Subgroups — C₆₇×#59744 #30738995

Order 17152.

1764 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2789	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2782	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2730	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2600	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2593	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2576	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2575	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2559	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2555	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#2536	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2525	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2510	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2367	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2364	C₂	1	2	yes	maximal, complemented
18	C₄×#126×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#124×C₆₇	C₂²	1	2	yes	—
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×#121×C₆₇	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	#401×C₆₇	C₂²	1	2	yes	—
31	#400×C₆₇	C₂²	1	1	yes	characteristic
32	#400×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	1	yes	characteristic
34	#400×C₆₇	C₂²	1	2	yes	—
35	#399×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	1	yes	characteristic
37	#398×C₆₇	C₂²	1	1	yes	characteristic
38	#397×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	2	yes	—
41	#396×C₆₇	C₂²	1	2	yes	—
42	#395×C₆₇	C₂²	1	1	yes	characteristic
43	#395×C₆₇	C₂²	1	1	yes	characteristic
44	#394×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	1	yes	characteristic
46	#394×C₆₇	C₂²	1	1	yes	characteristic
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	—
49	#392×C₆₇	C₂²	1	2	yes	—
50	#391×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	2	yes	—
53	#390×C₆₇	C₂²	1	1	yes	characteristic
54	#390×C₆₇	C₂²	1	2	yes	—
55	#389×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
61	#388×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#387×C₆₇	C₂²	1	2	yes	—
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	—
82	#386×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#385×C₆₇	C₂²	1	2	yes	—
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#383×C₆₇	C₂²	1	2	yes	—
89	#382×C₆₇	C₂²	1	1	yes	characteristic
90	#382×C₆₇	C₂²	1	1	yes	characteristic
91	#382×C₆₇	C₂²	1	1	yes	characteristic
92	#381×C₆₇	C₂²	1	2	yes	—
93	#380×C₆₇	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₄³×C₆₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
114	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
117	#126×C₆₇	—	2	8	no	—
118	#124×C₆₇	—	2	4	no	—
119	#124×C₆₇	—	2	8	no	—
120	C₂²⋊Q₈×C₆₇	—	2	8	no	—
121	#121×C₆₇	—	2	8	no	—
122	C₄×Q₈×C₆₇	—	4	2	no	—
123	C₄×Q₈×C₆₇	—	4	2	no	—
124	C₄×D₄×C₆₇	—	4	2	no	—
125	C₄×D₄×C₆₇	—	4	2	no	—
126	C₄×D₄×C₆₇	—	4	4	no	—
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	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	#95×C₆₇	C₂³	1	2	yes	—
177	#95×C₆₇	C₂³	1	2	yes	—
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	1	yes	characteristic
200	#95×C₆₇	C₂³	1	1	yes	characteristic
201	#95×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	2	yes	—
204	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
205	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₆₇	—	2	4	no	—
207	C₂×Q₈×C₆₇	—	4	1	no	—
208	C₂×Q₈×C₆₇	—	4	1	no	—
209	C₂×Q₈×C₆₇	—	4	1	no	—
210	C₂×Q₈×C₆₇	#41	1	4	yes	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	4	no	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	2	2	no	—
216	C₂×D₄×C₆₇	—	4	1	no	—
217	C₂×D₄×C₆₇	—	4	2	no	—
218	C₂×D₄×C₆₇	—	4	1	no	—
219	C₂×D₄×C₆₇	—	4	1	no	—
220	C₂×D₄×C₆₇	—	4	2	no	—
221	C₂×D₄×C₆₇	—	4	2	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	4	2	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	2	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	—	4	2	no	—
230	C₂²×C₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	4	2	no	—
232	C₂²×C₄×C₆₇	—	4	2	no	—
233	C₂²×C₄×C₆₇	—	4	2	no	—
234	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	—	2	4	no	—
259	C₄⋊C₄×C₆₇	—	4	2	no	—
260	C₄⋊C₄×C₆₇	—	4	2	no	—
261	C₄⋊C₄×C₆₇	—	4	2	no	—
262	C₄⋊C₄×C₆₇	—	4	1	no	—
263	C₄⋊C₄×C₆₇	—	4	1	no	—
264	C₄⋊C₄×C₆₇	—	4	1	no	—
265	C₄⋊C₄×C₆₇	—	4	1	no	—
266	C₄⋊C₄×C₆₇	—	4	1	no	—
267	C₄⋊C₄×C₆₇	—	4	1	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	no	—
277	C₂²⋊C₄×C₆₇	—	2	4	no	—
278	C₂²⋊C₄×C₆₇	—	2	4	no	—
279	C₂²⋊C₄×C₆₇	—	4	2	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	#41	1	8	yes	—
288	C₄²×C₆₇	—	2	4	no	—
289	C₄²×C₆₇	—	2	2	no	—
290	C₄²×C₆₇	—	2	4	no	—
291	C₄²×C₆₇	—	2	2	no	—
292	C₄²×C₆₇	—	2	2	no	—
293	C₄²×C₆₇	—	2	2	no	—
294	C₄²×C₆₇	—	4	1	no	—
295	C₄²×C₆₇	—	4	2	no	—
296	C₄²×C₆₇	—	4	2	no	—
297	C₄²×C₆₇	—	4	2	no	—
298	C₄²×C₆₇	—	4	2	no	—
299	C₄²×C₆₇	—	4	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	2	2	no	—
310	C₂³×C₆₇	—	2	2	no	—
311	C₂³×C₆₇	—	2	2	no	—
312	C₂³×C₆₇	—	2	2	no	—
313	C₂³×C₆₇	C₂×#41	1	4	yes	—
314	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
315	Q₈×C₆₇	—	4	4	no	—
316	Q₈×C₆₇	—	4	4	no	—
317	D₄×C₆₇	—	4	8	no	—
318	D₄×C₆₇	—	4	4	no	—
319	D₄×C₆₇	—	4	4	no	—
320	D₄×C₆₇	—	8	4	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	1	no	—
323	C₂×C₄×C₆₇	—	2	1	no	—
324	C₂×C₄×C₆₇	—	2	1	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	1	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	1	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	1	no	—
345	C₂×C₄×C₆₇	—	2	1	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	8	4	no	—
363	C₂×C₄×C₆₇	—	8	4	no	—
364	C₂×C₄×C₆₇	—	8	4	no	—
365	C₂×C₄×C₆₇	—	8	4	no	—
366	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
367	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
368	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
369	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
370	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
371	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
372	C₂²×C₆₇	—	2	4	no	—
373	C₂²×C₆₇	—	2	4	no	—
374	C₂²×C₆₇	—	2	4	no	—
375	C₂²×C₆₇	—	4	2	no	—
376	C₂²×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	4	2	no	—
378	C₂²×C₆₇	—	4	2	no	—
379	C₂²×C₆₇	—	4	2	no	—
380	C₂²×C₆₇	—	4	2	no	—
381	C₂²×C₆₇	—	4	2	no	—
382	C₂²×C₆₇	—	4	2	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
387	C₂²×C₆₇	C₂²×#41	1	2	yes	—
388	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂²×C₆₇	#585	1	2	yes	—
390	C₂²×C₆₇	#585	1	1	yes	characteristic
391	C₄×C₆₇	—	2	4	no	—
392	C₄×C₆₇	—	2	2	no	—
393	C₄×C₆₇	—	2	2	no	—
394	C₄×C₆₇	—	2	2	no	—
395	C₄×C₆₇	—	2	4	no	—
396	C₄×C₆₇	—	2	2	no	—
397	C₄×C₆₇	—	4	2	no	—
398	C₄×C₆₇	—	4	2	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	1	no	—
401	C₄×C₆₇	—	4	1	no	—
402	C₄×C₆₇	—	4	1	no	—
403	C₄×C₆₇	—	4	2	no	—
404	C₄×C₆₇	—	4	2	no	—
405	C₄×C₆₇	—	4	2	no	—
406	C₄×C₆₇	—	4	2	no	—
407	C₄×C₆₇	—	4	2	no	—
408	#59744	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
409	C₂×C₆₇	—	4	4	no	—
410	C₂×C₆₇	—	8	2	no	—
411	C₂×C₆₇	#3480	1	2	yes	—
412	C₂×C₆₇	#3481	1	1	yes	characteristic
413	C₂×C₆₇	#3505	1	1	yes	characteristic
414	C₂×C₆₇	#3521	1	2	yes	—
415	C₂×C₆₇	#3545	1	1	yes	characteristic
416	#2789	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#2782	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#2730	C₂×C₆₇	1	2	yes	complemented
419	#2600	C₂×C₆₇	1	2	yes	complemented
420	#2593	C₂×C₆₇	1	1	yes	characteristic, complemented
421	#2581	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#2576	C₂×C₆₇	1	2	yes	complemented
423	#2575	C₂×C₆₇	1	2	yes	complemented
424	#2559	C₂×C₆₇	1	2	yes	complemented
425	#2555	C₂×C₆₇	1	1	yes	characteristic
426	#2536	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#2525	C₂×C₆₇	1	2	yes	complemented
428	#2521	C₂×C₆₇	1	2	yes	complemented
429	#2510	C₂×C₆₇	1	2	yes	complemented
430	#2368	C₂×C₆₇	1	2	yes	complemented
431	#2367	C₂×C₆₇	1	2	yes	complemented
432	#2364	C₂×C₆₇	1	2	yes	complemented
433	C₄×#126	C₂×C₆₇	1	2	yes	complemented
434	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
435	C₆₇	#59744	1	1	yes	characteristic, direct product factor, Sylow
436	C₂×#126	C₂²×C₆₇	1	2	yes	—
437	C₂×#124	C₂²×C₆₇	1	2	yes	—
438	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
440	C₂×#121	C₂²×C₆₇	1	2	yes	—
441	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
445	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
446	#401	C₂²×C₆₇	1	2	yes	—
447	#400	C₂²×C₆₇	1	2	yes	—
448	#400	C₂²×C₆₇	1	2	yes	—
449	#400	C₂²×C₆₇	1	1	yes	characteristic
450	#400	C₂²×C₆₇	1	1	yes	characteristic
451	#399	C₂²×C₆₇	1	2	yes	—
452	#398	C₂²×C₆₇	1	1	yes	characteristic
453	#398	C₂²×C₆₇	1	1	yes	characteristic
454	#397	C₂²×C₆₇	1	2	yes	—
455	#397	C₂²×C₆₇	1	2	yes	—
456	#397	C₂²×C₆₇	1	2	yes	—
457	#396	C₂²×C₆₇	1	2	yes	—
458	#395	C₂²×C₆₇	1	1	yes	characteristic
459	#395	C₂²×C₆₇	1	1	yes	characteristic
460	#394	C₂²×C₆₇	1	2	yes	—
461	#394	C₂²×C₆₇	1	2	yes	—
462	#394	C₂²×C₆₇	1	2	yes	—
463	#394	C₂²×C₆₇	1	1	yes	characteristic
464	#394	C₂²×C₆₇	1	1	yes	characteristic
465	#392	C₂²×C₆₇	1	2	yes	—
466	#391	C₂²×C₆₇	1	2	yes	—
467	#391	C₂²×C₆₇	1	2	yes	—
468	#391	C₂²×C₆₇	1	1	yes	characteristic
469	#390	C₂²×C₆₇	1	1	yes	characteristic
470	#390	C₂²×C₆₇	1	2	yes	—
471	#389	C₂²×C₆₇	1	2	yes	—
472	#388	C₂²×C₆₇	1	2	yes	—
473	#388	C₂²×C₆₇	1	2	yes	—
474	#388	C₂²×C₆₇	1	2	yes	—
475	#388	C₂²×C₆₇	1	2	yes	—
476	#388	C₂²×C₆₇	1	2	yes	—
477	#388	C₂²×C₆₇	1	2	yes	—
478	#388	C₂²×C₆₇	1	2	yes	—
479	#388	C₂²×C₆₇	1	2	yes	—
480	#388	C₂²×C₆₇	1	2	yes	—
481	#388	C₂²×C₆₇	1	2	yes	—
482	#388	C₂²×C₆₇	1	2	yes	—
483	#388	C₂²×C₆₇	1	2	yes	—
484	#388	C₂²×C₆₇	1	2	yes	—
485	#387	C₂²×C₆₇	1	2	yes	—
486	#387	C₂²×C₆₇	1	2	yes	—
487	#387	C₂²×C₆₇	1	2	yes	—
488	#387	C₂²×C₆₇	1	2	yes	—
489	#387	C₂²×C₆₇	1	2	yes	—
490	#387	C₂²×C₆₇	1	2	yes	—
491	#387	C₂²×C₆₇	1	2	yes	—
492	#387	C₂²×C₆₇	1	2	yes	—
493	#387	C₂²×C₆₇	1	2	yes	—
494	#386	C₂²×C₆₇	1	2	yes	—
495	#386	C₂²×C₆₇	1	2	yes	—
496	#386	C₂²×C₆₇	1	2	yes	—
497	#386	C₂²×C₆₇	1	2	yes	—
498	#386	C₂²×C₆₇	1	2	yes	—
499	#386	C₂²×C₆₇	1	2	yes	—
500	#385	C₂²×C₆₇	1	2	yes	—
501	#385	C₂²×C₆₇	1	2	yes	—
502	#385	C₂²×C₆₇	1	2	yes	—
503	#385	C₂²×C₆₇	1	2	yes	—
504	#383	C₂²×C₆₇	1	2	yes	—
505	#382	C₂²×C₆₇	1	1	yes	characteristic
506	#382	C₂²×C₆₇	1	1	yes	characteristic
507	#382	C₂²×C₆₇	1	1	yes	characteristic
508	#381	C₂²×C₆₇	1	2	yes	—
509	#380	C₂²×C₆₇	1	2	yes	—
510	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
512	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
514	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
515	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
516	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
517	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
521	C₂×#95	C₂²×C₆₇	1	2	yes	—
522	C₄³	C₂²×C₆₇	1	1	yes	characteristic
523	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
524	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
527	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
529	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
530	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
531	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
532	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
533	#126	—	2	8	no	—
534	#124	—	2	4	no	—
535	#124	—	2	8	no	—
536	C₂²⋊Q₈	—	2	8	no	—
537	#121	—	2	8	no	—
538	C₄×Q₈	—	4	2	no	—
539	C₄×Q₈	—	4	2	no	—
540	C₄×D₄	—	4	2	no	—
541	C₄×D₄	—	4	2	no	—
542	C₄×D₄	—	4	4	no	—
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
580	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
587	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
588	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
592	#95	C₂³×C₆₇	1	2	yes	—
593	#95	C₂³×C₆₇	1	2	yes	—
594	#95	C₂³×C₆₇	1	2	yes	—
595	#95	C₂³×C₆₇	1	2	yes	—
596	#95	C₂³×C₆₇	1	2	yes	—
597	#95	C₂³×C₆₇	1	2	yes	—
598	#95	C₂³×C₆₇	1	2	yes	—
599	#95	C₂³×C₆₇	1	2	yes	—
600	#95	C₂³×C₆₇	1	2	yes	—
601	#95	C₂³×C₆₇	1	2	yes	—
602	#95	C₂³×C₆₇	1	2	yes	—
603	#95	C₂³×C₆₇	1	2	yes	—
604	#95	C₂³×C₆₇	1	2	yes	—
605	#95	C₂³×C₆₇	1	2	yes	—
606	#95	C₂³×C₆₇	1	2	yes	—
607	#95	C₂³×C₆₇	1	2	yes	—
608	#95	C₂³×C₆₇	1	2	yes	—
609	#95	C₂³×C₆₇	1	2	yes	—
610	#95	C₂³×C₆₇	1	2	yes	—
611	#95	C₂³×C₆₇	1	2	yes	—
612	#95	C₂³×C₆₇	1	2	yes	—
613	#95	C₂³×C₆₇	1	2	yes	—
614	#95	C₂³×C₆₇	1	2	yes	—
615	#95	C₂³×C₆₇	1	1	yes	characteristic
616	#95	C₂³×C₆₇	1	1	yes	characteristic
617	#95	C₂³×C₆₇	1	1	yes	characteristic
618	#95	C₂³×C₆₇	1	1	yes	characteristic
619	#95	C₂³×C₆₇	1	2	yes	—
620	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
621	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
622	C₂×Q₈	—	2	4	no	—
623	C₂×Q₈	—	4	1	no	—
624	C₂×Q₈	—	4	1	no	—
625	C₂×Q₈	—	4	1	no	—
626	C₂×Q₈	#41×C₆₇	1	4	yes	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	4	1	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	4	1	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	4	2	no	—
711	C₄²	—	4	2	no	—
712	C₄²	—	4	1	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	2	no	—
715	C₄²	—	4	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	C₂×#41×C₆₇	1	4	yes	—
730	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
731	Q₈	—	4	4	no	—
732	Q₈	—	4	4	no	—
733	D₄	—	4	8	no	—
734	D₄	—	4	4	no	—
735	D₄	—	4	4	no	—
736	D₄	—	8	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	8	4	no	—
779	C₂×C₄	—	8	4	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	—	8	4	no	—
782	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
783	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
784	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
785	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
786	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
787	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	C₂²×#41×C₆₇	1	2	yes	—
803	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
804	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
805	C₂²	#585×C₆₇	1	1	yes	characteristic
806	C₂²	#585×C₆₇	1	2	yes	—
807	C₄	—	2	4	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	4	no	—
810	C₄	—	2	2	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₂	—	4	4	no	—
825	C₂	—	8	2	no	—
826	C₂	C₆₇×#3480	1	2	yes	—
827	C₂	C₆₇×#3481	1	1	yes	characteristic
828	C₂	C₆₇×#3505	1	1	yes	characteristic
829	C₂	C₆₇×#3521	1	2	yes	—
830	C₂	C₆₇×#3545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2555	C₂
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×#2789	C₂	semidirect
2. C₆₇×#2782	C₂	semidirect
3. C₆₇×#2730	C₂	semidirect
4. C₆₇×#2600	C₂	semidirect
5. C₆₇×#2593	C₂	semidirect
6. C₆₇×#2581	C₂	semidirect
7. C₆₇×#2576	C₂	semidirect
8. C₆₇×#2575	C₂	semidirect
9. C₆₇×#2559	C₂	semidirect
11. C₆₇×#2536	C₂	semidirect
12. C₆₇×#2525	C₂	semidirect
13. C₆₇×#2521	C₂	semidirect
14. C₆₇×#2510	C₂	semidirect
15. C₆₇×#2368	C₂	semidirect
16. C₆₇×#2367	C₂	semidirect
17. C₆₇×#2364	C₂	semidirect
18. C₄×#126×C₆₇	C₂	semidirect
19. C₄×#124×C₆₇	C₂	semidirect
408. #59744	C₆₇	direct (N × H)
416. #2789	C₂×C₆₇	semidirect
417. #2782	C₂×C₆₇	semidirect
418. #2730	C₂×C₆₇	semidirect
419. #2600	C₂×C₆₇	semidirect
420. #2593	C₂×C₆₇	semidirect
421. #2581	C₂×C₆₇	semidirect
422. #2576	C₂×C₆₇	semidirect
423. #2575	C₂×C₆₇	semidirect
424. #2559	C₂×C₆₇	semidirect
426. #2536	C₂×C₆₇	semidirect
427. #2525	C₂×C₆₇	semidirect
428. #2521	C₂×C₆₇	semidirect
429. #2510	C₂×C₆₇	semidirect
430. #2368	C₂×C₆₇	semidirect
431. #2367	C₂×C₆₇	semidirect
432. #2364	C₂×C₆₇	semidirect
433. C₄×#126	C₂×C₆₇	semidirect
434. C₄×#124	C₂×C₆₇	semidirect
435. C₆₇	#59744	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×#2789	2
C₆₇×#2782	2
C₆₇×#2730	2
C₆₇×#2600	2
C₆₇×#2593	2
C₆₇×#2581	2
C₆₇×#2576	2
C₆₇×#2575	2
C₆₇×#2559	2
C₆₇×#2555	2
C₆₇×#2536	2
C₆₇×#2525	2
C₆₇×#2521	2
C₆₇×#2510	2
C₆₇×#2368	2
C₆₇×#2367	2
C₆₇×#2364	2
C₄×#126×C₆₇	2
C₄×#124×C₆₇	2
#59744	67

Subgroups — C67×#59744 #30738995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59744 #30738995