Subgroups — C₆₇×#60368 #30739619

Order 17152.

4726 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3013	C₂	1	8	yes	maximal, complemented
6	C₆₇×#3011	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3010	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3005	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3004	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#419×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×2₋¹⁺⁴×C₆₇	—	2	2	no	—
14	C₂×2₋¹⁺⁴×C₆₇	—	2	2	no	—
15	C₂×2₋¹⁺⁴×C₆₇	—	2	8	no	—
16	C₂×2₋¹⁺⁴×C₆₇	—	2	8	no	—
17	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	4	yes	—
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	4	yes	complemented
19	C₂²×#41×C₆₇	—	2	2	no	—
20	C₂²×#41×C₆₇	—	2	1	no	—
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
25	C₂³×Q₈×C₆₇	—	2	1	no	—
26	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂³×Q₈×C₆₇	C₂²	1	2	yes	complemented
28	#575×C₆₇	—	2	8	no	—
29	C₂×#137×C₆₇	—	2	8	no	—
30	C₂×#137×C₆₇	C₂²	1	4	yes	—
31	C₂×#137×C₆₇	C₂²	1	2	yes	—
32	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
35	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
36	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
37	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
38	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
39	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
41	#537×C₆₇	C₂²	1	4	yes	complemented
42	#536×C₆₇	—	2	1	no	—
43	#536×C₆₇	C₂²	1	2	yes	complemented
44	#535×C₆₇	—	2	1	no	—
45	#535×C₆₇	C₂²	1	2	yes	complemented
46	#534×C₆₇	—	2	2	no	—
47	#532×C₆₇	—	2	2	no	—
48	#525×C₆₇	—	2	2	no	—
49	#525×C₆₇	C₂²	1	4	yes	—
50	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
51	#452×C₆₇	C₂²	1	16	yes	complemented
52	#451×C₆₇	C₂²	1	16	yes	complemented
53	#449×C₆₇	C₂²	1	16	yes	complemented
54	#448×C₆₇	C₂²	1	16	yes	complemented
55	#419×C₆₇	C₂²	1	4	yes	complemented
56	#419×C₆₇	C₂²	1	4	yes	complemented
57	#419×C₆₇	C₂²	1	2	yes	complemented
58	#418×C₆₇	C₂²	1	2	yes	complemented
59	#417×C₆₇	C₂²	1	4	yes	complemented
60	#416×C₆₇	C₂²	1	4	yes	complemented
61	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
62	#408×C₆₇	C₂²	1	4	yes	complemented
63	#408×C₆₇	C₂²	1	4	yes	complemented
64	#407×C₆₇	C₂²	1	4	yes	complemented
65	2₋¹⁺⁴×C₆₇	—	2	32	no	—
66	2₋¹⁺⁴×C₆₇	—	2	32	no	—
67	2₋¹⁺⁴×C₆₇	—	2	16	no	—
68	2₋¹⁺⁴×C₆₇	—	2	16	no	—
69	2₋¹⁺⁴×C₆₇	—	2	16	no	—
70	2₋¹⁺⁴×C₆₇	—	2	16	no	—
71	C₂×#41×C₆₇	—	2	32	no	—
72	C₂×#41×C₆₇	—	2	16	no	—
73	C₂×#41×C₆₇	—	2	8	no	—
74	C₂×#41×C₆₇	—	2	8	no	—
75	C₂×#41×C₆₇	—	2	4	no	—
76	C₂×#41×C₆₇	—	2	4	no	—
77	C₂×#41×C₆₇	—	2	8	no	—
78	C₂×#41×C₆₇	—	2	8	no	—
79	C₂×#41×C₆₇	—	2	4	no	—
80	C₂×#41×C₆₇	—	2	1	no	—
81	C₂×#41×C₆₇	—	2	1	no	—
82	C₂×#41×C₆₇	—	2	4	no	—
83	C₂×#41×C₆₇	—	2	4	no	—
84	C₂×#41×C₆₇	—	2	4	no	—
85	C₂×#41×C₆₇	—	2	1	no	—
86	C₂×#41×C₆₇	—	2	1	no	—
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	2	4	no	—
89	C₂×#41×C₆₇	D₄	1	2	yes	—
90	C₂×#41×C₆₇	D₄	1	2	yes	—
91	C₂×#41×C₆₇	D₄	1	8	yes	complemented
92	C₂×#41×C₆₇	C₂³	1	8	yes	—
93	C₂×#41×C₆₇	C₂³	1	2	yes	—
94	C₂×#41×C₆₇	C₂³	1	2	yes	—
95	C₂×#41×C₆₇	C₂³	1	2	yes	—
96	C₂×#41×C₆₇	C₂³	1	2	yes	—
97	C₂×#41×C₆₇	C₂³	1	2	yes	—
98	C₂×#41×C₆₇	C₂³	1	2	yes	—
99	C₂²×Q₈×C₆₇	—	2	16	no	—
100	C₂²×Q₈×C₆₇	—	2	4	no	—
101	C₂²×Q₈×C₆₇	—	2	4	no	—
102	C₂²×Q₈×C₆₇	—	2	8	no	—
103	C₂²×Q₈×C₆₇	—	2	8	no	—
104	C₂²×Q₈×C₆₇	—	2	1	no	—
105	C₂²×Q₈×C₆₇	—	2	2	no	—
106	C₂²×Q₈×C₆₇	—	2	4	no	—
107	C₂²×Q₈×C₆₇	—	2	1	no	—
108	C₂²×Q₈×C₆₇	—	2	1	no	—
109	C₂²×Q₈×C₆₇	—	2	4	no	—
110	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₂²×Q₈×C₆₇	D₄	1	8	yes	complemented
112	C₂²×Q₈×C₆₇	C₂³	1	8	yes	—
113	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
115	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
116	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	—	2	1	no	—
119	C₂²×D₄×C₆₇	—	2	2	no	—
120	C₂²×D₄×C₆₇	—	2	1	no	—
121	C₂²×D₄×C₆₇	D₄	1	2	yes	—
122	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
123	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	—	2	1	no	—
126	C₂³×C₄×C₆₇	—	2	2	no	—
127	C₂³×C₄×C₆₇	—	2	1	no	—
128	C₂³×C₄×C₆₇	—	2	2	no	—
129	C₂³×C₄×C₆₇	—	2	1	no	—
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	#137×C₆₇	—	2	8	no	—
133	#137×C₆₇	—	2	16	no	—
134	#137×C₆₇	—	2	16	no	—
135	#137×C₆₇	—	2	8	no	—
136	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
137	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
138	#135×C₆₇	—	2	16	no	—
139	C₂×Q₁₆×C₆₇	—	2	8	no	—
140	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
141	C₂×Q₁₆×C₆₇	C₂³	1	8	yes	—
142	C₂×SD₁₆×C₆₇	—	2	8	no	—
143	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
144	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
145	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
146	C₂×D₈×C₆₇	C₂³	1	4	yes	—
147	C₂×M₁₆×C₆₇	—	2	4	no	—
148	C₂×M₁₆×C₆₇	—	2	4	no	—
149	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₇	—	2	2	no	—
156	#127×C₆₇	—	2	2	no	—
157	#124×C₆₇	—	2	2	no	—
158	#124×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	4	no	—
160	#123×C₆₇	—	2	4	no	—
161	C₂²⋊Q₈×C₆₇	—	2	4	no	—
162	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
163	#121×C₆₇	—	2	4	no	—
164	#121×C₆₇	—	2	8	no	—
165	#121×C₆₇	C₂³	1	8	yes	—
166	#120×C₆₇	—	2	4	no	—
167	#120×C₆₇	—	2	4	no	—
168	C₄×D₄×C₆₇	—	2	8	no	—
169	#117×C₆₇	—	2	1	no	—
170	#117×C₆₇	—	2	1	no	—
171	#117×C₆₇	C₂³	1	2	yes	—
172	#117×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
175	C₂×C₄²×C₆₇	—	2	1	no	—
176	#103×C₆₇	C₂³	1	8	yes	—
177	#103×C₆₇	C₂³	1	16	yes	—
178	#102×C₆₇	C₂³	1	8	yes	—
179	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	—
180	C₂⁴×C₆₇	—	2	1	no	—
181	C₂⁴×C₆₇	—	2	1	no	—
182	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
183	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
184	#41×C₆₇	—	2	64	no	—
185	#41×C₆₇	—	2	64	no	—
186	#41×C₆₇	—	2	32	no	—
187	#41×C₆₇	—	2	32	no	—
188	#41×C₆₇	—	2	32	no	—
189	#41×C₆₇	—	2	16	no	—
190	#41×C₆₇	—	2	16	no	—
191	#41×C₆₇	—	2	8	no	—
192	#41×C₆₇	—	2	8	no	—
193	#41×C₆₇	—	2	8	no	—
194	#41×C₆₇	—	2	8	no	—
195	#41×C₆₇	—	2	4	no	—
196	#41×C₆₇	—	2	4	no	—
197	#41×C₆₇	—	2	4	no	—
198	#41×C₆₇	—	2	4	no	—
199	#41×C₆₇	—	2	4	no	—
200	#41×C₆₇	—	2	4	no	—
201	#41×C₆₇	—	2	4	no	—
202	#41×C₆₇	—	2	4	no	—
203	#41×C₆₇	—	2	4	no	—
204	#41×C₆₇	—	2	4	no	—
205	#41×C₆₇	—	4	4	no	—
206	#41×C₆₇	—	4	4	no	—
207	#41×C₆₇	C₂×D₄	1	8	yes	—
208	#41×C₆₇	C₂×D₄	1	8	yes	—
209	C₂×Q₈×C₆₇	—	2	16	no	—
210	C₂×Q₈×C₆₇	—	2	32	no	—
211	C₂×Q₈×C₆₇	—	2	32	no	—
212	C₂×Q₈×C₆₇	—	2	32	no	—
213	C₂×Q₈×C₆₇	—	2	16	no	—
214	C₂×Q₈×C₆₇	—	2	16	no	—
215	C₂×Q₈×C₆₇	—	2	4	no	—
216	C₂×Q₈×C₆₇	—	2	8	no	—
217	C₂×Q₈×C₆₇	—	2	8	no	—
218	C₂×Q₈×C₆₇	—	2	8	no	—
219	C₂×Q₈×C₆₇	—	2	2	no	—
220	C₂×Q₈×C₆₇	—	2	4	no	—
221	C₂×Q₈×C₆₇	—	2	8	no	—
222	C₂×Q₈×C₆₇	—	2	2	no	—
223	C₂×Q₈×C₆₇	—	2	1	no	—
224	C₂×Q₈×C₆₇	—	2	2	no	—
225	C₂×Q₈×C₆₇	—	2	2	no	—
226	C₂×Q₈×C₆₇	—	2	4	no	—
227	C₂×Q₈×C₆₇	—	2	4	no	—
228	C₂×Q₈×C₆₇	—	2	1	no	—
229	C₂×Q₈×C₆₇	—	2	2	no	—
230	C₂×Q₈×C₆₇	—	2	2	no	—
231	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
232	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
233	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
234	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
235	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
237	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
240	C₂×D₄×C₆₇	—	2	16	no	—
241	C₂×D₄×C₆₇	—	2	8	no	—
242	C₂×D₄×C₆₇	—	2	8	no	—
243	C₂×D₄×C₆₇	—	2	8	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	8	no	—
249	C₂×D₄×C₆₇	—	2	4	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	1	no	—
255	C₂×D₄×C₆₇	—	4	4	no	—
256	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
257	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
258	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	—	2	16	no	—
264	C₂²×C₄×C₆₇	—	2	16	no	—
265	C₂²×C₄×C₆₇	—	2	8	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	1	no	—
268	C₂²×C₄×C₆₇	—	2	8	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	8	no	—
272	C₂²×C₄×C₆₇	—	2	8	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	4	no	—
276	C₂²×C₄×C₆₇	—	2	4	no	—
277	C₂²×C₄×C₆₇	—	2	1	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	4	4	no	—
282	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
283	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
288	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	Q₁₆×C₆₇	—	2	16	no	—
294	Q₁₆×C₆₇	—	2	8	no	—
295	SD₁₆×C₆₇	—	2	16	no	—
296	SD₁₆×C₆₇	—	2	8	no	—
297	SD₁₆×C₆₇	—	2	8	no	—
298	D₈×C₆₇	—	2	8	no	—
299	M₁₆×C₆₇	—	2	4	no	—
300	M₁₆×C₆₇	—	2	4	no	—
301	M₁₆×C₆₇	—	2	4	no	—
302	M₁₆×C₆₇	—	2	4	no	—
303	C₂×C₈×C₆₇	—	2	4	no	—
304	C₂×C₈×C₆₇	—	2	4	no	—
305	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
306	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	8	no	—
309	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	8	no	—
313	C₂²⋊C₄×C₆₇	—	2	8	no	—
314	C₄²×C₆₇	—	2	2	no	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	2	4	no	—
317	C₂³×C₆₇	—	2	4	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	4	2	no	—
321	C₂³×C₆₇	—	4	4	no	—
322	C₂³×C₆₇	—	4	4	no	—
323	C₂³×C₆₇	—	4	2	no	—
324	C₂³×C₆₇	—	8	2	no	—
325	C₂³×C₆₇	#120	1	4	yes	—
326	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
327	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
328	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
329	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₆₇	—	2	32	no	—
331	Q₈×C₆₇	—	2	4	no	—
332	Q₈×C₆₇	—	2	8	no	—
333	Q₈×C₆₇	—	2	8	no	—
334	Q₈×C₆₇	—	2	8	no	—
335	Q₈×C₆₇	—	2	4	no	—
336	Q₈×C₆₇	—	2	4	no	—
337	Q₈×C₆₇	—	2	2	no	—
338	Q₈×C₆₇	—	2	4	no	—
339	Q₈×C₆₇	—	2	2	no	—
340	Q₈×C₆₇	—	2	2	no	—
341	Q₈×C₆₇	—	4	2	no	—
342	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
343	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
344	D₄×C₆₇	—	2	32	no	—
345	D₄×C₆₇	—	2	8	no	—
346	D₄×C₆₇	—	2	8	no	—
347	D₄×C₆₇	—	2	8	no	—
348	D₄×C₆₇	—	2	8	no	—
349	D₄×C₆₇	—	2	4	no	—
350	D₄×C₆₇	—	2	4	no	—
351	D₄×C₆₇	—	2	4	no	—
352	D₄×C₆₇	—	2	2	no	—
353	D₄×C₆₇	—	2	2	no	—
354	D₄×C₆₇	—	2	2	no	—
355	D₄×C₆₇	—	4	4	no	—
356	D₄×C₆₇	—	4	4	no	—
357	D₄×C₆₇	—	4	2	no	—
358	D₄×C₆₇	—	8	8	no	—
359	D₄×C₆₇	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₆₇	—	2	32	no	—
361	C₂×C₄×C₆₇	—	2	32	no	—
362	C₂×C₄×C₆₇	—	2	8	no	—
363	C₂×C₄×C₆₇	—	2	4	no	—
364	C₂×C₄×C₆₇	—	2	4	no	—
365	C₂×C₄×C₆₇	—	2	8	no	—
366	C₂×C₄×C₆₇	—	2	8	no	—
367	C₂×C₄×C₆₇	—	2	4	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	8	no	—
370	C₂×C₄×C₆₇	—	2	8	no	—
371	C₂×C₄×C₆₇	—	2	8	no	—
372	C₂×C₄×C₆₇	—	2	4	no	—
373	C₂×C₄×C₆₇	—	2	4	no	—
374	C₂×C₄×C₆₇	—	2	4	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	4	2	no	—
377	C₂×C₄×C₆₇	—	4	4	no	—
378	C₂×C₄×C₆₇	—	4	4	no	—
379	C₂×C₄×C₆₇	—	8	2	no	—
380	C₂×C₄×C₆₇	#120	1	4	yes	—
381	C₂×C₄×C₆₇	#120	1	4	yes	—
382	C₂×C₄×C₆₇	#120	1	4	yes	—
383	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
384	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
394	C₈×C₆₇	—	2	4	no	—
395	C₈×C₆₇	—	2	4	no	—
396	C₂²×C₆₇	—	2	2	no	—
397	C₂²×C₆₇	—	2	2	no	—
398	C₂²×C₆₇	—	2	2	no	—
399	C₂²×C₆₇	—	2	8	no	—
400	C₂²×C₆₇	—	2	4	no	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	4	4	no	—
403	C₂²×C₆₇	—	4	8	no	—
404	C₂²×C₆₇	—	4	8	no	—
405	C₂²×C₆₇	—	4	4	no	—
406	C₂²×C₆₇	—	4	4	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	—	8	4	no	—
409	C₂²×C₆₇	C₂×#120	1	2	yes	—
410	C₂²×C₆₇	C₂×#120	1	2	yes	—
411	C₂²×C₆₇	C₂×#120	1	2	yes	—
412	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₆₇	—	2	8	no	—
414	C₄×C₆₇	—	2	4	no	—
415	C₄×C₆₇	—	2	4	no	—
416	C₄×C₆₇	—	4	4	no	—
417	C₄×C₆₇	—	4	2	no	—
418	C₄×C₆₇	C₂×#120	1	2	yes	—
419	C₄×C₆₇	C₂×#120	1	2	yes	—
420	C₄×C₆₇	C₂×#120	1	2	yes	—
421	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
423	#60368	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₆₇	—	2	2	no	—
425	C₂×C₆₇	—	2	2	no	—
426	C₂×C₆₇	—	2	2	no	—
427	C₂×C₆₇	—	4	4	no	—
428	C₂×C₆₇	—	4	4	no	—
429	C₂×C₆₇	—	8	2	no	—
430	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
431	C₂×C₆₇	#3586	1	2	yes	—
432	C₂²×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
433	C₂×#575	C₂×C₆₇	1	1	yes	characteristic, complemented
434	C₂²×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#3449	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#3013	C₂×C₆₇	1	8	yes	complemented
437	#3011	C₂×C₆₇	1	4	yes	complemented
438	#3010	C₂×C₆₇	1	4	yes	complemented
439	#3005	C₂×C₆₇	1	4	yes	complemented
440	#3004	C₂×C₆₇	1	4	yes	complemented
441	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
442	C₂×#419	C₂×C₆₇	1	1	yes	characteristic, complemented
443	#2879	C₂×C₆₇	1	1	yes	characteristic, complemented
444	C₆₇	#60368	1	1	yes	characteristic, direct product factor, Sylow
445	C₂×2₋¹⁺⁴	—	2	2	no	—
446	C₂×2₋¹⁺⁴	—	2	2	no	—
447	C₂×2₋¹⁺⁴	—	2	8	no	—
448	C₂×2₋¹⁺⁴	—	2	8	no	—
449	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	4	yes	—
450	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	4	yes	complemented
451	C₂²×#41	—	2	2	no	—
452	C₂²×#41	—	2	1	no	—
453	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
454	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
455	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
456	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
457	C₂³×Q₈	—	2	1	no	—
458	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
459	C₂³×Q₈	C₂²×C₆₇	1	2	yes	complemented
460	#575	—	2	8	no	—
461	C₂×#137	—	2	8	no	—
462	C₂×#137	C₂²×C₆₇	1	2	yes	—
463	C₂×#137	C₂²×C₆₇	1	4	yes	—
464	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
465	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
466	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
467	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
468	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
469	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
470	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
471	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
472	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
473	#537	C₂²×C₆₇	1	4	yes	complemented
474	#536	—	2	1	no	—
475	#536	C₂²×C₆₇	1	2	yes	complemented
476	#535	—	2	1	no	—
477	#535	C₂²×C₆₇	1	2	yes	complemented
478	#534	—	2	2	no	—
479	#532	—	2	2	no	—
480	#525	—	2	2	no	—
481	#525	C₂²×C₆₇	1	4	yes	—
482	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
483	#452	C₂²×C₆₇	1	16	yes	complemented
484	#451	C₂²×C₆₇	1	16	yes	complemented
485	#449	C₂²×C₆₇	1	16	yes	complemented
486	#448	C₂²×C₆₇	1	16	yes	complemented
487	#419	C₂²×C₆₇	1	4	yes	complemented
488	#419	C₂²×C₆₇	1	4	yes	complemented
489	#419	C₂²×C₆₇	1	2	yes	complemented
490	#418	C₂²×C₆₇	1	2	yes	complemented
491	#417	C₂²×C₆₇	1	4	yes	complemented
492	#416	C₂²×C₆₇	1	4	yes	complemented
493	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
494	#408	C₂²×C₆₇	1	4	yes	complemented
495	#408	C₂²×C₆₇	1	4	yes	complemented
496	#407	C₂²×C₆₇	1	4	yes	complemented
497	2₋¹⁺⁴	—	2	32	no	—
498	2₋¹⁺⁴	—	2	32	no	—
499	2₋¹⁺⁴	—	2	16	no	—
500	2₋¹⁺⁴	—	2	16	no	—
501	2₋¹⁺⁴	—	2	16	no	—
502	2₋¹⁺⁴	—	2	16	no	—
503	C₂×#41	—	2	32	no	—
504	C₂×#41	—	2	16	no	—
505	C₂×#41	—	2	8	no	—
506	C₂×#41	—	2	8	no	—
507	C₂×#41	—	2	4	no	—
508	C₂×#41	—	2	4	no	—
509	C₂×#41	—	2	8	no	—
510	C₂×#41	—	2	8	no	—
511	C₂×#41	—	2	4	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	—	2	1	no	—
514	C₂×#41	—	2	4	no	—
515	C₂×#41	—	2	4	no	—
516	C₂×#41	—	2	4	no	—
517	C₂×#41	—	2	1	no	—
518	C₂×#41	—	2	1	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	2	4	no	—
521	C₂×#41	D₄×C₆₇	1	2	yes	—
522	C₂×#41	D₄×C₆₇	1	2	yes	—
523	C₂×#41	D₄×C₆₇	1	8	yes	complemented
524	C₂×#41	C₂³×C₆₇	1	2	yes	—
525	C₂×#41	C₂³×C₆₇	1	2	yes	—
526	C₂×#41	C₂³×C₆₇	1	8	yes	—
527	C₂×#41	C₂³×C₆₇	1	2	yes	—
528	C₂×#41	C₂³×C₆₇	1	2	yes	—
529	C₂×#41	C₂³×C₆₇	1	2	yes	—
530	C₂×#41	C₂³×C₆₇	1	2	yes	—
531	C₂²×Q₈	—	2	16	no	—
532	C₂²×Q₈	—	2	4	no	—
533	C₂²×Q₈	—	2	4	no	—
534	C₂²×Q₈	—	2	8	no	—
535	C₂²×Q₈	—	2	8	no	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	—	2	2	no	—
538	C₂²×Q₈	—	2	4	no	—
539	C₂²×Q₈	—	2	1	no	—
540	C₂²×Q₈	—	2	1	no	—
541	C₂²×Q₈	—	2	4	no	—
542	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
543	C₂²×Q₈	D₄×C₆₇	1	8	yes	complemented
544	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₆₇	1	8	yes	—
546	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
547	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
548	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	2	no	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	D₄×C₆₇	1	2	yes	—
554	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂³×C₄	—	2	1	no	—
558	C₂³×C₄	—	2	2	no	—
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	2	no	—
561	C₂³×C₄	—	2	1	no	—
562	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
563	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
564	#137	—	2	8	no	—
565	#137	—	2	16	no	—
566	#137	—	2	16	no	—
567	#137	—	2	8	no	—
568	AGL(1,ℤ/8)	—	2	8	no	—
569	AGL(1,ℤ/8)	—	2	8	no	—
570	#135	—	2	16	no	—
571	C₂×Q₁₆	—	2	8	no	—
572	C₂×Q₁₆	C₂³×C₆₇	1	8	yes	—
573	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
574	C₂×SD₁₆	—	2	8	no	—
575	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
576	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
578	C₂×D₈	C₂³×C₆₇	1	4	yes	—
579	C₂×M₁₆	—	2	4	no	—
580	C₂×M₁₆	—	2	4	no	—
581	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
582	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
583	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
584	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
585	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
586	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
587	C₄⋊Q₈	—	2	2	no	—
588	#127	—	2	2	no	—
589	#124	—	2	2	no	—
590	#124	—	2	2	no	—
591	#123	—	2	4	no	—
592	#123	—	2	4	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
595	#121	—	2	4	no	—
596	#121	—	2	8	no	—
597	#121	C₂³×C₆₇	1	8	yes	—
598	#120	—	2	4	no	—
599	#120	—	2	4	no	—
600	C₄×D₄	—	2	8	no	—
601	#117	—	2	1	no	—
602	#117	—	2	1	no	—
603	#117	C₂³×C₆₇	1	2	yes	—
604	#117	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₄²	—	2	1	no	—
608	#103	C₂³×C₆₇	1	16	yes	—
609	#103	C₂³×C₆₇	1	8	yes	—
610	#102	C₂³×C₆₇	1	8	yes	—
611	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	—
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	1	no	—
614	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
615	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
616	#41	—	2	64	no	—
617	#41	—	2	64	no	—
618	#41	—	2	32	no	—
619	#41	—	2	32	no	—
620	#41	—	2	32	no	—
621	#41	—	2	16	no	—
622	#41	—	2	16	no	—
623	#41	—	2	8	no	—
624	#41	—	2	8	no	—
625	#41	—	2	8	no	—
626	#41	—	2	8	no	—
627	#41	—	2	4	no	—
628	#41	—	2	4	no	—
629	#41	—	2	4	no	—
630	#41	—	2	4	no	—
631	#41	—	2	4	no	—
632	#41	—	2	4	no	—
633	#41	—	2	4	no	—
634	#41	—	2	4	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	4	4	no	—
638	#41	—	4	4	no	—
639	#41	C₂×D₄×C₆₇	1	8	yes	—
640	#41	C₂×D₄×C₆₇	1	8	yes	—
641	C₂×Q₈	—	2	16	no	—
642	C₂×Q₈	—	2	32	no	—
643	C₂×Q₈	—	2	32	no	—
644	C₂×Q₈	—	2	32	no	—
645	C₂×Q₈	—	2	16	no	—
646	C₂×Q₈	—	2	16	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	2	8	no	—
649	C₂×Q₈	—	2	8	no	—
650	C₂×Q₈	—	2	8	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	8	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	4	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
664	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
665	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
666	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
667	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
668	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
669	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
670	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
672	C₂×D₄	—	2	16	no	—
673	C₂×D₄	—	2	8	no	—
674	C₂×D₄	—	2	8	no	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
689	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
690	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
692	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
693	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
694	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
695	C₂²×C₄	—	2	16	no	—
696	C₂²×C₄	—	2	16	no	—
697	C₂²×C₄	—	2	8	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	8	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	8	no	—
704	C₂²×C₄	—	2	8	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	4	4	no	—
714	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
715	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
720	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	Q₁₆	—	2	16	no	—
726	Q₁₆	—	2	8	no	—
727	SD₁₆	—	2	16	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	2	8	no	—
730	D₈	—	2	8	no	—
731	M₁₆	—	2	4	no	—
732	M₁₆	—	2	4	no	—
733	M₁₆	—	2	4	no	—
734	M₁₆	—	2	4	no	—
735	C₂×C₈	—	2	4	no	—
736	C₂×C₈	—	2	4	no	—
737	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
738	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	8	no	—
741	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	8	no	—
745	C₂²⋊C₄	—	2	8	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₂³	—	2	4	no	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	4	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	8	2	no	—
757	C₂³	#120×C₆₇	1	4	yes	—
758	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
759	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
760	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
761	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
762	Q₈	—	2	32	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	2	8	no	—
765	Q₈	—	2	8	no	—
766	Q₈	—	2	8	no	—
767	Q₈	—	2	4	no	—
768	Q₈	—	2	4	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	4	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
775	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
776	D₄	—	2	32	no	—
777	D₄	—	2	8	no	—
778	D₄	—	2	8	no	—
779	D₄	—	2	8	no	—
780	D₄	—	2	8	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	2	no	—
790	D₄	—	8	8	no	—
791	D₄	C₂²×D₄×C₆₇	1	4	yes	—
792	C₂×C₄	—	2	32	no	—
793	C₂×C₄	—	2	32	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	2	8	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	8	2	no	—
812	C₂×C₄	#120×C₆₇	1	4	yes	—
813	C₂×C₄	#120×C₆₇	1	4	yes	—
814	C₂×C₄	#120×C₆₇	1	4	yes	—
815	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
816	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
825	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
826	C₈	—	2	4	no	—
827	C₈	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	8	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	8	no	—
836	C₂²	—	4	8	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	4	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	4	no	—
841	C₂²	C₂×#120×C₆₇	1	2	yes	—
842	C₂²	C₂×#120×C₆₇	1	2	yes	—
843	C₂²	C₂×#120×C₆₇	1	2	yes	—
844	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
845	C₄	—	2	8	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	4	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	2	no	—
850	C₄	C₂×#120×C₆₇	1	2	yes	—
851	C₄	C₂×#120×C₆₇	1	2	yes	—
852	C₄	C₂×#120×C₆₇	1	2	yes	—
853	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
854	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
855	C₂	—	2	2	no	—
856	C₂	—	2	2	no	—
857	C₂	—	2	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	4	4	no	—
860	C₂	—	8	2	no	—
861	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
862	C₂	C₆₇×#3586	1	2	yes	—

	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 ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×2₋¹⁺⁴×C₆₇	C₂	semidirect
2. C₂×#575×C₆₇	C₂	semidirect
3. C₂²×#137×C₆₇	C₂	semidirect
4. C₆₇×#3449	C₂	semidirect
5. C₆₇×#3013	C₂	semidirect
6. C₆₇×#3011	C₂	semidirect
7. C₆₇×#3010	C₂	semidirect
8. C₆₇×#3005	C₂	semidirect
9. C₆₇×#3004	C₂	semidirect
10. C₆₇×#2896	C₂	semidirect
11. C₂×#419×C₆₇	C₂	semidirect
12. C₆₇×#2879	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
24. C₂²×#41×C₆₇	C₂²	semidirect
27. C₂³×Q₈×C₆₇	C₂²	semidirect
32. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×#137×C₆₇	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
36. C₂×#135×C₆₇	C₂²	semidirect
37. C₂²×Q₁₆×C₆₇	C₂²	semidirect
38. C₂²×SD₁₆×C₆₇	C₂²	semidirect
41. #537×C₆₇	C₂²	semidirect
43. #536×C₆₇	C₂²	semidirect
45. #535×C₆₇	C₂²	semidirect
51. #452×C₆₇	C₂²	semidirect
52. #451×C₆₇	C₂²	semidirect
53. #449×C₆₇	C₂²	semidirect
54. #448×C₆₇	C₂²	semidirect
55. #419×C₆₇	C₂²	semidirect
56. #419×C₆₇	C₂²	semidirect
57. #419×C₆₇	C₂²	semidirect
58. #418×C₆₇	C₂²	semidirect
59. #417×C₆₇	C₂²	semidirect
60. #416×C₆₇	C₂²	semidirect
61. C₂×#103×C₆₇	C₂²	semidirect
62. #408×C₆₇	C₂²	semidirect
63. #408×C₆₇	C₂²	semidirect
64. #407×C₆₇	C₂²	semidirect
91. C₂×#41×C₆₇	D₄	semidirect
111. C₂²×Q₈×C₆₇	D₄	semidirect
423. #60368	C₆₇	direct (N × H)
432. C₂²×2₋¹⁺⁴	C₂×C₆₇	semidirect
433. C₂×#575	C₂×C₆₇	semidirect
434. C₂²×#137	C₂×C₆₇	semidirect
435. #3449	C₂×C₆₇	semidirect
436. #3013	C₂×C₆₇	semidirect
437. #3011	C₂×C₆₇	semidirect
438. #3010	C₂×C₆₇	semidirect
439. #3005	C₂×C₆₇	semidirect
440. #3004	C₂×C₆₇	semidirect
441. #2896	C₂×C₆₇	semidirect
442. C₂×#419	C₂×C₆₇	semidirect
443. #2879	C₂×C₆₇	semidirect
444. C₆₇	#60368	direct (N × H)
450. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
456. C₂²×#41	C₂²×C₆₇	semidirect
459. C₂³×Q₈	C₂²×C₆₇	semidirect
464. C₂×#137	C₂²×C₆₇	semidirect
465. C₂×#137	C₂²×C₆₇	semidirect
467. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
468. C₂×#135	C₂²×C₆₇	semidirect
469. C₂²×Q₁₆	C₂²×C₆₇	semidirect
470. C₂²×SD₁₆	C₂²×C₆₇	semidirect
473. #537	C₂²×C₆₇	semidirect
475. #536	C₂²×C₆₇	semidirect
477. #535	C₂²×C₆₇	semidirect
483. #452	C₂²×C₆₇	semidirect
484. #451	C₂²×C₆₇	semidirect
485. #449	C₂²×C₆₇	semidirect
486. #448	C₂²×C₆₇	semidirect
487. #419	C₂²×C₆₇	semidirect
488. #419	C₂²×C₆₇	semidirect
489. #419	C₂²×C₆₇	semidirect
490. #418	C₂²×C₆₇	semidirect
491. #417	C₂²×C₆₇	semidirect
492. #416	C₂²×C₆₇	semidirect
493. C₂×#103	C₂²×C₆₇	semidirect
494. #408	C₂²×C₆₇	semidirect
495. #408	C₂²×C₆₇	semidirect
496. #407	C₂²×C₆₇	semidirect
523. C₂×#41	D₄×C₆₇	semidirect
543. C₂²×Q₈	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×2₋¹⁺⁴×C₆₇	2
C₂×#575×C₆₇	2
C₂²×#137×C₆₇	2
C₆₇×#3449	2
C₆₇×#3013	2
C₆₇×#3011	2
C₆₇×#3010	2
C₆₇×#3005	2
C₆₇×#3004	2
C₆₇×#2896	2
C₂×#419×C₆₇	2
C₆₇×#2879	2
#60368	67

Subgroups — C67×#60368 #30739619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60368 #30739619