Subgroups — C₆₇×#60215 #30739466

Order 17152.

1970 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2970	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2968	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2966	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2966	C₂	1	2	yes	maximal, complemented
7	C₈×#41×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2929	C₂	1	2	yes	maximal, complemented
13	C₂×C₈×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2924	C₂	1	2	yes	maximal, complemented
16	C₄×#131×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#405×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
21	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
22	#556×C₆₇	C₄	1	1	yes	characteristic
23	#555×C₆₇	C₄	1	1	yes	characteristic
24	#554×C₆₇	C₄	1	1	yes	characteristic
25	#553×C₆₇	C₄	1	2	yes	—
26	#552×C₆₇	C₄	1	2	yes	—
27	#552×C₆₇	C₄	1	2	yes	—
28	#551×C₆₇	C₄	1	4	yes	—
29	#547×C₆₇	C₄	1	1	yes	characteristic
30	#546×C₆₇	C₄	1	2	yes	—
31	#533×C₆₇	C₂²	1	1	yes	characteristic
32	#529×C₆₇	C₂²	1	4	yes	—
33	#529×C₆₇	C₂²	1	2	yes	—
34	#525×C₆₇	C₂²	1	2	yes	—
35	C₄×#41×C₆₇	C₂²	1	2	yes	—
36	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	2	yes	—
39	#446×C₆₇	C₂²	1	2	yes	complemented
40	#446×C₆₇	C₂²	1	2	yes	complemented
41	#446×C₆₇	C₂²	1	4	yes	complemented
42	#446×C₆₇	C₂²	1	2	yes	complemented
43	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
44	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
45	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
46	#436×C₆₇	C₂²	1	2	yes	—
47	#436×C₆₇	C₂²	1	4	yes	complemented
48	#435×C₆₇	C₂²	1	4	yes	—
49	#435×C₆₇	C₂²	1	4	yes	complemented
50	#435×C₆₇	C₂²	1	4	yes	complemented
51	#435×C₆₇	C₂²	1	4	yes	complemented
52	#435×C₆₇	C₂²	1	4	yes	complemented
53	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₆₇	C₂²	1	2	yes	—
56	C₈×D₄×C₆₇	C₂²	1	2	yes	—
57	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
58	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
59	C₈×D₄×C₆₇	C₂²	1	2	yes	—
60	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
61	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
62	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
63	#433×C₆₇	C₂²	1	4	yes	complemented
64	#433×C₆₇	C₂²	1	4	yes	complemented
65	#433×C₆₇	C₂²	1	4	yes	complemented
66	#432×C₆₇	C₂²	1	4	yes	complemented
67	#432×C₆₇	C₂²	1	2	yes	complemented
68	#431×C₆₇	C₂²	1	4	yes	complemented
69	#431×C₆₇	C₂²	1	2	yes	complemented
70	#424×C₆₇	C₂²	1	2	yes	—
71	#424×C₆₇	C₂²	1	2	yes	—
72	#423×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
74	#408×C₆₇	C₂²	1	2	yes	—
75	#407×C₆₇	C₂²	1	2	yes	—
76	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
77	#405×C₆₇	C₂²	1	1	yes	characteristic
78	#405×C₆₇	C₂²	1	2	yes	—
79	#405×C₆₇	C₂²	1	2	yes	—
80	#405×C₆₇	C₂²	1	2	yes	—
81	#405×C₆₇	C₂²	1	1	yes	characteristic
82	#405×C₆₇	C₂²	1	4	yes	complemented
83	#405×C₆₇	C₂²	1	4	yes	complemented
84	#405×C₆₇	C₂²	1	2	yes	complemented
85	#405×C₆₇	C₂²	1	2	yes	complemented
86	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
87	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
88	C₂×#97×C₆₇	C₂²	1	4	yes	complemented
89	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
90	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	complemented
91	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
92	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
93	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
96	#131×C₆₇	—	2	4	no	—
97	#131×C₆₇	—	2	4	no	—
98	C₂×M₁₆×C₆₇	—	2	8	no	—
99	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₆₇	—	2	8	no	—
106	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
110	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
112	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
113	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
114	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
115	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
118	#126×C₆₇	C₂×C₄	1	4	yes	—
119	#126×C₆₇	C₂×C₄	1	4	yes	—
120	#126×C₆₇	C₂×C₄	1	4	yes	—
121	#125×C₆₇	C₂×C₄	1	4	yes	—
122	#125×C₆₇	C₂×C₄	1	2	yes	—
123	#125×C₆₇	C₂×C₄	1	2	yes	—
124	#124×C₆₇	C₂×C₄	1	2	yes	—
125	#124×C₆₇	C₂×C₄	1	4	yes	—
126	#123×C₆₇	C₂×C₄	1	4	yes	—
127	#123×C₆₇	C₂×C₄	1	4	yes	—
128	#123×C₆₇	C₂×C₄	1	4	yes	—
129	#123×C₆₇	C₂×C₄	1	4	yes	—
130	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
131	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
132	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
133	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
134	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
135	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
136	#121×C₆₇	C₂×C₄	1	2	yes	—
137	#121×C₆₇	C₂×C₄	1	2	yes	—
138	#121×C₆₇	C₂×C₄	1	4	yes	—
139	#121×C₆₇	C₂×C₄	1	2	yes	—
140	#120×C₆₇	C₂×C₄	1	4	yes	—
141	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
142	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
143	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
144	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
145	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
147	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
148	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
150	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
151	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
153	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
154	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₄×D₄×C₆₇	C₂³	1	2	yes	—
157	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₆₇	C₂³	1	4	yes	—
159	C₄×D₄×C₆₇	C₂³	1	4	yes	—
160	#117×C₆₇	C₂×C₄	1	4	yes	—
161	#117×C₆₇	C₂×C₄	1	2	yes	—
162	#117×C₆₇	C₂×C₄	1	2	yes	—
163	#117×C₆₇	C₂×C₄	1	4	yes	—
164	#117×C₆₇	C₂×C₄	1	2	yes	—
165	#117×C₆₇	C₂³	1	1	yes	characteristic
166	#117×C₆₇	C₂³	1	2	yes	—
167	#117×C₆₇	C₂³	1	4	yes	—
168	#117×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
180	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
183	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
184	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
185	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
187	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
191	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
192	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
194	#97×C₆₇	C₂³	1	2	yes	—
195	#97×C₆₇	C₂³	1	4	yes	—
196	#97×C₆₇	C₂³	1	4	yes	—
197	#97×C₆₇	C₂³	1	4	yes	—
198	#97×C₆₇	C₂³	1	2	yes	—
199	#97×C₆₇	C₂³	1	2	yes	—
200	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
202	C₄×C₈×C₆₇	C₂³	1	2	yes	—
203	C₄×C₈×C₆₇	C₂³	1	4	yes	—
204	C₄×C₈×C₆₇	C₂³	1	2	yes	—
205	C₄×C₈×C₆₇	C₂³	1	4	yes	—
206	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₆₇	C₂³	1	2	yes	—
209	C₄×C₈×C₆₇	C₂³	1	4	yes	—
210	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
211	#41×C₆₇	—	2	8	no	—
212	#41×C₆₇	—	2	2	no	—
213	#41×C₆₇	—	2	2	no	—
214	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
216	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
217	C₂×D₄×C₆₇	—	2	4	no	—
218	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
219	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
220	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
221	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
222	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
223	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
224	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
228	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
230	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
235	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	M₁₆×C₆₇	—	2	4	no	—
241	M₁₆×C₆₇	—	2	2	no	—
242	M₁₆×C₆₇	—	2	8	no	—
243	M₁₆×C₆₇	—	2	4	no	—
244	M₁₆×C₆₇	—	2	4	no	—
245	M₁₆×C₆₇	#41	1	4	yes	complemented
246	C₂×C₈×C₆₇	—	2	4	no	—
247	C₂×C₈×C₆₇	—	2	2	no	—
248	C₂×C₈×C₆₇	—	2	4	no	—
249	C₂×C₈×C₆₇	—	2	4	no	—
250	C₂×C₈×C₆₇	—	2	4	no	—
251	C₂×C₈×C₆₇	—	2	4	no	—
252	C₂×C₈×C₆₇	—	2	8	no	—
253	C₂×C₈×C₆₇	—	2	4	no	—
254	C₂×C₈×C₆₇	—	2	4	no	—
255	C₂×C₈×C₆₇	#41	1	4	yes	complemented
256	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
257	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
259	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
260	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
261	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
266	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
267	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
268	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
270	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
271	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
272	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
273	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
274	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
276	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
280	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
281	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
282	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
283	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
284	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
285	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
287	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
288	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
289	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
290	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
291	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
293	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
294	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
295	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
296	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
297	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
298	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
299	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
300	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
301	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
302	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₄²×C₆₇	C₂⁴	1	4	yes	—
305	C₄²×C₆₇	C₂⁴	1	2	yes	—
306	C₂³×C₆₇	—	2	4	no	—
307	C₂³×C₆₇	—	2	4	no	—
308	C₂³×C₆₇	—	4	2	no	—
309	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
310	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
311	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
312	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
313	Q₈×C₆₇	—	2	2	no	—
314	Q₈×C₆₇	—	2	4	no	—
315	Q₈×C₆₇	—	4	2	no	—
316	D₄×C₆₇	—	2	4	no	—
317	D₄×C₆₇	—	2	4	no	—
318	D₄×C₆₇	—	2	8	no	—
319	D₄×C₆₇	—	2	2	no	—
320	D₄×C₆₇	—	2	2	no	—
321	D₄×C₆₇	—	4	4	no	—
322	D₄×C₆₇	#131	1	4	yes	complemented
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	8	no	—
325	C₂×C₄×C₆₇	—	2	4	no	—
326	C₂×C₄×C₆₇	—	2	4	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	4	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	4	2	no	—
336	C₂×C₄×C₆₇	—	4	4	no	—
337	C₂×C₄×C₆₇	—	4	1	no	—
338	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
339	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
340	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
342	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
343	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
345	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
346	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
350	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
351	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
352	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
353	C₈×C₆₇	—	2	2	no	—
354	C₈×C₆₇	—	2	2	no	—
355	C₈×C₆₇	—	2	1	no	—
356	C₈×C₆₇	—	2	1	no	—
357	C₈×C₆₇	—	2	4	no	—
358	C₈×C₆₇	—	2	2	no	—
359	C₈×C₆₇	C₂×#41	1	2	yes	—
360	C₈×C₆₇	C₂×#41	1	2	yes	—
361	C₈×C₆₇	C₂×#41	1	4	yes	—
362	C₂²×C₆₇	—	2	2	no	—
363	C₂²×C₆₇	—	2	1	no	—
364	C₂²×C₆₇	—	2	2	no	—
365	C₂²×C₆₇	—	2	1	no	—
366	C₂²×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	2	2	no	—
368	C₂²×C₆₇	—	2	2	no	—
369	C₂²×C₆₇	—	2	2	no	—
370	C₂²×C₆₇	—	2	2	no	—
371	C₂²×C₆₇	—	2	2	no	—
372	C₂²×C₆₇	—	4	8	no	—
373	C₂²×C₆₇	C₄×#41	1	2	yes	—
374	C₂²×C₆₇	C₂×#131	1	4	yes	—
375	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	2	no	—
378	C₄×C₆₇	—	2	2	no	—
379	C₄×C₆₇	—	2	2	no	—
380	C₄×C₆₇	—	2	1	no	—
381	C₄×C₆₇	—	2	4	no	—
382	C₄×C₆₇	—	2	1	no	—
383	C₄×C₆₇	—	2	2	no	—
384	C₄×C₆₇	—	2	4	no	—
385	C₄×C₆₇	—	2	1	no	—
386	C₄×C₆₇	C₄×#41	1	2	yes	—
387	C₄×C₆₇	C₂×#131	1	2	yes	—
388	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
389	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
390	#60215	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₆₇	—	2	2	no	—
392	C₂×C₆₇	—	2	4	no	—
393	C₂×C₆₇	—	4	2	no	—
394	C₂×C₆₇	—	4	2	no	—
395	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
396	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
397	C₂×C₆₇	#3573	1	1	yes	characteristic
398	#3475	C₂×C₆₇	1	1	yes	characteristic
399	#2970	C₂×C₆₇	1	2	yes	complemented
400	#2969	C₂×C₆₇	1	2	yes	complemented
401	#2968	C₂×C₆₇	1	4	yes	complemented
402	#2966	C₂×C₆₇	1	4	yes	complemented
403	#2966	C₂×C₆₇	1	2	yes	complemented
404	C₈×#41	C₂×C₆₇	1	2	yes	complemented
405	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
407	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
408	#2933	C₂×C₆₇	1	2	yes	complemented
409	#2929	C₂×C₆₇	1	2	yes	complemented
410	C₂×C₈×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
411	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#2924	C₂×C₆₇	1	2	yes	complemented
413	C₄×#131	C₂×C₆₇	1	1	yes	characteristic, complemented
414	C₂×#405	C₂×C₆₇	1	2	yes	complemented
415	C₆₇	#60215	1	1	yes	characteristic, direct product factor, Sylow
416	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
418	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
419	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
420	#556	C₄×C₆₇	1	1	yes	characteristic
421	#555	C₄×C₆₇	1	1	yes	characteristic
422	#554	C₄×C₆₇	1	1	yes	characteristic
423	#553	C₄×C₆₇	1	2	yes	—
424	#552	C₄×C₆₇	1	2	yes	—
425	#552	C₄×C₆₇	1	2	yes	—
426	#551	C₄×C₆₇	1	4	yes	—
427	#547	C₄×C₆₇	1	1	yes	characteristic
428	#546	C₄×C₆₇	1	2	yes	—
429	#533	C₂²×C₆₇	1	1	yes	characteristic
430	#529	C₂²×C₆₇	1	4	yes	—
431	#529	C₂²×C₆₇	1	2	yes	—
432	#525	C₂²×C₆₇	1	2	yes	—
433	C₄×#41	C₂²×C₆₇	1	2	yes	—
434	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×#117	C₂²×C₆₇	1	2	yes	—
437	#446	C₂²×C₆₇	1	2	yes	complemented
438	#446	C₂²×C₆₇	1	2	yes	complemented
439	#446	C₂²×C₆₇	1	4	yes	complemented
440	#446	C₂²×C₆₇	1	2	yes	complemented
441	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
442	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
443	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
444	#436	C₂²×C₆₇	1	2	yes	—
445	#436	C₂²×C₆₇	1	4	yes	complemented
446	#435	C₂²×C₆₇	1	4	yes	—
447	#435	C₂²×C₆₇	1	4	yes	complemented
448	#435	C₂²×C₆₇	1	4	yes	complemented
449	#435	C₂²×C₆₇	1	4	yes	complemented
450	#435	C₂²×C₆₇	1	4	yes	complemented
451	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
452	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
453	C₈×D₄	C₂²×C₆₇	1	2	yes	—
454	C₈×D₄	C₂²×C₆₇	1	2	yes	—
455	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
456	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
457	C₈×D₄	C₂²×C₆₇	1	2	yes	—
458	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
459	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
460	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
461	#433	C₂²×C₆₇	1	4	yes	complemented
462	#433	C₂²×C₆₇	1	4	yes	complemented
463	#433	C₂²×C₆₇	1	4	yes	complemented
464	#432	C₂²×C₆₇	1	4	yes	complemented
465	#432	C₂²×C₆₇	1	2	yes	complemented
466	#431	C₂²×C₆₇	1	4	yes	complemented
467	#431	C₂²×C₆₇	1	2	yes	complemented
468	#424	C₂²×C₆₇	1	2	yes	—
469	#424	C₂²×C₆₇	1	2	yes	—
470	#423	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
472	#408	C₂²×C₆₇	1	2	yes	—
473	#407	C₂²×C₆₇	1	2	yes	—
474	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
475	#405	C₂²×C₆₇	1	1	yes	characteristic
476	#405	C₂²×C₆₇	1	2	yes	—
477	#405	C₂²×C₆₇	1	2	yes	—
478	#405	C₂²×C₆₇	1	2	yes	—
479	#405	C₂²×C₆₇	1	1	yes	characteristic
480	#405	C₂²×C₆₇	1	4	yes	complemented
481	#405	C₂²×C₆₇	1	4	yes	complemented
482	#405	C₂²×C₆₇	1	2	yes	complemented
483	#405	C₂²×C₆₇	1	2	yes	complemented
484	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
485	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
486	C₂×#97	C₂²×C₆₇	1	4	yes	complemented
487	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	complemented
489	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
490	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
491	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
492	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
494	#131	—	2	4	no	—
495	#131	—	2	4	no	—
496	C₂×M₁₆	—	2	8	no	—
497	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
498	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
499	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
500	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
501	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
502	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
503	C₂²×C₈	—	2	8	no	—
504	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
505	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
506	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
507	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
508	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
509	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
510	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
512	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
513	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
514	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
515	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
516	#126	C₂×C₄×C₆₇	1	4	yes	—
517	#126	C₂×C₄×C₆₇	1	4	yes	—
518	#126	C₂×C₄×C₆₇	1	4	yes	—
519	#125	C₂×C₄×C₆₇	1	4	yes	—
520	#125	C₂×C₄×C₆₇	1	2	yes	—
521	#125	C₂×C₄×C₆₇	1	2	yes	—
522	#124	C₂×C₄×C₆₇	1	2	yes	—
523	#124	C₂×C₄×C₆₇	1	4	yes	—
524	#123	C₂×C₄×C₆₇	1	4	yes	—
525	#123	C₂×C₄×C₆₇	1	4	yes	—
526	#123	C₂×C₄×C₆₇	1	4	yes	—
527	#123	C₂×C₄×C₆₇	1	4	yes	—
528	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
529	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
530	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
531	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
532	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
533	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
534	#121	C₂×C₄×C₆₇	1	2	yes	—
535	#121	C₂×C₄×C₆₇	1	2	yes	—
536	#121	C₂×C₄×C₆₇	1	4	yes	—
537	#121	C₂×C₄×C₆₇	1	2	yes	—
538	#120	C₂×C₄×C₆₇	1	4	yes	—
539	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
540	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
541	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
542	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
543	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
544	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
545	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
546	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
547	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
548	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
549	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
550	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
551	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
552	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
553	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
554	C₄×D₄	C₂³×C₆₇	1	2	yes	—
555	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₆₇	1	4	yes	—
557	C₄×D₄	C₂³×C₆₇	1	4	yes	—
558	#117	C₂×C₄×C₆₇	1	4	yes	—
559	#117	C₂×C₄×C₆₇	1	2	yes	—
560	#117	C₂×C₄×C₆₇	1	2	yes	—
561	#117	C₂×C₄×C₆₇	1	4	yes	—
562	#117	C₂×C₄×C₆₇	1	2	yes	—
563	#117	C₂³×C₆₇	1	1	yes	characteristic
564	#117	C₂³×C₆₇	1	2	yes	—
565	#117	C₂³×C₆₇	1	4	yes	—
566	#117	C₂³×C₆₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
572	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
573	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
575	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
576	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
577	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
578	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
579	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
580	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
581	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
582	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
583	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
584	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
585	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
586	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
587	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
588	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
592	#97	C₂³×C₆₇	1	2	yes	—
593	#97	C₂³×C₆₇	1	4	yes	—
594	#97	C₂³×C₆₇	1	4	yes	—
595	#97	C₂³×C₆₇	1	4	yes	—
596	#97	C₂³×C₆₇	1	2	yes	—
597	#97	C₂³×C₆₇	1	2	yes	—
598	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
599	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
600	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
601	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
602	C₄×C₈	C₂³×C₆₇	1	2	yes	—
603	C₄×C₈	C₂³×C₆₇	1	2	yes	—
604	C₄×C₈	C₂³×C₆₇	1	4	yes	—
605	C₄×C₈	C₂³×C₆₇	1	2	yes	—
606	C₄×C₈	C₂³×C₆₇	1	4	yes	—
607	C₄×C₈	C₂³×C₆₇	1	4	yes	—
608	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
609	#41	—	2	8	no	—
610	#41	—	2	2	no	—
611	#41	—	2	2	no	—
612	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
613	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
614	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
617	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
618	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
619	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
620	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
621	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
622	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
626	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
627	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
628	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
629	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
630	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
631	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
632	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
633	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
638	M₁₆	—	2	4	no	—
639	M₁₆	—	2	2	no	—
640	M₁₆	—	2	8	no	—
641	M₁₆	—	2	4	no	—
642	M₁₆	—	2	4	no	—
643	M₁₆	#41×C₆₇	1	4	yes	complemented
644	C₂×C₈	—	2	4	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	4	no	—
647	C₂×C₈	—	2	4	no	—
648	C₂×C₈	—	2	4	no	—
649	C₂×C₈	—	2	4	no	—
650	C₂×C₈	—	2	8	no	—
651	C₂×C₈	—	2	4	no	—
652	C₂×C₈	—	2	4	no	—
653	C₂×C₈	#41×C₆₇	1	4	yes	complemented
654	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
655	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
656	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
657	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
658	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
659	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
660	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
661	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
662	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
664	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
666	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
667	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
668	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
669	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
670	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
671	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
672	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
673	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
674	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
675	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
676	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
677	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
678	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
679	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
681	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
682	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
683	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
684	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
688	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
689	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
690	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
691	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
692	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
693	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
694	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
695	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
696	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
697	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
698	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
699	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
700	C₄²	C₂⁴×C₆₇	1	2	yes	—
701	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
702	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
703	C₄²	C₂⁴×C₆₇	1	4	yes	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	4	2	no	—
707	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
708	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
709	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
710	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	4	no	—
713	Q₈	—	4	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	8	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	4	4	no	—
720	D₄	#131×C₆₇	1	4	yes	complemented
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
737	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
738	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
740	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
741	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
742	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
743	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
744	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
745	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
746	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
747	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
748	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
749	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
750	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
751	C₈	—	2	2	no	—
752	C₈	—	2	2	no	—
753	C₈	—	2	1	no	—
754	C₈	—	2	1	no	—
755	C₈	—	2	4	no	—
756	C₈	—	2	2	no	—
757	C₈	C₂×#41×C₆₇	1	2	yes	—
758	C₈	C₂×#41×C₆₇	1	2	yes	—
759	C₈	C₂×#41×C₆₇	1	4	yes	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	4	8	no	—
771	C₂²	C₄×#41×C₆₇	1	2	yes	—
772	C₂²	C₂×#131×C₆₇	1	4	yes	—
773	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	C₄×#41×C₆₇	1	2	yes	—
785	C₄	C₂×#131×C₆₇	1	2	yes	—
786	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
787	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
788	C₂	—	2	2	no	—
789	C₂	—	2	4	no	—
790	C₂	—	4	2	no	—
791	C₂	—	4	2	no	—
792	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
793	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
794	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₆₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3475	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2970	C₂	semidirect
3. C₆₇×#2969	C₂	semidirect
4. C₆₇×#2968	C₂	semidirect
5. C₆₇×#2966	C₂	semidirect
6. C₆₇×#2966	C₂	semidirect
7. C₈×#41×C₆₇	C₂	semidirect
8. C₆₇×#2962	C₂	semidirect
9. C₆₇×#2960	C₂	semidirect
10. D₄×M₁₆×C₆₇	C₂	semidirect
11. C₆₇×#2933	C₂	semidirect
12. C₆₇×#2929	C₂	semidirect
13. C₂×C₈×D₄×C₆₇	C₂	semidirect
14. C₆₇×#2925	C₂	semidirect
15. C₆₇×#2924	C₂	semidirect
16. C₄×#131×C₆₇	C₂	semidirect
17. C₂×#405×C₆₇	C₂	semidirect
39. #446×C₆₇	C₂²	semidirect
40. #446×C₆₇	C₂²	semidirect
41. #446×C₆₇	C₂²	semidirect
42. #446×C₆₇	C₂²	semidirect
43. C₈×Q₈×C₆₇	C₂²	semidirect
44. C₈×Q₈×C₆₇	C₂²	semidirect
45. C₈×Q₈×C₆₇	C₂²	semidirect
47. #436×C₆₇	C₂²	semidirect
49. #435×C₆₇	C₂²	semidirect
50. #435×C₆₇	C₂²	semidirect
51. #435×C₆₇	C₂²	semidirect
52. #435×C₆₇	C₂²	semidirect
60. C₈×D₄×C₆₇	C₂²	semidirect
61. C₈×D₄×C₆₇	C₂²	semidirect
62. C₈×D₄×C₆₇	C₂²	semidirect
63. #433×C₆₇	C₂²	semidirect
64. #433×C₆₇	C₂²	semidirect
65. #433×C₆₇	C₂²	semidirect
66. #432×C₆₇	C₂²	semidirect
67. #432×C₆₇	C₂²	semidirect
68. #431×C₆₇	C₂²	semidirect
69. #431×C₆₇	C₂²	semidirect
82. #405×C₆₇	C₂²	semidirect
83. #405×C₆₇	C₂²	semidirect
84. #405×C₆₇	C₂²	semidirect
85. #405×C₆₇	C₂²	semidirect
87. C₄×M₁₆×C₆₇	C₂²	semidirect
88. C₂×#97×C₆₇	C₂²	semidirect
90. C₂×C₄×C₈×C₆₇	C₂²	semidirect
91. C₂×C₄×C₈×C₆₇	C₂²	semidirect
245. M₁₆×C₆₇	#41	semidirect
255. C₂×C₈×C₆₇	#41	semidirect
322. D₄×C₆₇	#131	semidirect
390. #60215	C₆₇	direct (N × H)
399. #2970	C₂×C₆₇	semidirect
400. #2969	C₂×C₆₇	semidirect
401. #2968	C₂×C₆₇	semidirect
402. #2966	C₂×C₆₇	semidirect
403. #2966	C₂×C₆₇	semidirect
404. C₈×#41	C₂×C₆₇	semidirect
405. #2962	C₂×C₆₇	semidirect
406. #2960	C₂×C₆₇	semidirect
407. D₄×M₁₆	C₂×C₆₇	semidirect
408. #2933	C₂×C₆₇	semidirect
409. #2929	C₂×C₆₇	semidirect
410. C₂×C₈×D₄	C₂×C₆₇	semidirect
411. #2925	C₂×C₆₇	semidirect
412. #2924	C₂×C₆₇	semidirect
413. C₄×#131	C₂×C₆₇	semidirect
414. C₂×#405	C₂×C₆₇	semidirect
415. C₆₇	#60215	direct (N × H)
437. #446	C₂²×C₆₇	semidirect
438. #446	C₂²×C₆₇	semidirect
439. #446	C₂²×C₆₇	semidirect
440. #446	C₂²×C₆₇	semidirect
441. C₈×Q₈	C₂²×C₆₇	semidirect
442. C₈×Q₈	C₂²×C₆₇	semidirect
443. C₈×Q₈	C₂²×C₆₇	semidirect
445. #436	C₂²×C₆₇	semidirect
447. #435	C₂²×C₆₇	semidirect
448. #435	C₂²×C₆₇	semidirect
449. #435	C₂²×C₆₇	semidirect
450. #435	C₂²×C₆₇	semidirect
458. C₈×D₄	C₂²×C₆₇	semidirect
459. C₈×D₄	C₂²×C₆₇	semidirect
460. C₈×D₄	C₂²×C₆₇	semidirect
461. #433	C₂²×C₆₇	semidirect
462. #433	C₂²×C₆₇	semidirect
463. #433	C₂²×C₆₇	semidirect
464. #432	C₂²×C₆₇	semidirect
465. #432	C₂²×C₆₇	semidirect
466. #431	C₂²×C₆₇	semidirect
467. #431	C₂²×C₆₇	semidirect
480. #405	C₂²×C₆₇	semidirect
481. #405	C₂²×C₆₇	semidirect
482. #405	C₂²×C₆₇	semidirect
483. #405	C₂²×C₆₇	semidirect
485. C₄×M₁₆	C₂²×C₆₇	semidirect
486. C₂×#97	C₂²×C₆₇	semidirect
488. C₂×C₄×C₈	C₂²×C₆₇	semidirect
489. C₂×C₄×C₈	C₂²×C₆₇	semidirect
643. M₁₆	#41×C₆₇	semidirect
653. C₂×C₈	#41×C₆₇	semidirect
720. D₄	#131×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3475	2
C₆₇×#2970	2
C₆₇×#2969	2
C₆₇×#2968	2
C₆₇×#2966	2
C₈×#41×C₆₇	2
C₆₇×#2962	2
C₆₇×#2960	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2929	2
C₂×C₈×D₄×C₆₇	2
C₆₇×#2925	2
C₆₇×#2924	2
C₄×#131×C₆₇	2
C₂×#405×C₆₇	2
#60215	67

Subgroups — C67×#60215 #30739466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60215 #30739466