Subgroups — C₆₇×#34909 #30714160

Order 17152.

2726 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2600	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2599	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2598	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2580	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2536	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2535	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2485	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2407	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2395	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₄×#121×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2290	C₂	1	4	yes	maximal, complemented
17	C₆₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
21	C₂×#121×C₆₇	C₂²	1	2	yes	—
22	C₄×#41×C₆₇	—	2	8	no	—
23	C₄×#41×C₆₇	—	2	8	no	—
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	4	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	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×#117×C₆₇	C₂²	1	2	yes	—
38	C₂×#117×C₆₇	C₂²	1	2	yes	—
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#400×C₆₇	C₂²	1	2	yes	—
45	#399×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	4	yes	—
49	#395×C₆₇	C₂²	1	2	yes	—
50	#394×C₆₇	C₂²	1	2	yes	—
51	#394×C₆₇	C₂²	1	4	yes	—
52	#394×C₆₇	C₂²	1	4	yes	—
53	#393×C₆₇	C₂²	1	2	yes	—
54	#392×C₆₇	C₂²	1	2	yes	—
55	#392×C₆₇	C₂²	1	4	yes	—
56	#391×C₆₇	C₂²	1	2	yes	—
57	#390×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	4	yes	—
61	#388×C₆₇	C₂²	1	4	yes	—
62	#388×C₆₇	C₂²	1	4	yes	—
63	#387×C₆₇	C₂²	1	4	yes	—
64	#387×C₆₇	C₂²	1	4	yes	—
65	#387×C₆₇	C₂²	1	4	yes	—
66	#386×C₆₇	C₂²	1	4	yes	—
67	#386×C₆₇	C₂²	1	4	yes	—
68	#386×C₆₇	C₂²	1	4	yes	—
69	#385×C₆₇	C₂²	1	4	yes	—
70	#385×C₆₇	C₂²	1	4	yes	—
71	#385×C₆₇	C₂²	1	4	yes	—
72	#383×C₆₇	C₂²	1	2	yes	—
73	#382×C₆₇	C₂²	1	1	yes	characteristic
74	#382×C₆₇	C₂²	1	1	yes	characteristic
75	#381×C₆₇	C₂²	1	2	yes	—
76	#380×C₆₇	C₂²	1	2	yes	—
77	#380×C₆₇	C₂²	1	2	yes	—
78	#380×C₆₇	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
84	#376×C₆₇	C₂²	1	2	yes	—
85	C₂×#41×C₆₇	—	2	4	no	—
86	C₂×#41×C₆₇	—	2	4	no	—
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	2	4	no	—
89	C₂×#41×C₆₇	—	2	8	no	—
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
98	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
103	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²⋊Q₈×C₆₇	—	2	8	no	—
107	#121×C₆₇	—	2	8	no	—
108	C₄×Q₈×C₆₇	—	2	4	no	—
109	C₄×Q₈×C₆₇	—	2	4	no	—
110	C₄×Q₈×C₆₇	—	2	4	no	—
111	C₄×Q₈×C₆₇	—	2	4	no	—
112	C₄×D₄×C₆₇	—	2	8	no	—
113	C₄×D₄×C₆₇	—	2	8	no	—
114	C₄×D₄×C₆₇	—	2	8	no	—
115	C₄×D₄×C₆₇	—	2	8	no	—
116	C₄×D₄×C₆₇	—	2	16	no	—
117	C₄×D₄×C₆₇	—	2	4	no	—
118	C₄×D₄×C₆₇	—	2	4	no	—
119	C₄×D₄×C₆₇	—	2	4	no	—
120	C₄×D₄×C₆₇	—	2	4	no	—
121	#117×C₆₇	—	2	4	no	—
122	#117×C₆₇	—	2	4	no	—
123	#117×C₆₇	—	2	8	no	—
124	#117×C₆₇	—	2	8	no	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₄²×C₆₇	—	2	8	no	—
152	C₂×C₄²×C₆₇	—	2	8	no	—
153	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
154	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	2	yes	—
168	#95×C₆₇	C₂³	1	4	yes	—
169	#95×C₆₇	C₂³	1	2	yes	—
170	#95×C₆₇	C₂³	1	2	yes	—
171	#95×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	#95×C₆₇	C₂³	1	4	yes	—
175	#95×C₆₇	C₂³	1	4	yes	—
176	#95×C₆₇	C₂³	1	4	yes	—
177	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
178	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
179	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
180	#41×C₆₇	—	2	32	no	—
181	#41×C₆₇	—	2	32	no	—
182	C₂×Q₈×C₆₇	—	2	2	no	—
183	C₂×Q₈×C₆₇	—	2	2	no	—
184	C₂×Q₈×C₆₇	—	2	4	no	—
185	C₂×Q₈×C₆₇	—	2	2	no	—
186	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
187	C₂×D₄×C₆₇	—	2	4	no	—
188	C₂×D₄×C₆₇	—	2	4	no	—
189	C₂×D₄×C₆₇	—	2	4	no	—
190	C₂×D₄×C₆₇	—	2	4	no	—
191	C₂×D₄×C₆₇	—	2	4	no	—
192	C₂×D₄×C₆₇	—	2	8	no	—
193	C₂×D₄×C₆₇	—	2	8	no	—
194	C₂×D₄×C₆₇	—	2	2	no	—
195	C₂×D₄×C₆₇	—	2	2	no	—
196	C₂×D₄×C₆₇	—	2	4	no	—
197	C₂×D₄×C₆₇	—	2	4	no	—
198	C₂×D₄×C₆₇	—	2	2	no	—
199	C₂×D₄×C₆₇	—	4	4	no	—
200	C₂×D₄×C₆₇	#41	1	4	yes	complemented
201	C₂²×C₄×C₆₇	—	2	4	no	—
202	C₂²×C₄×C₆₇	—	2	4	no	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	2	4	no	—
205	C₂²×C₄×C₆₇	—	2	2	no	—
206	C₂²×C₄×C₆₇	—	2	2	no	—
207	C₂²×C₄×C₆₇	—	2	4	no	—
208	C₂²×C₄×C₆₇	—	2	4	no	—
209	C₂²×C₄×C₆₇	—	2	4	no	—
210	C₂²×C₄×C₆₇	—	2	4	no	—
211	C₂²×C₄×C₆₇	—	2	4	no	—
212	C₂²×C₄×C₆₇	—	2	4	no	—
213	C₂²×C₄×C₆₇	—	2	8	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	2	4	no	—
216	C₂²×C₄×C₆₇	—	4	2	no	—
217	C₂²×C₄×C₆₇	—	4	2	no	—
218	C₂²×C₄×C₆₇	—	4	4	no	—
219	C₂²×C₄×C₆₇	—	4	2	no	—
220	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
221	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₆₇	#41	1	8	yes	complemented
224	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	2	no	—
243	C₄⋊C₄×C₆₇	—	2	2	no	—
244	C₄⋊C₄×C₆₇	—	2	2	no	—
245	C₄⋊C₄×C₆₇	—	2	2	no	—
246	C₄⋊C₄×C₆₇	—	2	8	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	8	no	—
250	C₄⋊C₄×C₆₇	—	4	4	no	—
251	C₂²⋊C₄×C₆₇	—	2	4	no	—
252	C₂²⋊C₄×C₆₇	—	2	4	no	—
253	C₂²⋊C₄×C₆₇	—	2	8	no	—
254	C₂²⋊C₄×C₆₇	—	2	8	no	—
255	C₂²⋊C₄×C₆₇	—	2	4	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	4	no	—
259	C₂²⋊C₄×C₆₇	—	2	8	no	—
260	C₂²⋊C₄×C₆₇	—	2	8	no	—
261	C₂²⋊C₄×C₆₇	—	4	4	no	—
262	C₂²⋊C₄×C₆₇	—	4	4	no	—
263	C₂²⋊C₄×C₆₇	—	4	4	no	—
264	C₄²×C₆₇	—	2	4	no	—
265	C₄²×C₆₇	—	2	4	no	—
266	C₄²×C₆₇	—	2	4	no	—
267	C₄²×C₆₇	—	2	4	no	—
268	C₄²×C₆₇	—	2	4	no	—
269	C₄²×C₆₇	—	2	4	no	—
270	C₄²×C₆₇	—	2	8	no	—
271	C₄²×C₆₇	C₂×D₄	1	4	yes	—
272	C₄²×C₆₇	C₂×D₄	1	4	yes	—
273	C₄²×C₆₇	C₂×D₄	1	4	yes	—
274	C₄²×C₆₇	C₂×D₄	1	4	yes	—
275	C₂³×C₆₇	—	2	2	no	—
276	C₂³×C₆₇	—	2	2	no	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	4	no	—
279	C₂³×C₆₇	—	2	1	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	2	1	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	4	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
290	C₂³×C₆₇	C₂×#41	1	4	yes	—
291	C₂³×C₆₇	C₂×#41	1	4	yes	—
292	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
293	Q₈×C₆₇	—	2	8	no	—
294	Q₈×C₆₇	—	2	8	no	—
295	D₄×C₆₇	—	2	8	no	—
296	D₄×C₆₇	—	2	16	no	—
297	D₄×C₆₇	—	2	16	no	—
298	D₄×C₆₇	—	2	8	no	—
299	D₄×C₆₇	—	4	16	no	—
300	C₂×C₄×C₆₇	—	2	16	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	1	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	8	no	—
311	C₂×C₄×C₆₇	—	2	8	no	—
312	C₂×C₄×C₆₇	—	2	16	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	4	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	4	no	—
322	C₂×C₄×C₆₇	—	2	4	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	4	no	—
327	C₂×C₄×C₆₇	—	2	4	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	4	4	no	—
330	C₂×C₄×C₆₇	—	4	8	no	—
331	C₂×C₄×C₆₇	—	4	8	no	—
332	C₂×C₄×C₆₇	—	4	8	no	—
333	C₂×C₄×C₆₇	—	4	8	no	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
341	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
342	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
343	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
344	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	2	no	—
347	C₂²×C₆₇	—	2	4	no	—
348	C₂²×C₆₇	—	2	4	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	2	4	no	—
351	C₂²×C₆₇	—	2	8	no	—
352	C₂²×C₆₇	—	2	4	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	2	no	—
356	C₂²×C₆₇	—	4	2	no	—
357	C₂²×C₆₇	—	4	2	no	—
358	C₂²×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	4	2	no	—
360	C₂²×C₆₇	—	4	4	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
363	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₆₇	C₂²×#41	1	2	yes	—
365	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
366	C₂²×C₆₇	#585	1	2	yes	—
367	C₄×C₆₇	—	2	2	no	—
368	C₄×C₆₇	—	2	2	no	—
369	C₄×C₆₇	—	2	4	no	—
370	C₄×C₆₇	—	2	4	no	—
371	C₄×C₆₇	—	2	2	no	—
372	C₄×C₆₇	—	2	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	4	no	—
378	C₄×C₆₇	—	4	4	no	—
379	C₄×C₆₇	#525	1	4	yes	—
380	C₄×C₆₇	#525	1	4	yes	—
381	#34909	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂×C₆₇	—	4	2	no	—
383	C₂×C₆₇	—	4	4	no	—
384	C₂×C₆₇	—	4	4	no	—
385	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
386	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
387	C₂×C₆₇	#3449	1	1	yes	characteristic
388	C₂×C₆₇	#3475	1	2	yes	—
389	C₂×C₆₇	#3480	1	2	yes	—
390	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#2600	C₂×C₆₇	1	4	yes	complemented
393	#2599	C₂×C₆₇	1	2	yes	complemented
394	#2598	C₂×C₆₇	1	2	yes	complemented
395	#2581	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#2580	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#2536	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#2535	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#2485	C₂×C₆₇	1	2	yes	complemented
400	#2407	C₂×C₆₇	1	2	yes	complemented
401	#2395	C₂×C₆₇	1	2	yes	complemented
402	#2388	C₂×C₆₇	1	2	yes	complemented
403	C₄×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	complemented
404	C₄×#121	C₂×C₆₇	1	2	yes	complemented
405	#2290	C₂×C₆₇	1	4	yes	complemented
406	#2283	C₂×C₆₇	1	1	yes	characteristic, complemented
407	C₆₇	#34909	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
409	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
410	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
411	C₂×#121	C₂²×C₆₇	1	2	yes	—
412	C₄×#41	—	2	8	no	—
413	C₄×#41	—	2	8	no	—
414	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
423	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
424	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×#117	C₂²×C₆₇	1	2	yes	—
428	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×#117	C₂²×C₆₇	1	2	yes	—
431	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
432	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
433	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
434	#400	C₂²×C₆₇	1	2	yes	—
435	#399	C₂²×C₆₇	1	2	yes	—
436	#398	C₂²×C₆₇	1	2	yes	—
437	#397	C₂²×C₆₇	1	2	yes	—
438	#397	C₂²×C₆₇	1	4	yes	—
439	#395	C₂²×C₆₇	1	2	yes	—
440	#394	C₂²×C₆₇	1	2	yes	—
441	#394	C₂²×C₆₇	1	4	yes	—
442	#394	C₂²×C₆₇	1	4	yes	—
443	#393	C₂²×C₆₇	1	2	yes	—
444	#392	C₂²×C₆₇	1	2	yes	—
445	#392	C₂²×C₆₇	1	4	yes	—
446	#391	C₂²×C₆₇	1	2	yes	—
447	#390	C₂²×C₆₇	1	2	yes	—
448	#389	C₂²×C₆₇	1	2	yes	—
449	#389	C₂²×C₆₇	1	2	yes	—
450	#388	C₂²×C₆₇	1	4	yes	—
451	#388	C₂²×C₆₇	1	4	yes	—
452	#388	C₂²×C₆₇	1	4	yes	—
453	#387	C₂²×C₆₇	1	4	yes	—
454	#387	C₂²×C₆₇	1	4	yes	—
455	#387	C₂²×C₆₇	1	4	yes	—
456	#386	C₂²×C₆₇	1	4	yes	—
457	#386	C₂²×C₆₇	1	4	yes	—
458	#386	C₂²×C₆₇	1	4	yes	—
459	#385	C₂²×C₆₇	1	4	yes	—
460	#385	C₂²×C₆₇	1	4	yes	—
461	#385	C₂²×C₆₇	1	4	yes	—
462	#383	C₂²×C₆₇	1	2	yes	—
463	#382	C₂²×C₆₇	1	1	yes	characteristic
464	#382	C₂²×C₆₇	1	1	yes	characteristic
465	#381	C₂²×C₆₇	1	2	yes	—
466	#380	C₂²×C₆₇	1	2	yes	—
467	#380	C₂²×C₆₇	1	2	yes	—
468	#380	C₂²×C₆₇	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
470	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
474	#376	C₂²×C₆₇	1	2	yes	—
475	C₂×#41	—	2	4	no	—
476	C₂×#41	—	2	4	no	—
477	C₂×#41	—	2	4	no	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	8	no	—
480	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
481	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
484	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
485	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
486	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
488	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
489	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
490	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
493	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
494	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
495	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
496	C₂²⋊Q₈	—	2	8	no	—
497	#121	—	2	8	no	—
498	C₄×Q₈	—	2	4	no	—
499	C₄×Q₈	—	2	4	no	—
500	C₄×Q₈	—	2	4	no	—
501	C₄×Q₈	—	2	4	no	—
502	C₄×D₄	—	2	8	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	8	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	2	16	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	4	no	—
510	C₄×D₄	—	2	4	no	—
511	#117	—	2	4	no	—
512	#117	—	2	4	no	—
513	#117	—	2	8	no	—
514	#117	—	2	8	no	—
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
541	C₂×C₄²	—	2	8	no	—
542	C₂×C₄²	—	2	8	no	—
543	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
544	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
545	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
546	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
548	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
549	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
551	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
555	#95	C₂³×C₆₇	1	4	yes	—
556	#95	C₂³×C₆₇	1	2	yes	—
557	#95	C₂³×C₆₇	1	2	yes	—
558	#95	C₂³×C₆₇	1	4	yes	—
559	#95	C₂³×C₆₇	1	2	yes	—
560	#95	C₂³×C₆₇	1	2	yes	—
561	#95	C₂³×C₆₇	1	4	yes	—
562	#95	C₂³×C₆₇	1	4	yes	—
563	#95	C₂³×C₆₇	1	4	yes	—
564	#95	C₂³×C₆₇	1	4	yes	—
565	#95	C₂³×C₆₇	1	4	yes	—
566	#95	C₂³×C₆₇	1	4	yes	—
567	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
568	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
569	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
570	#41	—	2	32	no	—
571	#41	—	2	32	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	8	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	#41×C₆₇	1	4	yes	complemented
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
611	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
612	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
613	C₂²×C₄	#41×C₆₇	1	8	yes	complemented
614	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
616	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	8	no	—
640	C₄⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	4	4	no	—
652	C₂²⋊C₄	—	4	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	8	no	—
661	C₄²	C₂×D₄×C₆₇	1	4	yes	—
662	C₄²	C₂×D₄×C₆₇	1	4	yes	—
663	C₄²	C₂×D₄×C₆₇	1	4	yes	—
664	C₄²	C₂×D₄×C₆₇	1	4	yes	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	2	no	—
679	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
680	C₂³	C₂×#41×C₆₇	1	4	yes	—
681	C₂³	C₂×#41×C₆₇	1	4	yes	—
682	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
683	Q₈	—	2	8	no	—
684	Q₈	—	2	8	no	—
685	D₄	—	2	8	no	—
686	D₄	—	2	16	no	—
687	D₄	—	2	16	no	—
688	D₄	—	2	8	no	—
689	D₄	—	4	16	no	—
690	C₂×C₄	—	2	16	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	16	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
730	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
731	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
732	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
733	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
734	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	8	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
753	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
754	C₂²	C₂²×#41×C₆₇	1	2	yes	—
755	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
756	C₂²	#585×C₆₇	1	2	yes	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	4	no	—
769	C₄	#525×C₆₇	1	4	yes	—
770	C₄	#525×C₆₇	1	4	yes	—
771	C₂	—	4	2	no	—
772	C₂	—	4	4	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
775	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
776	C₂	C₆₇×#3449	1	1	yes	characteristic
777	C₂	C₆₇×#3475	1	2	yes	—
778	C₂	C₆₇×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
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. C₂×C₄×#41×C₆₇	C₂	semidirect
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#2600	C₂	semidirect
4. C₆₇×#2599	C₂	semidirect
5. C₆₇×#2598	C₂	semidirect
6. C₆₇×#2581	C₂	semidirect
7. C₆₇×#2580	C₂	semidirect
8. C₆₇×#2536	C₂	semidirect
9. C₆₇×#2535	C₂	semidirect
10. C₆₇×#2485	C₂	semidirect
11. C₆₇×#2407	C₂	semidirect
12. C₆₇×#2395	C₂	semidirect
13. C₆₇×#2388	C₂	semidirect
14. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
15. C₄×#121×C₆₇	C₂	semidirect
16. C₆₇×#2290	C₂	semidirect
17. C₆₇×#2283	C₂	semidirect
153. C₂×C₄²×C₆₇	D₄	semidirect
186. C₂×Q₈×C₆₇	#41	semidirect
200. C₂×D₄×C₆₇	#41	semidirect
223. C₂²×C₄×C₆₇	#41	semidirect
381. #34909	C₆₇	direct (N × H)
390. C₂×C₄×#41	C₂×C₆₇	semidirect
391. C₂×C₄×#41	C₂×C₆₇	semidirect
392. #2600	C₂×C₆₇	semidirect
393. #2599	C₂×C₆₇	semidirect
394. #2598	C₂×C₆₇	semidirect
395. #2581	C₂×C₆₇	semidirect
396. #2580	C₂×C₆₇	semidirect
397. #2536	C₂×C₆₇	semidirect
398. #2535	C₂×C₆₇	semidirect
399. #2485	C₂×C₆₇	semidirect
400. #2407	C₂×C₆₇	semidirect
401. #2395	C₂×C₆₇	semidirect
402. #2388	C₂×C₆₇	semidirect
403. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
404. C₄×#121	C₂×C₆₇	semidirect
405. #2290	C₂×C₆₇	semidirect
406. #2283	C₂×C₆₇	semidirect
407. C₆₇	#34909	direct (N × H)
543. C₂×C₄²	D₄×C₆₇	semidirect
576. C₂×Q₈	#41×C₆₇	semidirect
590. C₂×D₄	#41×C₆₇	semidirect
613. C₂²×C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₆₇	2
C₆₇×#2600	2
C₆₇×#2599	2
C₆₇×#2598	2
C₆₇×#2581	2
C₆₇×#2580	2
C₆₇×#2536	2
C₆₇×#2535	2
C₆₇×#2485	2
C₆₇×#2407	2
C₆₇×#2395	2
C₆₇×#2388	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2290	2
C₆₇×#2283	2
#34909	67

Subgroups — C67×#34909 #30714160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34909 #30714160