Subgroups — C₆₇×#34910 #30714161

Order 17152.

2570 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2602	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2601	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2500	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2499	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2431	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2392	C₂	1	4	yes	maximal, complemented
14	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2290	C₂	1	4	yes	maximal, complemented
19	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
23	#529×C₆₇	—	2	8	no	—
24	C₂×#126×C₆₇	C₂²	1	2	yes	—
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#123×C₆₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	C₄×#41×C₆₇	—	2	8	no	—
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
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	4	yes	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#117×C₆₇	C₂²	1	2	yes	—
45	C₂×#117×C₆₇	C₂²	1	2	yes	—
46	C₂×#117×C₆₇	C₂²	1	2	yes	—
47	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
48	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
49	#398×C₆₇	C₂²	1	4	yes	—
50	#397×C₆₇	C₂²	1	4	yes	—
51	#396×C₆₇	C₂²	1	4	yes	—
52	#396×C₆₇	C₂²	1	4	yes	—
53	#394×C₆₇	C₂²	1	4	yes	—
54	#394×C₆₇	C₂²	1	4	yes	—
55	#394×C₆₇	C₂²	1	4	yes	—
56	#392×C₆₇	C₂²	1	4	yes	—
57	#391×C₆₇	C₂²	1	1	yes	characteristic
58	#391×C₆₇	C₂²	1	1	yes	characteristic
59	#391×C₆₇	C₂²	1	1	yes	characteristic
60	#391×C₆₇	C₂²	1	1	yes	characteristic
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	#390×C₆₇	C₂²	1	4	yes	—
66	#389×C₆₇	C₂²	1	4	yes	—
67	#388×C₆₇	C₂²	1	4	yes	—
68	#388×C₆₇	C₂²	1	4	yes	—
69	#388×C₆₇	C₂²	1	4	yes	—
70	#388×C₆₇	C₂²	1	4	yes	—
71	#387×C₆₇	C₂²	1	4	yes	—
72	#387×C₆₇	C₂²	1	4	yes	—
73	#386×C₆₇	C₂²	1	4	yes	—
74	#386×C₆₇	C₂²	1	4	yes	—
75	#385×C₆₇	C₂²	1	4	yes	—
76	#385×C₆₇	C₂²	1	4	yes	—
77	#384×C₆₇	C₂²	1	1	yes	characteristic
78	#384×C₆₇	C₂²	1	1	yes	characteristic
79	#382×C₆₇	C₂²	1	1	yes	characteristic
80	#382×C₆₇	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
83	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
85	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
88	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
89	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
90	#376×C₆₇	C₂²	1	2	yes	—
91	C₄³×C₆₇	C₂²	1	1	yes	characteristic
92	C₄³×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	—	2	4	no	—
94	C₂×#41×C₆₇	—	2	4	no	—
95	C₂×#41×C₆₇	—	2	4	no	—
96	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
99	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
101	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
103	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₇	—	2	4	no	—
111	#127×C₆₇	—	2	4	no	—
112	#126×C₆₇	—	2	8	no	—
113	#125×C₆₇	—	2	4	no	—
114	#124×C₆₇	—	2	4	no	—
115	#124×C₆₇	—	2	4	no	—
116	#124×C₆₇	—	2	4	no	—
117	#123×C₆₇	—	2	8	no	—
118	C₂²⋊Q₈×C₆₇	—	2	4	no	—
119	#121×C₆₇	—	2	4	no	—
120	C₄×Q₈×C₆₇	—	2	4	no	—
121	C₄×Q₈×C₆₇	—	2	4	no	—
122	C₄×Q₈×C₆₇	—	2	4	no	—
123	C₄×D₄×C₆₇	—	2	8	no	—
124	C₄×D₄×C₆₇	—	2	8	no	—
125	C₄×D₄×C₆₇	—	2	8	no	—
126	C₄×D₄×C₆₇	—	2	4	no	—
127	C₄×D₄×C₆₇	—	2	4	no	—
128	C₄×D₄×C₆₇	—	2	4	no	—
129	C₄×D₄×C₆₇	—	2	16	no	—
130	#117×C₆₇	—	2	4	no	—
131	#117×C₆₇	—	2	8	no	—
132	#117×C₆₇	—	2	8	no	—
133	#117×C₆₇	—	2	8	no	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
165	C₂×C₄²×C₆₇	—	2	8	no	—
166	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
167	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	4	yes	—
188	#95×C₆₇	C₂³	1	4	yes	—
189	#95×C₆₇	C₂³	1	4	yes	—
190	#95×C₆₇	C₂³	1	4	yes	—
191	#95×C₆₇	C₂³	1	4	yes	—
192	#95×C₆₇	C₂³	1	4	yes	—
193	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
194	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
195	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
196	#41×C₆₇	—	2	32	no	—
197	C₂×Q₈×C₆₇	—	2	2	no	—
198	C₂×Q₈×C₆₇	—	2	2	no	—
199	C₂×Q₈×C₆₇	—	2	2	no	—
200	C₂×Q₈×C₆₇	—	2	2	no	—
201	C₂×Q₈×C₆₇	—	2	2	no	—
202	C₂×Q₈×C₆₇	#41	1	4	yes	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	8	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	—	2	2	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	2	no	—
211	C₂×D₄×C₆₇	—	2	8	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	2	no	—
214	C₂×D₄×C₆₇	—	4	4	no	—
215	C₂×D₄×C₆₇	—	4	4	no	—
216	C₂×D₄×C₆₇	#41	1	4	yes	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	8	no	—
227	C₂²×C₄×C₆₇	—	2	8	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	—	4	4	no	—
230	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	2	no	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	2	no	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	2	no	—
258	C₄⋊C₄×C₆₇	—	2	4	no	—
259	C₄⋊C₄×C₆₇	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	8	no	—
262	C₄⋊C₄×C₆₇	—	2	8	no	—
263	C₄⋊C₄×C₆₇	—	4	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	8	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	—	2	8	no	—
276	C₂²⋊C₄×C₆₇	—	2	8	no	—
277	C₂²⋊C₄×C₆₇	—	2	8	no	—
278	C₂²⋊C₄×C₆₇	—	4	4	no	—
279	C₂²⋊C₄×C₆₇	—	4	4	no	—
280	C₄²×C₆₇	—	2	4	no	—
281	C₄²×C₆₇	—	2	4	no	—
282	C₄²×C₆₇	—	2	4	no	—
283	C₄²×C₆₇	—	2	4	no	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	—	2	2	no	—
286	C₄²×C₆₇	—	2	2	no	—
287	C₄²×C₆₇	—	2	2	no	—
288	C₄²×C₆₇	—	2	2	no	—
289	C₄²×C₆₇	—	4	2	no	—
290	C₄²×C₆₇	—	4	2	no	—
291	C₄²×C₆₇	C₂×D₄	1	4	yes	—
292	C₄²×C₆₇	C₂×D₄	1	4	yes	—
293	C₄²×C₆₇	C₂×D₄	1	4	yes	—
294	C₄²×C₆₇	C₂×D₄	1	4	yes	—
295	C₄²×C₆₇	#41	1	8	yes	complemented
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	2	no	—
298	C₂³×C₆₇	—	2	4	no	—
299	C₂³×C₆₇	—	2	1	no	—
300	C₂³×C₆₇	—	2	1	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	4	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	4	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	4	no	—
309	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
310	C₂³×C₆₇	C₂×#41	1	4	yes	—
311	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
312	Q₈×C₆₇	—	2	8	no	—
313	Q₈×C₆₇	—	4	4	no	—
314	D₄×C₆₇	—	2	16	no	—
315	D₄×C₆₇	—	2	8	no	—
316	D₄×C₆₇	—	4	16	no	—
317	D₄×C₆₇	—	4	8	no	—
318	D₄×C₆₇	—	4	4	no	—
319	C₂×C₄×C₆₇	—	2	16	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	1	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	8	no	—
332	C₂×C₄×C₆₇	—	2	8	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	4	no	—
344	C₂×C₄×C₆₇	—	2	4	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	4	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	4	4	no	—
351	C₂×C₄×C₆₇	—	4	8	no	—
352	C₂×C₄×C₆₇	—	4	8	no	—
353	C₂×C₄×C₆₇	—	4	8	no	—
354	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
361	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
362	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
363	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
364	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
365	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
366	C₂²×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	2	4	no	—
368	C₂²×C₆₇	—	2	2	no	—
369	C₂²×C₆₇	—	2	2	no	—
370	C₂²×C₆₇	—	2	8	no	—
371	C₂²×C₆₇	—	4	2	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	4	4	no	—
376	C₂²×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	4	2	no	—
378	C₂²×C₆₇	—	4	2	no	—
379	C₂²×C₆₇	—	4	4	no	—
380	C₂²×C₆₇	—	4	4	no	—
381	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
382	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
383	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
384	C₂²×C₆₇	C₂²×#41	1	2	yes	—
385	C₂²×C₆₇	#585	1	2	yes	—
386	C₄×C₆₇	—	2	2	no	—
387	C₄×C₆₇	—	2	4	no	—
388	C₄×C₆₇	—	2	2	no	—
389	C₄×C₆₇	—	2	2	no	—
390	C₄×C₆₇	—	2	2	no	—
391	C₄×C₆₇	—	2	4	no	—
392	C₄×C₆₇	—	2	4	no	—
393	C₄×C₆₇	—	4	2	no	—
394	C₄×C₆₇	—	4	2	no	—
395	C₄×C₆₇	—	4	2	no	—
396	C₄×C₆₇	—	4	2	no	—
397	C₄×C₆₇	—	4	2	no	—
398	C₄×C₆₇	—	4	2	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	#525	1	4	yes	—
401	C₄×C₆₇	#532	1	4	yes	—
402	#34910	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂×C₆₇	—	4	2	no	—
404	C₂×C₆₇	—	4	4	no	—
405	C₂×C₆₇	—	8	2	no	—
406	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
407	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
408	C₂×C₆₇	#3449	1	1	yes	characteristic
409	C₂×C₆₇	#3475	1	2	yes	—
410	C₂×C₆₇	#3480	1	2	yes	—
411	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
412	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#2602	C₂×C₆₇	1	4	yes	complemented
414	#2601	C₂×C₆₇	1	4	yes	complemented
415	#2566	C₂×C₆₇	1	1	yes	characteristic, complemented
416	#2565	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#2545	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#2544	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#2500	C₂×C₆₇	1	1	yes	characteristic, complemented
420	#2499	C₂×C₆₇	1	1	yes	characteristic, complemented
421	#2432	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#2431	C₂×C₆₇	1	1	yes	characteristic
423	#2392	C₂×C₆₇	1	4	yes	complemented
424	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
426	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
427	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#2290	C₂×C₆₇	1	4	yes	complemented
429	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
430	C₆₇	#34910	1	1	yes	characteristic, direct product factor, Sylow
431	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
434	#529	—	2	8	no	—
435	C₂×#126	C₂²×C₆₇	1	2	yes	—
436	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
440	C₂×#123	C₂²×C₆₇	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
443	C₄×#41	—	2	8	no	—
444	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
448	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
452	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
453	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
454	C₂×#117	C₂²×C₆₇	1	2	yes	—
455	C₂×#117	C₂²×C₆₇	1	2	yes	—
456	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×#117	C₂²×C₆₇	1	2	yes	—
458	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
459	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
460	#398	C₂²×C₆₇	1	4	yes	—
461	#397	C₂²×C₆₇	1	4	yes	—
462	#396	C₂²×C₆₇	1	4	yes	—
463	#396	C₂²×C₆₇	1	4	yes	—
464	#394	C₂²×C₆₇	1	4	yes	—
465	#394	C₂²×C₆₇	1	4	yes	—
466	#394	C₂²×C₆₇	1	4	yes	—
467	#392	C₂²×C₆₇	1	4	yes	—
468	#391	C₂²×C₆₇	1	1	yes	characteristic
469	#391	C₂²×C₆₇	1	1	yes	characteristic
470	#391	C₂²×C₆₇	1	1	yes	characteristic
471	#391	C₂²×C₆₇	1	1	yes	characteristic
472	#390	C₂²×C₆₇	1	1	yes	characteristic
473	#390	C₂²×C₆₇	1	4	yes	—
474	#390	C₂²×C₆₇	1	1	yes	characteristic
475	#390	C₂²×C₆₇	1	1	yes	characteristic
476	#390	C₂²×C₆₇	1	1	yes	characteristic
477	#389	C₂²×C₆₇	1	4	yes	—
478	#388	C₂²×C₆₇	1	4	yes	—
479	#388	C₂²×C₆₇	1	4	yes	—
480	#388	C₂²×C₆₇	1	4	yes	—
481	#388	C₂²×C₆₇	1	4	yes	—
482	#387	C₂²×C₆₇	1	4	yes	—
483	#387	C₂²×C₆₇	1	4	yes	—
484	#386	C₂²×C₆₇	1	4	yes	—
485	#386	C₂²×C₆₇	1	4	yes	—
486	#385	C₂²×C₆₇	1	4	yes	—
487	#385	C₂²×C₆₇	1	4	yes	—
488	#384	C₂²×C₆₇	1	1	yes	characteristic
489	#384	C₂²×C₆₇	1	1	yes	characteristic
490	#382	C₂²×C₆₇	1	1	yes	characteristic
491	#382	C₂²×C₆₇	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
493	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
494	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
501	#376	C₂²×C₆₇	1	2	yes	—
502	C₄³	C₂²×C₆₇	1	1	yes	characteristic
503	C₄³	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×#41	—	2	4	no	—
505	C₂×#41	—	2	4	no	—
506	C₂×#41	—	2	4	no	—
507	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
508	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
510	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
512	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
514	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
515	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
516	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
517	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
520	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
521	C₄⋊Q₈	—	2	4	no	—
522	#127	—	2	4	no	—
523	#126	—	2	8	no	—
524	#125	—	2	4	no	—
525	#124	—	2	4	no	—
526	#124	—	2	4	no	—
527	#124	—	2	4	no	—
528	#123	—	2	8	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	#121	—	2	4	no	—
531	C₄×Q₈	—	2	4	no	—
532	C₄×Q₈	—	2	4	no	—
533	C₄×Q₈	—	2	4	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	2	8	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	—	2	16	no	—
541	#117	—	2	4	no	—
542	#117	—	2	8	no	—
543	#117	—	2	8	no	—
544	#117	—	2	8	no	—
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
559	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
576	C₂×C₄²	—	2	8	no	—
577	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
578	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
580	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
582	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
583	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
588	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
594	#95	C₂³×C₆₇	1	2	yes	—
595	#95	C₂³×C₆₇	1	2	yes	—
596	#95	C₂³×C₆₇	1	2	yes	—
597	#95	C₂³×C₆₇	1	2	yes	—
598	#95	C₂³×C₆₇	1	4	yes	—
599	#95	C₂³×C₆₇	1	4	yes	—
600	#95	C₂³×C₆₇	1	4	yes	—
601	#95	C₂³×C₆₇	1	4	yes	—
602	#95	C₂³×C₆₇	1	4	yes	—
603	#95	C₂³×C₆₇	1	4	yes	—
604	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
605	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
606	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
607	#41	—	2	32	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	#41×C₆₇	1	4	yes	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	#41×C₆₇	1	4	yes	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	8	no	—
638	C₂²×C₄	—	2	8	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	4	no	—
641	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
642	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
643	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
644	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	8	no	—
673	C₄⋊C₄	—	2	8	no	—
674	C₄⋊C₄	—	4	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	8	no	—
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	—	4	4	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	4	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₄²	C₂×D₄×C₆₇	1	4	yes	—
703	C₄²	C₂×D₄×C₆₇	1	4	yes	—
704	C₄²	C₂×D₄×C₆₇	1	4	yes	—
705	C₄²	C₂×D₄×C₆₇	1	4	yes	—
706	C₄²	#41×C₆₇	1	8	yes	complemented
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	4	no	—
720	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
721	C₂³	C₂×#41×C₆₇	1	4	yes	—
722	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
723	Q₈	—	2	8	no	—
724	Q₈	—	4	4	no	—
725	D₄	—	2	16	no	—
726	D₄	—	2	8	no	—
727	D₄	—	4	16	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	4	no	—
730	C₂×C₄	—	2	16	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	8	no	—
765	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
771	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
772	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
773	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
774	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
775	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
776	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
793	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
794	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
795	C₂²	C₂²×#41×C₆₇	1	2	yes	—
796	C₂²	#585×C₆₇	1	2	yes	—
797	C₄	—	2	2	no	—
798	C₄	—	2	4	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	4	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	#525×C₆₇	1	4	yes	—
812	C₄	#532×C₆₇	1	4	yes	—
813	C₂	—	4	2	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
817	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
818	C₂	C₆₇×#3449	1	1	yes	characteristic
819	C₂	C₆₇×#3475	1	2	yes	—
820	C₂	C₆₇×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₆₇×#2431	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#529×C₆₇	C₂	semidirect
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#2602	C₂	semidirect
4. C₆₇×#2601	C₂	semidirect
5. C₆₇×#2566	C₂	semidirect
6. C₆₇×#2565	C₂	semidirect
7. C₆₇×#2545	C₂	semidirect
8. C₆₇×#2544	C₂	semidirect
9. C₆₇×#2500	C₂	semidirect
10. C₆₇×#2499	C₂	semidirect
11. C₆₇×#2432	C₂	semidirect
13. C₆₇×#2392	C₂	semidirect
14. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
15. C₄×#127×C₆₇	C₂	semidirect
16. C₄×#124×C₆₇	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
18. C₆₇×#2290	C₂	semidirect
19. C₄×#117×C₆₇	C₂	semidirect
166. C₂×C₄²×C₆₇	D₄	semidirect
295. C₄²×C₆₇	#41	semidirect
402. #34910	C₆₇	direct (N × H)
411. C₂×#529	C₂×C₆₇	semidirect
412. C₂×C₄×#41	C₂×C₆₇	semidirect
413. #2602	C₂×C₆₇	semidirect
414. #2601	C₂×C₆₇	semidirect
415. #2566	C₂×C₆₇	semidirect
416. #2565	C₂×C₆₇	semidirect
417. #2545	C₂×C₆₇	semidirect
418. #2544	C₂×C₆₇	semidirect
419. #2500	C₂×C₆₇	semidirect
420. #2499	C₂×C₆₇	semidirect
421. #2432	C₂×C₆₇	semidirect
423. #2392	C₂×C₆₇	semidirect
424. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
425. C₄×#127	C₂×C₆₇	semidirect
426. C₄×#124	C₂×C₆₇	semidirect
427. C₄×#124	C₂×C₆₇	semidirect
428. #2290	C₂×C₆₇	semidirect
429. C₄×#117	C₂×C₆₇	semidirect
430. C₆₇	#34910	direct (N × H)
577. C₂×C₄²	D₄×C₆₇	semidirect
706. C₄²	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#2602	2
C₆₇×#2601	2
C₆₇×#2566	2
C₆₇×#2565	2
C₆₇×#2545	2
C₆₇×#2544	2
C₆₇×#2500	2
C₆₇×#2499	2
C₆₇×#2432	2
C₆₇×#2431	2
C₆₇×#2392	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#127×C₆₇	2
C₄×#124×C₆₇	2
C₆₇×#2290	2
C₄×#117×C₆₇	2
#34910	67

Subgroups — C67×#34910 #30714161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34910 #30714161