Subgroups — C₆₇×#61325 #30740576

Order 17152.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3370	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3367	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3366	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3361	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3360	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3358	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3136	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3083	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3041	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
19	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
20	#559×C₆₇	C₂²	1	4	yes	complemented
21	#556×C₆₇	C₂²	1	2	yes	complemented
22	#555×C₆₇	—	2	1	no	—
23	#554×C₆₇	—	2	1	no	—
24	#554×C₆₇	—	2	2	no	—
25	#554×C₆₇	C₂²	1	2	yes	complemented
26	#554×C₆₇	C₂²	1	4	yes	complemented
27	#553×C₆₇	—	2	2	no	—
28	#550×C₆₇	C₂²	1	2	yes	complemented
29	D₄×Q₈×C₆₇	—	2	1	no	—
30	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
31	#547×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	2	yes	—
33	#543×C₆₇	—	2	2	no	—
34	#538×C₆₇	—	2	2	no	—
35	#535×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	#525×C₆₇	—	2	2	no	—
40	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
41	#520×C₆₇	C₂²	1	2	yes	—
42	#518×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	#490×C₆₇	C₂²	1	4	yes	complemented
46	#489×C₆₇	C₂²	1	4	yes	complemented
47	#488×C₆₇	C₂²	1	4	yes	complemented
48	#488×C₆₇	C₂²	1	2	yes	complemented
49	#488×C₆₇	C₂²	1	2	yes	complemented
50	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#486×C₆₇	C₂²	1	4	yes	complemented
54	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	4	yes	complemented
57	#478×C₆₇	C₂²	1	4	yes	complemented
58	#477×C₆₇	C₂²	1	4	yes	complemented
59	#476×C₆₇	C₂²	1	2	yes	complemented
60	#474×C₆₇	C₂²	1	2	yes	complemented
61	#474×C₆₇	C₂²	1	4	yes	complemented
62	#463×C₆₇	C₂²	1	4	yes	—
63	#463×C₆₇	C₂²	1	4	yes	—
64	#463×C₆₇	C₂²	1	4	yes	complemented
65	#461×C₆₇	C₂²	1	2	yes	complemented
66	#459×C₆₇	C₂²	1	4	yes	—
67	#459×C₆₇	C₂²	1	4	yes	—
68	#459×C₆₇	C₂²	1	2	yes	complemented
69	#446×C₆₇	C₂²	1	2	yes	complemented
70	#446×C₆₇	C₂²	1	2	yes	complemented
71	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
73	#442×C₆₇	C₂²	1	4	yes	complemented
74	#440×C₆₇	C₂²	1	4	yes	complemented
75	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
76	C₄×D₈×C₆₇	C₂²	1	2	yes	—
77	C₄×D₈×C₆₇	C₂²	1	2	yes	—
78	C₄×D₈×C₆₇	C₂²	1	2	yes	—
79	C₄×D₈×C₆₇	C₂²	1	2	yes	—
80	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
81	#428×C₆₇	C₂²	1	2	yes	—
82	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
83	#424×C₆₇	C₂²	1	2	yes	—
84	#423×C₆₇	C₂²	1	1	yes	characteristic
85	#418×C₆₇	C₂²	1	2	yes	—
86	#417×C₆₇	C₂²	1	2	yes	—
87	#416×C₆₇	C₂²	1	2	yes	—
88	#416×C₆₇	C₂²	1	2	yes	—
89	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
90	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
91	#405×C₆₇	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	C₂³	1	2	yes	—
95	C₂²×Q₈×C₆₇	—	2	2	no	—
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	—	2	1	no	—
99	C₂³×C₄×C₆₇	—	2	1	no	—
100	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
101	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×D₈×C₆₇	—	2	4	no	—
103	C₂×D₈×C₆₇	C₂³	1	4	yes	—
104	C₂×D₈×C₆₇	C₂³	1	2	yes	—
105	C₂×D₈×C₆₇	C₂³	1	2	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
116	#127×C₆₇	C₂³	1	4	yes	—
117	#127×C₆₇	C₂³	1	1	yes	characteristic
118	#126×C₆₇	—	2	4	no	—
119	#125×C₆₇	—	2	2	no	—
120	#125×C₆₇	D₄	1	2	yes	—
121	#125×C₆₇	C₂³	1	2	yes	—
122	#125×C₆₇	C₂³	1	4	yes	—
123	#124×C₆₇	—	2	4	no	—
124	#124×C₆₇	C₂³	1	4	yes	—
125	#124×C₆₇	C₂³	1	2	yes	—
126	#123×C₆₇	—	2	4	no	—
127	#123×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	2	no	—
130	C₂²⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	1	no	—
132	C₂²⋊Q₈×C₆₇	—	2	1	no	—
133	C₂²⋊Q₈×C₆₇	—	2	2	no	—
134	C₂²⋊Q₈×C₆₇	—	2	4	no	—
135	C₂²⋊Q₈×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	—	2	4	no	—
138	C₂²⋊Q₈×C₆₇	—	2	4	no	—
139	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
140	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
141	#121×C₆₇	—	2	1	no	—
142	#121×C₆₇	—	2	1	no	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	2	no	—
146	#121×C₆₇	—	2	4	no	—
147	#120×C₆₇	—	2	4	no	—
148	C₄×Q₈×C₆₇	—	2	1	no	—
149	C₄×Q₈×C₆₇	—	2	1	no	—
150	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
151	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	—	2	4	no	—
156	C₄×D₄×C₆₇	—	2	4	no	—
157	C₄×D₄×C₆₇	—	2	1	no	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	—	2	1	no	—
160	C₄×D₄×C₆₇	—	2	1	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	C₂³	1	4	yes	—
164	C₄×D₄×C₆₇	C₂³	1	4	yes	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	C₄×D₄×C₆₇	C₂³	1	4	yes	—
169	C₄×D₄×C₆₇	C₂³	1	2	yes	—
170	#117×C₆₇	—	2	2	no	—
171	#117×C₆₇	—	2	2	no	—
172	#117×C₆₇	C₂³	1	2	yes	—
173	#117×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
175	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
176	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
182	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
183	#107×C₆₇	C₂³	1	4	yes	—
184	#107×C₆₇	C₂³	1	2	yes	—
185	#107×C₆₇	C₂³	1	2	yes	—
186	#106×C₆₇	C₂³	1	4	yes	—
187	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
188	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
189	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
190	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
191	#103×C₆₇	C₂³	1	4	yes	—
192	#103×C₆₇	C₂³	1	2	yes	—
193	#103×C₆₇	C₂³	1	2	yes	—
194	#103×C₆₇	C₂³	1	2	yes	—
195	#103×C₆₇	C₂³	1	2	yes	—
196	#102×C₆₇	C₂³	1	2	yes	—
197	#102×C₆₇	C₂³	1	2	yes	—
198	#102×C₆₇	C₂³	1	4	yes	—
199	#102×C₆₇	C₂³	1	4	yes	—
200	#102×C₆₇	C₂³	1	4	yes	—
201	#102×C₆₇	C₂³	1	2	yes	—
202	#102×C₆₇	C₂³	1	2	yes	—
203	#102×C₆₇	C₂³	1	2	yes	—
204	#102×C₆₇	C₂³	1	2	yes	—
205	#102×C₆₇	C₂³	1	2	yes	—
206	#102×C₆₇	C₂³	1	2	yes	—
207	#97×C₆₇	C₂³	1	4	yes	—
208	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₆₇	C₂³	1	4	yes	—
211	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₂⁴×C₆₇	—	2	1	no	—
214	C₂⁴×C₆₇	—	2	1	no	—
215	#41×C₆₇	—	2	4	no	—
216	#41×C₆₇	—	2	4	no	—
217	#41×C₆₇	—	8	4	no	—
218	C₂×Q₈×C₆₇	—	2	1	no	—
219	C₂×Q₈×C₆₇	—	2	1	no	—
220	C₂×Q₈×C₆₇	—	2	4	no	—
221	C₂×Q₈×C₆₇	—	8	4	no	—
222	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
225	C₂×D₄×C₆₇	—	2	2	no	—
226	C₂×D₄×C₆₇	—	2	1	no	—
227	C₂×D₄×C₆₇	—	2	1	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	2	4	no	—
232	C₂×D₄×C₆₇	—	2	2	no	—
233	C₂×D₄×C₆₇	—	2	2	no	—
234	C₂×D₄×C₆₇	—	2	2	no	—
235	C₂×D₄×C₆₇	#41	1	4	yes	complemented
236	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	8	2	no	—
250	C₂²×C₄×C₆₇	—	8	2	no	—
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₆₇	—	2	8	no	—
255	D₈×C₆₇	—	2	4	no	—
256	D₈×C₆₇	—	2	4	no	—
257	D₈×C₆₇	—	2	8	no	—
258	M₁₆×C₆₇	—	2	4	no	—
259	C₂×C₈×C₆₇	—	2	2	no	—
260	C₂×C₈×C₆₇	—	2	2	no	—
261	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	2	2	no	—
300	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
301	C₄²×C₆₇	—	2	4	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₄²×C₆₇	C₂⁴	1	4	yes	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	2	4	no	—
310	C₂³×C₆₇	—	2	2	no	—
311	C₂³×C₆₇	—	2	2	no	—
312	C₂³×C₆₇	—	4	2	no	—
313	C₂³×C₆₇	—	8	1	no	—
314	C₂³×C₆₇	—	8	1	no	—
315	C₂³×C₆₇	—	8	1	no	—
316	C₂³×C₆₇	—	8	1	no	—
317	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₆₇	—	2	4	no	—
319	Q₈×C₆₇	—	2	2	no	—
320	Q₈×C₆₇	—	2	2	no	—
321	Q₈×C₆₇	—	4	2	no	—
322	Q₈×C₆₇	—	4	2	no	—
323	Q₈×C₆₇	—	8	1	no	—
324	Q₈×C₆₇	—	8	4	no	—
325	D₄×C₆₇	—	2	4	no	—
326	D₄×C₆₇	—	2	2	no	—
327	D₄×C₆₇	—	2	2	no	—
328	D₄×C₆₇	—	2	2	no	—
329	D₄×C₆₇	—	2	2	no	—
330	D₄×C₆₇	—	2	2	no	—
331	D₄×C₆₇	—	4	4	no	—
332	D₄×C₆₇	—	4	2	no	—
333	D₄×C₆₇	—	4	2	no	—
334	D₄×C₆₇	—	8	1	no	—
335	D₄×C₆₇	—	8	4	no	—
336	D₄×C₆₇	—	8	4	no	—
337	D₄×C₆₇	C₂×#41	1	4	yes	—
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	2	no	—
344	C₂×C₄×C₆₇	—	4	1	no	—
345	C₂×C₄×C₆₇	—	4	4	no	—
346	C₂×C₄×C₆₇	—	4	4	no	—
347	C₂×C₄×C₆₇	—	4	4	no	—
348	C₂×C₄×C₆₇	—	8	4	no	—
349	C₂×C₄×C₆₇	—	8	2	no	—
350	C₂×C₄×C₆₇	—	8	2	no	—
351	C₂×C₄×C₆₇	—	8	4	no	—
352	C₂×C₄×C₆₇	—	8	4	no	—
353	C₂×C₄×C₆₇	—	8	1	no	—
354	C₂×C₄×C₆₇	—	8	1	no	—
355	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
363	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
364	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
365	C₈×C₆₇	—	2	1	no	—
366	C₈×C₆₇	—	2	1	no	—
367	C₈×C₆₇	—	2	4	no	—
368	C₈×C₆₇	—	2	1	no	—
369	C₈×C₆₇	—	2	1	no	—
370	C₂²×C₆₇	—	2	1	no	—
371	C₂²×C₆₇	—	2	1	no	—
372	C₂²×C₆₇	—	2	4	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	4	2	no	—
376	C₂²×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	4	2	no	—
378	C₂²×C₆₇	—	4	2	no	—
379	C₂²×C₆₇	—	4	2	no	—
380	C₂²×C₆₇	—	4	2	no	—
381	C₂²×C₆₇	—	8	4	no	—
382	C₂²×C₆₇	—	8	4	no	—
383	C₂²×C₆₇	#548	1	2	yes	—
384	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₆₇	—	2	1	no	—
386	C₄×C₆₇	—	2	1	no	—
387	C₄×C₆₇	—	2	4	no	—
388	C₄×C₆₇	—	2	1	no	—
389	C₄×C₆₇	—	2	4	no	—
390	C₄×C₆₇	—	4	2	no	—
391	C₄×C₆₇	—	4	2	no	—
392	C₄×C₆₇	—	4	2	no	—
393	C₄×C₆₇	—	4	2	no	—
394	C₄×C₆₇	—	4	2	no	—
395	C₄×C₆₇	#548	1	2	yes	—
396	C₄×C₆₇	#576	1	2	yes	—
397	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
398	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
399	#61325	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₂×C₆₇	—	2	2	no	—
401	C₂×C₆₇	—	4	4	no	—
402	C₂×C₆₇	—	8	2	no	—
403	C₂×C₆₇	—	8	2	no	—
404	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
405	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
406	C₂×C₆₇	#3584	1	1	yes	characteristic
407	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
408	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#3370	C₂×C₆₇	1	4	yes	complemented
410	#3367	C₂×C₆₇	1	2	yes	complemented
411	#3366	C₂×C₆₇	1	2	yes	complemented
412	#3361	C₂×C₆₇	1	4	yes	complemented
413	#3360	C₂×C₆₇	1	2	yes	complemented
414	#3358	C₂×C₆₇	1	2	yes	complemented
415	#3136	C₂×C₆₇	1	2	yes	complemented
416	#3131	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#3083	C₂×C₆₇	1	2	yes	complemented
418	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#3041	C₂×C₆₇	1	2	yes	complemented
420	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
421	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#2946	C₂×C₆₇	1	2	yes	complemented
423	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
424	C₆₇	#61325	1	1	yes	characteristic, direct product factor, Sylow
425	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
426	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
427	#559	C₂²×C₆₇	1	4	yes	complemented
428	#556	C₂²×C₆₇	1	2	yes	complemented
429	#555	—	2	1	no	—
430	#554	—	2	1	no	—
431	#554	—	2	2	no	—
432	#554	C₂²×C₆₇	1	2	yes	complemented
433	#554	C₂²×C₆₇	1	4	yes	complemented
434	#553	—	2	2	no	—
435	#550	C₂²×C₆₇	1	2	yes	complemented
436	D₄×Q₈	—	2	1	no	—
437	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
438	#547	—	2	1	no	—
439	#544	C₂²×C₆₇	1	2	yes	—
440	#543	—	2	2	no	—
441	#538	—	2	2	no	—
442	#535	C₂²×C₆₇	1	2	yes	—
443	#533	C₂²×C₆₇	1	1	yes	characteristic
444	#533	C₂²×C₆₇	1	1	yes	characteristic
445	#532	C₂²×C₆₇	1	1	yes	characteristic
446	#525	—	2	2	no	—
447	C₂×C₂²⋊Q₈	—	2	2	no	—
448	#520	C₂²×C₆₇	1	2	yes	—
449	#518	C₂²×C₆₇	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
452	#490	C₂²×C₆₇	1	4	yes	complemented
453	#489	C₂²×C₆₇	1	4	yes	complemented
454	#488	C₂²×C₆₇	1	4	yes	complemented
455	#488	C₂²×C₆₇	1	2	yes	complemented
456	#488	C₂²×C₆₇	1	2	yes	complemented
457	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
459	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
460	#486	C₂²×C₆₇	1	4	yes	complemented
461	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
462	#479	C₂²×C₆₇	1	4	yes	complemented
463	#478	C₂²×C₆₇	1	4	yes	complemented
464	#478	C₂²×C₆₇	1	4	yes	complemented
465	#477	C₂²×C₆₇	1	4	yes	complemented
466	#476	C₂²×C₆₇	1	2	yes	complemented
467	#474	C₂²×C₆₇	1	2	yes	complemented
468	#474	C₂²×C₆₇	1	4	yes	complemented
469	#463	C₂²×C₆₇	1	4	yes	—
470	#463	C₂²×C₆₇	1	4	yes	—
471	#463	C₂²×C₆₇	1	4	yes	complemented
472	#461	C₂²×C₆₇	1	2	yes	complemented
473	#459	C₂²×C₆₇	1	4	yes	—
474	#459	C₂²×C₆₇	1	4	yes	—
475	#459	C₂²×C₆₇	1	2	yes	complemented
476	#446	C₂²×C₆₇	1	2	yes	complemented
477	#446	C₂²×C₆₇	1	2	yes	complemented
478	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
479	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
480	#442	C₂²×C₆₇	1	4	yes	complemented
481	#440	C₂²×C₆₇	1	4	yes	complemented
482	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
483	C₄×D₈	C₂²×C₆₇	1	2	yes	—
484	C₄×D₈	C₂²×C₆₇	1	2	yes	—
485	C₄×D₈	C₂²×C₆₇	1	2	yes	—
486	C₄×D₈	C₂²×C₆₇	1	2	yes	—
487	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
488	#428	C₂²×C₆₇	1	2	yes	—
489	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
490	#424	C₂²×C₆₇	1	2	yes	—
491	#423	C₂²×C₆₇	1	1	yes	characteristic
492	#418	C₂²×C₆₇	1	2	yes	—
493	#417	C₂²×C₆₇	1	2	yes	—
494	#416	C₂²×C₆₇	1	2	yes	—
495	#416	C₂²×C₆₇	1	2	yes	—
496	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
498	#405	C₂²×C₆₇	1	2	yes	—
499	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×#41	—	2	2	no	—
501	C₂×#41	C₂³×C₆₇	1	2	yes	—
502	C₂²×Q₈	—	2	2	no	—
503	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	AGL(1,ℤ/8)	—	2	8	no	—
508	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
509	C₂×D₈	—	2	4	no	—
510	C₂×D₈	C₂³×C₆₇	1	2	yes	—
511	C₂×D₈	C₂³×C₆₇	1	2	yes	—
512	C₂×D₈	C₂³×C₆₇	1	4	yes	—
513	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
514	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
518	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
523	#127	C₂³×C₆₇	1	1	yes	characteristic
524	#127	C₂³×C₆₇	1	4	yes	—
525	#126	—	2	4	no	—
526	#125	—	2	2	no	—
527	#125	D₄×C₆₇	1	2	yes	—
528	#125	C₂³×C₆₇	1	2	yes	—
529	#125	C₂³×C₆₇	1	4	yes	—
530	#124	—	2	4	no	—
531	#124	C₂³×C₆₇	1	2	yes	—
532	#124	C₂³×C₆₇	1	4	yes	—
533	#123	—	2	4	no	—
534	#123	—	2	4	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	—	2	4	no	—
546	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
547	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
548	#121	—	2	1	no	—
549	#121	—	2	1	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	4	no	—
554	#120	—	2	4	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
558	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
559	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	C₂³×C₆₇	1	2	yes	—
571	C₄×D₄	C₂³×C₆₇	1	2	yes	—
572	C₄×D₄	C₂³×C₆₇	1	2	yes	—
573	C₄×D₄	C₂³×C₆₇	1	2	yes	—
574	C₄×D₄	C₂³×C₆₇	1	4	yes	—
575	C₄×D₄	C₂³×C₆₇	1	4	yes	—
576	C₄×D₄	C₂³×C₆₇	1	4	yes	—
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	#117	C₂³×C₆₇	1	2	yes	—
580	#117	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	4	no	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
590	#107	C₂³×C₆₇	1	2	yes	—
591	#107	C₂³×C₆₇	1	2	yes	—
592	#107	C₂³×C₆₇	1	4	yes	—
593	#106	C₂³×C₆₇	1	4	yes	—
594	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
595	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
596	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
597	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
598	#103	C₂³×C₆₇	1	2	yes	—
599	#103	C₂³×C₆₇	1	2	yes	—
600	#103	C₂³×C₆₇	1	2	yes	—
601	#103	C₂³×C₆₇	1	2	yes	—
602	#103	C₂³×C₆₇	1	4	yes	—
603	#102	C₂³×C₆₇	1	2	yes	—
604	#102	C₂³×C₆₇	1	2	yes	—
605	#102	C₂³×C₆₇	1	2	yes	—
606	#102	C₂³×C₆₇	1	2	yes	—
607	#102	C₂³×C₆₇	1	2	yes	—
608	#102	C₂³×C₆₇	1	2	yes	—
609	#102	C₂³×C₆₇	1	2	yes	—
610	#102	C₂³×C₆₇	1	2	yes	—
611	#102	C₂³×C₆₇	1	4	yes	—
612	#102	C₂³×C₆₇	1	4	yes	—
613	#102	C₂³×C₆₇	1	4	yes	—
614	#97	C₂³×C₆₇	1	4	yes	—
615	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
616	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
617	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
618	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
619	C₄×C₈	C₂³×C₆₇	1	4	yes	—
620	C₂⁴	—	2	1	no	—
621	C₂⁴	—	2	1	no	—
622	#41	—	2	4	no	—
623	#41	—	2	4	no	—
624	#41	—	8	4	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	4	no	—
628	C₂×Q₈	—	8	4	no	—
629	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
630	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	#41×C₆₇	1	4	yes	complemented
643	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
644	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
645	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	8	2	no	—
657	C₂²×C₄	—	8	2	no	—
658	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
661	SD₁₆	—	2	8	no	—
662	D₈	—	2	4	no	—
663	D₈	—	2	4	no	—
664	D₈	—	2	8	no	—
665	M₁₆	—	2	4	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	—	2	2	no	—
668	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
669	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
670	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
672	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
687	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
688	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
689	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
690	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
712	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
713	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₄²	C₂⁴×C₆₇	1	4	yes	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	8	1	no	—
721	C₂³	—	8	1	no	—
722	C₂³	—	8	1	no	—
723	C₂³	—	8	1	no	—
724	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
725	Q₈	—	2	4	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	4	2	no	—
730	Q₈	—	8	4	no	—
731	Q₈	—	8	1	no	—
732	D₄	—	2	4	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	2	no	—
741	D₄	—	8	4	no	—
742	D₄	—	8	1	no	—
743	D₄	—	8	4	no	—
744	D₄	C₂×#41×C₆₇	1	4	yes	—
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	—	4	1	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	8	2	no	—
756	C₂×C₄	—	8	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	4	no	—
760	C₂×C₄	—	8	1	no	—
761	C₂×C₄	—	8	1	no	—
762	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
767	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
769	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
770	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
771	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
772	C₈	—	2	1	no	—
773	C₈	—	2	1	no	—
774	C₈	—	2	4	no	—
775	C₈	—	2	1	no	—
776	C₈	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	8	4	no	—
789	C₂²	—	8	4	no	—
790	C₂²	#548×C₆₇	1	2	yes	—
791	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	4	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	#548×C₆₇	1	2	yes	—
803	C₄	#576×C₆₇	1	2	yes	—
804	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
805	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
806	C₂	—	2	2	no	—
807	C₂	—	4	4	no	—
808	C₂	—	8	2	no	—
809	C₂	—	8	2	no	—
810	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
811	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
812	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3506	C₂	semidirect
2. C₆₇×#3501	C₂	semidirect
3. C₆₇×#3370	C₂	semidirect
4. C₆₇×#3367	C₂	semidirect
5. C₆₇×#3366	C₂	semidirect
6. C₆₇×#3361	C₂	semidirect
7. C₆₇×#3360	C₂	semidirect
8. C₆₇×#3358	C₂	semidirect
9. C₆₇×#3136	C₂	semidirect
10. C₆₇×#3131	C₂	semidirect
11. C₆₇×#3083	C₂	semidirect
12. C₆₇×#3077	C₂	semidirect
13. C₆₇×#3041	C₂	semidirect
14. C₆₇×#3036	C₂	semidirect
15. C₆₇×#2960	C₂	semidirect
16. C₆₇×#2946	C₂	semidirect
17. C₂×C₄×D₈×C₆₇	C₂	semidirect
20. #559×C₆₇	C₂²	semidirect
21. #556×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
26. #554×C₆₇	C₂²	semidirect
28. #550×C₆₇	C₂²	semidirect
30. D₄×Q₈×C₆₇	C₂²	semidirect
45. #490×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #488×C₆₇	C₂²	semidirect
48. #488×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #487×C₆₇	C₂²	semidirect
51. #487×C₆₇	C₂²	semidirect
52. #486×C₆₇	C₂²	semidirect
53. #486×C₆₇	C₂²	semidirect
54. #486×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #478×C₆₇	C₂²	semidirect
57. #478×C₆₇	C₂²	semidirect
58. #477×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #474×C₆₇	C₂²	semidirect
61. #474×C₆₇	C₂²	semidirect
64. #463×C₆₇	C₂²	semidirect
65. #461×C₆₇	C₂²	semidirect
68. #459×C₆₇	C₂²	semidirect
69. #446×C₆₇	C₂²	semidirect
70. #446×C₆₇	C₂²	semidirect
71. C₈×Q₈×C₆₇	C₂²	semidirect
72. C₈×Q₈×C₆₇	C₂²	semidirect
73. #442×C₆₇	C₂²	semidirect
74. #440×C₆₇	C₂²	semidirect
75. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×D₈×C₆₇	C₂²	semidirect
235. C₂×D₄×C₆₇	#41	semidirect
399. #61325	C₆₇	direct (N × H)
407. #3506	C₂×C₆₇	semidirect
408. #3501	C₂×C₆₇	semidirect
409. #3370	C₂×C₆₇	semidirect
410. #3367	C₂×C₆₇	semidirect
411. #3366	C₂×C₆₇	semidirect
412. #3361	C₂×C₆₇	semidirect
413. #3360	C₂×C₆₇	semidirect
414. #3358	C₂×C₆₇	semidirect
415. #3136	C₂×C₆₇	semidirect
416. #3131	C₂×C₆₇	semidirect
417. #3083	C₂×C₆₇	semidirect
418. #3077	C₂×C₆₇	semidirect
419. #3041	C₂×C₆₇	semidirect
420. #3036	C₂×C₆₇	semidirect
421. #2960	C₂×C₆₇	semidirect
422. #2946	C₂×C₆₇	semidirect
423. C₂×C₄×D₈	C₂×C₆₇	semidirect
424. C₆₇	#61325	direct (N × H)
427. #559	C₂²×C₆₇	semidirect
428. #556	C₂²×C₆₇	semidirect
432. #554	C₂²×C₆₇	semidirect
433. #554	C₂²×C₆₇	semidirect
435. #550	C₂²×C₆₇	semidirect
437. D₄×Q₈	C₂²×C₆₇	semidirect
452. #490	C₂²×C₆₇	semidirect
453. #489	C₂²×C₆₇	semidirect
454. #488	C₂²×C₆₇	semidirect
455. #488	C₂²×C₆₇	semidirect
456. #488	C₂²×C₆₇	semidirect
457. #487	C₂²×C₆₇	semidirect
458. #487	C₂²×C₆₇	semidirect
459. #486	C₂²×C₆₇	semidirect
460. #486	C₂²×C₆₇	semidirect
461. #486	C₂²×C₆₇	semidirect
462. #479	C₂²×C₆₇	semidirect
463. #478	C₂²×C₆₇	semidirect
464. #478	C₂²×C₆₇	semidirect
465. #477	C₂²×C₆₇	semidirect
466. #476	C₂²×C₆₇	semidirect
467. #474	C₂²×C₆₇	semidirect
468. #474	C₂²×C₆₇	semidirect
471. #463	C₂²×C₆₇	semidirect
472. #461	C₂²×C₆₇	semidirect
475. #459	C₂²×C₆₇	semidirect
476. #446	C₂²×C₆₇	semidirect
477. #446	C₂²×C₆₇	semidirect
478. C₈×Q₈	C₂²×C₆₇	semidirect
479. C₈×Q₈	C₂²×C₆₇	semidirect
480. #442	C₂²×C₆₇	semidirect
481. #440	C₂²×C₆₇	semidirect
482. C₄×SD₁₆	C₂²×C₆₇	semidirect
487. C₄×D₈	C₂²×C₆₇	semidirect
642. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
C₆₇×#3501	2
C₆₇×#3370	2
C₆₇×#3367	2
C₆₇×#3366	2
C₆₇×#3361	2
C₆₇×#3360	2
C₆₇×#3358	2
C₆₇×#3136	2
C₆₇×#3131	2
C₆₇×#3083	2
C₆₇×#3077	2
C₆₇×#3041	2
C₆₇×#3036	2
C₆₇×#2960	2
C₆₇×#2946	2
C₂×C₄×D₈×C₆₇	2
#61325	67

Subgroups — C67×#61325 #30740576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61325 #30740576