#379×C₆₇	C₂²	1	2	yes	complemented
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
106	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂⁵×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	—	4	4	no	—
111	C₂²×D₄×C₆₇	—	4	4	no	—
112	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	#123×C₆₇	C₂×C₄	1	16	yes	complemented
132	#123×C₆₇	C₂×C₄	1	16	yes	complemented
133	#121×C₆₇	C₂×C₄	1	8	yes	complemented
134	#121×C₆₇	C₂×C₄	1	8	yes	complemented
135	#121×C₆₇	C₂×C₄	1	16	yes	complemented
136	#120×C₆₇	C₂×C₄	1	16	yes	complemented
137	#120×C₆₇	C₂×C₄	1	16	yes	complemented
138	C₄×D₄×C₆₇	—	4	2	no	—
139	C₄×D₄×C₆₇	—	4	2	no	—
140	C₄×D₄×C₆₇	—	4	4	no	—
141	C₄×D₄×C₆₇	—	4	4	no	—
142	C₄×D₄×C₆₇	—	4	4	no	—
143	C₄×D₄×C₆₇	—	4	4	no	—
144	C₄×D₄×C₆₇	—	4	4	no	—
145	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
160	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
161	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
162	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
163	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
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×C₄²×C₆₇	—	4	2	no	—
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×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	C₂⁴×C₆₇	—	2	2	no	—
220	C₂⁴×C₆₇	—	2	2	no	—
221	C₂⁴×C₆₇	—	4	1	no	—
222	C₂⁴×C₆₇	—	4	1	no	—
223	C₂⁴×C₆₇	—	4	2	no	—
224	C₂⁴×C₆₇	—	4	2	no	—
225	C₂⁴×C₆₇	—	4	2	no	—
226	C₂⁴×C₆₇	—	4	2	no	—
227	C₂⁴×C₆₇	—	4	1	no	—
228	C₂⁴×C₆₇	—	4	1	no	—
229	C₂⁴×C₆₇	—	4	2	no	—
230	C₂⁴×C₆₇	—	4	2	no	—
231	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
232	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
233	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
234	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
236	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₆₇	—	2	4	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	4	1	no	—
242	C₂×D₄×C₆₇	—	4	1	no	—
243	C₂×D₄×C₆₇	—	4	2	no	—
244	C₂×D₄×C₆₇	—	4	2	no	—
245	C₂×D₄×C₆₇	—	4	2	no	—
246	C₂×D₄×C₆₇	—	4	2	no	—
247	C₂×D₄×C₆₇	—	4	2	no	—
248	C₂×D₄×C₆₇	—	4	2	no	—
249	C₂×D₄×C₆₇	—	4	1	no	—
250	C₂×D₄×C₆₇	—	4	1	no	—
251	C₂×D₄×C₆₇	—	4	32	no	—
252	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
253	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
254	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
255	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
256	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
257	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
258	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
259	C₂²×C₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	2	4	no	—
267	C₂²×C₄×C₆₇	—	4	1	no	—
268	C₂²×C₄×C₆₇	—	4	1	no	—
269	C₂²×C₄×C₆₇	—	4	1	no	—
270	C₂²×C₄×C₆₇	—	4	1	no	—
271	C₂²×C₄×C₆₇	—	4	1	no	—
272	C₂²×C₄×C₆₇	—	4	1	no	—
273	C₂²×C₄×C₆₇	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	2	no	—
276	C₂²×C₄×C₆₇	—	4	1	no	—
277	C₂²×C₄×C₆₇	—	4	1	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	1	no	—
280	C₂²×C₄×C₆₇	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	2	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	—	4	2	no	—
288	C₂²×C₄×C₆₇	—	4	1	no	—
289	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
290	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
291	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₆₇	—	2	4	no	—
308	C₄⋊C₄×C₆₇	—	4	2	no	—
309	C₄⋊C₄×C₆₇	—	4	1	no	—
310	C₄⋊C₄×C₆₇	—	4	1	no	—
311	C₄⋊C₄×C₆₇	—	4	1	no	—
312	C₄⋊C₄×C₆₇	—	4	1	no	—
313	C₄⋊C₄×C₆₇	—	4	2	no	—
314	C₄⋊C₄×C₆₇	—	4	2	no	—
315	C₄⋊C₄×C₆₇	—	4	2	no	—
316	C₄⋊C₄×C₆₇	—	4	2	no	—
317	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
318	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
319	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	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	2	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	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	2	no	—
339	C₂²⋊C₄×C₆₇	—	4	2	no	—
340	C₂²⋊C₄×C₆₇	—	4	2	no	—
341	C₂²⋊C₄×C₆₇	—	4	2	no	—
342	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
343	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
344	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
345	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
346	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
347	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
348	C₄²×C₆₇	—	2	2	no	—
349	C₄²×C₆₇	—	2	2	no	—
350	C₄²×C₆₇	—	4	1	no	—
351	C₄²×C₆₇	—	4	1	no	—
352	C₄²×C₆₇	—	4	2	no	—
353	C₄²×C₆₇	—	4	2	no	—
354	C₄²×C₆₇	—	4	2	no	—
355	C₄²×C₆₇	—	4	2	no	—
356	C₄²×C₆₇	—	4	2	no	—
357	C₄²×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	2	1	no	—
359	C₂³×C₆₇	—	2	1	no	—
360	C₂³×C₆₇	—	2	1	no	—
361	C₂³×C₆₇	—	2	1	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	2	no	—
371	C₂³×C₆₇	—	2	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	2	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	8	no	—
381	C₂³×C₆₇	—	4	8	no	—
382	C₂³×C₆₇	—	4	4	no	—
383	C₂³×C₆₇	—	4	4	no	—
384	C₂³×C₆₇	—	4	8	no	—
385	C₂³×C₆₇	—	4	8	no	—
386	C₂³×C₆₇	—	8	2	no	—
387	C₂³×C₆₇	—	8	2	no	—
388	C₂³×C₆₇	—	8	2	no	—
389	C₂³×C₆₇	—	8	2	no	—
390	C₂³×C₆₇	—	8	4	no	—
391	C₂³×C₆₇	—	8	4	no	—
392	C₂³×C₆₇	—	8	4	no	—
393	C₂³×C₆₇	—	8	4	no	—
394	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
395	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
396	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
397	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
398	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
399	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
400	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
401	D₄×C₆₇	—	2	16	no	—
402	D₄×C₆₇	—	2	16	no	—
403	D₄×C₆₇	—	4	8	no	—
404	D₄×C₆₇	—	4	8	no	—
405	D₄×C₆₇	—	4	4	no	—
406	D₄×C₆₇	—	4	4	no	—
407	D₄×C₆₇	—	4	8	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	1	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	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	1	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	4	4	no	—
447	C₂×C₄×C₆₇	—	4	4	no	—
448	C₂×C₄×C₆₇	—	4	8	no	—
449	C₂×C₄×C₆₇	—	4	4	no	—
450	C₂×C₄×C₆₇	—	4	4	no	—
451	C₂×C₄×C₆₇	—	8	4	no	—
452	C₂×C₄×C₆₇	—	8	4	no	—
453	C₂×C₄×C₆₇	—	8	2	no	—
454	C₂×C₄×C₆₇	—	8	2	no	—
455	C₂×C₄×C₆₇	—	8	4	no	—
456	C₂×C₄×C₆₇	—	8	4	no	—
457	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
460	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
461	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
462	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
463	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
464	C₂²×C₆₇	—	2	2	no	—
465	C₂²×C₆₇	—	2	2	no	—
466	C₂²×C₆₇	—	2	2	no	—
467	C₂²×C₆₇	—	2	2	no	—
468	C₂²×C₆₇	—	2	2	no	—
469	C₂²×C₆₇	—	2	2	no	—
470	C₂²×C₆₇	—	2	4	no	—
471	C₂²×C₆₇	—	2	4	no	—
472	C₂²×C₆₇	—	2	4	no	—
473	C₂²×C₆₇	—	2	4	no	—
474	C₂²×C₆₇	—	2	4	no	—
475	C₂²×C₆₇	—	2	4	no	—
476	C₂²×C₆₇	—	2	4	no	—
477	C₂²×C₆₇	—	2	4	no	—
478	C₂²×C₆₇	—	2	4	no	—
479	C₂²×C₆₇	—	4	2	no	—
480	C₂²×C₆₇	—	4	2	no	—
481	C₂²×C₆₇	—	4	2	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	—	4	2	no	—
484	C₂²×C₆₇	—	4	2	no	—
485	C₂²×C₆₇	—	4	2	no	—
486	C₂²×C₆₇	—	4	2	no	—
487	C₂²×C₆₇	—	4	2	no	—
488	C₂²×C₆₇	—	4	2	no	—
489	C₂²×C₆₇	—	4	2	no	—
490	C₂²×C₆₇	—	4	2	no	—
491	C₂²×C₆₇	—	8	8	no	—
492	C₂²×C₆₇	—	8	16	no	—
493	C₂²×C₆₇	#518	1	4	yes	—
494	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
495	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
498	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂²×C₆₇	#585	1	1	yes	characteristic
500	C₂²×C₆₇	#585	1	1	yes	characteristic
501	C₄×C₆₇	—	2	4	no	—
502	C₄×C₆₇	—	2	4	no	—
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	4	no	—
506	C₄×C₆₇	—	2	2	no	—
507	C₄×C₆₇	—	2	2	no	—
508	C₄×C₆₇	—	4	1	no	—
509	C₄×C₆₇	—	4	2	no	—
510	C₄×C₆₇	—	4	1	no	—
511	C₄×C₆₇	—	4	2	no	—
512	C₄×C₆₇	—	4	2	no	—
513	C₄×C₆₇	—	4	2	no	—
514	C₄×C₆₇	—	4	2	no	—
515	C₄×C₆₇	—	4	2	no	—
516	#34437	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
517	C₂×C₆₇	—	2	4	no	—
518	C₂×C₆₇	—	4	4	no	—
519	C₂×C₆₇	—	4	4	no	—
520	C₂×C₆₇	—	4	4	no	—
521	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
522	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂×C₆₇	#3534	1	1	yes	characteristic
525	C₂×C₆₇	#3537	1	1	yes	characteristic
526	C₂×C₆₇	#3558	1	1	yes	characteristic
527	C₂×C₆₇	#3560	1	1	yes	characteristic
528	C₂×#534	C₂×C₆₇	1	1	yes	characteristic
529	#2376	C₂×C₆₇	1	2	yes	complemented
530	#2375	C₂×C₆₇	1	2	yes	complemented
531	#2374	C₂×C₆₇	1	2	yes	complemented
532	#2364	C₂×C₆₇	1	2	yes	complemented
533	#2361	C₂×C₆₇	1	2	yes	complemented
534	#2358	C₂×C₆₇	1	2	yes	complemented
535	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
536	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
537	#2335	C₂×C₆₇	1	2	yes	complemented
538	#2335	C₂×C₆₇	1	2	yes	complemented
539	#2325	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#2325	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#2321	C₂×C₆₇	1	2	yes	complemented
542	#2321	C₂×C₆₇	1	2	yes	complemented
543	#2312	C₂×C₆₇	1	1	yes	characteristic, complemented
544	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
545	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
546	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
547	C₆₇	#34437	1	1	yes	characteristic, direct product factor, Sylow
548	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
549	#534	C₄×C₆₇	1	16	yes	complemented
550	C₂×#123	C₂²×C₆₇	1	2	yes	—
551	C₂×#123	C₂²×C₆₇	1	2	yes	—
552	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
553	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
554	C₂×#121	C₂²×C₆₇	1	2	yes	—
555	C₂×#120	C₂²×C₆₇	1	2	yes	—
556	C₂×#120	C₂²×C₆₇	1	2	yes	—
557	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
558	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
559	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
560	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
561	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
562	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
563	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
565	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
566	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
567	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
568	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
569	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
570	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	#390	C₂²×C₆₇	1	2	yes	—
572	#390	C₂²×C₆₇	1	2	yes	—
573	#390	C₂²×C₆₇	1	2	yes	—
574	#390	C₂²×C₆₇	1	2	yes	—
575	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	#390	C₂²×C₆₇	1	2	yes	complemented
577	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
579	#389	C₂²×C₆₇	1	2	yes	complemented
580	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
581	#388	C₂²×C₆₇	1	2	yes	complemented
582	#388	C₂²×C₆₇	1	2	yes	complemented
583	#388	C₂²×C₆₇	1	2	yes	complemented
584	#388	C₂²×C₆₇	1	2	yes	complemented
585	#388	C₂²×C₆₇	1	2	yes	complemented
586	#388	C₂²×C₆₇	1	2	yes	complemented
587	#388	C₂²×C₆₇	1	2	yes	complemented
588	#388	C₂²×C₆₇	1	2	yes	complemented
589	#388	C₂²×C₆₇	1	2	yes	complemented
590	#388	C₂²×C₆₇	1	2	yes	complemented
591	#388	C₂²×C₆₇	1	2	yes	complemented
592	#388	C₂²×C₆₇	1	2	yes	complemented
593	#388	C₂²×C₆₇	1	2	yes	complemented
594	#388	C₂²×C₆₇	1	2	yes	complemented
595	#388	C₂²×C₆₇	1	2	yes	complemented
596	#388	C₂²×C₆₇	1	2	yes	complemented
597	#387	C₂²×C₆₇	1	2	yes	complemented
598	#387	C₂²×C₆₇	1	2	yes	complemented
599	#387	C₂²×C₆₇	1	2	yes	complemented
600	#387	C₂²×C₆₇	1	2	yes	complemented
601	#386	C₂²×C₆₇	1	2	yes	—
602	#386	C₂²×C₆₇	1	2	yes	—
603	#386	C₂²×C₆₇	1	2	yes	—
604	#386	C₂²×C₆₇	1	2	yes	—
605	#386	C₂²×C₆₇	1	2	yes	complemented
606	#386	C₂²×C₆₇	1	2	yes	complemented
607	#386	C₂²×C₆₇	1	2	yes	complemented
608	#386	C₂²×C₆₇	1	2	yes	complemented
609	#386	C₂²×C₆₇	1	2	yes	complemented
610	#386	C₂²×C₆₇	1	2	yes	complemented
611	#386	C₂²×C₆₇	1	2	yes	complemented
612	#386	C₂²×C₆₇	1	2	yes	complemented
613	#385	C₂²×C₆₇	1	2	yes	complemented
614	#385	C₂²×C₆₇	1	2	yes	complemented
615	#385	C₂²×C₆₇	1	2	yes	complemented
616	#385	C₂²×C₆₇	1	2	yes	complemented
617	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
618	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#380	C₂²×C₆₇	1	2	yes	complemented
620	#380	C₂²×C₆₇	1	2	yes	complemented
621	#379	C₂²×C₆₇	1	2	yes	—
622	#379	C₂²×C₆₇	1	2	yes	complemented
623	#379	C₂²×C₆₇	1	2	yes	complemented
624	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
626	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
628	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
629	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
630	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
631	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
632	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
633	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
634	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
637	C₂⁵	C₂³×C₆₇	1	2	yes	—
638	C₂²×D₄	—	4	4	no	—
639	C₂²×D₄	—	4	4	no	—
640	C₂²×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
641	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
642	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
643	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
645	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
647	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
648	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
649	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
652	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
653	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
654	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
655	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
656	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
659	#123	C₂×C₄×C₆₇	1	16	yes	complemented
660	#123	C₂×C₄×C₆₇	1	16	yes	complemented
661	#121	C₂×C₄×C₆₇	1	8	yes	complemented
662	#121	C₂×C₄×C₆₇	1	8	yes	complemented
663	#121	C₂×C₄×C₆₇	1	16	yes	complemented
664	#120	C₂×C₄×C₆₇	1	16	yes	complemented
665	#120	C₂×C₄×C₆₇	1	16	yes	complemented
666	C₄×D₄	—	4	2	no	—
667	C₄×D₄	—	4	2	no	—
668	C₄×D₄	—	4	4	no	—
669	C₄×D₄	—	4	4	no	—
670	C₄×D₄	—	4	4	no	—
671	C₄×D₄	—	4	4	no	—
672	C₄×D₄	—	4	4	no	—
673	C₂×C₄⋊C₄	—	4	2	no	—
674	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₄	—	4	2	no	—
688	C₂×C₂²⋊C₄	—	4	2	no	—
689	C₂×C₂²⋊C₄	—	4	4	no	—
690	C₂×C₂²⋊C₄	—	4	4	no	—
691	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
692	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
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×C₄²	—	4	2	no	—
721	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
724	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
725	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
726	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
727	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
728	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
729	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
731	#95	C₂³×C₆₇	1	2	yes	—
732	#95	C₂³×C₆₇	1	2	yes	—
733	#95	C₂³×C₆₇	1	2	yes	—
734	#95	C₂³×C₆₇	1	2	yes	—
735	#95	C₂³×C₆₇	1	2	yes	—
736	#95	C₂³×C₆₇	1	2	yes	—
737	#95	C₂³×C₆₇	1	2	yes	—
738	#95	C₂³×C₆₇	1	2	yes	—
739	#95	C₂³×C₆₇	1	2	yes	—
740	#95	C₂³×C₆₇	1	2	yes	—
741	#95	C₂³×C₆₇	1	2	yes	—
742	#95	C₂³×C₆₇	1	2	yes	—
743	#95	C₂³×C₆₇	1	2	yes	—
744	#95	C₂³×C₆₇	1	2	yes	—
745	#95	C₂³×C₆₇	1	2	yes	—
746	#95	C₂³×C₆₇	1	2	yes	—
747	C₂⁴	—	2	2	no	—
748	C₂⁴	—	2	2	no	—
749	C₂⁴	—	4	1	no	—
750	C₂⁴	—	4	1	no	—
751	C₂⁴	—	4	2	no	—
752	C₂⁴	—	4	2	no	—
753	C₂⁴	—	4	2	no	—
754	C₂⁴	—	4	2	no	—
755	C₂⁴	—	4	1	no	—
756	C₂⁴	—	4	1	no	—
757	C₂⁴	—	4	2	no	—
758	C₂⁴	—	4	2	no	—
759	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
760	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
761	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
762	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
763	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
764	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	4	no	—
767	C₂×D₄	—	2	4	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	4	1	no	—
770	C₂×D₄	—	4	1	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	4	2	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	1	no	—
778	C₂×D₄	—	4	1	no	—
779	C₂×D₄	—	4	32	no	—
780	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
781	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
782	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
783	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
784	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
785	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
786	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	4	1	no	—
796	C₂²×C₄	—	4	1	no	—
797	C₂²×C₄	—	4	1	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	1	no	—
801	C₂²×C₄	—	4	1	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	1	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
818	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
819	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
820	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	1	no	—
838	C₄⋊C₄	—	4	1	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₄⋊C₄	—	4	2	no	—
842	C₄⋊C₄	—	4	2	no	—
843	C₄⋊C₄	—	4	1	no	—
844	C₄⋊C₄	—	4	1	no	—
845	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
846	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
847	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
848	C₂²⋊C₄	—	2	4	no	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	4	2	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
871	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
872	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
873	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
874	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
875	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	4	1	no	—
879	C₄²	—	4	1	no	—
880	C₄²	—	4	2	no	—
881	C₄²	—	4	2	no	—
882	C₄²	—	4	2	no	—
883	C₄²	—	4	2	no	—
884	C₄²	—	4	2	no	—
885	C₄²	—	4	2	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	8	no	—
909	C₂³	—	4	8	no	—
910	C₂³	—	4	4	no	—
911	C₂³	—	4	4	no	—
912	C₂³	—	4	8	no	—
913	C₂³	—	4	8	no	—
914	C₂³	—	8	2	no	—
915	C₂³	—	8	2	no	—
916	C₂³	—	8	2	no	—
917	C₂³	—	8	2	no	—
918	C₂³	—	8	4	no	—
919	C₂³	—	8	4	no	—
920	C₂³	—	8	4	no	—
921	C₂³	—	8	4	no	—
922	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
923	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
924	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
925	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
926	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
927	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
928	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
929	D₄	—	2	16	no	—
930	D₄	—	2	16	no	—
931	D₄	—	4	8	no	—
932	D₄	—	4	8	no	—
933	D₄	—	4	4	no	—
934	D₄	—	4	4	no	—
935	D₄	—	4	8	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	4	8	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	8	4	no	—
980	C₂×C₄	—	8	4	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	8	2	no	—
983	C₂×C₄	—	8	4	no	—
984	C₂×C₄	—	8	4	no	—
985	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
990	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
991	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	8	8	no	—
1020	C₂²	—	8	16	no	—
1021	C₂²	#518×C₆₇	1	4	yes	—
1022	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1023	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1024	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1025	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1026	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1027	C₂²	#585×C₆₇	1	1	yes	characteristic
1028	C₂²	#585×C₆₇	1	1	yes	characteristic
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	4	no	—
1032	C₄	—	2	4	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	4	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	2	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₂	—	2	4	no	—
1045	C₂	—	4	4	no	—
1046	C₂	—	4	4	no	—
1047	C₂	—	4	4	no	—
1048	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
1049	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1050	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1051	C₂	C₆₇×#3534	1	1	yes	characteristic
1052	C₂	C₆₇×#3537	1	1	yes	characteristic
1053	C₂	C₆₇×#3558	1	1	yes	characteristic
1054	C₂	C₆₇×#3560	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×#534×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. C₆₇×#2376	C₂	semidirect
3. C₆₇×#2375	C₂	semidirect
4. C₆₇×#2374	C₂	semidirect
5. C₆₇×#2364	C₂	semidirect
6. C₆₇×#2361	C₂	semidirect
7. C₆₇×#2358	C₂	semidirect
8. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
9. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
10. C₆₇×#2335	C₂	semidirect
11. C₆₇×#2335	C₂	semidirect
12. C₆₇×#2325	C₂	semidirect
13. C₆₇×#2325	C₂	semidirect
14. C₆₇×#2321	C₂	semidirect
15. C₆₇×#2321	C₂	semidirect
16. C₆₇×#2312	C₂	semidirect
17. C₄×#121×C₆₇	C₂	semidirect
18. C₄×#121×C₆₇	C₂	semidirect
19. C₂×#388×C₆₇	C₂	semidirect
21. #534×C₆₇	C₄	semidirect
29. C₂×C₄×D₄×C₆₇	C₂²	semidirect
30. C₂×C₄×D₄×C₆₇	C₂²	semidirect
31. C₂×C₄×D₄×C₆₇	C₂²	semidirect
32. C₂×C₄×D₄×C₆₇	C₂²	semidirect
33. C₂×C₄×D₄×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
35. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
42. C₂²×C₄²×C₆₇	C₂²	semidirect
47. #390×C₆₇	C₂²	semidirect
48. #390×C₆₇	C₂²	semidirect
49. #390×C₆₇	C₂²	semidirect
50. #389×C₆₇	C₂²	semidirect
51. #389×C₆₇	C₂²	semidirect
52. #389×C₆₇	C₂²	semidirect
53. #388×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #388×C₆₇	C₂²	semidirect
57. #388×C₆₇	C₂²	semidirect
58. #388×C₆₇	C₂²	semidirect
59. #388×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #388×C₆₇	C₂²	semidirect
63. #388×C₆₇	C₂²	semidirect
64. #388×C₆₇	C₂²	semidirect
65. #388×C₆₇	C₂²	semidirect
66. #388×C₆₇	C₂²	semidirect
67. #388×C₆₇	C₂²	semidirect
68. #388×C₆₇	C₂²	semidirect
69. #387×C₆₇	C₂²	semidirect
70. #387×C₆₇	C₂²	semidirect
71. #387×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
77. #386×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. #385×C₆₇	C₂²	semidirect
86. #385×C₆₇	C₂²	semidirect
87. #385×C₆₇	C₂²	semidirect
88. #385×C₆₇	C₂²	semidirect
89. #380×C₆₇	C₂²	semidirect
90. #380×C₆₇	C₂²	semidirect
91. #380×C₆₇	C₂²	semidirect
92. #380×C₆₇	C₂²	semidirect
94. #379×C₆₇	C₂²	semidirect
95. #379×C₆₇	C₂²	semidirect
96. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
98. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
99. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. C₂×#95×C₆₇	C₂²	semidirect
107. C₂×#95×C₆₇	C₂²	semidirect
112. C₂²×D₄×C₆₇	C₂×C₄	semidirect
131. #123×C₆₇	C₂×C₄	semidirect
132. #123×C₆₇	C₂×C₄	semidirect
133. #121×C₆₇	C₂×C₄	semidirect
134. #121×C₆₇	C₂×C₄	semidirect
135. #121×C₆₇	C₂×C₄	semidirect
136. #120×C₆₇	C₂×C₄	semidirect
137. #120×C₆₇	C₂×C₄	semidirect
163. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
516. #34437	C₆₇	direct (N × H)
529. #2376	C₂×C₆₇	semidirect
530. #2375	C₂×C₆₇	semidirect
531. #2374	C₂×C₆₇	semidirect
532. #2364	C₂×C₆₇	semidirect
533. #2361	C₂×C₆₇	semidirect
534. #2358	C₂×C₆₇	semidirect
535. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
536. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
537. #2335	C₂×C₆₇	semidirect
538. #2335	C₂×C₆₇	semidirect
539. #2325	C₂×C₆₇	semidirect
540. #2325	C₂×C₆₇	semidirect
541. #2321	C₂×C₆₇	semidirect
542. #2321	C₂×C₆₇	semidirect
543. #2312	C₂×C₆₇	semidirect
544. C₄×#121	C₂×C₆₇	semidirect
545. C₄×#121	C₂×C₆₇	semidirect
546. C₂×#388	C₂×C₆₇	semidirect
547. C₆₇	#34437	direct (N × H)
549. #534	C₄×C₆₇	semidirect
557. C₂×C₄×D₄	C₂²×C₆₇	semidirect
558. C₂×C₄×D₄	C₂²×C₆₇	semidirect
559. C₂×C₄×D₄	C₂²×C₆₇	semidirect
560. C₂×C₄×D₄	C₂²×C₆₇	semidirect
561. C₂×C₄×D₄	C₂²×C₆₇	semidirect
562. C₂×C₄×D₄	C₂²×C₆₇	semidirect
563. C₂×C₄×D₄	C₂²×C₆₇	semidirect
564. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
568. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
569. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
570. C₂²×C₄²	C₂²×C₆₇	semidirect
575. #390	C₂²×C₆₇	semidirect
576. #390	C₂²×C₆₇	semidirect
577. #390	C₂²×C₆₇	semidirect
578. #389	C₂²×C₆₇	semidirect
579. #389	C₂²×C₆₇	semidirect
580. #389	C₂²×C₆₇	semidirect
581. #388	C₂²×C₆₇	semidirect
582. #388	C₂²×C₆₇	semidirect
583. #388	C₂²×C₆₇	semidirect
584. #388	C₂²×C₆₇	semidirect
585. #388	C₂²×C₆₇	semidirect
586. #388	C₂²×C₆₇	semidirect
587. #388	C₂²×C₆₇	semidirect
588. #388	C₂²×C₆₇	semidirect
589. #388	C₂²×C₆₇	semidirect
590. #388	C₂²×C₆₇	semidirect
591. #388	C₂²×C₆₇	semidirect
592. #388	C₂²×C₆₇	semidirect
593. #388	C₂²×C₆₇	semidirect
594. #388	C₂²×C₆₇	semidirect
595. #388	C₂²×C₆₇	semidirect
596. #388	C₂²×C₆₇	semidirect
597. #387	C₂²×C₆₇	semidirect
598. #387	C₂²×C₆₇	semidirect
599. #387	C₂²×C₆₇	semidirect
600. #387	C₂²×C₆₇	semidirect
605. #386	C₂²×C₆₇	semidirect
606. #386	C₂²×C₆₇	semidirect
607. #386	C₂²×C₆₇	semidirect
608. #386	C₂²×C₆₇	semidirect
609. #386	C₂²×C₆₇	semidirect
610. #386	C₂²×C₆₇	semidirect
611. #386	C₂²×C₆₇	semidirect
612. #386	C₂²×C₆₇	semidirect
613. #385	C₂²×C₆₇	semidirect
614. #385	C₂²×C₆₇	semidirect
615. #385	C₂²×C₆₇	semidirect
616. #385	C₂²×C₆₇	semidirect
617. #380	C₂²×C₆₇	semidirect
618. #380	C₂²×C₆₇	semidirect
619. #380	C₂²×C₆₇	semidirect
620. #380	C₂²×C₆₇	semidirect
622. #379	C₂²×C₆₇	semidirect
623. #379	C₂²×C₆₇	semidirect
624. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
625. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
626. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
627. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
628. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
629. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
630. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
631. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
632. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
633. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
634. C₂×#95	C₂²×C₆₇	semidirect
635. C₂×#95	C₂²×C₆₇	semidirect
640. C₂²×D₄	C₂×C₄×C₆₇	semidirect
659. #123	C₂×C₄×C₆₇	semidirect
660. #123	C₂×C₄×C₆₇	semidirect
661. #121	C₂×C₄×C₆₇	semidirect
662. #121	C₂×C₄×C₆₇	semidirect
663. #121	C₂×C₄×C₆₇	semidirect
664. #120	C₂×C₄×C₆₇	semidirect
665. #120	C₂×C₄×C₆₇	semidirect
691. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#534×C₆₇	2
C₆₇×#2376	2
C₆₇×#2375	2
C₆₇×#2374	2
C₆₇×#2364	2
C₆₇×#2361	2
C₆₇×#2358	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2335	2
C₆₇×#2325	2
C₆₇×#2321	2
C₆₇×#2312	2
C₄×#121×C₆₇	2
C₂×#388×C₆₇	2
#34437	67

Subgroups — C67×#34437 #30713688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34437 #30713688