Subgroups — C₆₇×#59402 #30738653

Order 17152.

1678 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2776	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2772	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2595	C₂	1	2	yes	maximal
4	C₆₇×#2594	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2587	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2558	C₂	1	2	yes	maximal
7	C₆₇×#2538	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2515	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2511	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2506	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2494	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2429	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2429	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2421	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2415	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2370	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	2	yes	—
26	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊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×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
38	#401×C₆₇	C₂²	1	2	yes	—
39	#400×C₆₇	C₂²	1	2	yes	—
40	#400×C₆₇	C₂²	1	2	yes	—
41	#400×C₆₇	C₂²	1	2	yes	—
42	#400×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	#397×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	—
49	#396×C₆₇	C₂²	1	2	yes	—
50	#396×C₆₇	C₂²	1	2	yes	—
51	#396×C₆₇	C₂²	1	2	yes	—
52	#396×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	1	yes	characteristic
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	#390×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	1	yes	characteristic
60	#389×C₆₇	C₂²	1	1	yes	characteristic
61	#389×C₆₇	C₂²	1	1	yes	characteristic
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
71	#389×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	1	yes	characteristic
75	#388×C₆₇	C₂²	1	2	yes	—
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	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	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	#387×C₆₇	C₂²	1	2	yes	—
90	#387×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	1	yes	characteristic
92	#387×C₆₇	C₂²	1	2	yes	—
93	#387×C₆₇	C₂²	1	2	yes	—
94	#387×C₆₇	C₂²	1	1	yes	characteristic
95	#386×C₆₇	C₂²	1	1	yes	characteristic
96	#385×C₆₇	C₂²	1	2	yes	—
97	#385×C₆₇	C₂²	1	1	yes	characteristic
98	#385×C₆₇	C₂²	1	2	yes	—
99	#384×C₆₇	C₂²	1	1	yes	characteristic
100	#383×C₆₇	C₂²	1	2	yes	—
101	#382×C₆₇	C₂²	1	2	yes	—
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#381×C₆₇	C₂²	1	1	yes	characteristic
104	#380×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
123	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₄⋊Q₈×C₆₇	—	2	4	no	—
131	#125×C₆₇	—	2	8	no	—
132	#123×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	—	2	4	no	—
134	C₂²⋊Q₈×C₆₇	—	2	4	no	—
135	C₂²⋊Q₈×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	4	2	no	—
137	C₄×Q₈×C₆₇	—	2	4	no	—
138	C₄×Q₈×C₆₇	—	4	2	no	—
139	C₄×Q₈×C₆₇	—	4	2	no	—
140	C₄×Q₈×C₆₇	—	4	2	no	—
141	C₄×D₄×C₆₇	—	4	2	no	—
142	#117×C₆₇	—	2	4	no	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊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	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	—	4	2	no	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	1	yes	characteristic
209	#95×C₆₇	C₂³	1	1	yes	characteristic
210	#95×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
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	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂×Q₈×C₆₇	—	2	2	no	—
239	C₂×Q₈×C₆₇	—	2	2	no	—
240	C₂×Q₈×C₆₇	—	2	2	no	—
241	C₂×Q₈×C₆₇	—	2	2	no	—
242	C₂×Q₈×C₆₇	—	2	2	no	—
243	C₂×Q₈×C₆₇	#41	1	4	yes	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	4	1	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	4	1	no	—
257	C₂²×C₄×C₆₇	—	4	1	no	—
258	C₂²×C₄×C₆₇	—	4	1	no	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	4	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	4	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	2	4	no	—
293	C₄⋊C₄×C₆₇	—	2	4	no	—
294	C₄⋊C₄×C₆₇	—	2	4	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	4	no	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	4	1	no	—
300	C₄⋊C₄×C₆₇	—	4	2	no	—
301	C₄⋊C₄×C₆₇	—	4	2	no	—
302	C₄⋊C₄×C₆₇	—	4	1	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	#41	1	4	yes	—
308	C₄⋊C₄×C₆₇	#41	1	4	yes	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	2	no	—
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	4	2	no	—
320	C₂²⋊C₄×C₆₇	—	4	2	no	—
321	C₂²⋊C₄×C₆₇	—	4	1	no	—
322	C₂²⋊C₄×C₆₇	—	4	1	no	—
323	C₂²⋊C₄×C₆₇	—	4	1	no	—
324	C₂²⋊C₄×C₆₇	—	4	2	no	—
325	C₄²×C₆₇	—	2	4	no	—
326	C₄²×C₆₇	—	2	4	no	—
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	—	4	1	no	—
334	C₄²×C₆₇	—	4	1	no	—
335	C₄²×C₆₇	—	4	2	no	—
336	C₄²×C₆₇	—	4	2	no	—
337	C₄²×C₆₇	—	4	2	no	—
338	C₄²×C₆₇	—	4	2	no	—
339	C₄²×C₆₇	—	4	2	no	—
340	C₂³×C₆₇	—	2	1	no	—
341	C₂³×C₆₇	—	2	1	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	—	2	1	no	—
344	C₂³×C₆₇	—	2	1	no	—
345	C₂³×C₆₇	—	2	1	no	—
346	C₂³×C₆₇	—	2	1	no	—
347	C₂³×C₆₇	—	2	1	no	—
348	C₂³×C₆₇	—	2	1	no	—
349	C₂³×C₆₇	—	2	1	no	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
354	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
355	Q₈×C₆₇	—	2	8	no	—
356	Q₈×C₆₇	—	4	4	no	—
357	D₄×C₆₇	—	4	4	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	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	2	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	2	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	2	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	1	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	2	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	1	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	2	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	—	4	4	no	—
413	C₂×C₄×C₆₇	—	4	4	no	—
414	C₂×C₄×C₆₇	—	4	4	no	—
415	C₂×C₄×C₆₇	—	4	4	no	—
416	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
417	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
418	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
419	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
420	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
421	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
422	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
423	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	2	2	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	4	1	no	—
429	C₂²×C₆₇	—	4	1	no	—
430	C₂²×C₆₇	—	4	1	no	—
431	C₂²×C₆₇	—	4	1	no	—
432	C₂²×C₆₇	—	4	1	no	—
433	C₂²×C₆₇	—	4	1	no	—
434	C₂²×C₆₇	—	4	1	no	—
435	C₂²×C₆₇	—	4	1	no	—
436	C₂²×C₆₇	—	4	1	no	—
437	C₂²×C₆₇	—	4	1	no	—
438	C₂²×C₆₇	—	4	1	no	—
439	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
440	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
441	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
442	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
444	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂²×C₆₇	#585	1	1	yes	characteristic
446	C₄×C₆₇	—	2	4	no	—
447	C₄×C₆₇	—	2	2	no	—
448	C₄×C₆₇	—	2	4	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	2	no	—
451	C₄×C₆₇	—	2	2	no	—
452	C₄×C₆₇	—	4	1	no	—
453	C₄×C₆₇	—	4	1	no	—
454	C₄×C₆₇	—	4	2	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	2	no	—
457	C₄×C₆₇	—	4	1	no	—
458	C₄×C₆₇	—	4	1	no	—
459	C₄×C₆₇	—	4	2	no	—
460	C₄×C₆₇	—	4	2	no	—
461	C₄×C₆₇	—	4	1	no	—
462	C₄×C₆₇	—	4	1	no	—
463	C₄×C₆₇	—	4	1	no	—
464	C₄×C₆₇	—	4	2	no	—
465	C₄×C₆₇	—	4	1	no	—
466	C₄×C₆₇	#553	1	4	yes	—
467	#59402	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
468	C₂×C₆₇	—	4	2	no	—
469	C₂×C₆₇	—	8	1	no	—
470	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
471	C₂×C₆₇	#3480	1	1	yes	characteristic
472	C₂×C₆₇	#3482	1	1	yes	characteristic
473	C₂×C₆₇	#3516	1	1	yes	characteristic
474	C₂×C₆₇	#3520	1	1	yes	characteristic
475	C₂×C₆₇	#3523	1	1	yes	characteristic
476	C₂×C₆₇	#3541	1	1	yes	characteristic
477	#2776	C₂×C₆₇	1	2	yes	complemented
478	#2772	C₂×C₆₇	1	2	yes	complemented
479	#2595	C₂×C₆₇	1	2	yes	—
480	#2594	C₂×C₆₇	1	2	yes	complemented
481	#2587	C₂×C₆₇	1	2	yes	complemented
482	#2558	C₂×C₆₇	1	2	yes	—
483	#2538	C₂×C₆₇	1	1	yes	characteristic
484	#2515	C₂×C₆₇	1	2	yes	complemented
485	#2511	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#2506	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#2494	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#2429	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#2429	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#2421	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#2415	C₂×C₆₇	1	1	yes	characteristic
492	#2370	C₂×C₆₇	1	2	yes	complemented
493	#2365	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#2362	C₂×C₆₇	1	1	yes	characteristic, complemented
495	#2351	C₂×C₆₇	1	1	yes	characteristic, complemented
496	#2347	C₂×C₆₇	1	1	yes	characteristic, complemented
497	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
498	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
499	C₄×#123	C₂×C₆₇	1	1	yes	characteristic
500	C₆₇	#59402	1	1	yes	characteristic, direct product factor, Sylow
501	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#125	C₂²×C₆₇	1	2	yes	—
503	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
505	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
506	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
507	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
508	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
509	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
510	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
511	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
512	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
513	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
514	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
515	#401	C₂²×C₆₇	1	2	yes	—
516	#400	C₂²×C₆₇	1	2	yes	—
517	#400	C₂²×C₆₇	1	2	yes	—
518	#400	C₂²×C₆₇	1	2	yes	—
519	#400	C₂²×C₆₇	1	2	yes	—
520	#398	C₂²×C₆₇	1	2	yes	—
521	#398	C₂²×C₆₇	1	2	yes	—
522	#398	C₂²×C₆₇	1	2	yes	—
523	#397	C₂²×C₆₇	1	2	yes	—
524	#397	C₂²×C₆₇	1	2	yes	—
525	#397	C₂²×C₆₇	1	2	yes	—
526	#396	C₂²×C₆₇	1	2	yes	—
527	#396	C₂²×C₆₇	1	2	yes	—
528	#396	C₂²×C₆₇	1	2	yes	—
529	#396	C₂²×C₆₇	1	2	yes	—
530	#394	C₂²×C₆₇	1	2	yes	—
531	#391	C₂²×C₆₇	1	1	yes	characteristic
532	#391	C₂²×C₆₇	1	1	yes	characteristic
533	#391	C₂²×C₆₇	1	1	yes	characteristic
534	#391	C₂²×C₆₇	1	1	yes	characteristic
535	#390	C₂²×C₆₇	1	2	yes	—
536	#389	C₂²×C₆₇	1	2	yes	—
537	#389	C₂²×C₆₇	1	2	yes	—
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	2	yes	—
543	#389	C₂²×C₆₇	1	1	yes	characteristic
544	#389	C₂²×C₆₇	1	2	yes	—
545	#389	C₂²×C₆₇	1	2	yes	—
546	#389	C₂²×C₆₇	1	2	yes	—
547	#389	C₂²×C₆₇	1	1	yes	characteristic
548	#389	C₂²×C₆₇	1	1	yes	characteristic
549	#388	C₂²×C₆₇	1	2	yes	—
550	#388	C₂²×C₆₇	1	2	yes	—
551	#388	C₂²×C₆₇	1	1	yes	characteristic
552	#388	C₂²×C₆₇	1	2	yes	—
553	#388	C₂²×C₆₇	1	2	yes	—
554	#388	C₂²×C₆₇	1	2	yes	—
555	#388	C₂²×C₆₇	1	2	yes	—
556	#388	C₂²×C₆₇	1	2	yes	—
557	#388	C₂²×C₆₇	1	2	yes	—
558	#388	C₂²×C₆₇	1	2	yes	—
559	#388	C₂²×C₆₇	1	1	yes	characteristic
560	#387	C₂²×C₆₇	1	2	yes	—
561	#387	C₂²×C₆₇	1	2	yes	—
562	#387	C₂²×C₆₇	1	2	yes	—
563	#387	C₂²×C₆₇	1	2	yes	—
564	#387	C₂²×C₆₇	1	2	yes	—
565	#387	C₂²×C₆₇	1	2	yes	—
566	#387	C₂²×C₆₇	1	1	yes	characteristic
567	#387	C₂²×C₆₇	1	2	yes	—
568	#387	C₂²×C₆₇	1	2	yes	—
569	#387	C₂²×C₆₇	1	2	yes	—
570	#387	C₂²×C₆₇	1	2	yes	—
571	#387	C₂²×C₆₇	1	1	yes	characteristic
572	#386	C₂²×C₆₇	1	1	yes	characteristic
573	#385	C₂²×C₆₇	1	1	yes	characteristic
574	#385	C₂²×C₆₇	1	2	yes	—
575	#385	C₂²×C₆₇	1	2	yes	—
576	#384	C₂²×C₆₇	1	1	yes	characteristic
577	#383	C₂²×C₆₇	1	2	yes	—
578	#382	C₂²×C₆₇	1	1	yes	characteristic
579	#382	C₂²×C₆₇	1	2	yes	—
580	#381	C₂²×C₆₇	1	1	yes	characteristic
581	#380	C₂²×C₆₇	1	1	yes	characteristic
582	#380	C₂²×C₆₇	1	1	yes	characteristic
583	#380	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×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
588	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
592	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
594	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
595	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
596	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
597	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
598	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
599	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
600	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
601	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
602	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₄⋊Q₈	—	2	4	no	—
608	#125	—	2	8	no	—
609	#123	—	2	4	no	—
610	C₂²⋊Q₈	—	2	4	no	—
611	C₂²⋊Q₈	—	2	4	no	—
612	C₂²⋊Q₈	—	2	4	no	—
613	C₂²⋊Q₈	—	4	2	no	—
614	C₄×Q₈	—	2	4	no	—
615	C₄×Q₈	—	4	2	no	—
616	C₄×Q₈	—	4	2	no	—
617	C₄×Q₈	—	4	2	no	—
618	C₄×D₄	—	4	2	no	—
619	#117	—	2	4	no	—
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₄²	—	4	2	no	—
666	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
671	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
673	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
675	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
677	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
678	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
680	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
681	#95	C₂³×C₆₇	1	1	yes	characteristic
682	#95	C₂³×C₆₇	1	1	yes	characteristic
683	#95	C₂³×C₆₇	1	1	yes	characteristic
684	#95	C₂³×C₆₇	1	2	yes	—
685	#95	C₂³×C₆₇	1	1	yes	characteristic
686	#95	C₂³×C₆₇	1	1	yes	characteristic
687	#95	C₂³×C₆₇	1	2	yes	—
688	#95	C₂³×C₆₇	1	1	yes	characteristic
689	#95	C₂³×C₆₇	1	2	yes	—
690	#95	C₂³×C₆₇	1	2	yes	—
691	#95	C₂³×C₆₇	1	2	yes	—
692	#95	C₂³×C₆₇	1	1	yes	characteristic
693	#95	C₂³×C₆₇	1	2	yes	—
694	#95	C₂³×C₆₇	1	2	yes	—
695	#95	C₂³×C₆₇	1	2	yes	—
696	#95	C₂³×C₆₇	1	1	yes	characteristic
697	#95	C₂³×C₆₇	1	1	yes	characteristic
698	#95	C₂³×C₆₇	1	2	yes	—
699	#95	C₂³×C₆₇	1	2	yes	—
700	#95	C₂³×C₆₇	1	2	yes	—
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	1	yes	characteristic
704	#95	C₂³×C₆₇	1	2	yes	—
705	#95	C₂³×C₆₇	1	2	yes	—
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	2	yes	—
708	#95	C₂³×C₆₇	1	2	yes	—
709	#95	C₂³×C₆₇	1	2	yes	—
710	#95	C₂³×C₆₇	1	2	yes	—
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	2	yes	—
713	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	#41×C₆₇	1	4	yes	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
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	2	yes	—
746	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
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	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	#41×C₆₇	1	4	yes	—
785	C₄⋊C₄	#41×C₆₇	1	4	yes	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	4	1	no	—
797	C₂²⋊C₄	—	4	1	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	1	no	—
802	C₄²	—	2	4	no	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	4	1	no	—
811	C₄²	—	4	1	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
831	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
832	Q₈	—	2	8	no	—
833	Q₈	—	4	4	no	—
834	D₄	—	4	4	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	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	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	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	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
894	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
895	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
896	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
897	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
898	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
899	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
900	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
901	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
917	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
918	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
919	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
920	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
921	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
922	C₂²	#585×C₆₇	1	1	yes	characteristic
923	C₄	—	2	2	no	—
924	C₄	—	2	4	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	4	no	—
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	1	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	#553×C₆₇	1	4	yes	—
944	C₂	—	4	2	no	—
945	C₂	—	8	1	no	—
946	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
947	C₂	C₆₇×#3480	1	1	yes	characteristic
948	C₂	C₆₇×#3482	1	1	yes	characteristic
949	C₂	C₆₇×#3516	1	1	yes	characteristic
950	C₂	C₆₇×#3520	1	1	yes	characteristic
951	C₂	C₆₇×#3523	1	1	yes	characteristic
952	C₂	C₆₇×#3541	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×#2776	C₂	semidirect
2. C₆₇×#2772	C₂	semidirect
4. C₆₇×#2594	C₂	semidirect
5. C₆₇×#2587	C₂	semidirect
8. C₆₇×#2515	C₂	semidirect
9. C₆₇×#2511	C₂	semidirect
10. C₆₇×#2506	C₂	semidirect
11. C₆₇×#2494	C₂	semidirect
12. C₆₇×#2429	C₂	semidirect
13. C₆₇×#2429	C₂	semidirect
14. C₆₇×#2421	C₂	semidirect
16. C₆₇×#2370	C₂	semidirect
17. C₆₇×#2365	C₂	semidirect
18. C₆₇×#2362	C₂	semidirect
19. C₆₇×#2351	C₂	semidirect
20. C₆₇×#2347	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
22. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
467. #59402	C₆₇	direct (N × H)
477. #2776	C₂×C₆₇	semidirect
478. #2772	C₂×C₆₇	semidirect
480. #2594	C₂×C₆₇	semidirect
481. #2587	C₂×C₆₇	semidirect
484. #2515	C₂×C₆₇	semidirect
485. #2511	C₂×C₆₇	semidirect
486. #2506	C₂×C₆₇	semidirect
487. #2494	C₂×C₆₇	semidirect
488. #2429	C₂×C₆₇	semidirect
489. #2429	C₂×C₆₇	semidirect
490. #2421	C₂×C₆₇	semidirect
492. #2370	C₂×C₆₇	semidirect
493. #2365	C₂×C₆₇	semidirect
494. #2362	C₂×C₆₇	semidirect
495. #2351	C₂×C₆₇	semidirect
496. #2347	C₂×C₆₇	semidirect
497. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
498. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
500. C₆₇	#59402	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2776	2
C₆₇×#2772	2
C₆₇×#2595	2
C₆₇×#2594	2
C₆₇×#2587	2
C₆₇×#2558	2
C₆₇×#2538	2
C₆₇×#2515	2
C₆₇×#2511	2
C₆₇×#2506	2
C₆₇×#2494	2
C₆₇×#2429	2
C₆₇×#2421	2
C₆₇×#2415	2
C₆₇×#2370	2
C₆₇×#2365	2
C₆₇×#2362	2
C₆₇×#2351	2
C₆₇×#2347	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#123×C₆₇	2
#59402	67

Subgroups — C67×#59402 #30738653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59402 #30738653