Subgroups — C₆₇×#34968 #30714219

Order 17152.

1940 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2525	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2520	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2515	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2468	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2465	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2461	C₂	1	2	yes	maximal
8	C₆₇×#2458	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2399	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2398	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2392	C₂	1	1	yes	maximal, characteristic
13	C₄×#126×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₄×#124×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₄×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2298	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×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×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
32	#400×C₆₇	C₂²	1	1	yes	characteristic
33	#400×C₆₇	C₂²	1	2	yes	—
34	#399×C₆₇	C₂²	1	1	yes	characteristic
35	#398×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	1	yes	characteristic
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	1	yes	characteristic
41	#396×C₆₇	C₂²	1	2	yes	—
42	#396×C₆₇	C₂²	1	2	yes	—
43	#395×C₆₇	C₂²	1	2	yes	—
44	#395×C₆₇	C₂²	1	2	yes	—
45	#395×C₆₇	C₂²	1	1	yes	characteristic
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	1	yes	characteristic
48	#394×C₆₇	C₂²	1	2	yes	—
49	#393×C₆₇	C₂²	1	1	yes	characteristic
50	#393×C₆₇	C₂²	1	2	yes	—
51	#392×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	2	yes	—
53	#391×C₆₇	C₂²	1	2	yes	—
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	#387×C₆₇	C₂²	1	2	yes	—
68	#387×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	#386×C₆₇	C₂²	1	2	yes	—
77	#385×C₆₇	C₂²	1	2	yes	—
78	#385×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#383×C₆₇	C₂²	1	2	yes	—
81	#382×C₆₇	C₂²	1	2	yes	—
82	#381×C₆₇	C₂²	1	2	yes	—
83	#380×C₆₇	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
85	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
86	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
89	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
105	C₄³×C₆₇	C₂²	1	1	yes	characteristic
106	C₄³×C₆₇	C₂²	1	2	yes	—
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
114	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
115	#126×C₆₇	—	2	8	no	—
116	#124×C₆₇	—	2	8	no	—
117	#123×C₆₇	—	2	8	no	—
118	C₂²⋊Q₈×C₆₇	—	2	8	no	—
119	C₄×Q₈×C₆₇	—	2	8	no	—
120	C₄×Q₈×C₆₇	—	2	4	no	—
121	C₄×Q₈×C₆₇	—	4	4	no	—
122	C₄×D₄×C₆₇	—	2	8	no	—
123	C₄×D₄×C₆₇	—	2	4	no	—
124	C₄×D₄×C₆₇	—	4	4	no	—
125	#117×C₆₇	—	2	4	no	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	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×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₄²×C₆₇	—	4	4	no	—
163	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄²×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	2	yes	—
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
185	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
199	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₆₇	—	2	4	no	—
209	C₂×Q₈×C₆₇	—	2	2	no	—
210	C₂×Q₈×C₆₇	—	2	4	no	—
211	C₂×Q₈×C₆₇	—	2	4	no	—
212	C₂×Q₈×C₆₇	—	4	2	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	—	2	4	no	—
217	C₂×D₄×C₆₇	—	4	2	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	4	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	—	2	2	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	—	4	2	no	—
230	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	—	2	2	no	—
248	C₄⋊C₄×C₆₇	—	2	2	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	2	no	—
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	2	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	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	4	2	no	—
262	C₄⋊C₄×C₆₇	—	4	2	no	—
263	C₄⋊C₄×C₆₇	—	4	2	no	—
264	C₄⋊C₄×C₆₇	—	4	2	no	—
265	C₄⋊C₄×C₆₇	#41	1	8	yes	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	2	no	—
270	C₂²⋊C₄×C₆₇	—	2	2	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	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	4	2	no	—
281	C₂²⋊C₄×C₆₇	—	4	2	no	—
282	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
283	C₄²×C₆₇	—	2	2	no	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	—	2	4	no	—
286	C₄²×C₆₇	—	2	4	no	—
287	C₄²×C₆₇	—	2	4	no	—
288	C₄²×C₆₇	—	2	4	no	—
289	C₄²×C₆₇	—	2	4	no	—
290	C₄²×C₆₇	—	2	4	no	—
291	C₄²×C₆₇	—	2	2	no	—
292	C₄²×C₆₇	—	2	4	no	—
293	C₄²×C₆₇	—	2	4	no	—
294	C₄²×C₆₇	—	2	2	no	—
295	C₄²×C₆₇	—	2	2	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	4	2	no	—
298	C₄²×C₆₇	—	4	2	no	—
299	C₄²×C₆₇	#41	1	4	yes	—
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	1	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	2	1	no	—
310	C₂³×C₆₇	—	2	1	no	—
311	C₂³×C₆₇	C₂×#41	1	4	yes	—
312	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
313	Q₈×C₆₇	—	2	8	no	—
314	Q₈×C₆₇	—	4	8	no	—
315	D₄×C₆₇	—	2	8	no	—
316	D₄×C₆₇	—	4	8	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	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	2	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	2	no	—
345	C₂×C₄×C₆₇	—	2	1	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	1	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	4	8	no	—
355	C₂×C₄×C₆₇	—	4	8	no	—
356	C₂×C₄×C₆₇	—	4	8	no	—
357	C₂×C₄×C₆₇	—	4	4	no	—
358	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
359	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
360	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
361	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
362	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
363	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
364	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
365	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
366	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
367	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
368	C₂²×C₆₇	—	2	4	no	—
369	C₂²×C₆₇	—	2	4	no	—
370	C₂²×C₆₇	—	2	4	no	—
371	C₂²×C₆₇	—	4	2	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	4	1	no	—
376	C₂²×C₆₇	—	4	1	no	—
377	C₂²×C₆₇	—	4	1	no	—
378	C₂²×C₆₇	—	4	2	no	—
379	C₂²×C₆₇	—	4	2	no	—
380	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
381	C₂²×C₆₇	C₂²×#41	1	2	yes	—
382	C₂²×C₆₇	C₂²×#41	1	2	yes	—
383	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
385	C₄×C₆₇	—	2	2	no	—
386	C₄×C₆₇	—	2	4	no	—
387	C₄×C₆₇	—	2	2	no	—
388	C₄×C₆₇	—	2	4	no	—
389	C₄×C₆₇	—	2	4	no	—
390	C₄×C₆₇	—	2	4	no	—
391	C₄×C₆₇	—	2	4	no	—
392	C₄×C₆₇	—	4	1	no	—
393	C₄×C₆₇	—	4	2	no	—
394	C₄×C₆₇	—	4	1	no	—
395	C₄×C₆₇	—	4	2	no	—
396	C₄×C₆₇	—	4	1	no	—
397	C₄×C₆₇	—	4	2	no	—
398	C₄×C₆₇	—	4	2	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	2	no	—
401	C₄×C₆₇	#542	1	4	yes	—
402	#34968	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂×C₆₇	—	4	4	no	—
404	C₂×C₆₇	—	8	1	no	—
405	C₂×C₆₇	#3444	1	1	yes	characteristic
406	C₂×C₆₇	#3444	1	1	yes	characteristic
407	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
408	C₂×C₆₇	#3481	1	2	yes	—
409	C₂×C₆₇	#3482	1	2	yes	—
410	#2525	C₂×C₆₇	1	2	yes	complemented
411	#2521	C₂×C₆₇	1	2	yes	complemented
412	#2520	C₂×C₆₇	1	2	yes	complemented
413	#2515	C₂×C₆₇	1	2	yes	complemented
414	#2468	C₂×C₆₇	1	2	yes	complemented
415	#2465	C₂×C₆₇	1	2	yes	complemented
416	#2461	C₂×C₆₇	1	2	yes	—
417	#2458	C₂×C₆₇	1	2	yes	complemented
418	#2399	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#2398	C₂×C₆₇	1	1	yes	characteristic, complemented
420	#2396	C₂×C₆₇	1	1	yes	characteristic, complemented
421	#2392	C₂×C₆₇	1	1	yes	characteristic
422	C₄×#126	C₂×C₆₇	1	2	yes	complemented
423	C₄×#124	C₂×C₆₇	1	2	yes	complemented
424	C₄×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	complemented
425	C₄×#123	C₂×C₆₇	1	2	yes	complemented
426	#2298	C₂×C₆₇	1	1	yes	characteristic, complemented
427	C₄²×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
428	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
429	C₆₇	#34968	1	1	yes	characteristic, direct product factor, Sylow
430	C₂×#126	C₂²×C₆₇	1	2	yes	—
431	C₂×#124	C₂²×C₆₇	1	2	yes	—
432	C₂×#123	C₂²×C₆₇	1	2	yes	—
433	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
434	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
436	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
437	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
439	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
440	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
441	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
442	#400	C₂²×C₆₇	1	1	yes	characteristic
443	#400	C₂²×C₆₇	1	2	yes	—
444	#399	C₂²×C₆₇	1	1	yes	characteristic
445	#398	C₂²×C₆₇	1	1	yes	characteristic
446	#398	C₂²×C₆₇	1	2	yes	—
447	#398	C₂²×C₆₇	1	2	yes	—
448	#398	C₂²×C₆₇	1	2	yes	—
449	#397	C₂²×C₆₇	1	1	yes	characteristic
450	#397	C₂²×C₆₇	1	2	yes	—
451	#396	C₂²×C₆₇	1	2	yes	—
452	#396	C₂²×C₆₇	1	2	yes	—
453	#395	C₂²×C₆₇	1	1	yes	characteristic
454	#395	C₂²×C₆₇	1	2	yes	—
455	#395	C₂²×C₆₇	1	2	yes	—
456	#394	C₂²×C₆₇	1	2	yes	—
457	#394	C₂²×C₆₇	1	1	yes	characteristic
458	#394	C₂²×C₆₇	1	2	yes	—
459	#393	C₂²×C₆₇	1	1	yes	characteristic
460	#393	C₂²×C₆₇	1	2	yes	—
461	#392	C₂²×C₆₇	1	1	yes	characteristic
462	#391	C₂²×C₆₇	1	2	yes	—
463	#391	C₂²×C₆₇	1	2	yes	—
464	#390	C₂²×C₆₇	1	2	yes	—
465	#389	C₂²×C₆₇	1	2	yes	—
466	#388	C₂²×C₆₇	1	2	yes	—
467	#388	C₂²×C₆₇	1	2	yes	—
468	#388	C₂²×C₆₇	1	2	yes	—
469	#388	C₂²×C₆₇	1	2	yes	—
470	#388	C₂²×C₆₇	1	2	yes	—
471	#388	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	#387	C₂²×C₆₇	1	2	yes	—
478	#387	C₂²×C₆₇	1	2	yes	—
479	#387	C₂²×C₆₇	1	2	yes	—
480	#387	C₂²×C₆₇	1	2	yes	—
481	#387	C₂²×C₆₇	1	2	yes	—
482	#387	C₂²×C₆₇	1	2	yes	—
483	#387	C₂²×C₆₇	1	2	yes	—
484	#387	C₂²×C₆₇	1	2	yes	—
485	#387	C₂²×C₆₇	1	2	yes	—
486	#386	C₂²×C₆₇	1	2	yes	—
487	#385	C₂²×C₆₇	1	2	yes	—
488	#385	C₂²×C₆₇	1	2	yes	—
489	#385	C₂²×C₆₇	1	2	yes	—
490	#383	C₂²×C₆₇	1	2	yes	—
491	#382	C₂²×C₆₇	1	2	yes	—
492	#381	C₂²×C₆₇	1	2	yes	—
493	#380	C₂²×C₆₇	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
503	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
504	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
506	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
510	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
511	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
512	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
513	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
514	#376	C₂²×C₆₇	1	1	yes	characteristic
515	C₄³	C₂²×C₆₇	1	2	yes	—
516	C₄³	C₂²×C₆₇	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
519	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
521	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
523	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
524	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
525	#126	—	2	8	no	—
526	#124	—	2	8	no	—
527	#123	—	2	8	no	—
528	C₂²⋊Q₈	—	2	8	no	—
529	C₄×Q₈	—	2	8	no	—
530	C₄×Q₈	—	2	4	no	—
531	C₄×Q₈	—	4	4	no	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	4	4	no	—
535	#117	—	2	4	no	—
536	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
559	C₂×C₂²⋊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×C₄²	—	4	4	no	—
573	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
575	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
576	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
580	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
582	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
583	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
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	#95	C₂³×C₆₇	1	2	yes	—
591	#95	C₂³×C₆₇	1	2	yes	—
592	#95	C₂³×C₆₇	1	2	yes	—
593	#95	C₂³×C₆₇	1	2	yes	—
594	#95	C₂³×C₆₇	1	1	yes	characteristic
595	#95	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
609	#95	C₂³×C₆₇	1	1	yes	characteristic
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	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
617	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
618	C₂×Q₈	—	2	4	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	4	2	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
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	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	#41×C₆₇	1	8	yes	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
691	C₂²⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	4	no	—
696	C₄²	—	2	4	no	—
697	C₄²	—	2	4	no	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	4	2	no	—
708	C₄²	—	4	2	no	—
709	C₄²	#41×C₆₇	1	4	yes	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	C₂×#41×C₆₇	1	4	yes	—
722	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
723	Q₈	—	2	8	no	—
724	Q₈	—	4	8	no	—
725	D₄	—	2	8	no	—
726	D₄	—	4	8	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	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	1	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	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	4	8	no	—
765	C₂×C₄	—	4	8	no	—
766	C₂×C₄	—	4	8	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
769	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
770	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
771	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
772	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
773	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
774	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
775	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
776	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
777	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
791	C₂²	C₂²×#41×C₆₇	1	2	yes	—
792	C₂²	C₂²×#41×C₆₇	1	2	yes	—
793	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
794	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
795	C₄	—	2	2	no	—
796	C₄	—	2	4	no	—
797	C₄	—	2	2	no	—
798	C₄	—	2	4	no	—
799	C₄	—	2	4	no	—
800	C₄	—	2	4	no	—
801	C₄	—	2	4	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	#542×C₆₇	1	4	yes	—
812	C₂	—	4	4	no	—
813	C₂	—	8	1	no	—
814	C₂	C₆₇×#3444	1	1	yes	characteristic
815	C₂	C₆₇×#3444	1	1	yes	characteristic
816	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
817	C₂	C₆₇×#3481	1	2	yes	—
818	C₂	C₆₇×#3482	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	#392×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2525	C₂	semidirect
2. C₆₇×#2521	C₂	semidirect
3. C₆₇×#2520	C₂	semidirect
4. C₆₇×#2515	C₂	semidirect
5. C₆₇×#2468	C₂	semidirect
6. C₆₇×#2465	C₂	semidirect
8. C₆₇×#2458	C₂	semidirect
9. C₆₇×#2399	C₂	semidirect
10. C₆₇×#2398	C₂	semidirect
11. C₆₇×#2396	C₂	semidirect
13. C₄×#126×C₆₇	C₂	semidirect
14. C₄×#124×C₆₇	C₂	semidirect
15. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
16. C₄×#123×C₆₇	C₂	semidirect
17. C₆₇×#2298	C₂	semidirect
18. C₄²×Q₈×C₆₇	C₂	semidirect
19. C₄²×D₄×C₆₇	C₂	semidirect
402. #34968	C₆₇	direct (N × H)
410. #2525	C₂×C₆₇	semidirect
411. #2521	C₂×C₆₇	semidirect
412. #2520	C₂×C₆₇	semidirect
413. #2515	C₂×C₆₇	semidirect
414. #2468	C₂×C₆₇	semidirect
415. #2465	C₂×C₆₇	semidirect
417. #2458	C₂×C₆₇	semidirect
418. #2399	C₂×C₆₇	semidirect
419. #2398	C₂×C₆₇	semidirect
420. #2396	C₂×C₆₇	semidirect
422. C₄×#126	C₂×C₆₇	semidirect
423. C₄×#124	C₂×C₆₇	semidirect
424. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
425. C₄×#123	C₂×C₆₇	semidirect
426. #2298	C₂×C₆₇	semidirect
427. C₄²×Q₈	C₂×C₆₇	semidirect
428. C₄²×D₄	C₂×C₆₇	semidirect
429. C₆₇	#34968	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×#2525	2
C₆₇×#2521	2
C₆₇×#2520	2
C₆₇×#2515	2
C₆₇×#2468	2
C₆₇×#2465	2
C₆₇×#2461	2
C₆₇×#2458	2
C₆₇×#2399	2
C₆₇×#2398	2
C₆₇×#2396	2
C₆₇×#2392	2
C₄×#126×C₆₇	2
C₄×#124×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#123×C₆₇	2
C₆₇×#2298	2
C₄²×Q₈×C₆₇	2
C₄²×D₄×C₆₇	2
#34968	67

Subgroups — C67×#34968 #30714219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34968 #30714219