Subgroups — C₆₇×#59880 #30739131

Order 17152.

1780 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2808	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2805	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2804	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2682	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2610	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2600	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2599	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2595	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2573	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2572	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2525	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2458	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2363	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2343	C₂	1	2	yes	maximal, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#123×C₆₇	C₂²	1	2	yes	—
22	C₂×#121×C₆₇	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×#117×C₆₇	C₂²	1	2	yes	—
29	C₂×#117×C₆₇	C₂²	1	2	yes	—
30	#400×C₆₇	C₂²	1	2	yes	—
31	#400×C₆₇	C₂²	1	2	yes	—
32	#400×C₆₇	C₂²	1	2	yes	—
33	#398×C₆₇	C₂²	1	2	yes	—
34	#397×C₆₇	C₂²	1	2	yes	—
35	#397×C₆₇	C₂²	1	2	yes	—
36	#397×C₆₇	C₂²	1	2	yes	—
37	#396×C₆₇	C₂²	1	2	yes	—
38	#395×C₆₇	C₂²	1	2	yes	—
39	#394×C₆₇	C₂²	1	2	yes	—
40	#394×C₆₇	C₂²	1	2	yes	—
41	#394×C₆₇	C₂²	1	2	yes	—
42	#393×C₆₇	C₂²	1	2	yes	—
43	#393×C₆₇	C₂²	1	2	yes	—
44	#393×C₆₇	C₂²	1	2	yes	—
45	#392×C₆₇	C₂²	1	2	yes	—
46	#391×C₆₇	C₂²	1	1	yes	characteristic
47	#391×C₆₇	C₂²	1	1	yes	characteristic
48	#391×C₆₇	C₂²	1	1	yes	characteristic
49	#390×C₆₇	C₂²	1	1	yes	characteristic
50	#390×C₆₇	C₂²	1	1	yes	characteristic
51	#390×C₆₇	C₂²	1	1	yes	characteristic
52	#390×C₆₇	C₂²	1	2	yes	—
53	#390×C₆₇	C₂²	1	2	yes	—
54	#389×C₆₇	C₂²	1	2	yes	—
55	#389×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	1	yes	characteristic
58	#389×C₆₇	C₂²	1	1	yes	characteristic
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	#388×C₆₇	C₂²	1	2	yes	—
70	#388×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	#387×C₆₇	C₂²	1	2	yes	—
79	#387×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	#386×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	#385×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#383×C₆₇	C₂²	1	2	yes	—
91	#383×C₆₇	C₂²	1	2	yes	—
92	#382×C₆₇	C₂²	1	1	yes	characteristic
93	#381×C₆₇	C₂²	1	2	yes	—
94	#381×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	#376×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	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
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	#124×C₆₇	—	2	4	no	—
118	#123×C₆₇	—	2	8	no	—
119	#121×C₆₇	—	2	8	no	—
120	C₄×Q₈×C₆₇	—	2	4	no	—
121	C₄×Q₈×C₆₇	—	4	2	no	—
122	C₄×D₄×C₆₇	—	2	4	no	—
123	C₄×D₄×C₆₇	—	4	2	no	—
124	C₄×D₄×C₆₇	—	4	4	no	—
125	#117×C₆₇	—	2	8	no	—
126	#117×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	1	yes	characteristic
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	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
205	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₆₇	—	2	2	no	—
207	C₂×Q₈×C₆₇	—	2	2	no	—
208	C₂×Q₈×C₆₇	—	4	1	no	—
209	C₂×Q₈×C₆₇	—	4	1	no	—
210	C₂×Q₈×C₆₇	—	4	1	no	—
211	C₂×Q₈×C₆₇	—	4	1	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	1	no	—
221	C₂×D₄×C₆₇	—	4	2	no	—
222	C₂×D₄×C₆₇	—	4	2	no	—
223	C₂×D₄×C₆₇	#41	1	4	yes	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	4	no	—
228	C₂²×C₄×C₆₇	—	2	4	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	—	4	2	no	—
235	C₂²×C₄×C₆₇	—	4	2	no	—
236	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
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	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	2	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	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	4	1	no	—
261	C₄⋊C₄×C₆₇	—	4	1	no	—
262	C₄⋊C₄×C₆₇	—	4	1	no	—
263	C₄⋊C₄×C₆₇	—	4	1	no	—
264	C₄⋊C₄×C₆₇	—	4	2	no	—
265	C₄⋊C₄×C₆₇	—	4	2	no	—
266	C₄⋊C₄×C₆₇	—	4	2	no	—
267	C₄⋊C₄×C₆₇	—	4	1	no	—
268	C₄⋊C₄×C₆₇	—	4	1	no	—
269	C₄⋊C₄×C₆₇	—	4	2	no	—
270	C₄⋊C₄×C₆₇	#41	1	4	yes	—
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	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	2	4	no	—
281	C₂²⋊C₄×C₆₇	—	2	4	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	—	4	2	no	—
288	C₂²⋊C₄×C₆₇	—	4	2	no	—
289	C₂²⋊C₄×C₆₇	—	4	2	no	—
290	C₂²⋊C₄×C₆₇	—	4	2	no	—
291	C₄²×C₆₇	—	2	4	no	—
292	C₄²×C₆₇	—	2	2	no	—
293	C₄²×C₆₇	—	2	2	no	—
294	C₄²×C₆₇	—	2	4	no	—
295	C₄²×C₆₇	—	2	4	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	4	1	no	—
298	C₄²×C₆₇	—	4	2	no	—
299	C₄²×C₆₇	—	4	1	no	—
300	C₄²×C₆₇	—	4	1	no	—
301	C₄²×C₆₇	—	4	2	no	—
302	C₄²×C₆₇	—	4	2	no	—
303	C₄²×C₆₇	#41	1	4	yes	—
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	—	2	2	no	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	C₂×#41	1	4	yes	—
318	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
319	Q₈×C₆₇	—	4	4	no	—
320	Q₈×C₆₇	—	4	4	no	—
321	D₄×C₆₇	—	4	4	no	—
322	D₄×C₆₇	—	4	8	no	—
323	D₄×C₆₇	—	4	4	no	—
324	D₄×C₆₇	—	8	4	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	1	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	1	no	—
332	C₂×C₄×C₆₇	—	2	1	no	—
333	C₂×C₄×C₆₇	—	2	1	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	1	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	1	no	—
339	C₂×C₄×C₆₇	—	2	1	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	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	1	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	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	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	2	no	—
369	C₂×C₄×C₆₇	—	4	8	no	—
370	C₂×C₄×C₆₇	—	4	8	no	—
371	C₂×C₄×C₆₇	—	8	4	no	—
372	C₂×C₄×C₆₇	—	8	4	no	—
373	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
374	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
375	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
376	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
377	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
378	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
379	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	2	4	no	—
382	C₂²×C₆₇	—	2	4	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	4	2	no	—
389	C₂²×C₆₇	—	4	2	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	2	no	—
393	C₂²×C₆₇	—	4	2	no	—
394	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
397	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²×C₆₇	#585	1	1	yes	characteristic
399	C₂²×C₆₇	#585	1	1	yes	characteristic
400	C₂²×C₆₇	#585	1	1	yes	characteristic
401	C₄×C₆₇	—	2	2	no	—
402	C₄×C₆₇	—	2	2	no	—
403	C₄×C₆₇	—	2	4	no	—
404	C₄×C₆₇	—	2	2	no	—
405	C₄×C₆₇	—	2	2	no	—
406	C₄×C₆₇	—	2	2	no	—
407	C₄×C₆₇	—	2	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	—	4	1	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	2	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	—	4	2	no	—
415	C₄×C₆₇	—	4	2	no	—
416	C₄×C₆₇	—	4	2	no	—
417	C₄×C₆₇	—	4	2	no	—
418	#59880	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂×C₆₇	—	4	4	no	—
420	C₂×C₆₇	—	8	2	no	—
421	C₂×C₆₇	#3475	1	1	yes	characteristic
422	C₂×C₆₇	#3480	1	1	yes	characteristic
423	C₂×C₆₇	#3481	1	1	yes	characteristic
424	C₂×C₆₇	#3491	1	1	yes	characteristic
425	C₂×C₆₇	#3493	1	1	yes	characteristic
426	C₂×C₆₇	#3506	1	1	yes	characteristic
427	C₂×C₆₇	#3545	1	1	yes	characteristic
428	#2808	C₂×C₆₇	1	1	yes	characteristic, complemented
429	#2805	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#2804	C₂×C₆₇	1	1	yes	characteristic, complemented
431	#2682	C₂×C₆₇	1	1	yes	characteristic
432	#2610	C₂×C₆₇	1	2	yes	complemented
433	#2600	C₂×C₆₇	1	2	yes	complemented
434	#2599	C₂×C₆₇	1	2	yes	complemented
435	#2595	C₂×C₆₇	1	2	yes	complemented
436	#2573	C₂×C₆₇	1	2	yes	complemented
437	#2572	C₂×C₆₇	1	2	yes	complemented
438	#2525	C₂×C₆₇	1	2	yes	complemented
439	#2458	C₂×C₆₇	1	2	yes	complemented
440	#2444	C₂×C₆₇	1	2	yes	complemented
441	#2363	C₂×C₆₇	1	2	yes	complemented
442	#2359	C₂×C₆₇	1	2	yes	complemented
443	#2343	C₂×C₆₇	1	2	yes	complemented
444	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
447	C₆₇	#59880	1	1	yes	characteristic, direct product factor, Sylow
448	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×#123	C₂²×C₆₇	1	2	yes	—
450	C₂×#121	C₂²×C₆₇	1	2	yes	—
451	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
456	C₂×#117	C₂²×C₆₇	1	2	yes	—
457	C₂×#117	C₂²×C₆₇	1	2	yes	—
458	#400	C₂²×C₆₇	1	2	yes	—
459	#400	C₂²×C₆₇	1	2	yes	—
460	#400	C₂²×C₆₇	1	2	yes	—
461	#398	C₂²×C₆₇	1	2	yes	—
462	#397	C₂²×C₆₇	1	2	yes	—
463	#397	C₂²×C₆₇	1	2	yes	—
464	#397	C₂²×C₆₇	1	2	yes	—
465	#396	C₂²×C₆₇	1	2	yes	—
466	#395	C₂²×C₆₇	1	2	yes	—
467	#394	C₂²×C₆₇	1	2	yes	—
468	#394	C₂²×C₆₇	1	2	yes	—
469	#394	C₂²×C₆₇	1	2	yes	—
470	#393	C₂²×C₆₇	1	2	yes	—
471	#393	C₂²×C₆₇	1	2	yes	—
472	#393	C₂²×C₆₇	1	2	yes	—
473	#392	C₂²×C₆₇	1	2	yes	—
474	#391	C₂²×C₆₇	1	1	yes	characteristic
475	#391	C₂²×C₆₇	1	1	yes	characteristic
476	#391	C₂²×C₆₇	1	1	yes	characteristic
477	#390	C₂²×C₆₇	1	2	yes	—
478	#390	C₂²×C₆₇	1	2	yes	—
479	#390	C₂²×C₆₇	1	1	yes	characteristic
480	#390	C₂²×C₆₇	1	1	yes	characteristic
481	#390	C₂²×C₆₇	1	1	yes	characteristic
482	#389	C₂²×C₆₇	1	1	yes	characteristic
483	#389	C₂²×C₆₇	1	1	yes	characteristic
484	#389	C₂²×C₆₇	1	2	yes	—
485	#389	C₂²×C₆₇	1	1	yes	characteristic
486	#389	C₂²×C₆₇	1	1	yes	characteristic
487	#388	C₂²×C₆₇	1	2	yes	—
488	#388	C₂²×C₆₇	1	2	yes	—
489	#388	C₂²×C₆₇	1	2	yes	—
490	#388	C₂²×C₆₇	1	2	yes	—
491	#388	C₂²×C₆₇	1	2	yes	—
492	#388	C₂²×C₆₇	1	2	yes	—
493	#388	C₂²×C₆₇	1	2	yes	—
494	#388	C₂²×C₆₇	1	2	yes	—
495	#388	C₂²×C₆₇	1	2	yes	—
496	#388	C₂²×C₆₇	1	2	yes	—
497	#388	C₂²×C₆₇	1	2	yes	—
498	#388	C₂²×C₆₇	1	2	yes	—
499	#387	C₂²×C₆₇	1	2	yes	—
500	#387	C₂²×C₆₇	1	2	yes	—
501	#387	C₂²×C₆₇	1	2	yes	—
502	#387	C₂²×C₆₇	1	2	yes	—
503	#387	C₂²×C₆₇	1	2	yes	—
504	#387	C₂²×C₆₇	1	2	yes	—
505	#387	C₂²×C₆₇	1	2	yes	—
506	#387	C₂²×C₆₇	1	2	yes	—
507	#387	C₂²×C₆₇	1	2	yes	—
508	#386	C₂²×C₆₇	1	2	yes	—
509	#386	C₂²×C₆₇	1	2	yes	—
510	#386	C₂²×C₆₇	1	2	yes	—
511	#386	C₂²×C₆₇	1	2	yes	—
512	#386	C₂²×C₆₇	1	2	yes	—
513	#385	C₂²×C₆₇	1	2	yes	—
514	#385	C₂²×C₆₇	1	2	yes	—
515	#385	C₂²×C₆₇	1	2	yes	—
516	#385	C₂²×C₆₇	1	2	yes	—
517	#385	C₂²×C₆₇	1	2	yes	—
518	#383	C₂²×C₆₇	1	2	yes	—
519	#383	C₂²×C₆₇	1	2	yes	—
520	#382	C₂²×C₆₇	1	1	yes	characteristic
521	#381	C₂²×C₆₇	1	2	yes	—
522	#381	C₂²×C₆₇	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
527	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
529	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
530	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
532	#376	C₂²×C₆₇	1	2	yes	—
533	C₂×#95	C₂²×C₆₇	1	2	yes	—
534	C₄³	C₂²×C₆₇	1	1	yes	characteristic
535	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
538	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
540	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
542	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
543	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
544	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
545	#124	—	2	4	no	—
546	#123	—	2	8	no	—
547	#121	—	2	8	no	—
548	C₄×Q₈	—	2	4	no	—
549	C₄×Q₈	—	4	2	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	4	2	no	—
552	C₄×D₄	—	4	4	no	—
553	#117	—	2	8	no	—
554	#117	—	4	4	no	—
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
616	#95	C₂³×C₆₇	1	2	yes	—
617	#95	C₂³×C₆₇	1	2	yes	—
618	#95	C₂³×C₆₇	1	2	yes	—
619	#95	C₂³×C₆₇	1	2	yes	—
620	#95	C₂³×C₆₇	1	2	yes	—
621	#95	C₂³×C₆₇	1	2	yes	—
622	#95	C₂³×C₆₇	1	2	yes	—
623	#95	C₂³×C₆₇	1	2	yes	—
624	#95	C₂³×C₆₇	1	2	yes	—
625	#95	C₂³×C₆₇	1	2	yes	—
626	#95	C₂³×C₆₇	1	2	yes	—
627	#95	C₂³×C₆₇	1	2	yes	—
628	#95	C₂³×C₆₇	1	2	yes	—
629	#95	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
633	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	4	1	no	—
637	C₂×Q₈	—	4	1	no	—
638	C₂×Q₈	—	4	1	no	—
639	C₂×Q₈	—	4	1	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	4	1	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	#41×C₆₇	1	4	yes	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	1	no	—
694	C₄⋊C₄	—	4	1	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	#41×C₆₇	1	4	yes	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
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	4	no	—
708	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	4	2	no	—
726	C₄²	—	4	2	no	—
727	C₄²	—	4	1	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	1	no	—
730	C₄²	—	4	1	no	—
731	C₄²	#41×C₆₇	1	4	yes	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	C₂×#41×C₆₇	1	4	yes	—
746	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
747	Q₈	—	4	4	no	—
748	Q₈	—	4	4	no	—
749	D₄	—	4	4	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	4	no	—
752	D₄	—	8	4	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	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	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
802	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
803	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
804	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
805	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
806	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
807	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
823	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
824	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
825	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
826	C₂²	#585×C₆₇	1	1	yes	characteristic
827	C₂²	#585×C₆₇	1	1	yes	characteristic
828	C₂²	#585×C₆₇	1	1	yes	characteristic
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₂	—	4	4	no	—
847	C₂	—	8	2	no	—
848	C₂	C₆₇×#3475	1	1	yes	characteristic
849	C₂	C₆₇×#3480	1	1	yes	characteristic
850	C₂	C₆₇×#3481	1	1	yes	characteristic
851	C₂	C₆₇×#3491	1	1	yes	characteristic
852	C₂	C₆₇×#3493	1	1	yes	characteristic
853	C₂	C₆₇×#3506	1	1	yes	characteristic
854	C₂	C₆₇×#3545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2682	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×#2808	C₂	semidirect
2. C₆₇×#2805	C₂	semidirect
3. C₆₇×#2804	C₂	semidirect
5. C₆₇×#2610	C₂	semidirect
6. C₆₇×#2600	C₂	semidirect
7. C₆₇×#2599	C₂	semidirect
8. C₆₇×#2595	C₂	semidirect
9. C₆₇×#2573	C₂	semidirect
10. C₆₇×#2572	C₂	semidirect
11. C₆₇×#2525	C₂	semidirect
12. C₆₇×#2458	C₂	semidirect
13. C₆₇×#2444	C₂	semidirect
14. C₆₇×#2363	C₂	semidirect
15. C₆₇×#2359	C₂	semidirect
16. C₆₇×#2343	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
18. C₆₇×#2295	C₂	semidirect
19. C₆₇×#2293	C₂	semidirect
418. #59880	C₆₇	direct (N × H)
428. #2808	C₂×C₆₇	semidirect
429. #2805	C₂×C₆₇	semidirect
430. #2804	C₂×C₆₇	semidirect
432. #2610	C₂×C₆₇	semidirect
433. #2600	C₂×C₆₇	semidirect
434. #2599	C₂×C₆₇	semidirect
435. #2595	C₂×C₆₇	semidirect
436. #2573	C₂×C₆₇	semidirect
437. #2572	C₂×C₆₇	semidirect
438. #2525	C₂×C₆₇	semidirect
439. #2458	C₂×C₆₇	semidirect
440. #2444	C₂×C₆₇	semidirect
441. #2363	C₂×C₆₇	semidirect
442. #2359	C₂×C₆₇	semidirect
443. #2343	C₂×C₆₇	semidirect
444. C₄×#124	C₂×C₆₇	semidirect
445. #2295	C₂×C₆₇	semidirect
446. #2293	C₂×C₆₇	semidirect
447. C₆₇	#59880	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×#2808	2
C₆₇×#2805	2
C₆₇×#2804	2
C₆₇×#2682	2
C₆₇×#2610	2
C₆₇×#2600	2
C₆₇×#2599	2
C₆₇×#2595	2
C₆₇×#2573	2
C₆₇×#2572	2
C₆₇×#2525	2
C₆₇×#2458	2
C₆₇×#2444	2
C₆₇×#2363	2
C₆₇×#2359	2
C₆₇×#2343	2
C₄×#124×C₆₇	2
C₆₇×#2295	2
C₆₇×#2293	2
#59880	67

Subgroups — C67×#59880 #30739131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59880 #30739131