Subgroups — C₆₇×#34974 #30714225

Order 17152.

1918 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2532	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2529	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2508	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2479	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2474	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2426	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2396	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2395	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#126×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#124×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
21	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#126×C₆₇	C₂²	1	2	yes	—
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₆₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	2	yes	—
39	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
40	#400×C₆₇	C₂²	1	2	yes	—
41	#400×C₆₇	C₂²	1	2	yes	—
42	#399×C₆₇	C₂²	1	2	yes	—
43	#399×C₆₇	C₂²	1	2	yes	—
44	#398×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	—
49	#397×C₆₇	C₂²	1	2	yes	—
50	#396×C₆₇	C₂²	1	2	yes	—
51	#396×C₆₇	C₂²	1	2	yes	—
52	#395×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#394×C₆₇	C₂²	1	2	yes	—
55	#393×C₆₇	C₂²	1	2	yes	—
56	#391×C₆₇	C₂²	1	2	yes	—
57	#391×C₆₇	C₂²	1	2	yes	—
58	#391×C₆₇	C₂²	1	1	yes	characteristic
59	#391×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	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#390×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic
69	#389×C₆₇	C₂²	1	2	yes	—
70	#389×C₆₇	C₂²	1	1	yes	characteristic
71	#389×C₆₇	C₂²	1	1	yes	characteristic
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
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	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#384×C₆₇	C₂²	1	1	yes	characteristic
91	#383×C₆₇	C₂²	1	2	yes	—
92	#382×C₆₇	C₂²	1	2	yes	—
93	#382×C₆₇	C₂²	1	1	yes	characteristic
94	#380×C₆₇	C₂²	1	1	yes	characteristic
95	#380×C₆₇	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
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	#376×C₆₇	C₂²	1	1	yes	characteristic
119	#376×C₆₇	C₂²	1	1	yes	characteristic
120	C₄³×C₆₇	C₂²	1	1	yes	characteristic
121	C₄³×C₆₇	C₂²	1	1	yes	characteristic
122	C₄³×C₆₇	C₂²	1	2	yes	—
123	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₆₇	—	2	4	no	—
132	#126×C₆₇	—	2	8	no	—
133	#124×C₆₇	—	2	4	no	—
134	#124×C₆₇	—	2	8	no	—
135	C₂²⋊Q₈×C₆₇	—	2	4	no	—
136	#121×C₆₇	—	2	4	no	—
137	C₄×Q₈×C₆₇	—	2	4	no	—
138	C₄×Q₈×C₆₇	—	2	4	no	—
139	C₄×Q₈×C₆₇	—	2	4	no	—
140	C₄×Q₈×C₆₇	—	4	4	no	—
141	C₄×D₄×C₆₇	—	2	4	no	—
142	C₄×D₄×C₆₇	—	4	4	no	—
143	#117×C₆₇	—	2	4	no	—
144	#117×C₆₇	—	2	4	no	—
145	#117×C₆₇	—	4	4	no	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
188	C₂×C₄²×C₆₇	—	2	4	no	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	#95×C₆₇	C₂³	1	1	yes	characteristic
213	#95×C₆₇	C₂³	1	1	yes	characteristic
214	#95×C₆₇	C₂³	1	1	yes	characteristic
215	#95×C₆₇	C₂³	1	1	yes	characteristic
216	#95×C₆₇	C₂³	1	1	yes	characteristic
217	#95×C₆₇	C₂³	1	1	yes	characteristic
218	#95×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
239	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₆₇	—	2	2	no	—
241	C₂×Q₈×C₆₇	—	2	2	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	2	4	no	—
244	C₂×Q₈×C₆₇	—	4	2	no	—
245	C₂×Q₈×C₆₇	#41	1	4	yes	—
246	C₂×D₄×C₆₇	—	2	4	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	4	no	—
258	C₂²×C₄×C₆₇	—	2	2	no	—
259	C₂²×C₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	4	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	2	4	no	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	2	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	4	no	—
296	C₄⋊C₄×C₆₇	—	2	4	no	—
297	C₄⋊C₄×C₆₇	—	2	4	no	—
298	C₄⋊C₄×C₆₇	—	2	4	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	4	2	no	—
301	C₄⋊C₄×C₆₇	—	4	2	no	—
302	C₄⋊C₄×C₆₇	—	4	2	no	—
303	C₄⋊C₄×C₆₇	—	4	2	no	—
304	C₄⋊C₄×C₆₇	—	4	2	no	—
305	C₄⋊C₄×C₆₇	—	4	2	no	—
306	C₄⋊C₄×C₆₇	#41	1	4	yes	—
307	C₄⋊C₄×C₆₇	#41	1	4	yes	—
308	C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	4	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	4	2	no	—
323	C₂²⋊C₄×C₆₇	—	4	2	no	—
324	C₂²⋊C₄×C₆₇	—	4	2	no	—
325	C₂²⋊C₄×C₆₇	—	4	2	no	—
326	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	2	2	no	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	2	no	—
331	C₄²×C₆₇	—	2	2	no	—
332	C₄²×C₆₇	—	2	2	no	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	4	no	—
335	C₄²×C₆₇	—	2	4	no	—
336	C₄²×C₆₇	—	2	2	no	—
337	C₄²×C₆₇	—	2	2	no	—
338	C₄²×C₆₇	—	2	4	no	—
339	C₄²×C₆₇	—	2	4	no	—
340	C₄²×C₆₇	—	2	2	no	—
341	C₄²×C₆₇	—	2	4	no	—
342	C₄²×C₆₇	—	2	2	no	—
343	C₄²×C₆₇	—	2	2	no	—
344	C₄²×C₆₇	—	2	4	no	—
345	C₄²×C₆₇	—	2	4	no	—
346	C₄²×C₆₇	—	2	2	no	—
347	C₄²×C₆₇	—	2	2	no	—
348	C₄²×C₆₇	—	2	2	no	—
349	C₄²×C₆₇	#41	1	4	yes	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	1	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	C₂×#41	1	2	yes	—
364	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
365	Q₈×C₆₇	—	2	8	no	—
366	Q₈×C₆₇	—	4	8	no	—
367	D₄×C₆₇	—	4	8	no	—
368	D₄×C₆₇	—	4	4	no	—
369	C₂×C₄×C₆₇	—	2	8	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	1	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	2	no	—
411	C₂×C₄×C₆₇	—	2	2	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	—	4	4	no	—
420	C₂×C₄×C₆₇	—	4	4	no	—
421	C₂×C₄×C₆₇	—	4	8	no	—
422	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
423	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
424	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
425	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
426	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
427	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
428	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
429	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
430	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
431	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
432	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
433	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
434	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	4	1	no	—
440	C₂²×C₆₇	—	4	1	no	—
441	C₂²×C₆₇	—	4	1	no	—
442	C₂²×C₆₇	—	4	1	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	4	2	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
451	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
452	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
453	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
454	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
455	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
457	C₄×C₆₇	—	2	4	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	2	no	—
460	C₄×C₆₇	—	2	4	no	—
461	C₄×C₆₇	—	2	2	no	—
462	C₄×C₆₇	—	2	2	no	—
463	C₄×C₆₇	—	2	2	no	—
464	C₄×C₆₇	—	2	2	no	—
465	C₄×C₆₇	—	4	1	no	—
466	C₄×C₆₇	—	4	2	no	—
467	C₄×C₆₇	—	4	1	no	—
468	C₄×C₆₇	—	4	2	no	—
469	C₄×C₆₇	—	4	1	no	—
470	C₄×C₆₇	—	4	2	no	—
471	C₄×C₆₇	—	4	1	no	—
472	C₄×C₆₇	—	4	1	no	—
473	C₄×C₆₇	—	4	1	no	—
474	C₄×C₆₇	—	4	2	no	—
475	C₄×C₆₇	—	4	2	no	—
476	C₄×C₆₇	#529	1	4	yes	—
477	C₄×C₆₇	#542	1	4	yes	—
478	#34974	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₂×C₆₇	—	4	2	no	—
480	C₂×C₆₇	—	8	2	no	—
481	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
482	C₂×C₆₇	#3444	1	1	yes	characteristic
483	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
484	C₂×C₆₇	#3481	1	1	yes	characteristic
485	C₂×C₆₇	#3482	1	1	yes	characteristic
486	C₂×C₆₇	#3482	1	1	yes	characteristic
487	C₂×C₆₇	#3483	1	1	yes	characteristic
488	#2532	C₂×C₆₇	1	2	yes	complemented
489	#2529	C₂×C₆₇	1	2	yes	complemented
490	#2512	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#2508	C₂×C₆₇	1	1	yes	characteristic, complemented
492	#2495	C₂×C₆₇	1	1	yes	characteristic, complemented
493	#2491	C₂×C₆₇	1	1	yes	characteristic
494	#2479	C₂×C₆₇	1	2	yes	complemented
495	#2474	C₂×C₆₇	1	2	yes	complemented
496	#2451	C₂×C₆₇	1	1	yes	characteristic, complemented
497	#2448	C₂×C₆₇	1	1	yes	characteristic, complemented
498	#2426	C₂×C₆₇	1	1	yes	characteristic
499	#2423	C₂×C₆₇	1	1	yes	characteristic, complemented
500	#2396	C₂×C₆₇	1	2	yes	complemented
501	#2395	C₂×C₆₇	1	2	yes	complemented
502	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
503	C₄×#126	C₂×C₆₇	1	2	yes	complemented
504	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
505	C₄×#124	C₂×C₆₇	1	2	yes	complemented
506	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
507	C₄×#121	C₂×C₆₇	1	1	yes	characteristic
508	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
509	C₄²×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
510	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
511	C₆₇	#34974	1	1	yes	characteristic, direct product factor, Sylow
512	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
513	C₂×#126	C₂²×C₆₇	1	2	yes	—
514	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
515	C₂×#124	C₂²×C₆₇	1	2	yes	—
516	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
517	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
518	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
519	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
520	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
521	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
524	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
525	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×#117	C₂²×C₆₇	1	2	yes	—
527	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
528	#400	C₂²×C₆₇	1	2	yes	—
529	#400	C₂²×C₆₇	1	2	yes	—
530	#399	C₂²×C₆₇	1	2	yes	—
531	#399	C₂²×C₆₇	1	2	yes	—
532	#398	C₂²×C₆₇	1	2	yes	—
533	#398	C₂²×C₆₇	1	2	yes	—
534	#398	C₂²×C₆₇	1	2	yes	—
535	#397	C₂²×C₆₇	1	2	yes	—
536	#397	C₂²×C₆₇	1	2	yes	—
537	#397	C₂²×C₆₇	1	2	yes	—
538	#396	C₂²×C₆₇	1	2	yes	—
539	#396	C₂²×C₆₇	1	2	yes	—
540	#395	C₂²×C₆₇	1	2	yes	—
541	#394	C₂²×C₆₇	1	2	yes	—
542	#394	C₂²×C₆₇	1	2	yes	—
543	#393	C₂²×C₆₇	1	2	yes	—
544	#391	C₂²×C₆₇	1	2	yes	—
545	#391	C₂²×C₆₇	1	1	yes	characteristic
546	#391	C₂²×C₆₇	1	1	yes	characteristic
547	#391	C₂²×C₆₇	1	2	yes	—
548	#390	C₂²×C₆₇	1	2	yes	—
549	#390	C₂²×C₆₇	1	1	yes	characteristic
550	#390	C₂²×C₆₇	1	1	yes	characteristic
551	#390	C₂²×C₆₇	1	1	yes	characteristic
552	#390	C₂²×C₆₇	1	1	yes	characteristic
553	#389	C₂²×C₆₇	1	1	yes	characteristic
554	#389	C₂²×C₆₇	1	1	yes	characteristic
555	#389	C₂²×C₆₇	1	2	yes	—
556	#389	C₂²×C₆₇	1	1	yes	characteristic
557	#389	C₂²×C₆₇	1	1	yes	characteristic
558	#389	C₂²×C₆₇	1	1	yes	characteristic
559	#389	C₂²×C₆₇	1	1	yes	characteristic
560	#388	C₂²×C₆₇	1	2	yes	—
561	#388	C₂²×C₆₇	1	2	yes	—
562	#388	C₂²×C₆₇	1	2	yes	—
563	#388	C₂²×C₆₇	1	2	yes	—
564	#388	C₂²×C₆₇	1	2	yes	—
565	#388	C₂²×C₆₇	1	2	yes	—
566	#388	C₂²×C₆₇	1	2	yes	—
567	#388	C₂²×C₆₇	1	2	yes	—
568	#388	C₂²×C₆₇	1	2	yes	—
569	#388	C₂²×C₆₇	1	2	yes	—
570	#388	C₂²×C₆₇	1	2	yes	—
571	#388	C₂²×C₆₇	1	2	yes	—
572	#387	C₂²×C₆₇	1	2	yes	—
573	#387	C₂²×C₆₇	1	2	yes	—
574	#387	C₂²×C₆₇	1	2	yes	—
575	#387	C₂²×C₆₇	1	2	yes	—
576	#386	C₂²×C₆₇	1	2	yes	—
577	#385	C₂²×C₆₇	1	2	yes	—
578	#384	C₂²×C₆₇	1	1	yes	characteristic
579	#383	C₂²×C₆₇	1	2	yes	—
580	#382	C₂²×C₆₇	1	1	yes	characteristic
581	#382	C₂²×C₆₇	1	2	yes	—
582	#380	C₂²×C₆₇	1	1	yes	characteristic
583	#380	C₂²×C₆₇	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
586	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
594	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
595	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
596	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
597	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
598	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
599	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
600	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
603	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
604	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
605	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
606	#376	C₂²×C₆₇	1	1	yes	characteristic
607	#376	C₂²×C₆₇	1	1	yes	characteristic
608	C₄³	C₂²×C₆₇	1	2	yes	—
609	C₄³	C₂²×C₆₇	1	1	yes	characteristic
610	C₄³	C₂²×C₆₇	1	1	yes	characteristic
611	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
612	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
613	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
615	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
617	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₄⋊Q₈	—	2	4	no	—
620	#126	—	2	8	no	—
621	#124	—	2	4	no	—
622	#124	—	2	8	no	—
623	C₂²⋊Q₈	—	2	4	no	—
624	#121	—	2	4	no	—
625	C₄×Q₈	—	2	4	no	—
626	C₄×Q₈	—	2	4	no	—
627	C₄×Q₈	—	2	4	no	—
628	C₄×Q₈	—	4	4	no	—
629	C₄×D₄	—	2	4	no	—
630	C₄×D₄	—	4	4	no	—
631	#117	—	2	4	no	—
632	#117	—	2	4	no	—
633	#117	—	4	4	no	—
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
676	C₂×C₄²	—	2	4	no	—
677	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
679	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
684	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
686	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
689	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
700	#95	C₂³×C₆₇	1	1	yes	characteristic
701	#95	C₂³×C₆₇	1	1	yes	characteristic
702	#95	C₂³×C₆₇	1	1	yes	characteristic
703	#95	C₂³×C₆₇	1	1	yes	characteristic
704	#95	C₂³×C₆₇	1	1	yes	characteristic
705	#95	C₂³×C₆₇	1	1	yes	characteristic
706	#95	C₂³×C₆₇	1	1	yes	characteristic
707	#95	C₂³×C₆₇	1	1	yes	characteristic
708	#95	C₂³×C₆₇	1	2	yes	—
709	#95	C₂³×C₆₇	1	2	yes	—
710	#95	C₂³×C₆₇	1	2	yes	—
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	2	yes	—
713	#95	C₂³×C₆₇	1	2	yes	—
714	#95	C₂³×C₆₇	1	2	yes	—
715	#95	C₂³×C₆₇	1	2	yes	—
716	#95	C₂³×C₆₇	1	2	yes	—
717	#95	C₂³×C₆₇	1	2	yes	—
718	#95	C₂³×C₆₇	1	2	yes	—
719	#95	C₂³×C₆₇	1	2	yes	—
720	#95	C₂³×C₆₇	1	2	yes	—
721	#95	C₂³×C₆₇	1	2	yes	—
722	#95	C₂³×C₆₇	1	2	yes	—
723	#95	C₂³×C₆₇	1	2	yes	—
724	#95	C₂³×C₆₇	1	2	yes	—
725	#95	C₂³×C₆₇	1	2	yes	—
726	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
727	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	4	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	4	2	no	—
733	C₂×Q₈	#41×C₆₇	1	4	yes	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	#41×C₆₇	1	4	yes	—
795	C₄⋊C₄	#41×C₆₇	1	4	yes	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	4	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	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	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	#41×C₆₇	1	4	yes	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	4	no	—
823	C₄²	—	2	4	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	4	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	4	no	—
833	C₄²	—	2	4	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	#41×C₆₇	1	4	yes	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	C₂×#41×C₆₇	1	2	yes	—
852	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
853	Q₈	—	2	8	no	—
854	Q₈	—	4	8	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	4	no	—
857	C₂×C₄	—	2	8	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
911	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
912	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
913	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
914	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
915	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
916	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
917	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
918	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
919	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
920	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
921	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
922	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
923	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
939	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
940	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
941	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
942	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
943	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
944	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	#529×C₆₇	1	4	yes	—
965	C₄	#542×C₆₇	1	4	yes	—
966	C₂	—	4	2	no	—
967	C₂	—	8	2	no	—
968	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
969	C₂	C₆₇×#3444	1	1	yes	characteristic
970	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
971	C₂	C₆₇×#3481	1	1	yes	characteristic
972	C₂	C₆₇×#3482	1	1	yes	characteristic
973	C₂	C₆₇×#3482	1	1	yes	characteristic
974	C₂	C₆₇×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#121×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2532	C₂	semidirect
2. C₆₇×#2529	C₂	semidirect
3. C₆₇×#2512	C₂	semidirect
4. C₆₇×#2508	C₂	semidirect
5. C₆₇×#2495	C₂	semidirect
7. C₆₇×#2479	C₂	semidirect
8. C₆₇×#2474	C₂	semidirect
9. C₆₇×#2451	C₂	semidirect
10. C₆₇×#2448	C₂	semidirect
12. C₆₇×#2423	C₂	semidirect
13. C₆₇×#2396	C₂	semidirect
14. C₆₇×#2395	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
16. C₄×#126×C₆₇	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
18. C₄×#124×C₆₇	C₂	semidirect
19. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
21. C₆₇×#2293	C₂	semidirect
22. C₄²×Q₈×C₆₇	C₂	semidirect
23. C₄×#117×C₆₇	C₂	semidirect
478. #34974	C₆₇	direct (N × H)
488. #2532	C₂×C₆₇	semidirect
489. #2529	C₂×C₆₇	semidirect
490. #2512	C₂×C₆₇	semidirect
491. #2508	C₂×C₆₇	semidirect
492. #2495	C₂×C₆₇	semidirect
494. #2479	C₂×C₆₇	semidirect
495. #2474	C₂×C₆₇	semidirect
496. #2451	C₂×C₆₇	semidirect
497. #2448	C₂×C₆₇	semidirect
499. #2423	C₂×C₆₇	semidirect
500. #2396	C₂×C₆₇	semidirect
501. #2395	C₂×C₆₇	semidirect
502. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
503. C₄×#126	C₂×C₆₇	semidirect
504. C₄×#124	C₂×C₆₇	semidirect
505. C₄×#124	C₂×C₆₇	semidirect
506. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
508. #2293	C₂×C₆₇	semidirect
509. C₄²×Q₈	C₂×C₆₇	semidirect
510. C₄×#117	C₂×C₆₇	semidirect
511. C₆₇	#34974	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×#2532	2
C₆₇×#2529	2
C₆₇×#2512	2
C₆₇×#2508	2
C₆₇×#2495	2
C₆₇×#2491	2
C₆₇×#2479	2
C₆₇×#2474	2
C₆₇×#2451	2
C₆₇×#2448	2
C₆₇×#2426	2
C₆₇×#2423	2
C₆₇×#2396	2
C₆₇×#2395	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#126×C₆₇	2
C₄×#124×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2293	2
C₄²×Q₈×C₆₇	2
C₄×#117×C₆₇	2
#34974	67

Subgroups — C67×#34974 #30714225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34974 #30714225