Subgroups — C₆₇×#60038 #30739289

Order 17152.

2036 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2795	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2792	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2673	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2610	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2602	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2593	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2555	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2543	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2531	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2471	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2464	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2461	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2414	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2364	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2363	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
18	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2298	C₂	1	2	yes	maximal, complemented
20	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₇	C₂²	1	2	yes	—
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₇	C₂²	1	2	yes	—
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×#117×C₆₇	C₂²	1	2	yes	—
35	C₂×#117×C₆₇	C₂²	1	2	yes	—
36	#400×C₆₇	C₂²	1	1	yes	characteristic
37	#399×C₆₇	C₂²	1	1	yes	characteristic
38	#398×C₆₇	C₂²	1	2	yes	—
39	#398×C₆₇	C₂²	1	1	yes	characteristic
40	#397×C₆₇	C₂²	1	1	yes	characteristic
41	#397×C₆₇	C₂²	1	2	yes	—
42	#396×C₆₇	C₂²	1	2	yes	—
43	#395×C₆₇	C₂²	1	1	yes	characteristic
44	#395×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	1	yes	characteristic
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	—
49	#394×C₆₇	C₂²	1	2	yes	—
50	#393×C₆₇	C₂²	1	1	yes	characteristic
51	#392×C₆₇	C₂²	1	1	yes	characteristic
52	#392×C₆₇	C₂²	1	2	yes	—
53	#392×C₆₇	C₂²	1	2	yes	—
54	#392×C₆₇	C₂²	1	2	yes	—
55	#392×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	2	yes	—
57	#390×C₆₇	C₂²	1	1	yes	characteristic
58	#390×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	1	yes	characteristic
60	#390×C₆₇	C₂²	1	2	yes	—
61	#390×C₆₇	C₂²	1	2	yes	—
62	#390×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×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	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	2	yes	—
71	#388×C₆₇	C₂²	1	2	yes	—
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	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	2	yes	—
81	#387×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#384×C₆₇	C₂²	1	1	yes	characteristic
95	#380×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	#376×C₆₇	C₂²	1	2	yes	—
104	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
105	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
106	C₄³×C₆₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
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	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
123	#127×C₆₇	—	2	4	no	—
124	#124×C₆₇	—	4	4	no	—
125	#123×C₆₇	—	2	8	no	—
126	#123×C₆₇	—	4	4	no	—
127	C₂²⋊Q₈×C₆₇	—	4	2	no	—
128	#121×C₆₇	—	2	8	no	—
129	#121×C₆₇	—	2	8	no	—
130	#121×C₆₇	—	4	4	no	—
131	#121×C₆₇	—	4	2	no	—
132	C₄×D₄×C₆₇	—	4	4	no	—
133	C₄×D₄×C₆₇	—	4	4	no	—
134	C₄×D₄×C₆₇	—	4	2	no	—
135	C₄×D₄×C₆₇	—	4	2	no	—
136	C₄×D₄×C₆₇	—	4	4	no	—
137	#117×C₆₇	—	2	8	no	—
138	#117×C₆₇	—	4	4	no	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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×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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	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×C₄²×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	1	yes	characteristic
193	#95×C₆₇	C₂³	1	1	yes	characteristic
194	#95×C₆₇	C₂³	1	1	yes	characteristic
195	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
211	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
212	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₂×Q₈×C₆₇	—	4	1	no	—
215	C₂×Q₈×C₆₇	—	4	2	no	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	4	no	—
218	C₂×D₄×C₆₇	—	2	4	no	—
219	C₂×D₄×C₆₇	—	2	4	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	2	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	4	1	no	—
226	C₂×D₄×C₆₇	—	4	2	no	—
227	C₂×D₄×C₆₇	—	4	2	no	—
228	C₂×D₄×C₆₇	—	4	1	no	—
229	C₂×D₄×C₆₇	—	4	2	no	—
230	C₂×D₄×C₆₇	—	4	1	no	—
231	C₂×D₄×C₆₇	—	4	1	no	—
232	C₂×D₄×C₆₇	—	4	2	no	—
233	C₂×D₄×C₆₇	—	4	2	no	—
234	C₂×D₄×C₆₇	—	4	2	no	—
235	C₂×D₄×C₆₇	—	4	2	no	—
236	C₂×D₄×C₆₇	—	4	1	no	—
237	C₂×D₄×C₆₇	—	4	2	no	—
238	C₂×D₄×C₆₇	—	4	2	no	—
239	C₂×D₄×C₆₇	—	4	2	no	—
240	C₂×D₄×C₆₇	—	4	2	no	—
241	C₂×D₄×C₆₇	#41	1	4	yes	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	4	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	2	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	4	2	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	1	no	—
282	C₄⋊C₄×C₆₇	—	4	1	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	1	no	—
285	C₄⋊C₄×C₆₇	—	4	1	no	—
286	C₄⋊C₄×C₆₇	—	4	2	no	—
287	C₄⋊C₄×C₆₇	#41	1	8	yes	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	1	no	—
307	C₂²⋊C₄×C₆₇	—	4	1	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₂²⋊C₄×C₆₇	—	4	2	no	—
311	C₂²⋊C₄×C₆₇	—	4	2	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	2	4	no	—
315	C₄²×C₆₇	—	2	4	no	—
316	C₄²×C₆₇	—	2	2	no	—
317	C₄²×C₆₇	—	2	4	no	—
318	C₄²×C₆₇	—	2	4	no	—
319	C₄²×C₆₇	—	2	2	no	—
320	C₄²×C₆₇	—	4	1	no	—
321	C₄²×C₆₇	—	4	2	no	—
322	C₄²×C₆₇	—	4	2	no	—
323	C₄²×C₆₇	—	4	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	1	no	—
329	C₂³×C₆₇	—	2	1	no	—
330	C₂³×C₆₇	—	2	1	no	—
331	C₂³×C₆₇	—	2	1	no	—
332	C₂³×C₆₇	—	2	2	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	C₂×#41	1	2	yes	—
347	C₂³×C₆₇	C₂×#41	1	2	yes	—
348	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
349	Q₈×C₆₇	—	8	2	no	—
350	D₄×C₆₇	—	4	4	no	—
351	D₄×C₆₇	—	4	8	no	—
352	D₄×C₆₇	—	4	8	no	—
353	D₄×C₆₇	—	4	8	no	—
354	D₄×C₆₇	—	4	4	no	—
355	D₄×C₆₇	—	8	4	no	—
356	D₄×C₆₇	—	8	4	no	—
357	D₄×C₆₇	—	8	2	no	—
358	D₄×C₆₇	—	8	4	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	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	4	8	no	—
395	C₂×C₄×C₆₇	—	4	8	no	—
396	C₂×C₄×C₆₇	—	8	4	no	—
397	C₂×C₄×C₆₇	—	8	4	no	—
398	C₂×C₄×C₆₇	—	8	2	no	—
399	C₂×C₄×C₆₇	—	8	2	no	—
400	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
401	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
402	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
403	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
404	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
405	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
406	C₂²×C₆₇	—	2	4	no	—
407	C₂²×C₆₇	—	2	4	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	4	1	no	—
411	C₂²×C₆₇	—	4	1	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	1	no	—
415	C₂²×C₆₇	—	4	1	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	2	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	—	4	2	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	2	no	—
430	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
431	C₂²×C₆₇	C₂²×#41	1	2	yes	—
432	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
433	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂²×C₆₇	#585	1	1	yes	characteristic
435	C₄×C₆₇	—	2	4	no	—
436	C₄×C₆₇	—	2	4	no	—
437	C₄×C₆₇	—	2	4	no	—
438	C₄×C₆₇	—	2	4	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	2	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	1	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	1	no	—
449	C₄×C₆₇	—	4	2	no	—
450	#60038	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂×C₆₇	—	4	2	no	—
452	C₂×C₆₇	—	4	2	no	—
453	C₂×C₆₇	—	8	2	no	—
454	C₂×C₆₇	—	8	2	no	—
455	C₂×C₆₇	#3481	1	2	yes	—
456	C₂×C₆₇	#3483	1	1	yes	characteristic
457	C₂×C₆₇	#3494	1	2	yes	—
458	C₂×C₆₇	#3505	1	1	yes	characteristic
459	C₂×C₆₇	#3543	1	1	yes	characteristic
460	#2795	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2792	C₂×C₆₇	1	1	yes	characteristic, complemented
462	#2673	C₂×C₆₇	1	2	yes	complemented
463	#2610	C₂×C₆₇	1	2	yes	complemented
464	#2602	C₂×C₆₇	1	2	yes	complemented
465	#2593	C₂×C₆₇	1	1	yes	characteristic, complemented
466	#2564	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#2555	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#2543	C₂×C₆₇	1	1	yes	characteristic, complemented
469	#2531	C₂×C₆₇	1	2	yes	complemented
470	#2471	C₂×C₆₇	1	2	yes	complemented
471	#2464	C₂×C₆₇	1	2	yes	complemented
472	#2461	C₂×C₆₇	1	2	yes	complemented
473	#2414	C₂×C₆₇	1	2	yes	complemented
474	#2364	C₂×C₆₇	1	2	yes	complemented
475	#2363	C₂×C₆₇	1	2	yes	complemented
476	#2359	C₂×C₆₇	1	2	yes	complemented
477	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
478	#2298	C₂×C₆₇	1	2	yes	complemented
479	C₆₇	#60038	1	1	yes	characteristic, direct product factor, Sylow
480	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×#124	C₂²×C₆₇	1	2	yes	—
482	C₂×#123	C₂²×C₆₇	1	2	yes	—
483	C₂×#123	C₂²×C₆₇	1	2	yes	—
484	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
485	C₂×#121	C₂²×C₆₇	1	2	yes	—
486	C₂×#121	C₂²×C₆₇	1	2	yes	—
487	C₂×#121	C₂²×C₆₇	1	2	yes	—
488	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
492	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
493	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
494	C₂×#117	C₂²×C₆₇	1	2	yes	—
495	C₂×#117	C₂²×C₆₇	1	2	yes	—
496	#400	C₂²×C₆₇	1	1	yes	characteristic
497	#399	C₂²×C₆₇	1	1	yes	characteristic
498	#398	C₂²×C₆₇	1	1	yes	characteristic
499	#398	C₂²×C₆₇	1	2	yes	—
500	#397	C₂²×C₆₇	1	2	yes	—
501	#397	C₂²×C₆₇	1	1	yes	characteristic
502	#396	C₂²×C₆₇	1	2	yes	—
503	#395	C₂²×C₆₇	1	1	yes	characteristic
504	#395	C₂²×C₆₇	1	2	yes	—
505	#394	C₂²×C₆₇	1	2	yes	—
506	#394	C₂²×C₆₇	1	2	yes	—
507	#394	C₂²×C₆₇	1	2	yes	—
508	#394	C₂²×C₆₇	1	2	yes	—
509	#394	C₂²×C₆₇	1	1	yes	characteristic
510	#393	C₂²×C₆₇	1	1	yes	characteristic
511	#392	C₂²×C₆₇	1	2	yes	—
512	#392	C₂²×C₆₇	1	2	yes	—
513	#392	C₂²×C₆₇	1	1	yes	characteristic
514	#392	C₂²×C₆₇	1	2	yes	—
515	#392	C₂²×C₆₇	1	2	yes	—
516	#390	C₂²×C₆₇	1	1	yes	characteristic
517	#390	C₂²×C₆₇	1	2	yes	—
518	#390	C₂²×C₆₇	1	1	yes	characteristic
519	#390	C₂²×C₆₇	1	2	yes	—
520	#390	C₂²×C₆₇	1	2	yes	—
521	#390	C₂²×C₆₇	1	2	yes	—
522	#390	C₂²×C₆₇	1	2	yes	—
523	#389	C₂²×C₆₇	1	2	yes	—
524	#389	C₂²×C₆₇	1	2	yes	—
525	#388	C₂²×C₆₇	1	2	yes	—
526	#388	C₂²×C₆₇	1	2	yes	—
527	#388	C₂²×C₆₇	1	2	yes	—
528	#388	C₂²×C₆₇	1	2	yes	—
529	#388	C₂²×C₆₇	1	2	yes	—
530	#388	C₂²×C₆₇	1	2	yes	—
531	#388	C₂²×C₆₇	1	2	yes	—
532	#388	C₂²×C₆₇	1	2	yes	—
533	#388	C₂²×C₆₇	1	2	yes	—
534	#388	C₂²×C₆₇	1	2	yes	—
535	#388	C₂²×C₆₇	1	2	yes	—
536	#388	C₂²×C₆₇	1	2	yes	—
537	#388	C₂²×C₆₇	1	2	yes	—
538	#387	C₂²×C₆₇	1	2	yes	—
539	#387	C₂²×C₆₇	1	2	yes	—
540	#387	C₂²×C₆₇	1	2	yes	—
541	#387	C₂²×C₆₇	1	2	yes	—
542	#387	C₂²×C₆₇	1	2	yes	—
543	#387	C₂²×C₆₇	1	2	yes	—
544	#386	C₂²×C₆₇	1	2	yes	—
545	#386	C₂²×C₆₇	1	2	yes	—
546	#386	C₂²×C₆₇	1	2	yes	—
547	#386	C₂²×C₆₇	1	2	yes	—
548	#386	C₂²×C₆₇	1	2	yes	—
549	#386	C₂²×C₆₇	1	2	yes	—
550	#386	C₂²×C₆₇	1	2	yes	—
551	#386	C₂²×C₆₇	1	2	yes	—
552	#385	C₂²×C₆₇	1	2	yes	—
553	#385	C₂²×C₆₇	1	2	yes	—
554	#384	C₂²×C₆₇	1	1	yes	characteristic
555	#380	C₂²×C₆₇	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
557	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
562	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
563	#376	C₂²×C₆₇	1	2	yes	—
564	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
565	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
566	C₄³	C₂²×C₆₇	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
569	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
570	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
571	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
573	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
574	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
576	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
578	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
579	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
582	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
583	#127	—	2	4	no	—
584	#124	—	4	4	no	—
585	#123	—	2	8	no	—
586	#123	—	4	4	no	—
587	C₂²⋊Q₈	—	4	2	no	—
588	#121	—	2	8	no	—
589	#121	—	2	8	no	—
590	#121	—	4	4	no	—
591	#121	—	4	2	no	—
592	C₄×D₄	—	4	4	no	—
593	C₄×D₄	—	4	4	no	—
594	C₄×D₄	—	4	2	no	—
595	C₄×D₄	—	4	2	no	—
596	C₄×D₄	—	4	4	no	—
597	#117	—	2	8	no	—
598	#117	—	4	4	no	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	1	yes	characteristic
653	#95	C₂³×C₆₇	1	1	yes	characteristic
654	#95	C₂³×C₆₇	1	1	yes	characteristic
655	#95	C₂³×C₆₇	1	1	yes	characteristic
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	#95	C₂³×C₆₇	1	2	yes	—
670	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
671	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
672	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
673	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
674	C₂×Q₈	—	4	1	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	4	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	1	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	#41×C₆₇	1	4	yes	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	—	4	1	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₄⋊C₄	—	4	1	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	#41×C₆₇	1	8	yes	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	1	no	—
766	C₂²⋊C₄	—	4	1	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	4	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	1	no	—
783	C₄²	—	4	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	C₂×#41×C₆₇	1	2	yes	—
807	C₂³	C₂×#41×C₆₇	1	2	yes	—
808	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
809	Q₈	—	8	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	8	no	—
813	D₄	—	4	8	no	—
814	D₄	—	4	4	no	—
815	D₄	—	8	4	no	—
816	D₄	—	8	4	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	4	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	8	2	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	—	8	4	no	—
860	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
861	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
862	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
863	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
864	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
865	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
891	C₂²	C₂²×#41×C₆₇	1	2	yes	—
892	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
893	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
894	C₂²	#585×C₆₇	1	1	yes	characteristic
895	C₄	—	2	2	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	4	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₂	—	4	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	8	2	no	—
913	C₂	—	8	2	no	—
914	C₂	C₆₇×#3481	1	2	yes	—
915	C₂	C₆₇×#3483	1	1	yes	characteristic
916	C₂	C₆₇×#3494	1	2	yes	—
917	C₂	C₆₇×#3505	1	1	yes	characteristic
918	C₂	C₆₇×#3543	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×#2795	C₂	semidirect
2. C₆₇×#2792	C₂	semidirect
3. C₆₇×#2673	C₂	semidirect
4. C₆₇×#2610	C₂	semidirect
5. C₆₇×#2602	C₂	semidirect
6. C₆₇×#2593	C₂	semidirect
7. C₆₇×#2564	C₂	semidirect
8. C₆₇×#2555	C₂	semidirect
9. C₆₇×#2543	C₂	semidirect
10. C₆₇×#2531	C₂	semidirect
11. C₆₇×#2471	C₂	semidirect
12. C₆₇×#2464	C₂	semidirect
13. C₆₇×#2461	C₂	semidirect
14. C₆₇×#2414	C₂	semidirect
15. C₆₇×#2364	C₂	semidirect
16. C₆₇×#2363	C₂	semidirect
17. C₆₇×#2359	C₂	semidirect
18. C₄×#127×C₆₇	C₂	semidirect
19. C₆₇×#2298	C₂	semidirect
450. #60038	C₆₇	direct (N × H)
460. #2795	C₂×C₆₇	semidirect
461. #2792	C₂×C₆₇	semidirect
462. #2673	C₂×C₆₇	semidirect
463. #2610	C₂×C₆₇	semidirect
464. #2602	C₂×C₆₇	semidirect
465. #2593	C₂×C₆₇	semidirect
466. #2564	C₂×C₆₇	semidirect
467. #2555	C₂×C₆₇	semidirect
468. #2543	C₂×C₆₇	semidirect
469. #2531	C₂×C₆₇	semidirect
470. #2471	C₂×C₆₇	semidirect
471. #2464	C₂×C₆₇	semidirect
472. #2461	C₂×C₆₇	semidirect
473. #2414	C₂×C₆₇	semidirect
474. #2364	C₂×C₆₇	semidirect
475. #2363	C₂×C₆₇	semidirect
476. #2359	C₂×C₆₇	semidirect
477. C₄×#127	C₂×C₆₇	semidirect
478. #2298	C₂×C₆₇	semidirect
479. C₆₇	#60038	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×#2795	2
C₆₇×#2792	2
C₆₇×#2673	2
C₆₇×#2610	2
C₆₇×#2602	2
C₆₇×#2593	2
C₆₇×#2564	2
C₆₇×#2555	2
C₆₇×#2543	2
C₆₇×#2531	2
C₆₇×#2471	2
C₆₇×#2464	2
C₆₇×#2461	2
C₆₇×#2414	2
C₆₇×#2364	2
C₆₇×#2363	2
C₆₇×#2359	2
C₄×#127×C₆₇	2
C₆₇×#2298	2
#60038	67

Subgroups — C67×#60038 #30739289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60038 #30739289