Subgroups — C₆₇×#59461 #30738712

Order 17152.

1772 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2768	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2720	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2589	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2549	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2542	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2522	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2465	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2452	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2423	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic
19	Q₈×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic
21	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	#400×C₆₇	C₂²	1	2	yes	—
40	#399×C₆₇	C₂²	1	2	yes	—
41	#399×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	#398×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	—
47	#398×C₆₇	C₂²	1	2	yes	—
48	#398×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	#395×C₆₇	C₂²	1	2	yes	—
53	#395×C₆₇	C₂²	1	2	yes	—
54	#393×C₆₇	C₂²	1	2	yes	—
55	#391×C₆₇	C₂²	1	2	yes	—
56	#391×C₆₇	C₂²	1	2	yes	—
57	#391×C₆₇	C₂²	1	2	yes	—
58	#391×C₆₇	C₂²	1	1	yes	characteristic
59	#391×C₆₇	C₂²	1	1	yes	characteristic
60	#391×C₆₇	C₂²	1	2	yes	—
61	#391×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	2	yes	—
66	#389×C₆₇	C₂²	1	2	yes	—
67	#389×C₆₇	C₂²	1	2	yes	—
68	#389×C₆₇	C₂²	1	2	yes	—
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	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	1	yes	characteristic
74	#389×C₆₇	C₂²	1	1	yes	characteristic
75	#389×C₆₇	C₂²	1	1	yes	characteristic
76	#389×C₆₇	C₂²	1	1	yes	characteristic
77	#388×C₆₇	C₂²	1	2	yes	—
78	#388×C₆₇	C₂²	1	2	yes	—
79	#388×C₆₇	C₂²	1	2	yes	—
80	#388×C₆₇	C₂²	1	2	yes	—
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	1	yes	characteristic
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	1	yes	characteristic
88	#387×C₆₇	C₂²	1	1	yes	characteristic
89	#387×C₆₇	C₂²	1	1	yes	characteristic
90	#387×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	2	yes	—
92	#387×C₆₇	C₂²	1	2	yes	—
93	#385×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	#385×C₆₇	C₂²	1	2	yes	—
98	#385×C₆₇	C₂²	1	2	yes	—
99	#384×C₆₇	C₂²	1	1	yes	characteristic
100	#384×C₆₇	C₂²	1	1	yes	characteristic
101	#384×C₆₇	C₂²	1	2	yes	—
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#382×C₆₇	C₂²	1	1	yes	characteristic
104	#382×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	2	yes	—
106	#380×C₆₇	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₂×#95×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₆₇	—	2	4	no	—
131	C₄⋊Q₈×C₆₇	—	4	2	no	—
132	#125×C₆₇	—	2	4	no	—
133	#125×C₆₇	—	4	2	no	—
134	#124×C₆₇	Q₈	1	8	yes	complemented
135	C₂²⋊Q₈×C₆₇	—	2	8	no	—
136	C₂²⋊Q₈×C₆₇	—	4	4	no	—
137	C₂²⋊Q₈×C₆₇	—	4	4	no	—
138	C₄×Q₈×C₆₇	—	2	4	no	—
139	C₄×Q₈×C₆₇	—	4	2	no	—
140	C₄×Q₈×C₆₇	—	4	4	no	—
141	C₄×Q₈×C₆₇	—	4	2	no	—
142	C₄×D₄×C₆₇	—	2	4	no	—
143	C₄×D₄×C₆₇	—	4	2	no	—
144	C₄×D₄×C₆₇	—	4	2	no	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄²×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	2	yes	—
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	1	yes	characteristic
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	1	yes	characteristic
212	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
219	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₆₇	—	2	2	no	—
239	C₂×Q₈×C₆₇	—	2	4	no	—
240	C₂×Q₈×C₆₇	—	2	4	no	—
241	C₂×Q₈×C₆₇	—	2	2	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	4	2	no	—
244	C₂×Q₈×C₆₇	—	4	2	no	—
245	C₂×Q₈×C₆₇	—	4	2	no	—
246	C₂×Q₈×C₆₇	C₂×Q₈	1	4	yes	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
250	C₂²×C₄×C₆₇	—	2	4	no	—
251	C₂²×C₄×C₆₇	—	2	4	no	—
252	C₂²×C₄×C₆₇	—	2	4	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	2	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	—	4	2	no	—
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	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	4	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	4	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	4	1	no	—
301	C₄⋊C₄×C₆₇	—	4	1	no	—
302	C₄⋊C₄×C₆₇	—	4	2	no	—
303	C₄⋊C₄×C₆₇	—	4	2	no	—
304	C₄⋊C₄×C₆₇	—	4	2	no	—
305	C₄⋊C₄×C₆₇	—	4	2	no	—
306	C₄⋊C₄×C₆₇	—	4	2	no	—
307	C₄⋊C₄×C₆₇	—	4	2	no	—
308	C₄⋊C₄×C₆₇	—	4	2	no	—
309	C₄⋊C₄×C₆₇	—	4	2	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	#41	1	4	yes	—
315	C₄⋊C₄×C₆₇	#41	1	4	yes	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	4	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	4	2	no	—
321	C₂²⋊C₄×C₆₇	—	4	2	no	—
322	C₂²⋊C₄×C₆₇	—	4	2	no	—
323	C₂²⋊C₄×C₆₇	—	4	2	no	—
324	C₂²⋊C₄×C₆₇	—	4	2	no	—
325	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
326	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	2	4	no	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	2	no	—
331	C₄²×C₆₇	—	2	2	no	—
332	C₄²×C₆₇	—	2	2	no	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	2	no	—
335	C₄²×C₆₇	—	2	2	no	—
336	C₄²×C₆₇	—	2	2	no	—
337	C₄²×C₆₇	—	4	1	no	—
338	C₄²×C₆₇	—	4	2	no	—
339	C₄²×C₆₇	—	4	2	no	—
340	C₄²×C₆₇	—	4	2	no	—
341	C₄²×C₆₇	—	4	2	no	—
342	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
350	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
351	Q₈×C₆₇	—	2	8	no	—
352	Q₈×C₆₇	—	4	8	no	—
353	Q₈×C₆₇	—	8	4	no	—
354	D₄×C₆₇	—	2	8	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	1	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	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	1	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	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	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	8	4	no	—
410	C₂×C₄×C₆₇	—	8	4	no	—
411	C₂×C₄×C₆₇	—	8	4	no	—
412	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
413	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
414	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
415	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
416	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
417	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
418	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
419	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
420	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
421	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
423	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
424	C₂²×C₆₇	—	2	4	no	—
425	C₂²×C₆₇	—	2	4	no	—
426	C₂²×C₆₇	—	2	4	no	—
427	C₂²×C₆₇	—	4	2	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	2	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
432	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
433	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
434	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
437	C₂²×C₆₇	#585	1	1	yes	characteristic
438	C₄×C₆₇	—	2	4	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	2	no	—
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	2	no	—
443	C₄×C₆₇	—	2	2	no	—
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	2	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	1	no	—
449	C₄×C₆₇	—	4	1	no	—
450	C₄×C₆₇	—	4	2	no	—
451	C₄×C₆₇	—	4	2	no	—
452	C₄×C₆₇	—	4	2	no	—
453	C₄×C₆₇	—	4	1	no	—
454	C₄×C₆₇	—	4	1	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	1	no	—
457	C₄×C₆₇	—	4	1	no	—
458	C₄×C₆₇	—	4	2	no	—
459	C₄×C₆₇	#554	1	4	yes	—
460	#59461	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂×C₆₇	—	4	4	no	—
462	C₂×C₆₇	C₂×#554	1	1	yes	characteristic
463	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
464	C₂×C₆₇	#3482	1	1	yes	characteristic
465	C₂×C₆₇	#3503	1	1	yes	characteristic
466	C₂×C₆₇	#3508	1	1	yes	characteristic
467	C₂×C₆₇	#3513	1	1	yes	characteristic
468	C₂×C₆₇	#3561	1	1	yes	characteristic
469	#2768	C₂×C₆₇	1	2	yes	complemented
470	#2720	C₂×C₆₇	1	2	yes	complemented
471	#2589	C₂×C₆₇	1	2	yes	complemented
472	#2570	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#2565	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#2550	C₂×C₆₇	1	1	yes	characteristic, complemented
475	#2549	C₂×C₆₇	1	2	yes	complemented
476	#2542	C₂×C₆₇	1	1	yes	characteristic
477	#2522	C₂×C₆₇	1	2	yes	complemented
478	#2465	C₂×C₆₇	1	2	yes	complemented
479	#2454	C₂×C₆₇	1	1	yes	characteristic
480	#2452	C₂×C₆₇	1	1	yes	characteristic
481	#2451	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#2451	C₂×C₆₇	1	1	yes	characteristic, complemented
483	#2423	C₂×C₆₇	1	2	yes	complemented
484	#2368	C₂×C₆₇	1	2	yes	complemented
485	#2367	C₂×C₆₇	1	1	yes	characteristic
486	#2367	C₂×C₆₇	1	1	yes	characteristic
487	Q₈×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#2349	C₂×C₆₇	1	1	yes	characteristic
489	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
490	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
491	C₄×#124	C₂×C₆₇	1	1	yes	characteristic
492	C₆₇	#59461	1	1	yes	characteristic, direct product factor, Sylow
493	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
494	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
495	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
496	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
498	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
499	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
500	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
501	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
503	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
508	#400	C₂²×C₆₇	1	2	yes	—
509	#399	C₂²×C₆₇	1	2	yes	—
510	#399	C₂²×C₆₇	1	2	yes	—
511	#399	C₂²×C₆₇	1	2	yes	—
512	#398	C₂²×C₆₇	1	2	yes	—
513	#398	C₂²×C₆₇	1	2	yes	—
514	#398	C₂²×C₆₇	1	2	yes	—
515	#398	C₂²×C₆₇	1	2	yes	—
516	#398	C₂²×C₆₇	1	2	yes	—
517	#398	C₂²×C₆₇	1	2	yes	—
518	#396	C₂²×C₆₇	1	2	yes	—
519	#396	C₂²×C₆₇	1	2	yes	—
520	#395	C₂²×C₆₇	1	2	yes	—
521	#395	C₂²×C₆₇	1	2	yes	—
522	#395	C₂²×C₆₇	1	2	yes	—
523	#393	C₂²×C₆₇	1	2	yes	—
524	#391	C₂²×C₆₇	1	2	yes	—
525	#391	C₂²×C₆₇	1	1	yes	characteristic
526	#391	C₂²×C₆₇	1	1	yes	characteristic
527	#391	C₂²×C₆₇	1	2	yes	—
528	#391	C₂²×C₆₇	1	1	yes	characteristic
529	#391	C₂²×C₆₇	1	2	yes	—
530	#391	C₂²×C₆₇	1	2	yes	—
531	#390	C₂²×C₆₇	1	1	yes	characteristic
532	#390	C₂²×C₆₇	1	1	yes	characteristic
533	#390	C₂²×C₆₇	1	1	yes	characteristic
534	#389	C₂²×C₆₇	1	1	yes	characteristic
535	#389	C₂²×C₆₇	1	1	yes	characteristic
536	#389	C₂²×C₆₇	1	1	yes	characteristic
537	#389	C₂²×C₆₇	1	1	yes	characteristic
538	#389	C₂²×C₆₇	1	2	yes	—
539	#389	C₂²×C₆₇	1	1	yes	characteristic
540	#389	C₂²×C₆₇	1	1	yes	characteristic
541	#389	C₂²×C₆₇	1	1	yes	characteristic
542	#389	C₂²×C₆₇	1	1	yes	characteristic
543	#389	C₂²×C₆₇	1	2	yes	—
544	#389	C₂²×C₆₇	1	2	yes	—
545	#389	C₂²×C₆₇	1	2	yes	—
546	#388	C₂²×C₆₇	1	2	yes	—
547	#388	C₂²×C₆₇	1	2	yes	—
548	#388	C₂²×C₆₇	1	2	yes	—
549	#388	C₂²×C₆₇	1	2	yes	—
550	#388	C₂²×C₆₇	1	2	yes	—
551	#388	C₂²×C₆₇	1	2	yes	—
552	#387	C₂²×C₆₇	1	1	yes	characteristic
553	#387	C₂²×C₆₇	1	1	yes	characteristic
554	#387	C₂²×C₆₇	1	1	yes	characteristic
555	#387	C₂²×C₆₇	1	1	yes	characteristic
556	#387	C₂²×C₆₇	1	2	yes	—
557	#387	C₂²×C₆₇	1	2	yes	—
558	#387	C₂²×C₆₇	1	2	yes	—
559	#387	C₂²×C₆₇	1	2	yes	—
560	#387	C₂²×C₆₇	1	2	yes	—
561	#387	C₂²×C₆₇	1	2	yes	—
562	#385	C₂²×C₆₇	1	2	yes	—
563	#385	C₂²×C₆₇	1	2	yes	—
564	#385	C₂²×C₆₇	1	2	yes	—
565	#385	C₂²×C₆₇	1	2	yes	—
566	#385	C₂²×C₆₇	1	2	yes	—
567	#385	C₂²×C₆₇	1	2	yes	—
568	#384	C₂²×C₆₇	1	1	yes	characteristic
569	#384	C₂²×C₆₇	1	1	yes	characteristic
570	#384	C₂²×C₆₇	1	2	yes	—
571	#382	C₂²×C₆₇	1	1	yes	characteristic
572	#382	C₂²×C₆₇	1	1	yes	characteristic
573	#382	C₂²×C₆₇	1	1	yes	characteristic
574	#380	C₂²×C₆₇	1	2	yes	—
575	#380	C₂²×C₆₇	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
586	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
587	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
588	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
589	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
590	C₂×#95	C₂²×C₆₇	1	2	yes	—
591	C₄³	C₂²×C₆₇	1	1	yes	characteristic
592	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
593	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
595	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
597	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
598	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
599	C₄⋊Q₈	—	2	4	no	—
600	C₄⋊Q₈	—	4	2	no	—
601	#125	—	2	4	no	—
602	#125	—	4	2	no	—
603	#124	Q₈×C₆₇	1	8	yes	complemented
604	C₂²⋊Q₈	—	2	8	no	—
605	C₂²⋊Q₈	—	4	4	no	—
606	C₂²⋊Q₈	—	4	4	no	—
607	C₄×Q₈	—	2	4	no	—
608	C₄×Q₈	—	4	2	no	—
609	C₄×Q₈	—	4	4	no	—
610	C₄×Q₈	—	4	2	no	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	—	4	2	no	—
613	C₄×D₄	—	4	2	no	—
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
666	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
673	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
674	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
676	#95	C₂³×C₆₇	1	1	yes	characteristic
677	#95	C₂³×C₆₇	1	2	yes	—
678	#95	C₂³×C₆₇	1	2	yes	—
679	#95	C₂³×C₆₇	1	2	yes	—
680	#95	C₂³×C₆₇	1	1	yes	characteristic
681	#95	C₂³×C₆₇	1	1	yes	characteristic
682	#95	C₂³×C₆₇	1	2	yes	—
683	#95	C₂³×C₆₇	1	2	yes	—
684	#95	C₂³×C₆₇	1	2	yes	—
685	#95	C₂³×C₆₇	1	2	yes	—
686	#95	C₂³×C₆₇	1	2	yes	—
687	#95	C₂³×C₆₇	1	2	yes	—
688	#95	C₂³×C₆₇	1	1	yes	characteristic
689	#95	C₂³×C₆₇	1	1	yes	characteristic
690	#95	C₂³×C₆₇	1	2	yes	—
691	#95	C₂³×C₆₇	1	1	yes	characteristic
692	#95	C₂³×C₆₇	1	1	yes	characteristic
693	#95	C₂³×C₆₇	1	1	yes	characteristic
694	#95	C₂³×C₆₇	1	2	yes	—
695	#95	C₂³×C₆₇	1	2	yes	—
696	#95	C₂³×C₆₇	1	2	yes	—
697	#95	C₂³×C₆₇	1	1	yes	characteristic
698	#95	C₂³×C₆₇	1	1	yes	characteristic
699	#95	C₂³×C₆₇	1	1	yes	characteristic
700	#95	C₂³×C₆₇	1	1	yes	characteristic
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	#95	C₂³×C₆₇	1	2	yes	—
706	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	4	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×Q₈	C₂×Q₈×C₆₇	1	4	yes	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	1	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	#41×C₆₇	1	4	yes	—
784	C₄⋊C₄	#41×C₆₇	1	4	yes	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
795	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	4	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	4	2	no	—
807	C₄²	—	4	2	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	1	no	—
811	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
819	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
820	Q₈	—	2	8	no	—
821	Q₈	—	4	8	no	—
822	Q₈	—	8	4	no	—
823	D₄	—	2	8	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	8	4	no	—
879	C₂×C₄	—	8	4	no	—
880	C₂×C₄	—	8	4	no	—
881	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
882	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
883	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
884	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
885	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
886	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
887	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
888	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
889	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
890	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
891	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
892	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
901	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
902	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
903	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
904	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
905	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
906	C₂²	#585×C₆₇	1	1	yes	characteristic
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	4	no	—
915	C₄	—	2	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	#554×C₆₇	1	4	yes	—
929	C₂	—	4	4	no	—
930	C₂	C₂×#554×C₆₇	1	1	yes	characteristic
931	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
932	C₂	C₆₇×#3482	1	1	yes	characteristic
933	C₂	C₆₇×#3503	1	1	yes	characteristic
934	C₂	C₆₇×#3508	1	1	yes	characteristic
935	C₂	C₆₇×#3513	1	1	yes	characteristic
936	C₂	C₆₇×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
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×#2768	C₂	semidirect
2. C₆₇×#2720	C₂	semidirect
3. C₆₇×#2589	C₂	semidirect
4. C₆₇×#2570	C₂	semidirect
5. C₆₇×#2565	C₂	semidirect
6. C₆₇×#2550	C₂	semidirect
7. C₆₇×#2549	C₂	semidirect
9. C₆₇×#2522	C₂	semidirect
10. C₆₇×#2465	C₂	semidirect
13. C₆₇×#2451	C₂	semidirect
14. C₆₇×#2451	C₂	semidirect
15. C₆₇×#2423	C₂	semidirect
16. C₆₇×#2368	C₂	semidirect
19. Q₈×C₄⋊C₄×C₆₇	C₂	semidirect
21. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#125×C₆₇	C₂	semidirect
134. #124×C₆₇	Q₈	semidirect
460. #59461	C₆₇	direct (N × H)
469. #2768	C₂×C₆₇	semidirect
470. #2720	C₂×C₆₇	semidirect
471. #2589	C₂×C₆₇	semidirect
472. #2570	C₂×C₆₇	semidirect
473. #2565	C₂×C₆₇	semidirect
474. #2550	C₂×C₆₇	semidirect
475. #2549	C₂×C₆₇	semidirect
477. #2522	C₂×C₆₇	semidirect
478. #2465	C₂×C₆₇	semidirect
481. #2451	C₂×C₆₇	semidirect
482. #2451	C₂×C₆₇	semidirect
483. #2423	C₂×C₆₇	semidirect
484. #2368	C₂×C₆₇	semidirect
487. Q₈×C₄⋊C₄	C₂×C₆₇	semidirect
489. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
490. C₄×#125	C₂×C₆₇	semidirect
492. C₆₇	#59461	direct (N × H)
603. #124	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2768	2
C₆₇×#2720	2
C₆₇×#2589	2
C₆₇×#2570	2
C₆₇×#2565	2
C₆₇×#2550	2
C₆₇×#2549	2
C₆₇×#2542	2
C₆₇×#2522	2
C₆₇×#2465	2
C₆₇×#2454	2
C₆₇×#2452	2
C₆₇×#2451	2
C₆₇×#2423	2
C₆₇×#2368	2
C₆₇×#2367	2
Q₈×C₄⋊C₄×C₆₇	2
C₆₇×#2349	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#125×C₆₇	2
C₄×#124×C₆₇	2
#59461	67

Subgroups — C67×#59461 #30738712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59461 #30738712