Subgroups — C₆₇×#34754 #30714005

Order 17152.

2182 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2518	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2517	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2510	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2505	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2493	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2437	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2412	C₂	1	2	yes	maximal
11	C₆₇×#2401	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2398	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2395	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₄×#120×C₆₇	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2290	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2283	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#123×C₆₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
23	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
32	#401×C₆₇	C₂²	1	2	yes	complemented
33	#400×C₆₇	C₂²	1	2	yes	complemented
34	#400×C₆₇	C₂²	1	2	yes	complemented
35	#400×C₆₇	C₂²	1	2	yes	complemented
36	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#400×C₆₇	C₂²	1	2	yes	complemented
38	#399×C₆₇	C₂²	1	1	yes	characteristic
39	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#397×C₆₇	C₂²	1	1	yes	characteristic
41	#397×C₆₇	C₂²	1	2	yes	—
42	#397×C₆₇	C₂²	1	2	yes	—
43	#397×C₆₇	C₂²	1	1	yes	characteristic
44	#397×C₆₇	C₂²	1	2	yes	—
45	#397×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#397×C₆₇	C₂²	1	2	yes	complemented
47	#396×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	#393×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#391×C₆₇	C₂²	1	2	yes	complemented
53	#389×C₆₇	C₂²	1	2	yes	complemented
54	#388×C₆₇	C₂²	1	2	yes	complemented
55	#388×C₆₇	C₂²	1	2	yes	complemented
56	#388×C₆₇	C₂²	1	2	yes	complemented
57	#388×C₆₇	C₂²	1	2	yes	complemented
58	#387×C₆₇	C₂²	1	2	yes	complemented
59	#387×C₆₇	C₂²	1	2	yes	complemented
60	#387×C₆₇	C₂²	1	2	yes	complemented
61	#387×C₆₇	C₂²	1	2	yes	complemented
62	#387×C₆₇	C₂²	1	2	yes	complemented
63	#387×C₆₇	C₂²	1	2	yes	complemented
64	#386×C₆₇	C₂²	1	2	yes	—
65	#386×C₆₇	C₂²	1	2	yes	—
66	#386×C₆₇	C₂²	1	2	yes	—
67	#386×C₆₇	C₂²	1	1	yes	characteristic
68	#386×C₆₇	C₂²	1	2	yes	—
69	#385×C₆₇	C₂²	1	2	yes	—
70	#385×C₆₇	C₂²	1	2	yes	—
71	#385×C₆₇	C₂²	1	2	yes	—
72	#385×C₆₇	C₂²	1	2	yes	—
73	#385×C₆₇	C₂²	1	2	yes	—
74	#385×C₆₇	C₂²	1	1	yes	characteristic
75	#385×C₆₇	C₂²	1	2	yes	—
76	#383×C₆₇	C₂²	1	2	yes	complemented
77	#383×C₆₇	C₂²	1	2	yes	complemented
78	#382×C₆₇	C₂²	1	2	yes	complemented
79	#382×C₆₇	C₂²	1	2	yes	complemented
80	#381×C₆₇	C₂²	1	2	yes	—
81	#381×C₆₇	C₂²	1	2	yes	—
82	#381×C₆₇	C₂²	1	2	yes	—
83	#380×C₆₇	C₂²	1	2	yes	—
84	#380×C₆₇	C₂²	1	2	yes	—
85	#380×C₆₇	C₂²	1	2	yes	—
86	#379×C₆₇	C₂²	1	1	yes	characteristic
87	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
88	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
89	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
90	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
92	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
94	C₄×C₂²⋊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	2	yes	—
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#376×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#376×C₆₇	C₂²	1	2	yes	complemented
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₂⁵×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	C₂³×C₄×C₆₇	—	2	8	no	—
112	C₂³×C₄×C₆₇	—	4	2	no	—
113	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	#123×C₆₇	—	2	8	no	—
123	C₂²⋊Q₈×C₆₇	—	2	8	no	—
124	#120×C₆₇	—	2	4	no	—
125	C₄×Q₈×C₆₇	—	4	2	no	—
126	C₄×D₄×C₆₇	—	2	8	no	—
127	C₄×D₄×C₆₇	—	4	2	no	—
128	#117×C₆₇	—	4	2	no	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	—	2	8	no	—
144	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
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	1	yes	characteristic
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	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	—	2	8	no	—
166	C₂×C₄²×C₆₇	—	4	4	no	—
167	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	#95×C₆₇	C₂³	1	2	yes	—
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	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	1	yes	characteristic
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	1	yes	characteristic
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	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	C₂⁴×C₆₇	—	2	4	no	—
208	C₂⁴×C₆₇	—	2	4	no	—
209	C₂⁴×C₆₇	—	4	1	no	—
210	C₂⁴×C₆₇	—	4	1	no	—
211	C₂⁴×C₆₇	#41	1	4	yes	—
212	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₆₇	—	2	4	no	—
216	C₂×Q₈×C₆₇	—	4	1	no	—
217	C₂×D₄×C₆₇	—	2	4	no	—
218	C₂×D₄×C₆₇	—	2	2	no	—
219	C₂×D₄×C₆₇	—	2	4	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	4	1	no	—
222	C₂×D₄×C₆₇	—	4	1	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
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	—	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	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	2	no	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	4	2	no	—
241	C₂²×C₄×C₆₇	—	4	2	no	—
242	C₂²×C₄×C₆₇	—	4	1	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	2	no	—
246	C₂²×C₄×C₆₇	—	4	16	no	—
247	C₂²×C₄×C₆₇	#41	1	8	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	2	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	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂⁴	1	2	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	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	4	no	—
266	C₄⋊C₄×C₆₇	—	2	4	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	4	2	no	—
271	C₄⋊C₄×C₆₇	—	4	2	no	—
272	C₄⋊C₄×C₆₇	—	4	2	no	—
273	C₄⋊C₄×C₆₇	—	4	1	no	—
274	C₄⋊C₄×C₆₇	—	4	1	no	—
275	C₄⋊C₄×C₆₇	—	4	1	no	—
276	C₄⋊C₄×C₆₇	—	4	2	no	—
277	C₄⋊C₄×C₆₇	—	4	1	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	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	2	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
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	—	4	1	no	—
293	C₂²⋊C₄×C₆₇	—	4	2	no	—
294	C₂²⋊C₄×C₆₇	—	4	2	no	—
295	C₂²⋊C₄×C₆₇	—	4	1	no	—
296	C₂²⋊C₄×C₆₇	—	4	1	no	—
297	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
298	C₄²×C₆₇	—	2	4	no	—
299	C₄²×C₆₇	—	2	4	no	—
300	C₄²×C₆₇	—	2	4	no	—
301	C₄²×C₆₇	—	2	4	no	—
302	C₄²×C₆₇	—	2	4	no	—
303	C₄²×C₆₇	—	2	4	no	—
304	C₄²×C₆₇	—	2	4	no	—
305	C₄²×C₆₇	—	2	2	no	—
306	C₄²×C₆₇	—	4	2	no	—
307	C₄²×C₆₇	—	4	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	16	no	—
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	1	no	—
316	C₂³×C₆₇	—	2	1	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	1	no	—
320	C₂³×C₆₇	—	2	1	no	—
321	C₂³×C₆₇	—	2	1	no	—
322	C₂³×C₆₇	—	4	4	no	—
323	C₂³×C₆₇	—	4	4	no	—
324	C₂³×C₆₇	—	4	8	no	—
325	C₂³×C₆₇	—	4	4	no	—
326	C₂³×C₆₇	C₂×#41	1	2	yes	—
327	C₂³×C₆₇	C₂×#41	1	4	yes	—
328	C₂³×C₆₇	C₂×#41	1	4	yes	—
329	C₂³×C₆₇	C₂×#41	1	4	yes	—
330	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
331	Q₈×C₆₇	—	4	4	no	—
332	D₄×C₆₇	—	4	4	no	—
333	D₄×C₆₇	—	4	8	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	16	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	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	2	no	—
353	C₂×C₄×C₆₇	—	2	1	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	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	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	1	no	—
374	C₂×C₄×C₆₇	—	4	4	no	—
375	C₂×C₄×C₆₇	—	4	8	no	—
376	C₂×C₄×C₆₇	—	4	8	no	—
377	C₂×C₄×C₆₇	—	4	8	no	—
378	C₂×C₄×C₆₇	—	4	8	no	—
379	C₂×C₄×C₆₇	—	4	8	no	—
380	C₂×C₄×C₆₇	—	4	4	no	—
381	C₂×C₄×C₆₇	—	4	4	no	—
382	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
383	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
384	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
385	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
386	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
387	C₂²×C₆₇	—	2	4	no	—
388	C₂²×C₆₇	—	2	4	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	4	no	—
394	C₂²×C₆₇	—	2	2	no	—
395	C₂²×C₆₇	—	4	16	no	—
396	C₂²×C₆₇	—	4	1	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	1	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	4	1	no	—
401	C₂²×C₆₇	—	4	1	no	—
402	C₂²×C₆₇	—	4	2	no	—
403	C₂²×C₆₇	—	4	1	no	—
404	C₂²×C₆₇	#529	1	8	yes	—
405	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₆₇	C₂²×#41	1	2	yes	—
407	C₂²×C₆₇	C₂²×#41	1	2	yes	—
408	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²×C₆₇	#585	1	1	yes	characteristic
410	C₄×C₆₇	—	2	4	no	—
411	C₄×C₆₇	—	2	4	no	—
412	C₄×C₆₇	—	2	4	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	C₄×C₆₇	—	4	1	no	—
419	C₄×C₆₇	—	4	1	no	—
420	C₄×C₆₇	—	4	1	no	—
421	C₄×C₆₇	—	4	2	no	—
422	C₄×C₆₇	—	4	2	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	1	no	—
425	C₄×C₆₇	#551	1	4	yes	—
426	#34754	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂×C₆₇	—	2	8	no	—
428	C₂×C₆₇	—	4	2	no	—
429	C₂×C₆₇	—	8	1	no	—
430	C₂×C₆₇	C₂×#529	1	2	yes	—
431	C₂×C₆₇	#3459	1	1	yes	characteristic
432	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
433	C₂×C₆₇	#3475	1	2	yes	—
434	C₂×C₆₇	#3481	1	1	yes	characteristic
435	#2523	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#2518	C₂×C₆₇	1	2	yes	complemented
437	#2517	C₂×C₆₇	1	1	yes	characteristic, complemented
438	#2510	C₂×C₆₇	1	2	yes	complemented
439	#2505	C₂×C₆₇	1	2	yes	complemented
440	#2493	C₂×C₆₇	1	2	yes	complemented
441	#2488	C₂×C₆₇	1	2	yes	complemented
442	#2483	C₂×C₆₇	1	1	yes	characteristic, complemented
443	#2437	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#2412	C₂×C₆₇	1	2	yes	—
445	#2401	C₂×C₆₇	1	2	yes	complemented
446	#2398	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#2395	C₂×C₆₇	1	1	yes	characteristic, complemented
448	C₄×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	complemented
449	C₄×#123	C₂×C₆₇	1	2	yes	complemented
450	C₄×#120	C₂×C₆₇	1	1	yes	characteristic
451	#2290	C₂×C₆₇	1	2	yes	complemented
452	#2283	C₂×C₆₇	1	2	yes	complemented
453	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
454	C₆₇	#34754	1	1	yes	characteristic, direct product factor, Sylow
455	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×#123	C₂²×C₆₇	1	2	yes	—
457	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
458	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
460	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
461	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
464	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
465	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
466	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
467	#401	C₂²×C₆₇	1	2	yes	complemented
468	#400	C₂²×C₆₇	1	1	yes	characteristic, complemented
469	#400	C₂²×C₆₇	1	2	yes	complemented
470	#400	C₂²×C₆₇	1	2	yes	complemented
471	#400	C₂²×C₆₇	1	2	yes	complemented
472	#400	C₂²×C₆₇	1	2	yes	complemented
473	#399	C₂²×C₆₇	1	1	yes	characteristic
474	#398	C₂²×C₆₇	1	1	yes	characteristic, complemented
475	#397	C₂²×C₆₇	1	1	yes	characteristic
476	#397	C₂²×C₆₇	1	1	yes	characteristic
477	#397	C₂²×C₆₇	1	2	yes	—
478	#397	C₂²×C₆₇	1	2	yes	—
479	#397	C₂²×C₆₇	1	2	yes	—
480	#397	C₂²×C₆₇	1	2	yes	complemented
481	#397	C₂²×C₆₇	1	1	yes	characteristic, complemented
482	#396	C₂²×C₆₇	1	2	yes	—
483	#394	C₂²×C₆₇	1	2	yes	—
484	#394	C₂²×C₆₇	1	2	yes	—
485	#393	C₂²×C₆₇	1	1	yes	characteristic
486	#393	C₂²×C₆₇	1	1	yes	characteristic, complemented
487	#391	C₂²×C₆₇	1	2	yes	complemented
488	#389	C₂²×C₆₇	1	2	yes	complemented
489	#388	C₂²×C₆₇	1	2	yes	complemented
490	#388	C₂²×C₆₇	1	2	yes	complemented
491	#388	C₂²×C₆₇	1	2	yes	complemented
492	#388	C₂²×C₆₇	1	2	yes	complemented
493	#387	C₂²×C₆₇	1	2	yes	complemented
494	#387	C₂²×C₆₇	1	2	yes	complemented
495	#387	C₂²×C₆₇	1	2	yes	complemented
496	#387	C₂²×C₆₇	1	2	yes	complemented
497	#387	C₂²×C₆₇	1	2	yes	complemented
498	#387	C₂²×C₆₇	1	2	yes	complemented
499	#386	C₂²×C₆₇	1	2	yes	—
500	#386	C₂²×C₆₇	1	2	yes	—
501	#386	C₂²×C₆₇	1	2	yes	—
502	#386	C₂²×C₆₇	1	2	yes	—
503	#386	C₂²×C₆₇	1	1	yes	characteristic
504	#385	C₂²×C₆₇	1	2	yes	—
505	#385	C₂²×C₆₇	1	2	yes	—
506	#385	C₂²×C₆₇	1	2	yes	—
507	#385	C₂²×C₆₇	1	2	yes	—
508	#385	C₂²×C₆₇	1	2	yes	—
509	#385	C₂²×C₆₇	1	2	yes	—
510	#385	C₂²×C₆₇	1	1	yes	characteristic
511	#383	C₂²×C₆₇	1	2	yes	complemented
512	#383	C₂²×C₆₇	1	2	yes	complemented
513	#382	C₂²×C₆₇	1	2	yes	complemented
514	#382	C₂²×C₆₇	1	2	yes	complemented
515	#381	C₂²×C₆₇	1	2	yes	—
516	#381	C₂²×C₆₇	1	2	yes	—
517	#381	C₂²×C₆₇	1	2	yes	—
518	#380	C₂²×C₆₇	1	2	yes	—
519	#380	C₂²×C₆₇	1	2	yes	—
520	#380	C₂²×C₆₇	1	2	yes	—
521	#379	C₂²×C₆₇	1	1	yes	characteristic
522	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
523	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
524	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
525	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
526	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
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	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
533	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
534	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
537	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
538	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
539	#376	C₂²×C₆₇	1	2	yes	complemented
540	C₂×#95	C₂²×C₆₇	1	2	yes	—
541	C₂×#95	C₂²×C₆₇	1	2	yes	—
542	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
543	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
545	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂³×C₄	—	2	8	no	—
547	C₂³×C₄	—	4	2	no	—
548	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
549	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
552	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
553	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
554	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
556	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
557	#123	—	2	8	no	—
558	C₂²⋊Q₈	—	2	8	no	—
559	#120	—	2	4	no	—
560	C₄×Q₈	—	4	2	no	—
561	C₄×D₄	—	2	8	no	—
562	C₄×D₄	—	4	2	no	—
563	#117	—	4	2	no	—
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₂²⋊C₄	—	2	8	no	—
579	C₂×C₂²⋊C₄	—	2	8	no	—
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	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄²	—	2	8	no	—
601	C₂×C₄²	—	4	4	no	—
602	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
611	C₂×C₄²	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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	1	yes	characteristic
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	#95	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	2	yes	—
642	C₂⁴	—	2	4	no	—
643	C₂⁴	—	2	4	no	—
644	C₂⁴	—	4	1	no	—
645	C₂⁴	—	4	1	no	—
646	C₂⁴	#41×C₆₇	1	4	yes	—
647	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
648	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
649	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
650	C₂×Q₈	—	2	4	no	—
651	C₂×Q₈	—	4	1	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	4	1	no	—
657	C₂×D₄	—	4	1	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	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	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	16	no	—
682	C₂²×C₄	#41×C₆₇	1	8	yes	—
683	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
728	C₂²⋊C₄	—	4	1	no	—
729	C₂²⋊C₄	—	4	1	no	—
730	C₂²⋊C₄	—	4	1	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	16	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	4	no	—
761	C₂³	C₂×#41×C₆₇	1	2	yes	—
762	C₂³	C₂×#41×C₆₇	1	4	yes	—
763	C₂³	C₂×#41×C₆₇	1	4	yes	—
764	C₂³	C₂×#41×C₆₇	1	4	yes	—
765	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
766	Q₈	—	4	4	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	8	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	16	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	2	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	1	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	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
818	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
819	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
820	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
821	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	16	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	#529×C₆₇	1	8	yes	—
840	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
841	C₂²	C₂²×#41×C₆₇	1	2	yes	—
842	C₂²	C₂²×#41×C₆₇	1	2	yes	—
843	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
844	C₂²	#585×C₆₇	1	1	yes	characteristic
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	4	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	#551×C₆₇	1	4	yes	—
861	C₂	—	2	8	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	1	no	—
864	C₂	C₂×#529×C₆₇	1	2	yes	—
865	C₂	C₆₇×#3459	1	1	yes	characteristic
866	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
867	C₂	C₆₇×#3475	1	2	yes	—
868	C₂	C₆₇×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#120×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×#2523	C₂	semidirect
2. C₆₇×#2518	C₂	semidirect
3. C₆₇×#2517	C₂	semidirect
4. C₆₇×#2510	C₂	semidirect
5. C₆₇×#2505	C₂	semidirect
6. C₆₇×#2493	C₂	semidirect
7. C₆₇×#2488	C₂	semidirect
8. C₆₇×#2483	C₂	semidirect
9. C₆₇×#2437	C₂	semidirect
11. C₆₇×#2401	C₂	semidirect
12. C₆₇×#2398	C₂	semidirect
13. C₆₇×#2395	C₂	semidirect
14. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
15. C₄×#123×C₆₇	C₂	semidirect
17. C₆₇×#2290	C₂	semidirect
18. C₆₇×#2283	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
24. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
27. C₂×#117×C₆₇	C₂²	semidirect
32. #401×C₆₇	C₂²	semidirect
33. #400×C₆₇	C₂²	semidirect
34. #400×C₆₇	C₂²	semidirect
35. #400×C₆₇	C₂²	semidirect
36. #400×C₆₇	C₂²	semidirect
37. #400×C₆₇	C₂²	semidirect
39. #398×C₆₇	C₂²	semidirect
45. #397×C₆₇	C₂²	semidirect
46. #397×C₆₇	C₂²	semidirect
51. #393×C₆₇	C₂²	semidirect
52. #391×C₆₇	C₂²	semidirect
53. #389×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #388×C₆₇	C₂²	semidirect
57. #388×C₆₇	C₂²	semidirect
58. #387×C₆₇	C₂²	semidirect
59. #387×C₆₇	C₂²	semidirect
60. #387×C₆₇	C₂²	semidirect
61. #387×C₆₇	C₂²	semidirect
62. #387×C₆₇	C₂²	semidirect
63. #387×C₆₇	C₂²	semidirect
76. #383×C₆₇	C₂²	semidirect
77. #383×C₆₇	C₂²	semidirect
78. #382×C₆₇	C₂²	semidirect
79. #382×C₆₇	C₂²	semidirect
87. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
88. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
89. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
90. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
103. #376×C₆₇	C₂²	semidirect
104. #376×C₆₇	C₂²	semidirect
426. #34754	C₆₇	direct (N × H)
435. #2523	C₂×C₆₇	semidirect
436. #2518	C₂×C₆₇	semidirect
437. #2517	C₂×C₆₇	semidirect
438. #2510	C₂×C₆₇	semidirect
439. #2505	C₂×C₆₇	semidirect
440. #2493	C₂×C₆₇	semidirect
441. #2488	C₂×C₆₇	semidirect
442. #2483	C₂×C₆₇	semidirect
443. #2437	C₂×C₆₇	semidirect
445. #2401	C₂×C₆₇	semidirect
446. #2398	C₂×C₆₇	semidirect
447. #2395	C₂×C₆₇	semidirect
448. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
449. C₄×#123	C₂×C₆₇	semidirect
451. #2290	C₂×C₆₇	semidirect
452. #2283	C₂×C₆₇	semidirect
453. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
454. C₆₇	#34754	direct (N × H)
459. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
462. C₂×#117	C₂²×C₆₇	semidirect
467. #401	C₂²×C₆₇	semidirect
468. #400	C₂²×C₆₇	semidirect
469. #400	C₂²×C₆₇	semidirect
470. #400	C₂²×C₆₇	semidirect
471. #400	C₂²×C₆₇	semidirect
472. #400	C₂²×C₆₇	semidirect
474. #398	C₂²×C₆₇	semidirect
480. #397	C₂²×C₆₇	semidirect
481. #397	C₂²×C₆₇	semidirect
486. #393	C₂²×C₆₇	semidirect
487. #391	C₂²×C₆₇	semidirect
488. #389	C₂²×C₆₇	semidirect
489. #388	C₂²×C₆₇	semidirect
490. #388	C₂²×C₆₇	semidirect
491. #388	C₂²×C₆₇	semidirect
492. #388	C₂²×C₆₇	semidirect
493. #387	C₂²×C₆₇	semidirect
494. #387	C₂²×C₆₇	semidirect
495. #387	C₂²×C₆₇	semidirect
496. #387	C₂²×C₆₇	semidirect
497. #387	C₂²×C₆₇	semidirect
498. #387	C₂²×C₆₇	semidirect
511. #383	C₂²×C₆₇	semidirect
512. #383	C₂²×C₆₇	semidirect
513. #382	C₂²×C₆₇	semidirect
514. #382	C₂²×C₆₇	semidirect
522. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
523. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
524. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
525. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
536. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
537. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
538. #376	C₂²×C₆₇	semidirect
539. #376	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2523	2
C₆₇×#2518	2
C₆₇×#2517	2
C₆₇×#2510	2
C₆₇×#2505	2
C₆₇×#2493	2
C₆₇×#2488	2
C₆₇×#2483	2
C₆₇×#2437	2
C₆₇×#2412	2
C₆₇×#2401	2
C₆₇×#2398	2
C₆₇×#2395	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#123×C₆₇	2
C₄×#120×C₆₇	2
C₆₇×#2290	2
C₆₇×#2283	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
#34754	67

Subgroups — C67×#34754 #30714005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34754 #30714005