Subgroups — C₆₇×#59854 #30739105

Order 17152.

1930 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2803	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2783	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2591	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2543	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2526	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2518	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2508	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2504	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2485	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2414	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2346	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#121×C₆₇	C₂²	1	2	yes	—
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
41	#400×C₆₇	C₂²	1	2	yes	—
42	#400×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#397×C₆₇	C₂²	1	2	yes	—
45	#397×C₆₇	C₂²	1	2	yes	—
46	#397×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	—
49	#396×C₆₇	C₂²	1	2	yes	—
50	#396×C₆₇	C₂²	1	2	yes	—
51	#394×C₆₇	C₂²	1	2	yes	—
52	#394×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#394×C₆₇	C₂²	1	2	yes	—
55	#394×C₆₇	C₂²	1	2	yes	—
56	#392×C₆₇	C₂²	1	2	yes	—
57	#390×C₆₇	C₂²	1	2	yes	—
58	#390×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	1	yes	characteristic
60	#390×C₆₇	C₂²	1	1	yes	characteristic
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#390×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	1	yes	characteristic
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	1	yes	characteristic
68	#389×C₆₇	C₂²	1	2	yes	—
69	#389×C₆₇	C₂²	1	1	yes	characteristic
70	#389×C₆₇	C₂²	1	2	yes	—
71	#389×C₆₇	C₂²	1	1	yes	characteristic
72	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	1	yes	characteristic
76	#388×C₆₇	C₂²	1	2	yes	—
77	#388×C₆₇	C₂²	1	2	yes	—
78	#388×C₆₇	C₂²	1	2	yes	—
79	#388×C₆₇	C₂²	1	1	yes	characteristic
80	#388×C₆₇	C₂²	1	2	yes	—
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×C₆₇	C₂²	1	2	yes	—
83	#388×C₆₇	C₂²	1	2	yes	—
84	#388×C₆₇	C₂²	1	2	yes	—
85	#388×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#387×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	1	yes	characteristic
91	#386×C₆₇	C₂²	1	2	yes	—
92	#386×C₆₇	C₂²	1	2	yes	—
93	#386×C₆₇	C₂²	1	2	yes	—
94	#386×C₆₇	C₂²	1	2	yes	—
95	#386×C₆₇	C₂²	1	2	yes	—
96	#386×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	1	yes	characteristic
98	#386×C₆₇	C₂²	1	2	yes	—
99	#383×C₆₇	C₂²	1	2	yes	—
100	#382×C₆₇	C₂²	1	2	yes	—
101	#382×C₆₇	C₂²	1	2	yes	—
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#382×C₆₇	C₂²	1	1	yes	characteristic
104	#381×C₆₇	C₂²	1	2	yes	—
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	1	yes	characteristic
107	#380×C₆₇	C₂²	1	1	yes	characteristic
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	#376×C₆₇	C₂²	1	2	yes	—
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
138	#121×C₆₇	—	2	4	no	—
139	#121×C₆₇	—	2	4	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	—	4	2	no	—
142	#121×C₆₇	—	4	4	no	—
143	#121×C₆₇	—	4	4	no	—
144	C₄×D₄×C₆₇	—	2	4	no	—
145	C₄×D₄×C₆₇	—	2	4	no	—
146	C₄×D₄×C₆₇	—	2	8	no	—
147	C₄×D₄×C₆₇	—	4	2	no	—
148	C₄×D₄×C₆₇	—	4	2	no	—
149	#117×C₆₇	—	2	4	no	—
150	#117×C₆₇	—	4	2	no	—
151	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
152	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
153	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
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	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₄²×C₆₇	—	4	2	no	—
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×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	1	yes	characteristic
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
241	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	2	4	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	4	1	no	—
258	C₂×D₄×C₆₇	—	4	1	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	—	4	2	no	—
262	C₂×D₄×C₆₇	—	4	2	no	—
263	C₂×D₄×C₆₇	—	4	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	4	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	4	no	—
277	C₂²×C₄×C₆₇	—	4	1	no	—
278	C₂²×C₄×C₆₇	—	4	1	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	1	no	—
281	C₂²×C₄×C₆₇	—	4	1	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	#41	1	4	yes	—
287	C₂²×C₄×C₆₇	#41	1	4	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₆₇	—	2	4	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	4	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	4	2	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₄⋊C₄×C₆₇	—	4	2	no	—
321	C₄⋊C₄×C₆₇	—	4	2	no	—
322	C₄⋊C₄×C₆₇	—	4	2	no	—
323	C₄⋊C₄×C₆₇	—	4	1	no	—
324	C₄⋊C₄×C₆₇	—	4	1	no	—
325	C₄⋊C₄×C₆₇	—	4	2	no	—
326	C₄⋊C₄×C₆₇	—	4	2	no	—
327	C₄⋊C₄×C₆₇	#41	1	4	yes	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	—	2	2	no	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
337	C₂²⋊C₄×C₆₇	—	2	2	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	4	1	no	—
340	C₂²⋊C₄×C₆₇	—	4	2	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	1	no	—
345	C₂²⋊C₄×C₆₇	—	4	2	no	—
346	C₂²⋊C₄×C₆₇	—	4	2	no	—
347	C₂²⋊C₄×C₆₇	—	4	1	no	—
348	C₂²⋊C₄×C₆₇	—	4	2	no	—
349	C₂²⋊C₄×C₆₇	—	4	1	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	C₄²×C₆₇	—	2	4	no	—
356	C₄²×C₆₇	—	2	4	no	—
357	C₄²×C₆₇	—	2	2	no	—
358	C₄²×C₆₇	—	2	2	no	—
359	C₄²×C₆₇	—	2	2	no	—
360	C₄²×C₆₇	—	2	2	no	—
361	C₄²×C₆₇	—	4	1	no	—
362	C₄²×C₆₇	—	4	1	no	—
363	C₄²×C₆₇	—	4	2	no	—
364	C₄²×C₆₇	—	4	2	no	—
365	C₄²×C₆₇	—	4	2	no	—
366	C₂³×C₆₇	—	2	1	no	—
367	C₂³×C₆₇	—	2	1	no	—
368	C₂³×C₆₇	—	2	1	no	—
369	C₂³×C₆₇	—	2	1	no	—
370	C₂³×C₆₇	—	2	1	no	—
371	C₂³×C₆₇	—	2	1	no	—
372	C₂³×C₆₇	—	2	1	no	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	2	2	no	—
375	C₂³×C₆₇	—	2	2	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	—	2	1	no	—
378	C₂³×C₆₇	—	2	1	no	—
379	C₂³×C₆₇	—	2	1	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	1	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	1	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	1	no	—
386	C₂³×C₆₇	—	2	2	no	—
387	C₂³×C₆₇	—	2	1	no	—
388	C₂³×C₆₇	—	2	2	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	C₂×#41	1	2	yes	—
392	C₂³×C₆₇	C₂×#41	1	2	yes	—
393	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
394	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
395	D₄×C₆₇	—	4	4	no	—
396	D₄×C₆₇	—	4	4	no	—
397	D₄×C₆₇	—	4	4	no	—
398	D₄×C₆₇	—	4	8	no	—
399	D₄×C₆₇	—	4	4	no	—
400	D₄×C₆₇	—	8	4	no	—
401	D₄×C₆₇	—	8	4	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	8	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	1	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	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	1	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	2	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	1	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	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	4	4	no	—
454	C₂×C₄×C₆₇	—	4	8	no	—
455	C₂×C₄×C₆₇	—	4	4	no	—
456	C₂×C₄×C₆₇	—	4	4	no	—
457	C₂×C₄×C₆₇	—	4	4	no	—
458	C₂×C₄×C₆₇	—	8	4	no	—
459	C₂×C₄×C₆₇	—	8	4	no	—
460	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
461	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
462	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
463	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
464	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
465	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
466	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
467	C₂²×C₆₇	—	2	2	no	—
468	C₂²×C₆₇	—	2	2	no	—
469	C₂²×C₆₇	—	2	2	no	—
470	C₂²×C₆₇	—	2	2	no	—
471	C₂²×C₆₇	—	2	2	no	—
472	C₂²×C₆₇	—	2	2	no	—
473	C₂²×C₆₇	—	4	1	no	—
474	C₂²×C₆₇	—	4	1	no	—
475	C₂²×C₆₇	—	4	2	no	—
476	C₂²×C₆₇	—	4	1	no	—
477	C₂²×C₆₇	—	4	1	no	—
478	C₂²×C₆₇	—	4	2	no	—
479	C₂²×C₆₇	—	4	1	no	—
480	C₂²×C₆₇	—	4	2	no	—
481	C₂²×C₆₇	—	4	1	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	—	4	1	no	—
484	C₂²×C₆₇	—	4	1	no	—
485	C₂²×C₆₇	—	4	1	no	—
486	C₂²×C₆₇	—	4	1	no	—
487	C₂²×C₆₇	—	4	2	no	—
488	C₂²×C₆₇	—	4	1	no	—
489	C₂²×C₆₇	—	4	2	no	—
490	C₂²×C₆₇	—	4	1	no	—
491	C₂²×C₆₇	—	4	1	no	—
492	C₂²×C₆₇	—	4	2	no	—
493	C₂²×C₆₇	—	4	1	no	—
494	C₂²×C₆₇	#555	1	4	yes	—
495	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
496	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
497	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²×C₆₇	#585	1	1	yes	characteristic
501	C₂²×C₆₇	#585	1	1	yes	characteristic
502	C₄×C₆₇	—	2	2	no	—
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	4	no	—
506	C₄×C₆₇	—	4	1	no	—
507	C₄×C₆₇	—	4	1	no	—
508	C₄×C₆₇	—	4	1	no	—
509	C₄×C₆₇	—	4	1	no	—
510	C₄×C₆₇	—	4	2	no	—
511	C₄×C₆₇	—	4	2	no	—
512	C₄×C₆₇	—	4	2	no	—
513	C₄×C₆₇	—	4	1	no	—
514	C₄×C₆₇	—	4	1	no	—
515	C₄×C₆₇	—	4	2	no	—
516	C₄×C₆₇	—	4	1	no	—
517	C₄×C₆₇	—	4	1	no	—
518	C₄×C₆₇	—	4	2	no	—
519	C₄×C₆₇	—	4	2	no	—
520	C₄×C₆₇	#553	1	4	yes	—
521	#59854	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
522	C₂×C₆₇	—	2	4	no	—
523	C₂×C₆₇	—	8	1	no	—
524	C₂×C₆₇	—	8	1	no	—
525	C₂×C₆₇	—	8	2	no	—
526	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
527	C₂×C₆₇	C₂×#555	1	1	yes	characteristic
528	C₂×C₆₇	#3480	1	1	yes	characteristic
529	C₂×C₆₇	#3505	1	1	yes	characteristic
530	C₂×C₆₇	#3512	1	1	yes	characteristic
531	C₂×C₆₇	#3513	1	1	yes	characteristic
532	C₂×C₆₇	#3542	1	1	yes	characteristic
533	#2803	C₂×C₆₇	1	2	yes	complemented
534	#2783	C₂×C₆₇	1	2	yes	complemented
535	#2591	C₂×C₆₇	1	2	yes	complemented
536	#2543	C₂×C₆₇	1	2	yes	complemented
537	#2526	C₂×C₆₇	1	2	yes	complemented
538	#2518	C₂×C₆₇	1	2	yes	complemented
539	#2513	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#2508	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#2504	C₂×C₆₇	1	2	yes	complemented
542	#2495	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#2485	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#2420	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#2416	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#2416	C₂×C₆₇	1	1	yes	characteristic, complemented
547	#2414	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#2363	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#2353	C₂×C₆₇	1	2	yes	complemented
550	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#2346	C₂×C₆₇	1	1	yes	characteristic, complemented
553	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
554	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
555	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
556	C₆₇	#59854	1	1	yes	characteristic, direct product factor, Sylow
557	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
558	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
559	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
560	C₂×#121	C₂²×C₆₇	1	2	yes	—
561	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×#121	C₂²×C₆₇	1	2	yes	—
563	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
566	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
568	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
569	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
570	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
571	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
572	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
573	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
574	#400	C₂²×C₆₇	1	2	yes	—
575	#400	C₂²×C₆₇	1	2	yes	—
576	#398	C₂²×C₆₇	1	2	yes	—
577	#397	C₂²×C₆₇	1	2	yes	—
578	#397	C₂²×C₆₇	1	2	yes	—
579	#397	C₂²×C₆₇	1	2	yes	—
580	#397	C₂²×C₆₇	1	2	yes	—
581	#397	C₂²×C₆₇	1	2	yes	—
582	#396	C₂²×C₆₇	1	2	yes	—
583	#396	C₂²×C₆₇	1	2	yes	—
584	#394	C₂²×C₆₇	1	2	yes	—
585	#394	C₂²×C₆₇	1	2	yes	—
586	#394	C₂²×C₆₇	1	2	yes	—
587	#394	C₂²×C₆₇	1	2	yes	—
588	#394	C₂²×C₆₇	1	2	yes	—
589	#392	C₂²×C₆₇	1	2	yes	—
590	#390	C₂²×C₆₇	1	1	yes	characteristic
591	#390	C₂²×C₆₇	1	2	yes	—
592	#390	C₂²×C₆₇	1	2	yes	—
593	#390	C₂²×C₆₇	1	1	yes	characteristic
594	#390	C₂²×C₆₇	1	1	yes	characteristic
595	#390	C₂²×C₆₇	1	1	yes	characteristic
596	#389	C₂²×C₆₇	1	1	yes	characteristic
597	#389	C₂²×C₆₇	1	1	yes	characteristic
598	#389	C₂²×C₆₇	1	1	yes	characteristic
599	#389	C₂²×C₆₇	1	1	yes	characteristic
600	#389	C₂²×C₆₇	1	1	yes	characteristic
601	#389	C₂²×C₆₇	1	1	yes	characteristic
602	#389	C₂²×C₆₇	1	1	yes	characteristic
603	#389	C₂²×C₆₇	1	2	yes	—
604	#389	C₂²×C₆₇	1	1	yes	characteristic
605	#389	C₂²×C₆₇	1	2	yes	—
606	#388	C₂²×C₆₇	1	2	yes	—
607	#388	C₂²×C₆₇	1	2	yes	—
608	#388	C₂²×C₆₇	1	2	yes	—
609	#388	C₂²×C₆₇	1	2	yes	—
610	#388	C₂²×C₆₇	1	2	yes	—
611	#388	C₂²×C₆₇	1	2	yes	—
612	#388	C₂²×C₆₇	1	2	yes	—
613	#388	C₂²×C₆₇	1	2	yes	—
614	#388	C₂²×C₆₇	1	2	yes	—
615	#388	C₂²×C₆₇	1	2	yes	—
616	#388	C₂²×C₆₇	1	1	yes	characteristic
617	#388	C₂²×C₆₇	1	1	yes	characteristic
618	#388	C₂²×C₆₇	1	2	yes	—
619	#387	C₂²×C₆₇	1	2	yes	—
620	#387	C₂²×C₆₇	1	2	yes	—
621	#387	C₂²×C₆₇	1	2	yes	—
622	#387	C₂²×C₆₇	1	2	yes	—
623	#386	C₂²×C₆₇	1	1	yes	characteristic
624	#386	C₂²×C₆₇	1	2	yes	—
625	#386	C₂²×C₆₇	1	2	yes	—
626	#386	C₂²×C₆₇	1	2	yes	—
627	#386	C₂²×C₆₇	1	2	yes	—
628	#386	C₂²×C₆₇	1	2	yes	—
629	#386	C₂²×C₆₇	1	2	yes	—
630	#386	C₂²×C₆₇	1	2	yes	—
631	#386	C₂²×C₆₇	1	1	yes	characteristic
632	#383	C₂²×C₆₇	1	2	yes	—
633	#382	C₂²×C₆₇	1	2	yes	—
634	#382	C₂²×C₆₇	1	1	yes	characteristic
635	#382	C₂²×C₆₇	1	1	yes	characteristic
636	#382	C₂²×C₆₇	1	2	yes	—
637	#381	C₂²×C₆₇	1	2	yes	—
638	#380	C₂²×C₆₇	1	1	yes	characteristic
639	#380	C₂²×C₆₇	1	1	yes	characteristic
640	#380	C₂²×C₆₇	1	1	yes	characteristic
641	#380	C₂²×C₆₇	1	1	yes	characteristic
642	#380	C₂²×C₆₇	1	1	yes	characteristic
643	#380	C₂²×C₆₇	1	1	yes	characteristic
644	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
645	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
646	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
647	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
648	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
649	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
650	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
651	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
652	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
653	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
654	#376	C₂²×C₆₇	1	2	yes	—
655	C₂×#95	C₂²×C₆₇	1	2	yes	—
656	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
659	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
661	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
662	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
663	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
666	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
668	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
670	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
671	#121	—	2	4	no	—
672	#121	—	2	4	no	—
673	#121	—	2	4	no	—
674	#121	—	4	2	no	—
675	#121	—	4	4	no	—
676	#121	—	4	4	no	—
677	C₄×D₄	—	2	4	no	—
678	C₄×D₄	—	2	4	no	—
679	C₄×D₄	—	2	8	no	—
680	C₄×D₄	—	4	2	no	—
681	C₄×D₄	—	4	2	no	—
682	#117	—	2	4	no	—
683	#117	—	4	2	no	—
684	C₂×C₄⋊C₄	—	2	4	no	—
685	C₂×C₄⋊C₄	—	4	2	no	—
686	C₂×C₄⋊C₄	—	4	4	no	—
687	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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×C₄²	—	4	2	no	—
736	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
737	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
738	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
743	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
744	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
745	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
747	#95	C₂³×C₆₇	1	2	yes	—
748	#95	C₂³×C₆₇	1	2	yes	—
749	#95	C₂³×C₆₇	1	2	yes	—
750	#95	C₂³×C₆₇	1	2	yes	—
751	#95	C₂³×C₆₇	1	1	yes	characteristic
752	#95	C₂³×C₆₇	1	2	yes	—
753	#95	C₂³×C₆₇	1	2	yes	—
754	#95	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
760	#95	C₂³×C₆₇	1	2	yes	—
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	1	yes	characteristic
763	#95	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
768	#95	C₂³×C₆₇	1	2	yes	—
769	#95	C₂³×C₆₇	1	2	yes	—
770	#95	C₂³×C₆₇	1	2	yes	—
771	#95	C₂³×C₆₇	1	2	yes	—
772	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
774	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	4	1	no	—
791	C₂×D₄	—	4	1	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	#41×C₆₇	1	4	yes	—
820	C₂²×C₄	#41×C₆₇	1	4	yes	—
821	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
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	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	1	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	—	4	2	no	—
859	C₄⋊C₄	—	4	1	no	—
860	C₄⋊C₄	#41×C₆₇	1	4	yes	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	1	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	1	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	1	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	—	4	2	no	—
884	C₂²⋊C₄	—	4	2	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	1	no	—
887	C₂²⋊C₄	—	4	2	no	—
888	C₄²	—	2	4	no	—
889	C₄²	—	2	4	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	1	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	C₂×#41×C₆₇	1	2	yes	—
925	C₂³	C₂×#41×C₆₇	1	2	yes	—
926	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
927	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
928	D₄	—	4	4	no	—
929	D₄	—	4	4	no	—
930	D₄	—	4	4	no	—
931	D₄	—	4	8	no	—
932	D₄	—	4	4	no	—
933	D₄	—	8	4	no	—
934	D₄	—	8	4	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	8	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	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	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	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	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	4	4	no	—
987	C₂×C₄	—	4	8	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	8	4	no	—
992	C₂×C₄	—	8	4	no	—
993	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
994	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
995	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
996	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
997	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
998	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
999	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	#555×C₆₇	1	4	yes	—
1028	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1029	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1030	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1031	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1032	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1033	C₂²	#585×C₆₇	1	1	yes	characteristic
1034	C₂²	#585×C₆₇	1	1	yes	characteristic
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	#553×C₆₇	1	4	yes	—
1054	C₂	—	2	4	no	—
1055	C₂	—	8	1	no	—
1056	C₂	—	8	2	no	—
1057	C₂	—	8	1	no	—
1058	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
1059	C₂	C₂×#555×C₆₇	1	1	yes	characteristic
1060	C₂	C₆₇×#3480	1	1	yes	characteristic
1061	C₂	C₆₇×#3505	1	1	yes	characteristic
1062	C₂	C₆₇×#3512	1	1	yes	characteristic
1063	C₂	C₆₇×#3513	1	1	yes	characteristic
1064	C₂	C₆₇×#3542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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. C₆₇×#2803	C₂	semidirect
2. C₆₇×#2783	C₂	semidirect
3. C₆₇×#2591	C₂	semidirect
4. C₆₇×#2543	C₂	semidirect
5. C₆₇×#2526	C₂	semidirect
6. C₆₇×#2518	C₂	semidirect
7. C₆₇×#2513	C₂	semidirect
8. C₆₇×#2508	C₂	semidirect
9. C₆₇×#2504	C₂	semidirect
10. C₆₇×#2495	C₂	semidirect
11. C₆₇×#2485	C₂	semidirect
12. C₆₇×#2420	C₂	semidirect
13. C₆₇×#2416	C₂	semidirect
14. C₆₇×#2416	C₂	semidirect
15. C₆₇×#2414	C₂	semidirect
16. C₆₇×#2363	C₂	semidirect
17. C₆₇×#2353	C₂	semidirect
18. C₆₇×#2352	C₂	semidirect
19. C₆₇×#2352	C₂	semidirect
20. C₆₇×#2346	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×#389×C₆₇	C₂	semidirect
521. #59854	C₆₇	direct (N × H)
533. #2803	C₂×C₆₇	semidirect
534. #2783	C₂×C₆₇	semidirect
535. #2591	C₂×C₆₇	semidirect
536. #2543	C₂×C₆₇	semidirect
537. #2526	C₂×C₆₇	semidirect
538. #2518	C₂×C₆₇	semidirect
539. #2513	C₂×C₆₇	semidirect
540. #2508	C₂×C₆₇	semidirect
541. #2504	C₂×C₆₇	semidirect
542. #2495	C₂×C₆₇	semidirect
543. #2485	C₂×C₆₇	semidirect
544. #2420	C₂×C₆₇	semidirect
545. #2416	C₂×C₆₇	semidirect
546. #2416	C₂×C₆₇	semidirect
547. #2414	C₂×C₆₇	semidirect
548. #2363	C₂×C₆₇	semidirect
549. #2353	C₂×C₆₇	semidirect
550. #2352	C₂×C₆₇	semidirect
551. #2352	C₂×C₆₇	semidirect
552. #2346	C₂×C₆₇	semidirect
553. C₄×#121	C₂×C₆₇	semidirect
554. C₄×#121	C₂×C₆₇	semidirect
555. C₂×#389	C₂×C₆₇	semidirect
556. C₆₇	#59854	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2803	2
C₆₇×#2783	2
C₆₇×#2591	2
C₆₇×#2543	2
C₆₇×#2526	2
C₆₇×#2518	2
C₆₇×#2513	2
C₆₇×#2508	2
C₆₇×#2504	2
C₆₇×#2495	2
C₆₇×#2485	2
C₆₇×#2420	2
C₆₇×#2416	2
C₆₇×#2414	2
C₆₇×#2363	2
C₆₇×#2353	2
C₆₇×#2352	2
C₆₇×#2346	2
C₄×#121×C₆₇	2
C₂×#389×C₆₇	2
#59854	67

Subgroups — C67×#59854 #30739105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59854 #30739105