Subgroups — C₆₇×#35077 #30714328

Order 17152.

3078 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2847	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2630	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2579	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2534	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2485	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2417	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2416	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2412	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2410	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2407	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2325	C₂	1	4	yes	maximal, complemented
17	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	#525×C₆₇	—	2	8	no	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#121×C₆₇	C₂²	1	4	yes	—
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#120×C₆₇	C₂²	1	2	yes	—
33	C₂×#120×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	—	2	8	no	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
47	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
48	#398×C₆₇	C₂²	1	4	yes	complemented
49	#397×C₆₇	C₂²	1	4	yes	complemented
50	#396×C₆₇	C₂²	1	4	yes	complemented
51	#396×C₆₇	C₂²	1	4	yes	complemented
52	#394×C₆₇	C₂²	1	4	yes	—
53	#394×C₆₇	C₂²	1	4	yes	complemented
54	#394×C₆₇	C₂²	1	4	yes	complemented
55	#392×C₆₇	C₂²	1	4	yes	—
56	#391×C₆₇	C₂²	1	2	yes	complemented
57	#390×C₆₇	C₂²	1	2	yes	complemented
58	#389×C₆₇	C₂²	1	2	yes	complemented
59	#389×C₆₇	C₂²	1	2	yes	complemented
60	#388×C₆₇	C₂²	1	4	yes	complemented
61	#388×C₆₇	C₂²	1	4	yes	complemented
62	#387×C₆₇	C₂²	1	4	yes	complemented
63	#387×C₆₇	C₂²	1	4	yes	complemented
64	#386×C₆₇	C₂²	1	2	yes	—
65	#386×C₆₇	C₂²	1	2	yes	—
66	#386×C₆₇	C₂²	1	4	yes	—
67	#386×C₆₇	C₂²	1	4	yes	complemented
68	#386×C₆₇	C₂²	1	4	yes	complemented
69	#386×C₆₇	C₂²	1	4	yes	complemented
70	#385×C₆₇	C₂²	1	2	yes	—
71	#385×C₆₇	C₂²	1	2	yes	—
72	#385×C₆₇	C₂²	1	4	yes	complemented
73	#385×C₆₇	C₂²	1	4	yes	complemented
74	#381×C₆₇	C₂²	1	2	yes	—
75	#380×C₆₇	C₂²	1	2	yes	—
76	#380×C₆₇	C₂²	1	1	yes	characteristic
77	#380×C₆₇	C₂²	1	1	yes	characteristic
78	#380×C₆₇	C₂²	1	2	yes	complemented
79	#380×C₆₇	C₂²	1	2	yes	complemented
80	#380×C₆₇	C₂²	1	4	yes	complemented
81	#380×C₆₇	C₂²	1	2	yes	complemented
82	#380×C₆₇	C₂²	1	2	yes	complemented
83	#379×C₆₇	C₂²	1	2	yes	—
84	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	4	4	no	—
89	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	—	2	4	no	—
91	C₂²×D₄×C₆₇	—	2	8	no	—
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
98	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₆₇	—	2	4	no	—
100	C₂³×C₄×C₆₇	—	4	4	no	—
101	C₂³×C₄×C₆₇	—	4	4	no	—
102	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
103	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	#123×C₆₇	—	2	8	no	—
117	#123×C₆₇	—	4	4	no	—
118	C₂²⋊Q₈×C₆₇	—	2	4	no	—
119	C₂²⋊Q₈×C₆₇	—	2	4	no	—
120	C₂²⋊Q₈×C₆₇	—	4	4	no	—
121	#121×C₆₇	—	2	16	no	—
122	#121×C₆₇	—	2	4	no	—
123	#121×C₆₇	—	2	4	no	—
124	#121×C₆₇	—	4	4	no	—
125	#120×C₆₇	—	2	8	no	—
126	#120×C₆₇	—	4	4	no	—
127	C₄×D₄×C₆₇	—	2	8	no	—
128	C₄×D₄×C₆₇	—	2	8	no	—
129	C₄×D₄×C₆₇	—	2	8	no	—
130	C₄×D₄×C₆₇	—	2	8	no	—
131	C₄×D₄×C₆₇	—	2	8	no	—
132	C₄×D₄×C₆₇	—	2	8	no	—
133	#117×C₆₇	—	2	4	no	—
134	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
135	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
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	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	4	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
149	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
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	4	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
169	C₂×C₄²×C₆₇	—	2	4	no	—
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	#95×C₆₇	C₂³	1	2	yes	—
174	#95×C₆₇	C₂³	1	4	yes	—
175	#95×C₆₇	C₂³	1	2	yes	—
176	#95×C₆₇	C₂³	1	4	yes	—
177	#95×C₆₇	C₂³	1	4	yes	—
178	#95×C₆₇	C₂³	1	4	yes	—
179	#95×C₆₇	C₂³	1	4	yes	—
180	#95×C₆₇	C₂³	1	4	yes	—
181	#95×C₆₇	C₂³	1	4	yes	—
182	C₂⁴×C₆₇	—	2	2	no	—
183	C₂⁴×C₆₇	—	2	4	no	—
184	C₂⁴×C₆₇	—	2	4	no	—
185	C₂⁴×C₆₇	—	2	2	no	—
186	C₂⁴×C₆₇	—	2	2	no	—
187	C₂⁴×C₆₇	—	2	2	no	—
188	C₂⁴×C₆₇	—	2	2	no	—
189	C₂⁴×C₆₇	—	4	2	no	—
190	C₂⁴×C₆₇	—	4	2	no	—
191	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
192	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
193	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
195	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
197	#41×C₆₇	—	4	16	no	—
198	C₂×Q₈×C₆₇	—	2	2	no	—
199	C₂×Q₈×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	32	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	4	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	8	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	8	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	4	4	no	—
216	C₂×D₄×C₆₇	—	4	4	no	—
217	C₂×D₄×C₆₇	—	4	4	no	—
218	C₂×D₄×C₆₇	#41	1	8	yes	complemented
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	2	no	—
225	C₂²×C₄×C₆₇	—	2	2	no	—
226	C₂²×C₄×C₆₇	—	2	2	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	2	8	no	—
229	C₂²×C₄×C₆₇	—	2	4	no	—
230	C₂²×C₄×C₆₇	—	2	4	no	—
231	C₂²×C₄×C₆₇	—	2	4	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	4	16	no	—
235	C₂²×C₄×C₆₇	—	4	2	no	—
236	C₂²×C₄×C₆₇	—	4	2	no	—
237	C₂²×C₄×C₆₇	—	4	2	no	—
238	C₂²×C₄×C₆₇	—	4	2	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	—	4	2	no	—
241	C₂²×C₄×C₆₇	—	4	4	no	—
242	C₂²×C₄×C₆₇	—	4	4	no	—
243	C₂²×C₄×C₆₇	—	4	4	no	—
244	C₂²×C₄×C₆₇	—	4	16	no	—
245	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
247	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
249	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
250	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	8	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	4	4	no	—
273	C₄⋊C₄×C₆₇	—	4	4	no	—
274	C₄⋊C₄×C₆₇	—	4	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	8	no	—
281	C₂²⋊C₄×C₆₇	—	2	4	no	—
282	C₂²⋊C₄×C₆₇	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	8	no	—
288	C₂²⋊C₄×C₆₇	—	4	4	no	—
289	C₂²⋊C₄×C₆₇	—	4	4	no	—
290	C₂²⋊C₄×C₆₇	—	4	4	no	—
291	C₂²⋊C₄×C₆₇	—	4	4	no	—
292	C₂²⋊C₄×C₆₇	—	4	4	no	—
293	C₄²×C₆₇	—	2	4	no	—
294	C₄²×C₆₇	—	2	4	no	—
295	C₄²×C₆₇	—	2	4	no	—
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	2	no	—
298	C₂³×C₆₇	—	2	2	no	—
299	C₂³×C₆₇	—	2	1	no	—
300	C₂³×C₆₇	—	2	1	no	—
301	C₂³×C₆₇	—	2	8	no	—
302	C₂³×C₆₇	—	2	8	no	—
303	C₂³×C₆₇	—	2	8	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	2	1	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	1	no	—
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	4	no	—
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	—	2	4	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	4	4	no	—
320	C₂³×C₆₇	—	4	8	no	—
321	C₂³×C₆₇	—	4	8	no	—
322	C₂³×C₆₇	—	4	8	no	—
323	C₂³×C₆₇	—	4	8	no	—
324	C₂³×C₆₇	—	4	4	no	—
325	C₂³×C₆₇	—	4	4	no	—
326	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
327	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
329	C₂³×C₆₇	C₂×#41	1	4	yes	—
330	C₂³×C₆₇	C₂×#41	1	4	yes	—
331	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
332	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
333	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
334	Q₈×C₆₇	—	4	4	no	—
335	D₄×C₆₇	—	2	16	no	—
336	D₄×C₆₇	—	2	16	no	—
337	D₄×C₆₇	—	4	8	no	—
338	D₄×C₆₇	—	4	8	no	—
339	D₄×C₆₇	—	4	8	no	—
340	D₄×C₆₇	—	4	4	no	—
341	D₄×C₆₇	—	8	8	no	—
342	C₂×C₄×C₆₇	—	2	8	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	8	no	—
349	C₂×C₄×C₆₇	—	2	8	no	—
350	C₂×C₄×C₆₇	—	2	8	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	4	no	—
357	C₂×C₄×C₆₇	—	2	4	no	—
358	C₂×C₄×C₆₇	—	2	4	no	—
359	C₂×C₄×C₆₇	—	2	4	no	—
360	C₂×C₄×C₆₇	—	2	4	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	4	no	—
365	C₂×C₄×C₆₇	—	2	4	no	—
366	C₂×C₄×C₆₇	—	2	4	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	4	4	no	—
371	C₂×C₄×C₆₇	—	4	4	no	—
372	C₂×C₄×C₆₇	—	4	4	no	—
373	C₂×C₄×C₆₇	—	4	8	no	—
374	C₂×C₄×C₆₇	—	4	8	no	—
375	C₂×C₄×C₆₇	—	4	4	no	—
376	C₂×C₄×C₆₇	—	4	4	no	—
377	C₂×C₄×C₆₇	—	4	8	no	—
378	C₂×C₄×C₆₇	—	8	8	no	—
379	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
384	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
385	C₂²×C₆₇	—	2	2	no	—
386	C₂²×C₆₇	—	2	2	no	—
387	C₂²×C₆₇	—	2	2	no	—
388	C₂²×C₆₇	—	2	2	no	—
389	C₂²×C₆₇	—	2	4	no	—
390	C₂²×C₆₇	—	2	4	no	—
391	C₂²×C₆₇	—	2	4	no	—
392	C₂²×C₆₇	—	2	4	no	—
393	C₂²×C₆₇	—	2	2	no	—
394	C₂²×C₆₇	—	2	4	no	—
395	C₂²×C₆₇	—	2	2	no	—
396	C₂²×C₆₇	—	2	2	no	—
397	C₂²×C₆₇	—	2	4	no	—
398	C₂²×C₆₇	—	2	4	no	—
399	C₂²×C₆₇	—	4	16	no	—
400	C₂²×C₆₇	—	4	16	no	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	2	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	—	4	2	no	—
409	C₂²×C₆₇	—	4	2	no	—
410	C₂²×C₆₇	—	4	4	no	—
411	C₂²×C₆₇	—	4	4	no	—
412	C₂²×C₆₇	#525	1	4	yes	—
413	C₂²×C₆₇	#537	1	4	yes	—
414	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
415	C₂²×C₆₇	C₂²×#41	1	2	yes	—
416	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
417	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	C₄×C₆₇	—	2	4	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	2	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	2	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	4	no	—
429	C₄×C₆₇	—	4	4	no	—
430	C₄×C₆₇	#534	1	4	yes	—
431	#35077	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂×C₆₇	—	2	4	no	—
433	C₂×C₆₇	—	2	4	no	—
434	C₂×C₆₇	—	4	2	no	—
435	C₂×C₆₇	—	4	4	no	—
436	C₂×C₆₇	—	8	2	no	—
437	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
438	C₂×C₆₇	C₂×#534	1	1	yes	characteristic
439	C₂×C₆₇	C₂×#537	1	1	yes	characteristic
440	C₂×C₆₇	#3519	1	2	yes	—
441	C₂×C₆₇	#3520	1	2	yes	—
442	C₂×#525	C₂×C₆₇	1	1	yes	characteristic, complemented
443	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#2855	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#2854	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#2848	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#2847	C₂×C₆₇	1	1	yes	characteristic, complemented
448	#2630	C₂×C₆₇	1	4	yes	complemented
449	#2579	C₂×C₆₇	1	2	yes	complemented
450	#2534	C₂×C₆₇	1	2	yes	complemented
451	#2485	C₂×C₆₇	1	2	yes	complemented
452	#2417	C₂×C₆₇	1	2	yes	complemented
453	#2416	C₂×C₆₇	1	2	yes	complemented
454	#2412	C₂×C₆₇	1	2	yes	complemented
455	#2410	C₂×C₆₇	1	2	yes	complemented
456	#2407	C₂×C₆₇	1	2	yes	complemented
457	#2325	C₂×C₆₇	1	4	yes	complemented
458	C₂×#380	C₂×C₆₇	1	1	yes	characteristic, complemented
459	C₆₇	#35077	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
462	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
463	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
464	#525	—	2	8	no	—
465	C₂×#123	C₂²×C₆₇	1	2	yes	—
466	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
467	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
469	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
470	C₂×#121	C₂²×C₆₇	1	4	yes	—
471	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
473	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
474	C₂×#120	C₂²×C₆₇	1	2	yes	—
475	C₂×#120	C₂²×C₆₇	1	2	yes	—
476	C₂×C₄×D₄	—	2	8	no	—
477	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
480	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
481	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
483	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
484	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
486	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
487	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
488	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
489	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
490	#398	C₂²×C₆₇	1	4	yes	complemented
491	#397	C₂²×C₆₇	1	4	yes	complemented
492	#396	C₂²×C₆₇	1	4	yes	complemented
493	#396	C₂²×C₆₇	1	4	yes	complemented
494	#394	C₂²×C₆₇	1	4	yes	—
495	#394	C₂²×C₆₇	1	4	yes	complemented
496	#394	C₂²×C₆₇	1	4	yes	complemented
497	#392	C₂²×C₆₇	1	4	yes	—
498	#391	C₂²×C₆₇	1	2	yes	complemented
499	#390	C₂²×C₆₇	1	2	yes	complemented
500	#389	C₂²×C₆₇	1	2	yes	complemented
501	#389	C₂²×C₆₇	1	2	yes	complemented
502	#388	C₂²×C₆₇	1	4	yes	complemented
503	#388	C₂²×C₆₇	1	4	yes	complemented
504	#387	C₂²×C₆₇	1	4	yes	complemented
505	#387	C₂²×C₆₇	1	4	yes	complemented
506	#386	C₂²×C₆₇	1	2	yes	—
507	#386	C₂²×C₆₇	1	2	yes	—
508	#386	C₂²×C₆₇	1	4	yes	—
509	#386	C₂²×C₆₇	1	4	yes	complemented
510	#386	C₂²×C₆₇	1	4	yes	complemented
511	#386	C₂²×C₆₇	1	4	yes	complemented
512	#385	C₂²×C₆₇	1	2	yes	—
513	#385	C₂²×C₆₇	1	2	yes	—
514	#385	C₂²×C₆₇	1	4	yes	complemented
515	#385	C₂²×C₆₇	1	4	yes	complemented
516	#381	C₂²×C₆₇	1	2	yes	—
517	#380	C₂²×C₆₇	1	2	yes	—
518	#380	C₂²×C₆₇	1	1	yes	characteristic
519	#380	C₂²×C₆₇	1	1	yes	characteristic
520	#380	C₂²×C₆₇	1	4	yes	complemented
521	#380	C₂²×C₆₇	1	2	yes	complemented
522	#380	C₂²×C₆₇	1	2	yes	complemented
523	#380	C₂²×C₆₇	1	2	yes	complemented
524	#380	C₂²×C₆₇	1	2	yes	complemented
525	#379	C₂²×C₆₇	1	2	yes	—
526	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
527	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
528	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
529	C₂×#41	—	2	4	no	—
530	C₂×#41	—	4	4	no	—
531	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
532	C₂²×D₄	—	2	4	no	—
533	C₂²×D₄	—	2	8	no	—
534	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
535	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
536	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
537	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
539	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
540	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
541	C₂³×C₄	—	2	4	no	—
542	C₂³×C₄	—	4	4	no	—
543	C₂³×C₄	—	4	4	no	—
544	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
545	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
548	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
553	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
554	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
555	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
558	#123	—	2	8	no	—
559	#123	—	4	4	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	4	4	no	—
563	#121	—	2	16	no	—
564	#121	—	2	4	no	—
565	#121	—	2	4	no	—
566	#121	—	4	4	no	—
567	#120	—	2	8	no	—
568	#120	—	4	4	no	—
569	C₄×D₄	—	2	8	no	—
570	C₄×D₄	—	2	8	no	—
571	C₄×D₄	—	2	8	no	—
572	C₄×D₄	—	2	8	no	—
573	C₄×D₄	—	2	8	no	—
574	C₄×D₄	—	2	8	no	—
575	#117	—	2	4	no	—
576	C₂×C₄⋊C₄	—	2	4	no	—
577	C₂×C₄⋊C₄	—	4	4	no	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
590	C₂×C₂²⋊C₄	—	2	4	no	—
591	C₂×C₂²⋊C₄	—	2	4	no	—
592	C₂×C₂²⋊C₄	—	4	4	no	—
593	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
611	C₂×C₄²	—	2	4	no	—
612	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
615	#95	C₂³×C₆₇	1	2	yes	—
616	#95	C₂³×C₆₇	1	4	yes	—
617	#95	C₂³×C₆₇	1	2	yes	—
618	#95	C₂³×C₆₇	1	4	yes	—
619	#95	C₂³×C₆₇	1	4	yes	—
620	#95	C₂³×C₆₇	1	4	yes	—
621	#95	C₂³×C₆₇	1	4	yes	—
622	#95	C₂³×C₆₇	1	4	yes	—
623	#95	C₂³×C₆₇	1	4	yes	—
624	C₂⁴	—	2	2	no	—
625	C₂⁴	—	2	4	no	—
626	C₂⁴	—	2	4	no	—
627	C₂⁴	—	2	2	no	—
628	C₂⁴	—	2	2	no	—
629	C₂⁴	—	2	2	no	—
630	C₂⁴	—	2	2	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
634	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
635	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
636	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
637	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
638	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
639	#41	—	4	16	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×D₄	—	2	32	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	8	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	8	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	—	4	4	no	—
660	C₂×D₄	#41×C₆₇	1	8	yes	complemented
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	8	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	4	16	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	4	no	—
684	C₂²×C₄	—	4	4	no	—
685	C₂²×C₄	—	4	4	no	—
686	C₂²×C₄	—	4	16	no	—
687	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
688	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
689	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
690	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
691	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
692	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
693	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
694	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
698	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	8	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	4	4	no	—
715	C₄⋊C₄	—	4	4	no	—
716	C₄⋊C₄	—	4	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	8	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	8	no	—
730	C₂²⋊C₄	—	4	4	no	—
731	C₂²⋊C₄	—	4	4	no	—
732	C₂²⋊C₄	—	4	4	no	—
733	C₂²⋊C₄	—	4	4	no	—
734	C₂²⋊C₄	—	4	4	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	4	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	8	no	—
744	C₂³	—	2	8	no	—
745	C₂³	—	2	8	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	4	4	no	—
762	C₂³	—	4	8	no	—
763	C₂³	—	4	8	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	4	no	—
768	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
769	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
770	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
771	C₂³	C₂×#41×C₆₇	1	4	yes	—
772	C₂³	C₂×#41×C₆₇	1	4	yes	—
773	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
774	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
775	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
776	Q₈	—	4	4	no	—
777	D₄	—	2	16	no	—
778	D₄	—	2	16	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	4	no	—
783	D₄	—	8	8	no	—
784	C₂×C₄	—	2	8	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	8	no	—
791	C₂×C₄	—	2	8	no	—
792	C₂×C₄	—	2	8	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	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	8	no	—
820	C₂×C₄	—	8	8	no	—
821	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
825	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
826	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	4	16	no	—
842	C₂²	—	4	16	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	4	no	—
853	C₂²	—	4	4	no	—
854	C₂²	#525×C₆₇	1	4	yes	—
855	C₂²	#537×C₆₇	1	4	yes	—
856	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
857	C₂²	C₂²×#41×C₆₇	1	2	yes	—
858	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
859	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
860	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	4	no	—
871	C₄	—	4	4	no	—
872	C₄	#534×C₆₇	1	4	yes	—
873	C₂	—	2	4	no	—
874	C₂	—	2	4	no	—
875	C₂	—	4	2	no	—
876	C₂	—	4	4	no	—
877	C₂	—	8	2	no	—
878	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
879	C₂	C₂×#534×C₆₇	1	1	yes	characteristic
880	C₂	C₂×#537×C₆₇	1	1	yes	characteristic
881	C₂	C₆₇×#3519	1	2	yes	—
882	C₂	C₆₇×#3520	1	2	yes	—

	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. C₂×#525×C₆₇	C₂	semidirect
2. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2855	C₂	semidirect
4. C₆₇×#2854	C₂	semidirect
5. C₆₇×#2848	C₂	semidirect
6. C₆₇×#2847	C₂	semidirect
7. C₆₇×#2630	C₂	semidirect
8. C₆₇×#2579	C₂	semidirect
9. C₆₇×#2534	C₂	semidirect
10. C₆₇×#2485	C₂	semidirect
11. C₆₇×#2417	C₂	semidirect
12. C₆₇×#2416	C₂	semidirect
13. C₆₇×#2412	C₂	semidirect
14. C₆₇×#2410	C₂	semidirect
15. C₆₇×#2407	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₂×#380×C₆₇	C₂	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
24. C₂×#123×C₆₇	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
30. C₂×#121×C₆₇	C₂²	semidirect
31. C₂×#121×C₆₇	C₂²	semidirect
40. C₂×C₄×D₄×C₆₇	C₂²	semidirect
41. C₂×#117×C₆₇	C₂²	semidirect
43. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
48. #398×C₆₇	C₂²	semidirect
49. #397×C₆₇	C₂²	semidirect
50. #396×C₆₇	C₂²	semidirect
51. #396×C₆₇	C₂²	semidirect
53. #394×C₆₇	C₂²	semidirect
54. #394×C₆₇	C₂²	semidirect
56. #391×C₆₇	C₂²	semidirect
57. #390×C₆₇	C₂²	semidirect
58. #389×C₆₇	C₂²	semidirect
59. #389×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #387×C₆₇	C₂²	semidirect
63. #387×C₆₇	C₂²	semidirect
67. #386×C₆₇	C₂²	semidirect
68. #386×C₆₇	C₂²	semidirect
69. #386×C₆₇	C₂²	semidirect
72. #385×C₆₇	C₂²	semidirect
73. #385×C₆₇	C₂²	semidirect
78. #380×C₆₇	C₂²	semidirect
79. #380×C₆₇	C₂²	semidirect
80. #380×C₆₇	C₂²	semidirect
81. #380×C₆₇	C₂²	semidirect
82. #380×C₆₇	C₂²	semidirect
84. C₂×#95×C₆₇	C₂²	semidirect
102. C₂³×C₄×C₆₇	D₄	semidirect
218. C₂×D₄×C₆₇	#41	semidirect
431. #35077	C₆₇	direct (N × H)
442. C₂×#525	C₂×C₆₇	semidirect
443. C₂²×C₄×D₄	C₂×C₆₇	semidirect
444. #2855	C₂×C₆₇	semidirect
445. #2854	C₂×C₆₇	semidirect
446. #2848	C₂×C₆₇	semidirect
447. #2847	C₂×C₆₇	semidirect
448. #2630	C₂×C₆₇	semidirect
449. #2579	C₂×C₆₇	semidirect
450. #2534	C₂×C₆₇	semidirect
451. #2485	C₂×C₆₇	semidirect
452. #2417	C₂×C₆₇	semidirect
453. #2416	C₂×C₆₇	semidirect
454. #2412	C₂×C₆₇	semidirect
455. #2410	C₂×C₆₇	semidirect
456. #2407	C₂×C₆₇	semidirect
457. #2325	C₂×C₆₇	semidirect
458. C₂×#380	C₂×C₆₇	semidirect
459. C₆₇	#35077	direct (N × H)
460. C₂²×#41	C₂²×C₆₇	semidirect
466. C₂×#123	C₂²×C₆₇	semidirect
468. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
469. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
472. C₂×#121	C₂²×C₆₇	semidirect
473. C₂×#121	C₂²×C₆₇	semidirect
482. C₂×C₄×D₄	C₂²×C₆₇	semidirect
483. C₂×#117	C₂²×C₆₇	semidirect
485. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
490. #398	C₂²×C₆₇	semidirect
491. #397	C₂²×C₆₇	semidirect
492. #396	C₂²×C₆₇	semidirect
493. #396	C₂²×C₆₇	semidirect
495. #394	C₂²×C₆₇	semidirect
496. #394	C₂²×C₆₇	semidirect
498. #391	C₂²×C₆₇	semidirect
499. #390	C₂²×C₆₇	semidirect
500. #389	C₂²×C₆₇	semidirect
501. #389	C₂²×C₆₇	semidirect
502. #388	C₂²×C₆₇	semidirect
503. #388	C₂²×C₆₇	semidirect
504. #387	C₂²×C₆₇	semidirect
505. #387	C₂²×C₆₇	semidirect
509. #386	C₂²×C₆₇	semidirect
510. #386	C₂²×C₆₇	semidirect
511. #386	C₂²×C₆₇	semidirect
514. #385	C₂²×C₆₇	semidirect
515. #385	C₂²×C₆₇	semidirect
520. #380	C₂²×C₆₇	semidirect
521. #380	C₂²×C₆₇	semidirect
522. #380	C₂²×C₆₇	semidirect
523. #380	C₂²×C₆₇	semidirect
524. #380	C₂²×C₆₇	semidirect
526. C₂×#95	C₂²×C₆₇	semidirect
544. C₂³×C₄	D₄×C₆₇	semidirect
660. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2855	2
C₆₇×#2854	2
C₆₇×#2848	2
C₆₇×#2847	2
C₆₇×#2630	2
C₆₇×#2579	2
C₆₇×#2534	2
C₆₇×#2485	2
C₆₇×#2417	2
C₆₇×#2416	2
C₆₇×#2412	2
C₆₇×#2410	2
C₆₇×#2407	2
C₆₇×#2325	2
C₂×#380×C₆₇	2
#35077	67

Subgroups — C67×#35077 #30714328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35077 #30714328