Subgroups — C₆₇×#59546 #30738797

Order 17152.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2786	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2743	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2526	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2515	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2486	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2471	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2461	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2438	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2423	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2341	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#123×C₆₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	#400×C₆₇	C₂²	1	2	yes	—
40	#400×C₆₇	C₂²	1	2	yes	—
41	#400×C₆₇	C₂²	1	2	yes	—
42	#399×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#398×C₆₇	C₂²	1	2	yes	—
45	#397×C₆₇	C₂²	1	2	yes	—
46	#397×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#396×C₆₇	C₂²	1	2	yes	—
49	#396×C₆₇	C₂²	1	2	yes	—
50	#396×C₆₇	C₂²	1	2	yes	—
51	#395×C₆₇	C₂²	1	2	yes	—
52	#394×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#392×C₆₇	C₂²	1	2	yes	—
55	#391×C₆₇	C₂²	1	1	yes	characteristic
56	#391×C₆₇	C₂²	1	1	yes	characteristic
57	#391×C₆₇	C₂²	1	1	yes	characteristic
58	#391×C₆₇	C₂²	1	1	yes	characteristic
59	#390×C₆₇	C₂²	1	2	yes	—
60	#390×C₆₇	C₂²	1	2	yes	—
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#390×C₆₇	C₂²	1	1	yes	characteristic
63	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#390×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	1	yes	characteristic
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	2	yes	—
68	#389×C₆₇	C₂²	1	1	yes	characteristic
69	#389×C₆₇	C₂²	1	1	yes	characteristic
70	#389×C₆₇	C₂²	1	1	yes	characteristic
71	#389×C₆₇	C₂²	1	1	yes	characteristic
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	1	yes	characteristic
76	#388×C₆₇	C₂²	1	2	yes	—
77	#388×C₆₇	C₂²	1	1	yes	characteristic
78	#388×C₆₇	C₂²	1	2	yes	—
79	#388×C₆₇	C₂²	1	1	yes	characteristic
80	#388×C₆₇	C₂²	1	1	yes	characteristic
81	#388×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	2	yes	—
92	#386×C₆₇	C₂²	1	2	yes	—
93	#386×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#385×C₆₇	C₂²	1	2	yes	—
97	#384×C₆₇	C₂²	1	1	yes	characteristic
98	#383×C₆₇	C₂²	1	2	yes	—
99	#382×C₆₇	C₂²	1	1	yes	characteristic
100	#382×C₆₇	C₂²	1	1	yes	characteristic
101	#381×C₆₇	C₂²	1	2	yes	—
102	#381×C₆₇	C₂²	1	2	yes	—
103	#381×C₆₇	C₂²	1	2	yes	—
104	#380×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	2	yes	—
107	#380×C₆₇	C₂²	1	1	yes	characteristic
108	#380×C₆₇	C₂²	1	2	yes	—
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	#376×C₆₇	C₂²	1	2	yes	—
121	C₂×#95×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂×#41×C₆₇	—	2	4	no	—
124	C₂×#41×C₆₇	—	2	4	no	—
125	C₂×#41×C₆₇	—	4	2	no	—
126	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	#124×C₆₇	—	2	4	no	—
139	#123×C₆₇	—	4	4	no	—
140	C₂²⋊Q₈×C₆₇	—	2	4	no	—
141	C₂²⋊Q₈×C₆₇	—	4	4	no	—
142	#121×C₆₇	—	2	4	no	—
143	C₄×Q₈×C₆₇	—	2	4	no	—
144	C₄×Q₈×C₆₇	—	4	2	no	—
145	C₄×Q₈×C₆₇	—	4	2	no	—
146	C₄×D₄×C₆₇	—	2	4	no	—
147	C₄×D₄×C₆₇	—	2	8	no	—
148	C₄×D₄×C₆₇	—	4	2	no	—
149	C₄×D₄×C₆₇	—	4	2	no	—
150	#117×C₆₇	—	4	4	no	—
151	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	#95×C₆₇	C₂³	1	1	yes	characteristic
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	1	yes	characteristic
223	#95×C₆₇	C₂³	1	1	yes	characteristic
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
242	#41×C₆₇	—	4	16	no	—
243	C₂×Q₈×C₆₇	—	2	2	no	—
244	C₂×Q₈×C₆₇	—	2	2	no	—
245	C₂×Q₈×C₆₇	—	2	2	no	—
246	C₂×Q₈×C₆₇	—	2	2	no	—
247	C₂×Q₈×C₆₇	—	4	1	no	—
248	C₂×Q₈×C₆₇	#41	1	4	yes	—
249	C₂×D₄×C₆₇	—	2	4	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	4	1	no	—
258	C₂×D₄×C₆₇	—	4	2	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	#41	1	4	yes	—
261	C₂²×C₄×C₆₇	—	2	4	no	—
262	C₂²×C₄×C₆₇	—	2	4	no	—
263	C₂²×C₄×C₆₇	—	2	4	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	4	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	2	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	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	2	no	—
276	C₂²×C₄×C₆₇	—	4	2	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₆₇	—	2	4	no	—
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	4	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	4	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	4	no	—
309	C₄⋊C₄×C₆₇	—	2	4	no	—
310	C₄⋊C₄×C₆₇	—	4	2	no	—
311	C₄⋊C₄×C₆₇	—	4	2	no	—
312	C₄⋊C₄×C₆₇	—	4	2	no	—
313	C₄⋊C₄×C₆₇	—	4	2	no	—
314	C₄⋊C₄×C₆₇	—	4	1	no	—
315	C₄⋊C₄×C₆₇	—	4	1	no	—
316	C₄⋊C₄×C₆₇	—	4	1	no	—
317	C₄⋊C₄×C₆₇	—	4	2	no	—
318	C₄⋊C₄×C₆₇	—	4	1	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₄⋊C₄×C₆₇	—	4	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	2	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	—	2	2	no	—
331	C₂²⋊C₄×C₆₇	—	4	1	no	—
332	C₂²⋊C₄×C₆₇	—	4	2	no	—
333	C₂²⋊C₄×C₆₇	—	4	1	no	—
334	C₂²⋊C₄×C₆₇	—	4	2	no	—
335	C₂²⋊C₄×C₆₇	—	4	2	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	—	4	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	1	no	—
339	C₂²⋊C₄×C₆₇	—	4	1	no	—
340	C₂²⋊C₄×C₆₇	—	4	2	no	—
341	C₂²⋊C₄×C₆₇	—	4	2	no	—
342	C₂²⋊C₄×C₆₇	—	4	2	no	—
343	C₂²⋊C₄×C₆₇	—	4	2	no	—
344	C₂²⋊C₄×C₆₇	#41	1	4	yes	complemented
345	C₄²×C₆₇	—	2	2	no	—
346	C₄²×C₆₇	—	2	4	no	—
347	C₄²×C₆₇	—	2	4	no	—
348	C₄²×C₆₇	—	2	2	no	—
349	C₄²×C₆₇	—	2	2	no	—
350	C₄²×C₆₇	—	2	2	no	—
351	C₄²×C₆₇	—	2	2	no	—
352	C₄²×C₆₇	—	2	2	no	—
353	C₄²×C₆₇	—	2	2	no	—
354	C₄²×C₆₇	—	2	2	no	—
355	C₄²×C₆₇	—	4	1	no	—
356	C₄²×C₆₇	—	4	2	no	—
357	C₄²×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	2	1	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	1	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	1	no	—
364	C₂³×C₆₇	—	2	1	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	1	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	1	no	—
370	C₂³×C₆₇	—	2	1	no	—
371	C₂³×C₆₇	—	2	1	no	—
372	C₂³×C₆₇	—	2	1	no	—
373	C₂³×C₆₇	—	2	1	no	—
374	C₂³×C₆₇	—	2	1	no	—
375	C₂³×C₆₇	—	2	1	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	C₂×#41	1	4	yes	—
378	C₂³×C₆₇	C₂×#41	1	2	yes	—
379	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
380	Q₈×C₆₇	—	2	8	no	—
381	Q₈×C₆₇	—	4	4	no	—
382	D₄×C₆₇	—	2	8	no	—
383	D₄×C₆₇	—	4	4	no	—
384	D₄×C₆₇	—	4	8	no	—
385	D₄×C₆₇	—	4	8	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	4	8	no	—
439	C₂×C₄×C₆₇	—	4	8	no	—
440	C₂×C₄×C₆₇	—	4	4	no	—
441	C₂×C₄×C₆₇	—	4	4	no	—
442	C₂×C₄×C₆₇	—	8	4	no	—
443	C₂×C₄×C₆₇	—	8	4	no	—
444	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
445	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
446	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
447	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
448	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
449	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
450	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
451	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
452	C₂²×C₆₇	—	2	4	no	—
453	C₂²×C₆₇	—	2	2	no	—
454	C₂²×C₆₇	—	2	4	no	—
455	C₂²×C₆₇	—	2	2	no	—
456	C₂²×C₆₇	—	2	2	no	—
457	C₂²×C₆₇	—	2	4	no	—
458	C₂²×C₆₇	—	4	1	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	1	no	—
461	C₂²×C₆₇	—	4	2	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	1	no	—
464	C₂²×C₆₇	—	4	1	no	—
465	C₂²×C₆₇	—	4	2	no	—
466	C₂²×C₆₇	—	4	1	no	—
467	C₂²×C₆₇	—	4	1	no	—
468	C₂²×C₆₇	—	4	1	no	—
469	C₂²×C₆₇	—	4	1	no	—
470	C₂²×C₆₇	—	4	1	no	—
471	C₂²×C₆₇	—	4	1	no	—
472	C₂²×C₆₇	—	4	1	no	—
473	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
474	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
475	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
476	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
479	C₂²×C₆₇	#585	1	1	yes	characteristic
480	C₄×C₆₇	—	2	4	no	—
481	C₄×C₆₇	—	2	2	no	—
482	C₄×C₆₇	—	2	2	no	—
483	C₄×C₆₇	—	2	2	no	—
484	C₄×C₆₇	—	2	2	no	—
485	C₄×C₆₇	—	4	1	no	—
486	C₄×C₆₇	—	4	1	no	—
487	C₄×C₆₇	—	4	1	no	—
488	C₄×C₆₇	—	4	2	no	—
489	C₄×C₆₇	—	4	1	no	—
490	C₄×C₆₇	—	4	2	no	—
491	C₄×C₆₇	—	4	2	no	—
492	C₄×C₆₇	—	4	2	no	—
493	C₄×C₆₇	—	4	2	no	—
494	C₄×C₆₇	—	4	1	no	—
495	C₄×C₆₇	—	4	2	no	—
496	C₄×C₆₇	—	4	1	no	—
497	C₄×C₆₇	—	4	1	no	—
498	C₄×C₆₇	—	4	1	no	—
499	C₄×C₆₇	#551	1	4	yes	—
500	#59546	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
501	C₂×C₆₇	—	4	4	no	—
502	C₂×C₆₇	—	4	2	no	—
503	C₂×C₆₇	—	8	1	no	—
504	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
505	C₂×C₆₇	#3475	1	1	yes	characteristic
506	C₂×C₆₇	#3482	1	1	yes	characteristic
507	C₂×C₆₇	#3517	1	1	yes	characteristic
508	C₂×C₆₇	#3519	1	1	yes	characteristic
509	C₂×C₆₇	#3520	1	1	yes	characteristic
510	C₂×C₆₇	#3547	1	1	yes	characteristic
511	#2786	C₂×C₆₇	1	2	yes	complemented
512	#2743	C₂×C₆₇	1	2	yes	complemented
513	#2581	C₂×C₆₇	1	1	yes	characteristic, complemented
514	#2538	C₂×C₆₇	1	1	yes	characteristic, complemented
515	#2526	C₂×C₆₇	1	2	yes	complemented
516	#2515	C₂×C₆₇	1	2	yes	complemented
517	#2497	C₂×C₆₇	1	1	yes	characteristic, complemented
518	#2495	C₂×C₆₇	1	1	yes	characteristic, complemented
519	#2486	C₂×C₆₇	1	1	yes	characteristic, complemented
520	#2471	C₂×C₆₇	1	2	yes	complemented
521	#2461	C₂×C₆₇	1	2	yes	complemented
522	#2438	C₂×C₆₇	1	2	yes	complemented
523	#2423	C₂×C₆₇	1	1	yes	characteristic, complemented
524	#2420	C₂×C₆₇	1	1	yes	characteristic, complemented
525	#2407	C₂×C₆₇	1	1	yes	characteristic
526	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
527	#2360	C₂×C₆₇	1	1	yes	characteristic, complemented
528	#2353	C₂×C₆₇	1	2	yes	complemented
529	#2341	C₂×C₆₇	1	1	yes	characteristic, complemented
530	#2339	C₂×C₆₇	1	1	yes	characteristic, complemented
531	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
532	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
533	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
534	C₆₇	#59546	1	1	yes	characteristic, direct product factor, Sylow
535	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
536	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
537	C₂×#123	C₂²×C₆₇	1	2	yes	—
538	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
539	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
540	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
541	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
545	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
546	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
547	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
548	C₂×#117	C₂²×C₆₇	1	2	yes	—
549	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
550	#400	C₂²×C₆₇	1	2	yes	—
551	#400	C₂²×C₆₇	1	2	yes	—
552	#400	C₂²×C₆₇	1	2	yes	—
553	#399	C₂²×C₆₇	1	2	yes	—
554	#398	C₂²×C₆₇	1	2	yes	—
555	#398	C₂²×C₆₇	1	2	yes	—
556	#397	C₂²×C₆₇	1	2	yes	—
557	#397	C₂²×C₆₇	1	2	yes	—
558	#397	C₂²×C₆₇	1	2	yes	—
559	#396	C₂²×C₆₇	1	2	yes	—
560	#396	C₂²×C₆₇	1	2	yes	—
561	#396	C₂²×C₆₇	1	2	yes	—
562	#395	C₂²×C₆₇	1	2	yes	—
563	#394	C₂²×C₆₇	1	2	yes	—
564	#394	C₂²×C₆₇	1	2	yes	—
565	#392	C₂²×C₆₇	1	2	yes	—
566	#391	C₂²×C₆₇	1	1	yes	characteristic
567	#391	C₂²×C₆₇	1	1	yes	characteristic
568	#391	C₂²×C₆₇	1	1	yes	characteristic
569	#391	C₂²×C₆₇	1	1	yes	characteristic
570	#390	C₂²×C₆₇	1	1	yes	characteristic
571	#390	C₂²×C₆₇	1	1	yes	characteristic
572	#390	C₂²×C₆₇	1	2	yes	—
573	#390	C₂²×C₆₇	1	2	yes	—
574	#390	C₂²×C₆₇	1	1	yes	characteristic
575	#390	C₂²×C₆₇	1	1	yes	characteristic
576	#389	C₂²×C₆₇	1	1	yes	characteristic
577	#389	C₂²×C₆₇	1	1	yes	characteristic
578	#389	C₂²×C₆₇	1	2	yes	—
579	#389	C₂²×C₆₇	1	1	yes	characteristic
580	#389	C₂²×C₆₇	1	1	yes	characteristic
581	#389	C₂²×C₆₇	1	1	yes	characteristic
582	#389	C₂²×C₆₇	1	1	yes	characteristic
583	#388	C₂²×C₆₇	1	1	yes	characteristic
584	#388	C₂²×C₆₇	1	2	yes	—
585	#388	C₂²×C₆₇	1	2	yes	—
586	#388	C₂²×C₆₇	1	2	yes	—
587	#388	C₂²×C₆₇	1	2	yes	—
588	#388	C₂²×C₆₇	1	2	yes	—
589	#388	C₂²×C₆₇	1	1	yes	characteristic
590	#388	C₂²×C₆₇	1	2	yes	—
591	#388	C₂²×C₆₇	1	1	yes	characteristic
592	#388	C₂²×C₆₇	1	1	yes	characteristic
593	#387	C₂²×C₆₇	1	2	yes	—
594	#387	C₂²×C₆₇	1	2	yes	—
595	#387	C₂²×C₆₇	1	2	yes	—
596	#387	C₂²×C₆₇	1	2	yes	—
597	#387	C₂²×C₆₇	1	2	yes	—
598	#387	C₂²×C₆₇	1	2	yes	—
599	#387	C₂²×C₆₇	1	2	yes	—
600	#386	C₂²×C₆₇	1	2	yes	—
601	#386	C₂²×C₆₇	1	2	yes	—
602	#386	C₂²×C₆₇	1	2	yes	—
603	#386	C₂²×C₆₇	1	2	yes	—
604	#386	C₂²×C₆₇	1	2	yes	—
605	#385	C₂²×C₆₇	1	2	yes	—
606	#385	C₂²×C₆₇	1	2	yes	—
607	#385	C₂²×C₆₇	1	2	yes	—
608	#384	C₂²×C₆₇	1	1	yes	characteristic
609	#383	C₂²×C₆₇	1	2	yes	—
610	#382	C₂²×C₆₇	1	1	yes	characteristic
611	#382	C₂²×C₆₇	1	1	yes	characteristic
612	#381	C₂²×C₆₇	1	2	yes	—
613	#381	C₂²×C₆₇	1	2	yes	—
614	#381	C₂²×C₆₇	1	2	yes	—
615	#380	C₂²×C₆₇	1	1	yes	characteristic
616	#380	C₂²×C₆₇	1	2	yes	—
617	#380	C₂²×C₆₇	1	1	yes	characteristic
618	#380	C₂²×C₆₇	1	2	yes	—
619	#380	C₂²×C₆₇	1	1	yes	characteristic
620	#380	C₂²×C₆₇	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
624	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
625	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
626	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
627	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
628	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
629	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
630	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
631	#376	C₂²×C₆₇	1	2	yes	—
632	C₂×#95	C₂²×C₆₇	1	2	yes	—
633	C₄³	C₂²×C₆₇	1	1	yes	characteristic
634	C₂×#41	—	2	4	no	—
635	C₂×#41	—	2	4	no	—
636	C₂×#41	—	4	2	no	—
637	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
638	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
639	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
640	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
642	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
643	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
646	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
647	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
648	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
649	#124	—	2	4	no	—
650	#123	—	4	4	no	—
651	C₂²⋊Q₈	—	2	4	no	—
652	C₂²⋊Q₈	—	4	4	no	—
653	#121	—	2	4	no	—
654	C₄×Q₈	—	2	4	no	—
655	C₄×Q₈	—	4	2	no	—
656	C₄×Q₈	—	4	2	no	—
657	C₄×D₄	—	2	4	no	—
658	C₄×D₄	—	2	8	no	—
659	C₄×D₄	—	4	2	no	—
660	C₄×D₄	—	4	2	no	—
661	#117	—	4	4	no	—
662	C₂×C₄⋊C₄	—	4	2	no	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
714	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
717	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
720	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
721	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
722	#95	C₂³×C₆₇	1	1	yes	characteristic
723	#95	C₂³×C₆₇	1	2	yes	—
724	#95	C₂³×C₆₇	1	2	yes	—
725	#95	C₂³×C₆₇	1	2	yes	—
726	#95	C₂³×C₆₇	1	2	yes	—
727	#95	C₂³×C₆₇	1	2	yes	—
728	#95	C₂³×C₆₇	1	2	yes	—
729	#95	C₂³×C₆₇	1	1	yes	characteristic
730	#95	C₂³×C₆₇	1	2	yes	—
731	#95	C₂³×C₆₇	1	1	yes	characteristic
732	#95	C₂³×C₆₇	1	2	yes	—
733	#95	C₂³×C₆₇	1	1	yes	characteristic
734	#95	C₂³×C₆₇	1	1	yes	characteristic
735	#95	C₂³×C₆₇	1	2	yes	—
736	#95	C₂³×C₆₇	1	1	yes	characteristic
737	#95	C₂³×C₆₇	1	1	yes	characteristic
738	#95	C₂³×C₆₇	1	2	yes	—
739	#95	C₂³×C₆₇	1	1	yes	characteristic
740	#95	C₂³×C₆₇	1	2	yes	—
741	#95	C₂³×C₆₇	1	2	yes	—
742	#95	C₂³×C₆₇	1	2	yes	—
743	#95	C₂³×C₆₇	1	2	yes	—
744	#95	C₂³×C₆₇	1	2	yes	—
745	#95	C₂³×C₆₇	1	2	yes	—
746	#95	C₂³×C₆₇	1	2	yes	—
747	#95	C₂³×C₆₇	1	2	yes	—
748	#95	C₂³×C₆₇	1	2	yes	—
749	#95	C₂³×C₆₇	1	2	yes	—
750	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
752	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
753	#41	—	4	16	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	4	1	no	—
759	C₂×Q₈	#41×C₆₇	1	4	yes	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	4	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	4	1	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	#41×C₆₇	1	4	yes	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	—	2	4	no	—
774	C₂²×C₄	—	2	4	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	4	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	4	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	—	4	1	no	—
824	C₄⋊C₄	—	4	1	no	—
825	C₄⋊C₄	—	4	1	no	—
826	C₄⋊C₄	—	4	2	no	—
827	C₄⋊C₄	—	4	1	no	—
828	C₄⋊C₄	—	4	2	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	1	no	—
845	C₂²⋊C₄	—	4	1	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	1	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	4	1	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	2	no	—
855	C₂²⋊C₄	#41×C₆₇	1	4	yes	complemented
856	C₄²	—	2	2	no	—
857	C₄²	—	2	4	no	—
858	C₄²	—	2	4	no	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	4	2	no	—
867	C₄²	—	4	2	no	—
868	C₄²	—	4	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	2	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	C₂×#41×C₆₇	1	4	yes	—
889	C₂³	C₂×#41×C₆₇	1	2	yes	—
890	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
891	Q₈	—	2	8	no	—
892	Q₈	—	4	4	no	—
893	D₄	—	2	8	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	8	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	4	8	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	8	4	no	—
954	C₂×C₄	—	8	4	no	—
955	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
956	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
957	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
958	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
959	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
960	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
961	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
962	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
963	C₂²	—	2	4	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	4	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	4	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	1	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	4	1	no	—
983	C₂²	—	4	1	no	—
984	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
985	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
986	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
987	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
988	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
989	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
990	C₂²	#585×C₆₇	1	1	yes	characteristic
991	C₄	—	2	4	no	—
992	C₄	—	2	2	no	—
993	C₄	—	2	2	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	2	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	#551×C₆₇	1	4	yes	—
1011	C₂	—	4	4	no	—
1012	C₂	—	4	2	no	—
1013	C₂	—	8	1	no	—
1014	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
1015	C₂	C₆₇×#3475	1	1	yes	characteristic
1016	C₂	C₆₇×#3482	1	1	yes	characteristic
1017	C₂	C₆₇×#3517	1	1	yes	characteristic
1018	C₂	C₆₇×#3519	1	1	yes	characteristic
1019	C₂	C₆₇×#3520	1	1	yes	characteristic
1020	C₂	C₆₇×#3547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2407	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×#2786	C₂	semidirect
2. C₆₇×#2743	C₂	semidirect
3. C₆₇×#2581	C₂	semidirect
4. C₆₇×#2538	C₂	semidirect
5. C₆₇×#2526	C₂	semidirect
6. C₆₇×#2515	C₂	semidirect
7. C₆₇×#2497	C₂	semidirect
8. C₆₇×#2495	C₂	semidirect
9. C₆₇×#2486	C₂	semidirect
10. C₆₇×#2471	C₂	semidirect
11. C₆₇×#2461	C₂	semidirect
12. C₆₇×#2438	C₂	semidirect
13. C₆₇×#2423	C₂	semidirect
14. C₆₇×#2420	C₂	semidirect
16. C₆₇×#2361	C₂	semidirect
17. C₆₇×#2360	C₂	semidirect
18. C₆₇×#2353	C₂	semidirect
19. C₆₇×#2341	C₂	semidirect
20. C₆₇×#2339	C₂	semidirect
21. C₄×#124×C₆₇	C₂	semidirect
22. C₆₇×#2295	C₂	semidirect
23. C₆₇×#2293	C₂	semidirect
344. C₂²⋊C₄×C₆₇	#41	semidirect
500. #59546	C₆₇	direct (N × H)
511. #2786	C₂×C₆₇	semidirect
512. #2743	C₂×C₆₇	semidirect
513. #2581	C₂×C₆₇	semidirect
514. #2538	C₂×C₆₇	semidirect
515. #2526	C₂×C₆₇	semidirect
516. #2515	C₂×C₆₇	semidirect
517. #2497	C₂×C₆₇	semidirect
518. #2495	C₂×C₆₇	semidirect
519. #2486	C₂×C₆₇	semidirect
520. #2471	C₂×C₆₇	semidirect
521. #2461	C₂×C₆₇	semidirect
522. #2438	C₂×C₆₇	semidirect
523. #2423	C₂×C₆₇	semidirect
524. #2420	C₂×C₆₇	semidirect
526. #2361	C₂×C₆₇	semidirect
527. #2360	C₂×C₆₇	semidirect
528. #2353	C₂×C₆₇	semidirect
529. #2341	C₂×C₆₇	semidirect
530. #2339	C₂×C₆₇	semidirect
531. C₄×#124	C₂×C₆₇	semidirect
532. #2295	C₂×C₆₇	semidirect
533. #2293	C₂×C₆₇	semidirect
534. C₆₇	#59546	direct (N × H)
855. C₂²⋊C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2786	2
C₆₇×#2743	2
C₆₇×#2581	2
C₆₇×#2538	2
C₆₇×#2526	2
C₆₇×#2515	2
C₆₇×#2497	2
C₆₇×#2495	2
C₆₇×#2486	2
C₆₇×#2471	2
C₆₇×#2461	2
C₆₇×#2438	2
C₆₇×#2423	2
C₆₇×#2420	2
C₆₇×#2407	2
C₆₇×#2361	2
C₆₇×#2360	2
C₆₇×#2353	2
C₆₇×#2341	2
C₆₇×#2339	2
C₄×#124×C₆₇	2
C₆₇×#2295	2
C₆₇×#2293	2
#59546	67

Subgroups — C67×#59546 #30738797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59546 #30738797