Subgroups — C₆₇×#60170 #30739421

Order 17152.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2952	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2951	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2947	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2946	C₂	1	4	yes	maximal, complemented
8	C₄×#137×C₆₇	C₂	1	4	yes	maximal, complemented
9	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	4	yes	maximal, complemented
10	C₂×#428×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
16	#575×C₆₇	C₄	1	16	yes	complemented
17	C₂×#137×C₆₇	C₂²	1	2	yes	—
18	C₂×#137×C₆₇	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
21	C₂×#135×C₆₇	C₂²	1	4	yes	—
22	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
24	#520×C₆₇	—	2	2	no	—
25	#520×C₆₇	—	2	2	no	—
26	#520×C₆₇	—	2	1	no	—
27	#520×C₆₇	—	2	1	no	—
28	#520×C₆₇	C₂²	1	4	yes	—
29	#520×C₆₇	C₂²	1	4	yes	complemented
30	#520×C₆₇	C₂²	1	2	yes	complemented
31	#520×C₆₇	C₂²	1	2	yes	complemented
32	#519×C₆₇	C₂²	1	2	yes	complemented
33	#518×C₆₇	—	2	2	no	—
34	#518×C₆₇	C₂²	1	2	yes	complemented
35	C₄×#41×C₆₇	—	2	2	no	—
36	C₄×#41×C₆₇	C₂²	1	4	yes	—
37	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₆₇	—	2	2	no	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
40	C₂×#117×C₆₇	—	2	2	no	—
41	C₂×#117×C₆₇	—	2	1	no	—
42	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	#442×C₆₇	C₂²	1	8	yes	complemented
47	#441×C₆₇	C₂²	1	8	yes	complemented
48	#440×C₆₇	C₂²	1	8	yes	complemented
49	#440×C₆₇	C₂²	1	8	yes	complemented
50	C₄×Q₁₆×C₆₇	C₂²	1	8	yes	complemented
51	C₄×SD₁₆×C₆₇	C₂²	1	8	yes	complemented
52	C₄×SD₁₆×C₆₇	C₂²	1	8	yes	complemented
53	C₄×D₈×C₆₇	C₂²	1	8	yes	complemented
54	#428×C₆₇	C₂²	1	4	yes	complemented
55	#428×C₆₇	C₂²	1	4	yes	complemented
56	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
57	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
58	#419×C₆₇	C₂²	1	2	yes	complemented
59	#418×C₆₇	C₂²	1	2	yes	complemented
60	#417×C₆₇	C₂²	1	4	yes	—
61	#417×C₆₇	C₂²	1	4	yes	complemented
62	#417×C₆₇	C₂²	1	2	yes	complemented
63	#417×C₆₇	C₂²	1	2	yes	complemented
64	#416×C₆₇	C₂²	1	4	yes	—
65	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
66	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
67	#405×C₆₇	C₂²	1	4	yes	complemented
68	#405×C₆₇	C₂²	1	4	yes	complemented
69	C₄×M₁₆×C₆₇	C₂²	1	4	yes	complemented
70	C₂×#41×C₆₇	—	2	1	no	—
71	C₂×#41×C₆₇	—	2	1	no	—
72	C₂×#41×C₆₇	—	2	1	no	—
73	C₂×#41×C₆₇	—	2	1	no	—
74	C₂×#41×C₆₇	—	2	4	no	—
75	C₂×#41×C₆₇	—	2	4	no	—
76	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
77	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
78	C₂×#41×C₆₇	C₂³	1	2	yes	—
79	C₂×#41×C₆₇	C₂³	1	2	yes	—
80	C₂×#41×C₆₇	C₂³	1	2	yes	—
81	C₂×#41×C₆₇	C₂³	1	2	yes	—
82	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	—	2	1	no	—
85	C₂²×D₄×C₆₇	—	2	1	no	—
86	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	—	2	1	no	—
89	C₂³×C₄×C₆₇	—	2	1	no	—
90	C₂³×C₄×C₆₇	—	2	1	no	—
91	C₂³×C₄×C₆₇	—	2	2	no	—
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	#137×C₆₇	C₂×C₄	1	16	yes	complemented
94	#137×C₆₇	C₂×C₄	1	16	yes	complemented
95	AGL(1,ℤ/8)×C₆₇	C₂×C₄	1	16	yes	complemented
96	AGL(1,ℤ/8)×C₆₇	C₂×C₄	1	16	yes	complemented
97	#135×C₆₇	C₂×C₄	1	32	yes	complemented
98	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂×D₈×C₆₇	C₂³	1	4	yes	—
102	C₂×M₁₆×C₆₇	—	2	4	no	—
103	C₂×M₁₆×C₆₇	C₂×C₄	1	8	yes	complemented
104	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
105	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
110	C₄×Q₈×C₆₇	—	2	2	no	—
111	C₄×Q₈×C₆₇	—	2	2	no	—
112	C₄×Q₈×C₆₇	—	2	4	no	—
113	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
114	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
115	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
116	C₄×D₄×C₆₇	—	2	4	no	—
117	C₄×D₄×C₆₇	—	2	4	no	—
118	C₄×D₄×C₆₇	—	2	2	no	—
119	C₄×D₄×C₆₇	—	2	2	no	—
120	C₄×D₄×C₆₇	—	2	8	no	—
121	C₄×D₄×C₆₇	—	2	8	no	—
122	C₄×D₄×C₆₇	—	2	4	no	—
123	C₄×D₄×C₆₇	—	2	4	no	—
124	C₄×D₄×C₆₇	—	2	4	no	—
125	C₄×D₄×C₆₇	C₂³	1	8	yes	—
126	C₄×D₄×C₆₇	C₂³	1	4	yes	—
127	C₄×D₄×C₆₇	C₂³	1	4	yes	—
128	#117×C₆₇	—	2	1	no	—
129	#117×C₆₇	—	2	1	no	—
130	#117×C₆₇	—	2	4	no	—
131	#117×C₆₇	—	2	4	no	—
132	#117×C₆₇	—	2	2	no	—
133	#117×C₆₇	—	2	2	no	—
134	#117×C₆₇	—	2	4	no	—
135	#117×C₆₇	—	2	4	no	—
136	#117×C₆₇	D₄	1	2	yes	—
137	#117×C₆₇	D₄	1	2	yes	—
138	#117×C₆₇	C₂³	1	2	yes	—
139	#117×C₆₇	C₂³	1	2	yes	—
140	#117×C₆₇	C₂³	1	2	yes	—
141	#117×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
144	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
145	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
146	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
147	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
148	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
149	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
150	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	D₄	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	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
159	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
160	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
161	C₂×C₄²×C₆₇	—	2	2	no	—
162	C₂×C₄²×C₆₇	—	2	1	no	—
163	C₂×C₄²×C₆₇	—	2	4	no	—
164	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
165	#107×C₆₇	C₂³	1	8	yes	—
166	#106×C₆₇	C₂³	1	8	yes	—
167	#103×C₆₇	C₂³	1	8	yes	—
168	#103×C₆₇	C₂³	1	4	yes	—
169	#103×C₆₇	C₂³	1	4	yes	—
170	#102×C₆₇	C₂³	1	8	yes	—
171	#102×C₆₇	C₂³	1	4	yes	—
172	#102×C₆₇	C₂³	1	4	yes	—
173	#97×C₆₇	C₂³	1	8	yes	—
174	C₄×C₈×C₆₇	C₂³	1	8	yes	—
175	C₂⁴×C₆₇	—	2	1	no	—
176	C₂⁴×C₆₇	—	2	1	no	—
177	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
178	#41×C₆₇	—	2	8	no	—
179	#41×C₆₇	—	2	8	no	—
180	#41×C₆₇	—	2	8	no	—
181	#41×C₆₇	—	2	8	no	—
182	#41×C₆₇	—	2	4	no	—
183	#41×C₆₇	—	2	4	no	—
184	#41×C₆₇	—	2	4	no	—
185	#41×C₆₇	—	2	4	no	—
186	#41×C₆₇	C₂²×C₄	1	8	yes	—
187	#41×C₆₇	C₂²×C₄	1	8	yes	—
188	#41×C₆₇	C₂²×C₄	1	8	yes	—
189	#41×C₆₇	C₂²×C₄	1	8	yes	complemented
190	C₂×Q₈×C₆₇	—	2	1	no	—
191	C₂×Q₈×C₆₇	—	2	1	no	—
192	C₂×Q₈×C₆₇	—	2	2	no	—
193	C₂×Q₈×C₆₇	—	2	2	no	—
194	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
195	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	complemented
196	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
198	C₂×D₄×C₆₇	—	2	8	no	—
199	C₂×D₄×C₆₇	—	2	8	no	—
200	C₂×D₄×C₆₇	—	2	2	no	—
201	C₂×D₄×C₆₇	—	2	2	no	—
202	C₂×D₄×C₆₇	—	2	2	no	—
203	C₂×D₄×C₆₇	—	2	2	no	—
204	C₂×D₄×C₆₇	—	2	1	no	—
205	C₂×D₄×C₆₇	—	2	1	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
209	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	complemented
210	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	—	2	1	no	—
213	C₂²×C₄×C₆₇	—	2	1	no	—
214	C₂²×C₄×C₆₇	—	2	8	no	—
215	C₂²×C₄×C₆₇	—	2	8	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	2	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	1	no	—
222	C₂²×C₄×C₆₇	—	2	1	no	—
223	C₂²×C₄×C₆₇	—	2	2	no	—
224	C₂²×C₄×C₆₇	—	2	2	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	8	no	—
228	C₂²×C₄×C₆₇	—	8	4	no	—
229	C₂²×C₄×C₆₇	—	8	2	no	—
230	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
231	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	#41	1	4	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	Q₁₆×C₆₇	C₂²×C₄	1	16	yes	complemented
241	SD₁₆×C₆₇	C₂²×C₄	1	16	yes	complemented
242	SD₁₆×C₆₇	C₂²×C₄	1	16	yes	complemented
243	D₈×C₆₇	C₂²×C₄	1	16	yes	complemented
244	M₁₆×C₆₇	—	2	4	no	—
245	M₁₆×C₆₇	—	2	4	no	—
246	M₁₆×C₆₇	C₂²×C₄	1	8	yes	—
247	M₁₆×C₆₇	C₂²×C₄	1	8	yes	complemented
248	C₂×C₈×C₆₇	—	2	4	no	—
249	C₂×C₈×C₆₇	C₂²×C₄	1	8	yes	complemented
250	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
251	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	2	no	—
254	C₄⋊C₄×C₆₇	—	2	8	no	—
255	C₄⋊C₄×C₆₇	—	2	1	no	—
256	C₄⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂²⋊C₄×C₆₇	—	2	2	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	8	no	—
272	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
273	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
274	C₄²×C₆₇	—	2	2	no	—
275	C₄²×C₆₇	—	2	4	no	—
276	C₄²×C₆₇	—	2	4	no	—
277	C₄²×C₆₇	—	2	8	no	—
278	C₄²×C₆₇	—	2	2	no	—
279	C₄²×C₆₇	C₂×D₄	1	4	yes	—
280	C₄²×C₆₇	C₂⁴	1	4	yes	—
281	C₂³×C₆₇	—	2	4	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	4	no	—
285	C₂³×C₆₇	—	4	1	no	—
286	C₂³×C₆₇	—	4	1	no	—
287	C₂³×C₆₇	—	4	2	no	—
288	C₂³×C₆₇	—	4	2	no	—
289	C₂³×C₆₇	—	8	1	no	—
290	C₂³×C₆₇	—	8	1	no	—
291	C₂³×C₆₇	C₄×D₄	1	4	yes	—
292	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₆₇	—	2	4	no	—
296	Q₈×C₆₇	—	2	4	no	—
297	Q₈×C₆₇	—	2	2	no	—
298	Q₈×C₆₇	—	2	2	no	—
299	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
300	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
301	D₄×C₆₇	—	2	8	no	—
302	D₄×C₆₇	—	2	8	no	—
303	D₄×C₆₇	—	2	8	no	—
304	D₄×C₆₇	—	2	8	no	—
305	D₄×C₆₇	—	2	4	no	—
306	D₄×C₆₇	—	2	4	no	—
307	D₄×C₆₇	—	2	2	no	—
308	D₄×C₆₇	—	2	2	no	—
309	D₄×C₆₇	C₂³×C₄	1	4	yes	—
310	D₄×C₆₇	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₆₇	—	2	4	no	—
312	C₂×C₄×C₆₇	—	2	4	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	8	no	—
316	C₂×C₄×C₆₇	—	2	8	no	—
317	C₂×C₄×C₆₇	—	2	8	no	—
318	C₂×C₄×C₆₇	—	2	8	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	4	no	—
322	C₂×C₄×C₆₇	—	4	2	no	—
323	C₂×C₄×C₆₇	—	4	2	no	—
324	C₂×C₄×C₆₇	—	4	4	no	—
325	C₂×C₄×C₆₇	—	8	4	no	—
326	C₂×C₄×C₆₇	—	8	4	no	—
327	C₂×C₄×C₆₇	—	8	8	no	—
328	C₂×C₄×C₆₇	—	8	1	no	—
329	C₂×C₄×C₆₇	—	8	1	no	—
330	C₂×C₄×C₆₇	—	8	2	no	—
331	C₂×C₄×C₆₇	—	8	2	no	—
332	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
333	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
334	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
335	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
336	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
344	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
345	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
346	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
347	C₈×C₆₇	—	2	4	no	—
348	C₈×C₆₇	C₂³×C₄	1	8	yes	—
349	C₂²×C₆₇	—	2	1	no	—
350	C₂²×C₆₇	—	2	1	no	—
351	C₂²×C₆₇	—	2	1	no	—
352	C₂²×C₆₇	—	2	1	no	—
353	C₂²×C₆₇	—	2	1	no	—
354	C₂²×C₆₇	—	2	1	no	—
355	C₂²×C₆₇	—	2	4	no	—
356	C₂²×C₆₇	—	2	4	no	—
357	C₂²×C₆₇	—	4	4	no	—
358	C₂²×C₆₇	—	4	8	no	—
359	C₂²×C₆₇	—	4	2	no	—
360	C₂²×C₆₇	—	4	2	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	—	4	2	no	—
363	C₂²×C₆₇	—	8	4	no	—
364	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
365	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
366	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
367	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₆₇	—	2	4	no	—
369	C₄×C₆₇	—	2	4	no	—
370	C₄×C₆₇	—	2	4	no	—
371	C₄×C₆₇	—	2	4	no	—
372	C₄×C₆₇	—	4	4	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
376	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
377	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
378	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
379	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
380	#60170	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₆₇	—	2	2	no	—
382	C₂×C₆₇	—	2	2	no	—
383	C₂×C₆₇	—	2	2	no	—
384	C₂×C₆₇	—	4	4	no	—
385	C₂×C₆₇	—	4	4	no	—
386	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
387	C₂×C₆₇	#3585	1	1	yes	characteristic
388	C₂×C₆₇	#3586	1	1	yes	characteristic
389	C₂×#575	C₂×C₆₇	1	1	yes	characteristic
390	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#2952	C₂×C₆₇	1	4	yes	complemented
393	#2951	C₂×C₆₇	1	4	yes	complemented
394	#2947	C₂×C₆₇	1	4	yes	complemented
395	#2946	C₂×C₆₇	1	4	yes	complemented
396	C₄×#137	C₂×C₆₇	1	4	yes	complemented
397	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	4	yes	complemented
398	C₂×#428	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#2873	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₆₇	#60170	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
404	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
405	#575	C₄×C₆₇	1	16	yes	complemented
406	C₂×#137	C₂²×C₆₇	1	2	yes	—
407	C₂×#137	C₂²×C₆₇	1	2	yes	—
408	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
409	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
410	C₂×#135	C₂²×C₆₇	1	4	yes	—
411	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
412	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
413	#520	—	2	2	no	—
414	#520	—	2	2	no	—
415	#520	—	2	1	no	—
416	#520	—	2	1	no	—
417	#520	C₂²×C₆₇	1	4	yes	—
418	#520	C₂²×C₆₇	1	4	yes	complemented
419	#520	C₂²×C₆₇	1	2	yes	complemented
420	#520	C₂²×C₆₇	1	2	yes	complemented
421	#519	C₂²×C₆₇	1	2	yes	complemented
422	#518	—	2	2	no	—
423	#518	C₂²×C₆₇	1	2	yes	complemented
424	C₄×#41	—	2	2	no	—
425	C₄×#41	C₂²×C₆₇	1	4	yes	—
426	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
427	C₂×C₄×D₄	—	2	2	no	—
428	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
429	C₂×#117	—	2	2	no	—
430	C₂×#117	—	2	1	no	—
431	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	—	2	1	no	—
434	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
435	#442	C₂²×C₆₇	1	8	yes	complemented
436	#441	C₂²×C₆₇	1	8	yes	complemented
437	#440	C₂²×C₆₇	1	8	yes	complemented
438	#440	C₂²×C₆₇	1	8	yes	complemented
439	C₄×Q₁₆	C₂²×C₆₇	1	8	yes	complemented
440	C₄×SD₁₆	C₂²×C₆₇	1	8	yes	complemented
441	C₄×SD₁₆	C₂²×C₆₇	1	8	yes	complemented
442	C₄×D₈	C₂²×C₆₇	1	8	yes	complemented
443	#428	C₂²×C₆₇	1	4	yes	complemented
444	#428	C₂²×C₆₇	1	4	yes	complemented
445	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
446	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
447	#419	C₂²×C₆₇	1	2	yes	complemented
448	#418	C₂²×C₆₇	1	2	yes	complemented
449	#417	C₂²×C₆₇	1	4	yes	—
450	#417	C₂²×C₆₇	1	4	yes	complemented
451	#417	C₂²×C₆₇	1	2	yes	complemented
452	#417	C₂²×C₆₇	1	2	yes	complemented
453	#416	C₂²×C₆₇	1	4	yes	—
454	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
455	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
456	#405	C₂²×C₆₇	1	4	yes	complemented
457	#405	C₂²×C₆₇	1	4	yes	complemented
458	C₄×M₁₆	C₂²×C₆₇	1	4	yes	complemented
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	4	no	—
464	C₂×#41	—	2	4	no	—
465	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
466	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
467	C₂×#41	C₂³×C₆₇	1	2	yes	—
468	C₂×#41	C₂³×C₆₇	1	2	yes	—
469	C₂×#41	C₂³×C₆₇	1	2	yes	—
470	C₂×#41	C₂³×C₆₇	1	2	yes	—
471	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	2	no	—
481	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
482	#137	C₂×C₄×C₆₇	1	16	yes	complemented
483	#137	C₂×C₄×C₆₇	1	16	yes	complemented
484	AGL(1,ℤ/8)	C₂×C₄×C₆₇	1	16	yes	complemented
485	AGL(1,ℤ/8)	C₂×C₄×C₆₇	1	16	yes	complemented
486	#135	C₂×C₄×C₆₇	1	32	yes	complemented
487	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
488	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
489	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
490	C₂×D₈	C₂³×C₆₇	1	4	yes	—
491	C₂×M₁₆	—	2	4	no	—
492	C₂×M₁₆	C₂×C₄×C₆₇	1	8	yes	complemented
493	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
494	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
495	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
496	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
497	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
498	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	4	no	—
502	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
503	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
504	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
505	C₄×D₄	—	2	4	no	—
506	C₄×D₄	—	2	4	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	8	no	—
510	C₄×D₄	—	2	8	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	C₂³×C₆₇	1	8	yes	—
515	C₄×D₄	C₂³×C₆₇	1	4	yes	—
516	C₄×D₄	C₂³×C₆₇	1	4	yes	—
517	#117	—	2	1	no	—
518	#117	—	2	1	no	—
519	#117	—	2	4	no	—
520	#117	—	2	4	no	—
521	#117	—	2	2	no	—
522	#117	—	2	2	no	—
523	#117	—	2	4	no	—
524	#117	—	2	4	no	—
525	#117	D₄×C₆₇	1	2	yes	—
526	#117	D₄×C₆₇	1	2	yes	—
527	#117	C₂³×C₆₇	1	2	yes	—
528	#117	C₂³×C₆₇	1	2	yes	—
529	#117	C₂³×C₆₇	1	2	yes	—
530	#117	C₂³×C₆₇	1	2	yes	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	2	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	4	no	—
536	C₂×C₄⋊C₄	—	2	4	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	2	no	—
539	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	2	no	—
548	C₂×C₂²⋊C₄	—	2	4	no	—
549	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
550	C₂×C₄²	—	2	2	no	—
551	C₂×C₄²	—	2	1	no	—
552	C₂×C₄²	—	2	4	no	—
553	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
554	#107	C₂³×C₆₇	1	8	yes	—
555	#106	C₂³×C₆₇	1	8	yes	—
556	#103	C₂³×C₆₇	1	8	yes	—
557	#103	C₂³×C₆₇	1	4	yes	—
558	#103	C₂³×C₆₇	1	4	yes	—
559	#102	C₂³×C₆₇	1	8	yes	—
560	#102	C₂³×C₆₇	1	4	yes	—
561	#102	C₂³×C₆₇	1	4	yes	—
562	#97	C₂³×C₆₇	1	8	yes	—
563	C₄×C₈	C₂³×C₆₇	1	8	yes	—
564	C₂⁴	—	2	1	no	—
565	C₂⁴	—	2	1	no	—
566	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
567	#41	—	2	8	no	—
568	#41	—	2	8	no	—
569	#41	—	2	8	no	—
570	#41	—	2	8	no	—
571	#41	—	2	4	no	—
572	#41	—	2	4	no	—
573	#41	—	2	4	no	—
574	#41	—	2	4	no	—
575	#41	C₂²×C₄×C₆₇	1	8	yes	—
576	#41	C₂²×C₄×C₆₇	1	8	yes	—
577	#41	C₂²×C₄×C₆₇	1	8	yes	—
578	#41	C₂²×C₄×C₆₇	1	8	yes	complemented
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
584	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	complemented
585	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
586	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
598	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	complemented
599	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
600	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	8	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	8	4	no	—
618	C₂²×C₄	—	8	2	no	—
619	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
620	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
621	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
622	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
625	C₂²×C₄	#41×C₆₇	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
629	Q₁₆	C₂²×C₄×C₆₇	1	16	yes	complemented
630	SD₁₆	C₂²×C₄×C₆₇	1	16	yes	complemented
631	SD₁₆	C₂²×C₄×C₆₇	1	16	yes	complemented
632	D₈	C₂²×C₄×C₆₇	1	16	yes	complemented
633	M₁₆	—	2	4	no	—
634	M₁₆	—	2	4	no	—
635	M₁₆	C₂²×C₄×C₆₇	1	8	yes	—
636	M₁₆	C₂²×C₄×C₆₇	1	8	yes	complemented
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	C₂²×C₄×C₆₇	1	8	yes	complemented
639	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
640	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
655	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
662	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
663	C₄²	—	2	2	no	—
664	C₄²	—	2	4	no	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	8	no	—
667	C₄²	—	2	2	no	—
668	C₄²	C₂×D₄×C₆₇	1	4	yes	—
669	C₄²	C₂⁴×C₆₇	1	4	yes	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	2	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	8	1	no	—
679	C₂³	—	8	1	no	—
680	C₂³	C₄×D₄×C₆₇	1	4	yes	—
681	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
682	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
683	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
684	Q₈	—	2	4	no	—
685	Q₈	—	2	4	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	C₂³×C₄×C₆₇	1	4	yes	—
689	Q₈	C₂³×C₄×C₆₇	1	4	yes	—
690	D₄	—	2	8	no	—
691	D₄	—	2	8	no	—
692	D₄	—	2	8	no	—
693	D₄	—	2	8	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	C₂³×C₄×C₆₇	1	4	yes	—
699	D₄	C₂³×C₄×C₆₇	1	4	yes	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	8	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	8	8	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	1	no	—
720	C₂×C₄	—	8	1	no	—
721	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
722	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
723	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
724	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
725	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
726	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
728	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
729	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
732	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
733	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
734	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
735	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
736	C₈	—	2	4	no	—
737	C₈	C₂³×C₄×C₆₇	1	8	yes	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	4	8	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	8	4	no	—
753	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
754	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
755	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
756	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
757	C₄	—	2	4	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	4	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
765	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
766	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
767	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
768	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	2	2	no	—
772	C₂	—	4	4	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
775	C₂	C₆₇×#3585	1	1	yes	characteristic
776	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#575×C₆₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3428	C₂	semidirect
3. C₂×#520×C₆₇	C₂	semidirect
4. C₆₇×#2952	C₂	semidirect
5. C₆₇×#2951	C₂	semidirect
6. C₆₇×#2947	C₂	semidirect
7. C₆₇×#2946	C₂	semidirect
8. C₄×#137×C₆₇	C₂	semidirect
9. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
10. C₂×#428×C₆₇	C₂	semidirect
11. C₆₇×#2896	C₂	semidirect
12. C₂×#417×C₆₇	C₂	semidirect
13. C₆₇×#2873	C₂	semidirect
16. #575×C₆₇	C₄	semidirect
29. #520×C₆₇	C₂²	semidirect
30. #520×C₆₇	C₂²	semidirect
31. #520×C₆₇	C₂²	semidirect
32. #519×C₆₇	C₂²	semidirect
34. #518×C₆₇	C₂²	semidirect
37. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
39. C₂×C₄×D₄×C₆₇	C₂²	semidirect
46. #442×C₆₇	C₂²	semidirect
47. #441×C₆₇	C₂²	semidirect
48. #440×C₆₇	C₂²	semidirect
49. #440×C₆₇	C₂²	semidirect
50. C₄×Q₁₆×C₆₇	C₂²	semidirect
51. C₄×SD₁₆×C₆₇	C₂²	semidirect
52. C₄×SD₁₆×C₆₇	C₂²	semidirect
53. C₄×D₈×C₆₇	C₂²	semidirect
54. #428×C₆₇	C₂²	semidirect
55. #428×C₆₇	C₂²	semidirect
56. C₂×#107×C₆₇	C₂²	semidirect
57. C₂×#106×C₆₇	C₂²	semidirect
58. #419×C₆₇	C₂²	semidirect
59. #418×C₆₇	C₂²	semidirect
61. #417×C₆₇	C₂²	semidirect
62. #417×C₆₇	C₂²	semidirect
63. #417×C₆₇	C₂²	semidirect
65. C₂×#103×C₆₇	C₂²	semidirect
66. C₂×#102×C₆₇	C₂²	semidirect
67. #405×C₆₇	C₂²	semidirect
68. #405×C₆₇	C₂²	semidirect
69. C₄×M₁₆×C₆₇	C₂²	semidirect
76. C₂×#41×C₆₇	C₂×C₄	semidirect
77. C₂×#41×C₆₇	C₂×C₄	semidirect
93. #137×C₆₇	C₂×C₄	semidirect
94. #137×C₆₇	C₂×C₄	semidirect
95. AGL(1,ℤ/8)×C₆₇	C₂×C₄	semidirect
96. AGL(1,ℤ/8)×C₆₇	C₂×C₄	semidirect
97. #135×C₆₇	C₂×C₄	semidirect
103. C₂×M₁₆×C₆₇	C₂×C₄	semidirect
189. #41×C₆₇	C₂²×C₄	semidirect
195. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
209. C₂×D₄×C₆₇	C₂²×C₄	semidirect
240. Q₁₆×C₆₇	C₂²×C₄	semidirect
241. SD₁₆×C₆₇	C₂²×C₄	semidirect
242. SD₁₆×C₆₇	C₂²×C₄	semidirect
243. D₈×C₆₇	C₂²×C₄	semidirect
247. M₁₆×C₆₇	C₂²×C₄	semidirect
249. C₂×C₈×C₆₇	C₂²×C₄	semidirect
380. #60170	C₆₇	direct (N × H)
390. #3428	C₂×C₆₇	semidirect
391. C₂×#520	C₂×C₆₇	semidirect
392. #2952	C₂×C₆₇	semidirect
393. #2951	C₂×C₆₇	semidirect
394. #2947	C₂×C₆₇	semidirect
395. #2946	C₂×C₆₇	semidirect
396. C₄×#137	C₂×C₆₇	semidirect
397. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
398. C₂×#428	C₂×C₆₇	semidirect
399. #2896	C₂×C₆₇	semidirect
400. C₂×#417	C₂×C₆₇	semidirect
401. #2873	C₂×C₆₇	semidirect
402. C₆₇	#60170	direct (N × H)
405. #575	C₄×C₆₇	semidirect
418. #520	C₂²×C₆₇	semidirect
419. #520	C₂²×C₆₇	semidirect
420. #520	C₂²×C₆₇	semidirect
421. #519	C₂²×C₆₇	semidirect
423. #518	C₂²×C₆₇	semidirect
426. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
428. C₂×C₄×D₄	C₂²×C₆₇	semidirect
435. #442	C₂²×C₆₇	semidirect
436. #441	C₂²×C₆₇	semidirect
437. #440	C₂²×C₆₇	semidirect
438. #440	C₂²×C₆₇	semidirect
439. C₄×Q₁₆	C₂²×C₆₇	semidirect
440. C₄×SD₁₆	C₂²×C₆₇	semidirect
441. C₄×SD₁₆	C₂²×C₆₇	semidirect
442. C₄×D₈	C₂²×C₆₇	semidirect
443. #428	C₂²×C₆₇	semidirect
444. #428	C₂²×C₆₇	semidirect
445. C₂×#107	C₂²×C₆₇	semidirect
446. C₂×#106	C₂²×C₆₇	semidirect
447. #419	C₂²×C₆₇	semidirect
448. #418	C₂²×C₆₇	semidirect
450. #417	C₂²×C₆₇	semidirect
451. #417	C₂²×C₆₇	semidirect
452. #417	C₂²×C₆₇	semidirect
454. C₂×#103	C₂²×C₆₇	semidirect
455. C₂×#102	C₂²×C₆₇	semidirect
456. #405	C₂²×C₆₇	semidirect
457. #405	C₂²×C₆₇	semidirect
458. C₄×M₁₆	C₂²×C₆₇	semidirect
465. C₂×#41	C₂×C₄×C₆₇	semidirect
466. C₂×#41	C₂×C₄×C₆₇	semidirect
482. #137	C₂×C₄×C₆₇	semidirect
483. #137	C₂×C₄×C₆₇	semidirect
484. AGL(1,ℤ/8)	C₂×C₄×C₆₇	semidirect
485. AGL(1,ℤ/8)	C₂×C₄×C₆₇	semidirect
486. #135	C₂×C₄×C₆₇	semidirect
492. C₂×M₁₆	C₂×C₄×C₆₇	semidirect
578. #41	C₂²×C₄×C₆₇	semidirect
584. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
598. C₂×D₄	C₂²×C₄×C₆₇	semidirect
629. Q₁₆	C₂²×C₄×C₆₇	semidirect
630. SD₁₆	C₂²×C₄×C₆₇	semidirect
631. SD₁₆	C₂²×C₄×C₆₇	semidirect
632. D₈	C₂²×C₄×C₆₇	semidirect
636. M₁₆	C₂²×C₄×C₆₇	semidirect
638. C₂×C₈	C₂²×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₆₇	2
C₆₇×#3428	2
C₂×#520×C₆₇	2
C₆₇×#2952	2
C₆₇×#2951	2
C₆₇×#2947	2
C₆₇×#2946	2
C₄×#137×C₆₇	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₂×#428×C₆₇	2
C₆₇×#2896	2
C₂×#417×C₆₇	2
C₆₇×#2873	2
#60170	67

Subgroups — C67×#60170 #30739421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60170 #30739421