Subgroups — C₆₇×#60322 #30739573

Order 17152.

1858 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3459	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2978	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2977	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2974	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×M₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2930	C₂	1	2	yes	maximal, complemented
19	C₂×#436×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
21	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
24	#543×C₆₇	C₄	1	1	yes	characteristic
25	#539×C₆₇	C₄	1	2	yes	—
26	#539×C₆₇	C₄	1	2	yes	—
27	#539×C₆₇	C₄	1	2	yes	—
28	#538×C₆₇	C₄	1	1	yes	characteristic
29	#538×C₆₇	C₄	1	1	yes	characteristic
30	#538×C₆₇	C₄	1	2	yes	—
31	#538×C₆₇	C₄	1	2	yes	—
32	#534×C₆₇	C₄	1	1	yes	characteristic
33	#534×C₆₇	C₄	1	2	yes	—
34	#529×C₆₇	C₂²	1	1	yes	characteristic
35	#529×C₆₇	C₂²	1	1	yes	characteristic
36	#529×C₆₇	C₂²	1	2	yes	—
37	#529×C₆₇	C₂²	1	2	yes	—
38	#525×C₆₇	C₂²	1	2	yes	—
39	#525×C₆₇	C₂²	1	2	yes	—
40	#525×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
43	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#446×C₆₇	C₂²	1	2	yes	complemented
46	#446×C₆₇	C₂²	1	2	yes	complemented
47	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#436×C₆₇	C₂²	1	2	yes	complemented
50	#436×C₆₇	C₂²	1	2	yes	complemented
51	#436×C₆₇	C₂²	1	2	yes	complemented
52	#436×C₆₇	C₂²	1	2	yes	complemented
53	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#436×C₆₇	C₂²	1	2	yes	complemented
55	#436×C₆₇	C₂²	1	2	yes	complemented
56	#436×C₆₇	C₂²	1	2	yes	complemented
57	#436×C₆₇	C₂²	1	2	yes	complemented
58	#436×C₆₇	C₂²	1	2	yes	complemented
59	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#436×C₆₇	C₂²	1	2	yes	complemented
61	#435×C₆₇	C₂²	1	2	yes	complemented
62	#435×C₆₇	C₂²	1	2	yes	complemented
63	#435×C₆₇	C₂²	1	2	yes	complemented
64	#435×C₆₇	C₂²	1	2	yes	complemented
65	#435×C₆₇	C₂²	1	2	yes	complemented
66	#435×C₆₇	C₂²	1	2	yes	complemented
67	#435×C₆₇	C₂²	1	2	yes	complemented
68	#435×C₆₇	C₂²	1	2	yes	complemented
69	#435×C₆₇	C₂²	1	2	yes	complemented
70	#435×C₆₇	C₂²	1	2	yes	complemented
71	#435×C₆₇	C₂²	1	2	yes	complemented
72	#435×C₆₇	C₂²	1	2	yes	complemented
73	#435×C₆₇	C₂²	1	2	yes	complemented
74	#435×C₆₇	C₂²	1	2	yes	complemented
75	#435×C₆₇	C₂²	1	2	yes	complemented
76	#435×C₆₇	C₂²	1	2	yes	complemented
77	#435×C₆₇	C₂²	1	2	yes	complemented
78	#435×C₆₇	C₂²	1	2	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
81	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	#433×C₆₇	C₂²	1	2	yes	complemented
88	#433×C₆₇	C₂²	1	2	yes	complemented
89	#433×C₆₇	C₂²	1	2	yes	complemented
90	#433×C₆₇	C₂²	1	2	yes	complemented
91	#433×C₆₇	C₂²	1	2	yes	complemented
92	#433×C₆₇	C₂²	1	2	yes	complemented
93	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#432×C₆₇	C₂²	1	2	yes	complemented
96	#431×C₆₇	C₂²	1	2	yes	complemented
97	#424×C₆₇	C₂²	1	2	yes	complemented
98	#424×C₆₇	C₂²	1	2	yes	complemented
99	#424×C₆₇	C₂²	1	2	yes	complemented
100	#423×C₆₇	C₂²	1	2	yes	complemented
101	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#408×C₆₇	C₂²	1	2	yes	complemented
103	#408×C₆₇	C₂²	1	2	yes	complemented
104	#408×C₆₇	C₂²	1	2	yes	complemented
105	#407×C₆₇	C₂²	1	2	yes	—
106	#407×C₆₇	C₂²	1	2	yes	complemented
107	#407×C₆₇	C₂²	1	2	yes	complemented
108	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
109	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
111	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
112	#405×C₆₇	C₂²	1	2	yes	complemented
113	#405×C₆₇	C₂²	1	2	yes	complemented
114	#405×C₆₇	C₂²	1	2	yes	complemented
115	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
116	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
123	#131×C₆₇	—	4	4	no	—
124	C₂×M₁₆×C₆₇	—	4	2	no	—
125	C₂×M₁₆×C₆₇	—	4	2	no	—
126	C₂×M₁₆×C₆₇	—	4	4	no	—
127	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
129	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
133	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
134	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
136	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
137	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
139	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
142	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
143	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
144	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
146	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
147	#126×C₆₇	C₂×C₄	1	2	yes	—
148	#126×C₆₇	C₂×C₄	1	2	yes	—
149	#126×C₆₇	C₂×C₄	1	2	yes	—
150	#126×C₆₇	C₂×C₄	1	2	yes	—
151	#126×C₆₇	C₂×C₄	1	2	yes	—
152	#126×C₆₇	C₂×C₄	1	2	yes	—
153	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
154	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
155	#125×C₆₇	C₂×C₄	1	2	yes	—
156	#125×C₆₇	C₂×C₄	1	2	yes	—
157	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
158	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
159	#124×C₆₇	C₂×C₄	1	2	yes	—
160	#124×C₆₇	C₂×C₄	1	2	yes	—
161	#123×C₆₇	C₂×C₄	1	2	yes	—
162	#123×C₆₇	C₂×C₄	1	2	yes	—
163	#123×C₆₇	C₂×C₄	1	2	yes	—
164	#123×C₆₇	C₂×C₄	1	2	yes	—
165	#123×C₆₇	C₂×C₄	1	2	yes	—
166	#123×C₆₇	C₂×C₄	1	2	yes	—
167	#123×C₆₇	C₂×C₄	1	2	yes	—
168	#123×C₆₇	C₂×C₄	1	2	yes	—
169	#123×C₆₇	C₂×C₄	1	2	yes	—
170	#123×C₆₇	C₂×C₄	1	2	yes	—
171	#123×C₆₇	C₂×C₄	1	2	yes	—
172	#123×C₆₇	C₂×C₄	1	2	yes	—
173	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
174	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
175	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
176	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
177	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
178	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
179	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
180	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
181	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
182	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
183	#121×C₆₇	C₂×C₄	1	2	yes	—
184	#121×C₆₇	C₂×C₄	1	2	yes	—
185	#121×C₆₇	C₂×C₄	1	2	yes	—
186	#121×C₆₇	C₂×C₄	1	2	yes	—
187	#121×C₆₇	C₂×C₄	1	2	yes	—
188	#121×C₆₇	C₂×C₄	1	2	yes	—
189	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
190	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
191	#121×C₆₇	C₂×C₄	1	2	yes	—
192	#121×C₆₇	C₂×C₄	1	2	yes	—
193	#120×C₆₇	C₂×C₄	1	2	yes	—
194	#120×C₆₇	C₂×C₄	1	2	yes	—
195	#120×C₆₇	C₂×C₄	1	2	yes	—
196	#120×C₆₇	C₂×C₄	1	2	yes	—
197	#120×C₆₇	C₂×C₄	1	2	yes	—
198	#120×C₆₇	C₂×C₄	1	2	yes	—
199	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
202	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
203	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
204	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
205	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
206	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
207	C₄×D₄×C₆₇	C₂³	1	2	yes	—
208	C₄×D₄×C₆₇	C₂³	1	2	yes	—
209	C₄×D₄×C₆₇	C₂³	1	2	yes	—
210	C₄×D₄×C₆₇	C₂³	1	2	yes	—
211	C₄×D₄×C₆₇	C₂³	1	2	yes	—
212	C₄×D₄×C₆₇	C₂³	1	2	yes	—
213	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₆₇	C₂³	1	2	yes	—
215	C₄×D₄×C₆₇	C₂³	1	2	yes	—
216	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
217	#117×C₆₇	C₂³	1	2	yes	—
218	#117×C₆₇	C₂³	1	2	yes	—
219	#117×C₆₇	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
225	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
228	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
229	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
230	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
231	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
232	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
238	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
239	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
240	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
241	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
242	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
243	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
244	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
245	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
247	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
248	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
249	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
250	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
251	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
260	#97×C₆₇	C₂³	1	2	yes	—
261	#97×C₆₇	C₂³	1	2	yes	—
262	#97×C₆₇	C₂³	1	2	yes	—
263	#97×C₆₇	C₂³	1	2	yes	—
264	#97×C₆₇	C₂³	1	2	yes	—
265	#97×C₆₇	C₂³	1	2	yes	—
266	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
267	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₆₇	C₂³	1	2	yes	—
271	C₄×C₈×C₆₇	C₂³	1	2	yes	—
272	C₄×C₈×C₆₇	C₂³	1	2	yes	—
273	C₄×C₈×C₆₇	C₂³	1	2	yes	—
274	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
275	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
276	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
277	#41×C₆₇	—	4	2	no	—
278	#41×C₆₇	—	4	2	no	—
279	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
280	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
281	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
282	C₂×D₄×C₆₇	—	4	2	no	—
283	C₂×D₄×C₆₇	—	4	4	no	—
284	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
285	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
286	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
287	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
288	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
289	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
291	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
292	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
297	C₂²×C₄×C₆₇	—	4	1	no	—
298	C₂²×C₄×C₆₇	—	4	1	no	—
299	C₂²×C₄×C₆₇	—	4	2	no	—
300	C₂²×C₄×C₆₇	—	4	1	no	—
301	C₂²×C₄×C₆₇	—	4	1	no	—
302	C₂²×C₄×C₆₇	—	4	2	no	—
303	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
305	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
307	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
308	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
319	M₁₆×C₆₇	—	2	4	no	—
320	M₁₆×C₆₇	—	2	4	no	—
321	M₁₆×C₆₇	—	2	4	no	—
322	M₁₆×C₆₇	—	4	2	no	—
323	M₁₆×C₆₇	—	4	2	no	—
324	M₁₆×C₆₇	—	4	2	no	—
325	M₁₆×C₆₇	—	4	2	no	—
326	M₁₆×C₆₇	—	4	2	no	—
327	M₁₆×C₆₇	—	4	2	no	—
328	M₁₆×C₆₇	—	4	2	no	—
329	C₂×C₈×C₆₇	—	2	2	no	—
330	C₂×C₈×C₆₇	—	2	4	no	—
331	C₂×C₈×C₆₇	—	4	2	no	—
332	C₂×C₈×C₆₇	—	4	1	no	—
333	C₂×C₈×C₆₇	—	4	2	no	—
334	C₂×C₈×C₆₇	—	4	1	no	—
335	C₂×C₈×C₆₇	—	4	1	no	—
336	C₂×C₈×C₆₇	—	4	2	no	—
337	C₂×C₈×C₆₇	—	4	2	no	—
338	C₂×C₈×C₆₇	—	4	2	no	—
339	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
340	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
341	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
342	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
343	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
346	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
347	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
350	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
352	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
353	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
354	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
355	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
357	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
358	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
360	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
362	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
365	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
368	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
369	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
370	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
372	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
391	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
393	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
394	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
395	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
396	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
397	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
399	C₄²×C₆₇	C₂⁴	1	2	yes	—
400	C₄²×C₆₇	C₂⁴	1	2	yes	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	4	1	no	—
404	C₂³×C₆₇	—	4	1	no	—
405	C₂³×C₆₇	—	4	2	no	—
406	C₂³×C₆₇	—	4	2	no	—
407	C₂³×C₆₇	—	4	1	no	—
408	C₂³×C₆₇	—	4	1	no	—
409	C₂³×C₆₇	—	4	2	no	—
410	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
411	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
412	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
413	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
414	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
415	Q₈×C₆₇	—	4	1	no	—
416	Q₈×C₆₇	—	4	1	no	—
417	Q₈×C₆₇	—	4	2	no	—
418	D₄×C₆₇	—	2	4	no	—
419	D₄×C₆₇	—	2	4	no	—
420	D₄×C₆₇	—	4	2	no	—
421	D₄×C₆₇	—	4	2	no	—
422	D₄×C₆₇	—	4	2	no	—
423	D₄×C₆₇	—	4	2	no	—
424	D₄×C₆₇	—	4	1	no	—
425	D₄×C₆₇	—	4	1	no	—
426	D₄×C₆₇	—	4	2	no	—
427	D₄×C₆₇	—	4	2	no	—
428	D₄×C₆₇	—	4	2	no	—
429	D₄×C₆₇	—	4	2	no	—
430	D₄×C₆₇	—	4	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	4	1	no	—
443	C₂×C₄×C₆₇	—	4	2	no	—
444	C₂×C₄×C₆₇	—	4	2	no	—
445	C₂×C₄×C₆₇	—	4	2	no	—
446	C₂×C₄×C₆₇	—	4	2	no	—
447	C₂×C₄×C₆₇	—	4	1	no	—
448	C₂×C₄×C₆₇	—	4	2	no	—
449	C₂×C₄×C₆₇	—	4	1	no	—
450	C₂×C₄×C₆₇	—	4	2	no	—
451	C₂×C₄×C₆₇	—	4	2	no	—
452	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
453	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
454	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
455	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
456	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
459	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
460	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
466	C₈×C₆₇	—	2	2	no	—
467	C₈×C₆₇	—	2	1	no	—
468	C₈×C₆₇	—	2	2	no	—
469	C₈×C₆₇	—	2	2	no	—
470	C₈×C₆₇	—	2	2	no	—
471	C₈×C₆₇	—	2	1	no	—
472	C₈×C₆₇	—	2	2	no	—
473	C₈×C₆₇	—	2	1	no	—
474	C₈×C₆₇	—	2	2	no	—
475	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
476	C₂²×C₆₇	—	2	1	no	—
477	C₂²×C₆₇	—	2	1	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	2	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	2	2	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	2	no	—
489	C₂²×C₆₇	—	2	2	no	—
490	C₂²×C₆₇	—	8	2	no	—
491	C₂²×C₆₇	—	8	2	no	—
492	C₂²×C₆₇	—	8	4	no	—
493	C₂²×C₆₇	#568	1	2	yes	—
494	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
495	C₄×C₆₇	—	2	1	no	—
496	C₄×C₆₇	—	2	2	no	—
497	C₄×C₆₇	—	2	2	no	—
498	C₄×C₆₇	—	2	2	no	—
499	C₄×C₆₇	—	2	2	no	—
500	C₄×C₆₇	—	2	1	no	—
501	C₄×C₆₇	—	2	1	no	—
502	C₄×C₆₇	—	2	2	no	—
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	1	no	—
505	C₄×C₆₇	—	2	1	no	—
506	C₄×C₆₇	—	2	2	no	—
507	C₄×C₆₇	—	2	2	no	—
508	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
509	C₄×C₆₇	#585	1	1	yes	characteristic
510	#60322	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
511	C₂×C₆₇	—	2	2	no	—
512	C₂×C₆₇	—	4	2	no	—
513	C₂×C₆₇	—	4	2	no	—
514	C₂×C₆₇	—	4	2	no	—
515	C₂×C₆₇	—	4	2	no	—
516	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
518	C₂×C₆₇	#3573	1	1	yes	characteristic
519	#3459	C₂×C₆₇	1	1	yes	characteristic
520	#2995	C₂×C₆₇	1	2	yes	complemented
521	#2993	C₂×C₆₇	1	2	yes	complemented
522	#2992	C₂×C₆₇	1	1	yes	characteristic, complemented
523	#2992	C₂×C₆₇	1	1	yes	characteristic, complemented
524	#2978	C₂×C₆₇	1	2	yes	complemented
525	#2977	C₂×C₆₇	1	2	yes	complemented
526	#2976	C₂×C₆₇	1	2	yes	complemented
527	#2974	C₂×C₆₇	1	2	yes	complemented
528	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
529	#2969	C₂×C₆₇	1	2	yes	complemented
530	#2967	C₂×C₆₇	1	2	yes	complemented
531	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
532	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
533	D₄×M₁₆	C₂×C₆₇	1	2	yes	complemented
534	#2933	C₂×C₆₇	1	2	yes	complemented
535	#2933	C₂×C₆₇	1	2	yes	complemented
536	#2930	C₂×C₆₇	1	2	yes	complemented
537	C₂×#436	C₂×C₆₇	1	1	yes	characteristic, complemented
538	C₆₇	#60322	1	1	yes	characteristic, direct product factor, Sylow
539	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
540	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
541	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
543	#543	C₄×C₆₇	1	1	yes	characteristic
544	#539	C₄×C₆₇	1	2	yes	—
545	#539	C₄×C₆₇	1	2	yes	—
546	#539	C₄×C₆₇	1	2	yes	—
547	#538	C₄×C₆₇	1	1	yes	characteristic
548	#538	C₄×C₆₇	1	1	yes	characteristic
549	#538	C₄×C₆₇	1	2	yes	—
550	#538	C₄×C₆₇	1	2	yes	—
551	#534	C₄×C₆₇	1	1	yes	characteristic
552	#534	C₄×C₆₇	1	2	yes	—
553	#529	C₂²×C₆₇	1	1	yes	characteristic
554	#529	C₂²×C₆₇	1	1	yes	characteristic
555	#529	C₂²×C₆₇	1	2	yes	—
556	#529	C₂²×C₆₇	1	2	yes	—
557	#525	C₂²×C₆₇	1	2	yes	—
558	#525	C₂²×C₆₇	1	2	yes	—
559	#525	C₂²×C₆₇	1	2	yes	—
560	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
562	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
563	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	#446	C₂²×C₆₇	1	2	yes	complemented
565	#446	C₂²×C₆₇	1	2	yes	complemented
566	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
567	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#436	C₂²×C₆₇	1	2	yes	complemented
569	#436	C₂²×C₆₇	1	2	yes	complemented
570	#436	C₂²×C₆₇	1	2	yes	complemented
571	#436	C₂²×C₆₇	1	2	yes	complemented
572	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
573	#436	C₂²×C₆₇	1	2	yes	complemented
574	#436	C₂²×C₆₇	1	2	yes	complemented
575	#436	C₂²×C₆₇	1	2	yes	complemented
576	#436	C₂²×C₆₇	1	2	yes	complemented
577	#436	C₂²×C₆₇	1	2	yes	complemented
578	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
579	#436	C₂²×C₆₇	1	2	yes	complemented
580	#435	C₂²×C₆₇	1	2	yes	complemented
581	#435	C₂²×C₆₇	1	2	yes	complemented
582	#435	C₂²×C₆₇	1	2	yes	complemented
583	#435	C₂²×C₆₇	1	2	yes	complemented
584	#435	C₂²×C₆₇	1	2	yes	complemented
585	#435	C₂²×C₆₇	1	2	yes	complemented
586	#435	C₂²×C₆₇	1	2	yes	complemented
587	#435	C₂²×C₆₇	1	2	yes	complemented
588	#435	C₂²×C₆₇	1	2	yes	complemented
589	#435	C₂²×C₆₇	1	2	yes	complemented
590	#435	C₂²×C₆₇	1	2	yes	complemented
591	#435	C₂²×C₆₇	1	2	yes	complemented
592	#435	C₂²×C₆₇	1	2	yes	complemented
593	#435	C₂²×C₆₇	1	2	yes	complemented
594	#435	C₂²×C₆₇	1	2	yes	complemented
595	#435	C₂²×C₆₇	1	2	yes	complemented
596	#435	C₂²×C₆₇	1	2	yes	complemented
597	#435	C₂²×C₆₇	1	2	yes	complemented
598	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
599	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
600	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
601	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
602	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
603	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
604	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
605	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
606	#433	C₂²×C₆₇	1	2	yes	complemented
607	#433	C₂²×C₆₇	1	2	yes	complemented
608	#433	C₂²×C₆₇	1	2	yes	complemented
609	#433	C₂²×C₆₇	1	2	yes	complemented
610	#433	C₂²×C₆₇	1	2	yes	complemented
611	#433	C₂²×C₆₇	1	2	yes	complemented
612	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
614	#432	C₂²×C₆₇	1	2	yes	complemented
615	#431	C₂²×C₆₇	1	2	yes	complemented
616	#424	C₂²×C₆₇	1	2	yes	complemented
617	#424	C₂²×C₆₇	1	2	yes	complemented
618	#424	C₂²×C₆₇	1	2	yes	complemented
619	#423	C₂²×C₆₇	1	2	yes	complemented
620	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#408	C₂²×C₆₇	1	2	yes	complemented
622	#408	C₂²×C₆₇	1	2	yes	complemented
623	#408	C₂²×C₆₇	1	2	yes	complemented
624	#407	C₂²×C₆₇	1	2	yes	—
625	#407	C₂²×C₆₇	1	2	yes	complemented
626	#407	C₂²×C₆₇	1	2	yes	complemented
627	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
628	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
630	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
631	#405	C₂²×C₆₇	1	2	yes	complemented
632	#405	C₂²×C₆₇	1	2	yes	complemented
633	#405	C₂²×C₆₇	1	2	yes	complemented
634	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
635	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	C₂×#41	C₂³×C₆₇	1	2	yes	—
637	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
638	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
639	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
642	#131	—	4	4	no	—
643	C₂×M₁₆	—	4	2	no	—
644	C₂×M₁₆	—	4	2	no	—
645	C₂×M₁₆	—	4	4	no	—
646	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
647	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
648	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
649	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
650	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
651	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
652	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
653	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
654	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
655	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
656	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
657	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
658	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
659	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
660	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
661	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
662	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
663	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
664	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
665	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
666	#126	C₂×C₄×C₆₇	1	2	yes	—
667	#126	C₂×C₄×C₆₇	1	2	yes	—
668	#126	C₂×C₄×C₆₇	1	2	yes	—
669	#126	C₂×C₄×C₆₇	1	2	yes	—
670	#126	C₂×C₄×C₆₇	1	2	yes	—
671	#126	C₂×C₄×C₆₇	1	2	yes	—
672	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
673	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
674	#125	C₂×C₄×C₆₇	1	2	yes	—
675	#125	C₂×C₄×C₆₇	1	2	yes	—
676	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
677	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
678	#124	C₂×C₄×C₆₇	1	2	yes	—
679	#124	C₂×C₄×C₆₇	1	2	yes	—
680	#123	C₂×C₄×C₆₇	1	2	yes	—
681	#123	C₂×C₄×C₆₇	1	2	yes	—
682	#123	C₂×C₄×C₆₇	1	2	yes	—
683	#123	C₂×C₄×C₆₇	1	2	yes	—
684	#123	C₂×C₄×C₆₇	1	2	yes	—
685	#123	C₂×C₄×C₆₇	1	2	yes	—
686	#123	C₂×C₄×C₆₇	1	2	yes	—
687	#123	C₂×C₄×C₆₇	1	2	yes	—
688	#123	C₂×C₄×C₆₇	1	2	yes	—
689	#123	C₂×C₄×C₆₇	1	2	yes	—
690	#123	C₂×C₄×C₆₇	1	2	yes	—
691	#123	C₂×C₄×C₆₇	1	2	yes	—
692	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
693	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
694	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
695	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
696	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
697	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
698	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
699	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
701	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
702	#121	C₂×C₄×C₆₇	1	2	yes	—
703	#121	C₂×C₄×C₆₇	1	2	yes	—
704	#121	C₂×C₄×C₆₇	1	2	yes	—
705	#121	C₂×C₄×C₆₇	1	2	yes	—
706	#121	C₂×C₄×C₆₇	1	2	yes	—
707	#121	C₂×C₄×C₆₇	1	2	yes	—
708	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
709	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
710	#121	C₂×C₄×C₆₇	1	2	yes	—
711	#121	C₂×C₄×C₆₇	1	2	yes	—
712	#120	C₂×C₄×C₆₇	1	2	yes	—
713	#120	C₂×C₄×C₆₇	1	2	yes	—
714	#120	C₂×C₄×C₆₇	1	2	yes	—
715	#120	C₂×C₄×C₆₇	1	2	yes	—
716	#120	C₂×C₄×C₆₇	1	2	yes	—
717	#120	C₂×C₄×C₆₇	1	2	yes	—
718	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
721	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
722	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
723	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
724	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
725	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
726	C₄×D₄	C₂³×C₆₇	1	2	yes	—
727	C₄×D₄	C₂³×C₆₇	1	2	yes	—
728	C₄×D₄	C₂³×C₆₇	1	2	yes	—
729	C₄×D₄	C₂³×C₆₇	1	2	yes	—
730	C₄×D₄	C₂³×C₆₇	1	2	yes	—
731	C₄×D₄	C₂³×C₆₇	1	2	yes	—
732	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₄×D₄	C₂³×C₆₇	1	2	yes	—
734	C₄×D₄	C₂³×C₆₇	1	2	yes	—
735	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
736	#117	C₂³×C₆₇	1	2	yes	—
737	#117	C₂³×C₆₇	1	2	yes	—
738	#117	C₂³×C₆₇	1	2	yes	—
739	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
745	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
747	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
748	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
749	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
750	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
751	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
752	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
753	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
754	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
755	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
756	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
757	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
758	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
759	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
760	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
761	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
766	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
768	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
779	#97	C₂³×C₆₇	1	2	yes	—
780	#97	C₂³×C₆₇	1	2	yes	—
781	#97	C₂³×C₆₇	1	2	yes	—
782	#97	C₂³×C₆₇	1	2	yes	—
783	#97	C₂³×C₆₇	1	2	yes	—
784	#97	C₂³×C₆₇	1	2	yes	—
785	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
786	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
787	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
788	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₄×C₈	C₂³×C₆₇	1	2	yes	—
790	C₄×C₈	C₂³×C₆₇	1	2	yes	—
791	C₄×C₈	C₂³×C₆₇	1	2	yes	—
792	C₄×C₈	C₂³×C₆₇	1	2	yes	—
793	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
794	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
795	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
796	#41	—	4	2	no	—
797	#41	—	4	2	no	—
798	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
799	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
800	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	4	4	no	—
803	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
804	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
805	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
806	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
807	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
808	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
809	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
810	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
811	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
812	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
813	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
814	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
815	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
823	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
824	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
825	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
826	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
827	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
829	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
830	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
831	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
832	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
838	M₁₆	—	2	4	no	—
839	M₁₆	—	2	4	no	—
840	M₁₆	—	2	4	no	—
841	M₁₆	—	4	2	no	—
842	M₁₆	—	4	2	no	—
843	M₁₆	—	4	2	no	—
844	M₁₆	—	4	2	no	—
845	M₁₆	—	4	2	no	—
846	M₁₆	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	2	2	no	—
849	C₂×C₈	—	2	4	no	—
850	C₂×C₈	—	4	1	no	—
851	C₂×C₈	—	4	1	no	—
852	C₂×C₈	—	4	2	no	—
853	C₂×C₈	—	4	2	no	—
854	C₂×C₈	—	4	2	no	—
855	C₂×C₈	—	4	2	no	—
856	C₂×C₈	—	4	1	no	—
857	C₂×C₈	—	4	2	no	—
858	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
859	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
860	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
861	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
862	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
863	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
864	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
865	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
866	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
867	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
868	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
869	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
870	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
871	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
872	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
873	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
874	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
875	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
877	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
878	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
879	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
880	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
881	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
882	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
883	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
884	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
885	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
886	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
887	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
888	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
891	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
892	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
894	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
896	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
903	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
904	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
905	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
906	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
907	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
908	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
909	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
912	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
913	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
914	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
915	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
916	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
917	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
918	C₄²	C₂⁴×C₆₇	1	2	yes	—
919	C₄²	C₂⁴×C₆₇	1	2	yes	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	4	1	no	—
923	C₂³	—	4	1	no	—
924	C₂³	—	4	2	no	—
925	C₂³	—	4	2	no	—
926	C₂³	—	4	1	no	—
927	C₂³	—	4	1	no	—
928	C₂³	—	4	2	no	—
929	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
930	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
931	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
932	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
933	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
934	Q₈	—	4	2	no	—
935	Q₈	—	4	1	no	—
936	Q₈	—	4	1	no	—
937	D₄	—	2	4	no	—
938	D₄	—	2	4	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	1	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	2	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
972	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
973	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
974	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
975	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
976	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
977	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
978	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
979	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
980	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
981	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
982	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
984	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	1	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	—	2	2	no	—
990	C₈	—	2	1	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	2	no	—
994	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	8	2	no	—
1010	C₂²	—	8	2	no	—
1011	C₂²	—	8	4	no	—
1012	C₂²	#568×C₆₇	1	2	yes	—
1013	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1028	C₄	#585×C₆₇	1	1	yes	characteristic
1029	C₂	—	2	2	no	—
1030	C₂	—	4	2	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	2	no	—
1034	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1035	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
1036	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3459	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2993	C₂	semidirect
4. C₆₇×#2992	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2978	C₂	semidirect
7. C₆₇×#2977	C₂	semidirect
8. C₆₇×#2976	C₂	semidirect
9. C₆₇×#2974	C₂	semidirect
10. C₆₇×#2973	C₂	semidirect
11. C₆₇×#2969	C₂	semidirect
12. C₆₇×#2967	C₂	semidirect
13. C₆₇×#2966	C₂	semidirect
14. C₆₇×#2966	C₂	semidirect
15. D₄×M₁₆×C₆₇	C₂	semidirect
16. C₆₇×#2933	C₂	semidirect
17. C₆₇×#2933	C₂	semidirect
18. C₆₇×#2930	C₂	semidirect
19. C₂×#436×C₆₇	C₂	semidirect
20. C₂×#131×C₆₇	C₂²	semidirect
22. C₂²×M₁₆×C₆₇	C₂²	semidirect
23. C₂²×M₁₆×C₆₇	C₂²	semidirect
43. #446×C₆₇	C₂²	semidirect
44. #446×C₆₇	C₂²	semidirect
45. #446×C₆₇	C₂²	semidirect
46. #446×C₆₇	C₂²	semidirect
47. C₈×Q₈×C₆₇	C₂²	semidirect
48. C₈×Q₈×C₆₇	C₂²	semidirect
49. #436×C₆₇	C₂²	semidirect
50. #436×C₆₇	C₂²	semidirect
51. #436×C₆₇	C₂²	semidirect
52. #436×C₆₇	C₂²	semidirect
53. #436×C₆₇	C₂²	semidirect
54. #436×C₆₇	C₂²	semidirect
55. #436×C₆₇	C₂²	semidirect
56. #436×C₆₇	C₂²	semidirect
57. #436×C₆₇	C₂²	semidirect
58. #436×C₆₇	C₂²	semidirect
59. #436×C₆₇	C₂²	semidirect
60. #436×C₆₇	C₂²	semidirect
61. #435×C₆₇	C₂²	semidirect
62. #435×C₆₇	C₂²	semidirect
63. #435×C₆₇	C₂²	semidirect
64. #435×C₆₇	C₂²	semidirect
65. #435×C₆₇	C₂²	semidirect
66. #435×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #435×C₆₇	C₂²	semidirect
71. #435×C₆₇	C₂²	semidirect
72. #435×C₆₇	C₂²	semidirect
73. #435×C₆₇	C₂²	semidirect
74. #435×C₆₇	C₂²	semidirect
75. #435×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
77. #435×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. C₈×D₄×C₆₇	C₂²	semidirect
80. C₈×D₄×C₆₇	C₂²	semidirect
81. C₈×D₄×C₆₇	C₂²	semidirect
82. C₈×D₄×C₆₇	C₂²	semidirect
83. C₈×D₄×C₆₇	C₂²	semidirect
84. C₈×D₄×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
87. #433×C₆₇	C₂²	semidirect
88. #433×C₆₇	C₂²	semidirect
89. #433×C₆₇	C₂²	semidirect
90. #433×C₆₇	C₂²	semidirect
91. #433×C₆₇	C₂²	semidirect
92. #433×C₆₇	C₂²	semidirect
93. #432×C₆₇	C₂²	semidirect
94. #432×C₆₇	C₂²	semidirect
95. #432×C₆₇	C₂²	semidirect
96. #431×C₆₇	C₂²	semidirect
97. #424×C₆₇	C₂²	semidirect
98. #424×C₆₇	C₂²	semidirect
99. #424×C₆₇	C₂²	semidirect
100. #423×C₆₇	C₂²	semidirect
101. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
102. #408×C₆₇	C₂²	semidirect
103. #408×C₆₇	C₂²	semidirect
104. #408×C₆₇	C₂²	semidirect
106. #407×C₆₇	C₂²	semidirect
107. #407×C₆₇	C₂²	semidirect
109. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
110. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
111. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
112. #405×C₆₇	C₂²	semidirect
113. #405×C₆₇	C₂²	semidirect
114. #405×C₆₇	C₂²	semidirect
115. C₄×M₁₆×C₆₇	C₂²	semidirect
116. C₂×C₄×C₈×C₆₇	C₂²	semidirect
510. #60322	C₆₇	direct (N × H)
520. #2995	C₂×C₆₇	semidirect
521. #2993	C₂×C₆₇	semidirect
522. #2992	C₂×C₆₇	semidirect
523. #2992	C₂×C₆₇	semidirect
524. #2978	C₂×C₆₇	semidirect
525. #2977	C₂×C₆₇	semidirect
526. #2976	C₂×C₆₇	semidirect
527. #2974	C₂×C₆₇	semidirect
528. #2973	C₂×C₆₇	semidirect
529. #2969	C₂×C₆₇	semidirect
530. #2967	C₂×C₆₇	semidirect
531. #2966	C₂×C₆₇	semidirect
532. #2966	C₂×C₆₇	semidirect
533. D₄×M₁₆	C₂×C₆₇	semidirect
534. #2933	C₂×C₆₇	semidirect
535. #2933	C₂×C₆₇	semidirect
536. #2930	C₂×C₆₇	semidirect
537. C₂×#436	C₂×C₆₇	semidirect
538. C₆₇	#60322	direct (N × H)
539. C₂×#131	C₂²×C₆₇	semidirect
541. C₂²×M₁₆	C₂²×C₆₇	semidirect
542. C₂²×M₁₆	C₂²×C₆₇	semidirect
562. #446	C₂²×C₆₇	semidirect
563. #446	C₂²×C₆₇	semidirect
564. #446	C₂²×C₆₇	semidirect
565. #446	C₂²×C₆₇	semidirect
566. C₈×Q₈	C₂²×C₆₇	semidirect
567. C₈×Q₈	C₂²×C₆₇	semidirect
568. #436	C₂²×C₆₇	semidirect
569. #436	C₂²×C₆₇	semidirect
570. #436	C₂²×C₆₇	semidirect
571. #436	C₂²×C₆₇	semidirect
572. #436	C₂²×C₆₇	semidirect
573. #436	C₂²×C₆₇	semidirect
574. #436	C₂²×C₆₇	semidirect
575. #436	C₂²×C₆₇	semidirect
576. #436	C₂²×C₆₇	semidirect
577. #436	C₂²×C₆₇	semidirect
578. #436	C₂²×C₆₇	semidirect
579. #436	C₂²×C₆₇	semidirect
580. #435	C₂²×C₆₇	semidirect
581. #435	C₂²×C₆₇	semidirect
582. #435	C₂²×C₆₇	semidirect
583. #435	C₂²×C₆₇	semidirect
584. #435	C₂²×C₆₇	semidirect
585. #435	C₂²×C₆₇	semidirect
586. #435	C₂²×C₆₇	semidirect
587. #435	C₂²×C₆₇	semidirect
588. #435	C₂²×C₆₇	semidirect
589. #435	C₂²×C₆₇	semidirect
590. #435	C₂²×C₆₇	semidirect
591. #435	C₂²×C₆₇	semidirect
592. #435	C₂²×C₆₇	semidirect
593. #435	C₂²×C₆₇	semidirect
594. #435	C₂²×C₆₇	semidirect
595. #435	C₂²×C₆₇	semidirect
596. #435	C₂²×C₆₇	semidirect
597. #435	C₂²×C₆₇	semidirect
598. C₈×D₄	C₂²×C₆₇	semidirect
599. C₈×D₄	C₂²×C₆₇	semidirect
600. C₈×D₄	C₂²×C₆₇	semidirect
601. C₈×D₄	C₂²×C₆₇	semidirect
602. C₈×D₄	C₂²×C₆₇	semidirect
603. C₈×D₄	C₂²×C₆₇	semidirect
604. C₈×D₄	C₂²×C₆₇	semidirect
605. C₈×D₄	C₂²×C₆₇	semidirect
606. #433	C₂²×C₆₇	semidirect
607. #433	C₂²×C₆₇	semidirect
608. #433	C₂²×C₆₇	semidirect
609. #433	C₂²×C₆₇	semidirect
610. #433	C₂²×C₆₇	semidirect
611. #433	C₂²×C₆₇	semidirect
612. #432	C₂²×C₆₇	semidirect
613. #432	C₂²×C₆₇	semidirect
614. #432	C₂²×C₆₇	semidirect
615. #431	C₂²×C₆₇	semidirect
616. #424	C₂²×C₆₇	semidirect
617. #424	C₂²×C₆₇	semidirect
618. #424	C₂²×C₆₇	semidirect
619. #423	C₂²×C₆₇	semidirect
620. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
621. #408	C₂²×C₆₇	semidirect
622. #408	C₂²×C₆₇	semidirect
623. #408	C₂²×C₆₇	semidirect
625. #407	C₂²×C₆₇	semidirect
626. #407	C₂²×C₆₇	semidirect
628. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
629. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
630. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
631. #405	C₂²×C₆₇	semidirect
632. #405	C₂²×C₆₇	semidirect
633. #405	C₂²×C₆₇	semidirect
634. C₄×M₁₆	C₂²×C₆₇	semidirect
635. C₂×C₄×C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3459	2
C₆₇×#2995	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2978	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2974	2
C₆₇×#2973	2
C₆₇×#2969	2
C₆₇×#2967	2
C₆₇×#2966	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2930	2
C₂×#436×C₆₇	2
#60322	67

Subgroups — C67×#60322 #30739573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60322 #30739573