Subgroups — C₆₇×#60271 #30739522

Order 17152.

1882 conjugacy classes of subgroups.

The subgroup lattice has 790 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×#2994	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2994	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2992	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2990	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2988	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×#2924	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#424×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×#131×C₆₇	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
20	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
21	#556×C₆₇	C₄	1	1	yes	characteristic
22	#555×C₆₇	C₄	1	1	yes	characteristic
23	#554×C₆₇	C₄	1	1	yes	characteristic
24	#553×C₆₇	C₄	1	2	yes	—
25	#552×C₆₇	C₄	1	2	yes	—
26	#552×C₆₇	C₄	1	2	yes	—
27	#551×C₆₇	C₄	1	4	yes	—
28	#547×C₆₇	C₄	1	1	yes	characteristic
29	#546×C₆₇	C₄	1	2	yes	—
30	#533×C₆₇	C₂²	1	1	yes	characteristic
31	#529×C₆₇	C₂²	1	4	yes	—
32	#529×C₆₇	C₂²	1	2	yes	—
33	#525×C₆₇	C₂²	1	2	yes	—
34	C₄×#41×C₆₇	C₂²	1	2	yes	—
35	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	2	yes	—
38	#446×C₆₇	C₂²	1	2	yes	complemented
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	C₈×Q₈×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	#436×C₆₇	C₂²	1	2	yes	—
46	#436×C₆₇	C₂²	1	4	yes	complemented
47	#435×C₆₇	C₂²	1	4	yes	—
48	#435×C₆₇	C₂²	1	4	yes	complemented
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	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₆₇	C₂²	1	2	yes	—
55	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
56	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
57	C₈×D₄×C₆₇	C₂²	1	2	yes	—
58	C₈×D₄×C₆₇	C₂²	1	2	yes	—
59	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
60	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
61	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
62	#433×C₆₇	C₂²	1	2	yes	complemented
63	#433×C₆₇	C₂²	1	2	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	#431×C₆₇	C₂²	1	2	yes	complemented
68	#431×C₆₇	C₂²	1	2	yes	complemented
69	#431×C₆₇	C₂²	1	4	yes	complemented
70	#424×C₆₇	C₂²	1	1	yes	characteristic
71	#424×C₆₇	C₂²	1	2	yes	—
72	#424×C₆₇	C₂²	1	2	yes	—
73	#424×C₆₇	C₂²	1	2	yes	—
74	#424×C₆₇	C₂²	1	1	yes	characteristic
75	#424×C₆₇	C₂²	1	4	yes	complemented
76	#424×C₆₇	C₂²	1	4	yes	complemented
77	#424×C₆₇	C₂²	1	4	yes	complemented
78	#423×C₆₇	C₂²	1	1	yes	characteristic
79	#423×C₆₇	C₂²	1	2	yes	complemented
80	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
81	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
82	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
83	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
84	#408×C₆₇	C₂²	1	1	yes	characteristic
85	#408×C₆₇	C₂²	1	1	yes	characteristic
86	#407×C₆₇	C₂²	1	2	yes	—
87	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
88	#405×C₆₇	C₂²	1	2	yes	—
89	#405×C₆₇	C₂²	1	2	yes	—
90	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
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	—	4	4	no	—
97	C₂×M₁₆×C₆₇	—	4	4	no	—
98	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂²×C₈×C₆₇	—	4	4	no	—
104	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
110	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
111	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
112	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
115	#126×C₆₇	C₂×C₄	1	4	yes	—
116	#126×C₆₇	C₂×C₄	1	4	yes	—
117	#126×C₆₇	C₂×C₄	1	4	yes	—
118	#125×C₆₇	C₂×C₄	1	4	yes	—
119	#125×C₆₇	C₂×C₄	1	2	yes	—
120	#125×C₆₇	C₂×C₄	1	2	yes	—
121	#124×C₆₇	C₂×C₄	1	2	yes	—
122	#124×C₆₇	C₂×C₄	1	4	yes	—
123	#123×C₆₇	C₂×C₄	1	4	yes	—
124	#123×C₆₇	C₂×C₄	1	4	yes	—
125	#123×C₆₇	C₂×C₄	1	4	yes	—
126	#123×C₆₇	C₂×C₄	1	4	yes	—
127	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
128	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
129	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
130	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
131	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
132	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
133	#121×C₆₇	C₂×C₄	1	2	yes	—
134	#121×C₆₇	C₂×C₄	1	2	yes	—
135	#121×C₆₇	C₂×C₄	1	4	yes	—
136	#121×C₆₇	C₂×C₄	1	2	yes	—
137	#120×C₆₇	C₂×C₄	1	4	yes	—
138	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
140	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
142	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
143	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
145	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
146	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
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	4	yes	—
151	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₆₇	C₂³	1	2	yes	—
154	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₄×D₄×C₆₇	C₂³	1	4	yes	—
156	C₄×D₄×C₆₇	C₂³	1	4	yes	—
157	#117×C₆₇	C₂×C₄	1	4	yes	—
158	#117×C₆₇	C₂×C₄	1	2	yes	—
159	#117×C₆₇	C₂×C₄	1	2	yes	—
160	#117×C₆₇	C₂×C₄	1	4	yes	—
161	#117×C₆₇	C₂×C₄	1	2	yes	—
162	#117×C₆₇	C₂³	1	1	yes	characteristic
163	#117×C₆₇	C₂³	1	2	yes	—
164	#117×C₆₇	C₂³	1	4	yes	—
165	#117×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
178	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
180	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	4	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	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
187	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
188	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
199	#97×C₆₇	C₂³	1	2	yes	—
200	#97×C₆₇	C₂³	1	4	yes	—
201	#97×C₆₇	C₂³	1	4	yes	—
202	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
203	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₄×C₈×C₆₇	C₂³	1	2	yes	—
207	C₄×C₈×C₆₇	C₂³	1	4	yes	—
208	C₄×C₈×C₆₇	C₂³	1	4	yes	—
209	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
210	#41×C₆₇	—	2	8	no	—
211	#41×C₆₇	—	2	2	no	—
212	#41×C₆₇	—	2	2	no	—
213	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
214	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
215	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
218	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
219	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
220	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
221	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
222	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
223	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
227	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
234	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	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	1	yes	characteristic
239	M₁₆×C₆₇	—	2	2	no	—
240	M₁₆×C₆₇	—	2	4	no	—
241	M₁₆×C₆₇	—	2	2	no	—
242	M₁₆×C₆₇	—	4	4	no	—
243	M₁₆×C₆₇	—	4	4	no	—
244	C₂×C₈×C₆₇	—	2	2	no	—
245	C₂×C₈×C₆₇	—	2	4	no	—
246	C₂×C₈×C₆₇	—	2	2	no	—
247	C₂×C₈×C₆₇	—	4	2	no	—
248	C₂×C₈×C₆₇	—	4	2	no	—
249	C₂×C₈×C₆₇	—	4	2	no	—
250	C₂×C₈×C₆₇	—	4	2	no	—
251	C₂×C₈×C₆₇	—	4	4	no	—
252	C₂×C₈×C₆₇	—	4	4	no	—
253	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
254	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
257	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
258	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
259	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
263	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
264	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
265	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
266	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
267	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
268	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
269	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
270	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
271	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
272	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
273	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
274	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
276	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
278	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
279	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
280	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
281	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
282	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
283	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
284	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
285	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
286	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
287	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
288	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
289	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
290	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
291	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
293	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
294	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
295	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
296	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
297	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
298	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
299	C₄²×C₆₇	C₂⁴	1	2	yes	—
300	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄²×C₆₇	C₂⁴	1	4	yes	—
303	C₂³×C₆₇	—	2	4	no	—
304	C₂³×C₆₇	—	2	4	no	—
305	C₂³×C₆₇	—	4	2	no	—
306	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
307	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
308	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
309	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
310	Q₈×C₆₇	—	2	2	no	—
311	Q₈×C₆₇	—	2	4	no	—
312	Q₈×C₆₇	—	4	2	no	—
313	D₄×C₆₇	—	2	4	no	—
314	D₄×C₆₇	—	2	4	no	—
315	D₄×C₆₇	—	2	8	no	—
316	D₄×C₆₇	—	2	2	no	—
317	D₄×C₆₇	—	2	2	no	—
318	D₄×C₆₇	—	4	4	no	—
319	D₄×C₆₇	#131	1	4	yes	complemented
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	8	no	—
322	C₂×C₄×C₆₇	—	2	4	no	—
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	4	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	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	—	4	2	no	—
333	C₂×C₄×C₆₇	—	4	4	no	—
334	C₂×C₄×C₆₇	—	4	1	no	—
335	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
336	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
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	4	yes	—
342	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
343	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
345	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
346	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
348	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
349	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
350	C₈×C₆₇	—	2	1	no	—
351	C₈×C₆₇	—	2	1	no	—
352	C₈×C₆₇	—	2	2	no	—
353	C₈×C₆₇	—	2	2	no	—
354	C₈×C₆₇	—	2	2	no	—
355	C₈×C₆₇	—	2	4	no	—
356	C₈×C₆₇	—	2	1	no	—
357	C₈×C₆₇	—	2	1	no	—
358	C₈×C₆₇	—	2	2	no	—
359	C₂²×C₆₇	—	2	2	no	—
360	C₂²×C₆₇	—	2	1	no	—
361	C₂²×C₆₇	—	2	2	no	—
362	C₂²×C₆₇	—	2	1	no	—
363	C₂²×C₆₇	—	2	2	no	—
364	C₂²×C₆₇	—	2	2	no	—
365	C₂²×C₆₇	—	2	2	no	—
366	C₂²×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	2	2	no	—
368	C₂²×C₆₇	—	2	2	no	—
369	C₂²×C₆₇	—	4	8	no	—
370	C₂²×C₆₇	#520	1	2	yes	—
371	C₂²×C₆₇	C₂×#131	1	4	yes	—
372	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
373	C₄×C₆₇	—	2	2	no	—
374	C₄×C₆₇	—	2	2	no	—
375	C₄×C₆₇	—	2	2	no	—
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	1	no	—
378	C₄×C₆₇	—	2	4	no	—
379	C₄×C₆₇	—	2	1	no	—
380	C₄×C₆₇	—	2	2	no	—
381	C₄×C₆₇	—	2	4	no	—
382	C₄×C₆₇	—	2	1	no	—
383	C₄×C₆₇	#520	1	2	yes	—
384	C₄×C₆₇	C₂×#131	1	2	yes	—
385	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
386	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
387	#60271	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂×C₆₇	—	2	2	no	—
389	C₂×C₆₇	—	2	4	no	—
390	C₂×C₆₇	—	4	2	no	—
391	C₂×C₆₇	—	4	2	no	—
392	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
393	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
394	C₂×C₆₇	#3573	1	1	yes	characteristic
395	#3475	C₂×C₆₇	1	1	yes	characteristic
396	#2994	C₂×C₆₇	1	4	yes	complemented
397	#2994	C₂×C₆₇	1	2	yes	complemented
398	#2993	C₂×C₆₇	1	2	yes	complemented
399	#2992	C₂×C₆₇	1	4	yes	complemented
400	#2990	C₂×C₆₇	1	2	yes	complemented
401	#2988	C₂×C₆₇	1	2	yes	complemented
402	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
403	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
404	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
405	#2933	C₂×C₆₇	1	2	yes	complemented
406	#2929	C₂×C₆₇	1	2	yes	complemented
407	C₂×C₈×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
408	#2924	C₂×C₆₇	1	2	yes	complemented
409	#2922	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#2906	C₂×C₆₇	1	1	yes	characteristic, complemented
411	C₂×#424	C₂×C₆₇	1	2	yes	complemented
412	C₆₇	#60271	1	1	yes	characteristic, direct product factor, Sylow
413	C₂×#131	C₂²×C₆₇	1	2	yes	—
414	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
415	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
416	#556	C₄×C₆₇	1	1	yes	characteristic
417	#555	C₄×C₆₇	1	1	yes	characteristic
418	#554	C₄×C₆₇	1	1	yes	characteristic
419	#553	C₄×C₆₇	1	2	yes	—
420	#552	C₄×C₆₇	1	2	yes	—
421	#552	C₄×C₆₇	1	2	yes	—
422	#551	C₄×C₆₇	1	4	yes	—
423	#547	C₄×C₆₇	1	1	yes	characteristic
424	#546	C₄×C₆₇	1	2	yes	—
425	#533	C₂²×C₆₇	1	1	yes	characteristic
426	#529	C₂²×C₆₇	1	4	yes	—
427	#529	C₂²×C₆₇	1	2	yes	—
428	#525	C₂²×C₆₇	1	2	yes	—
429	C₄×#41	C₂²×C₆₇	1	2	yes	—
430	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×#117	C₂²×C₆₇	1	2	yes	—
433	#446	C₂²×C₆₇	1	2	yes	complemented
434	#446	C₂²×C₆₇	1	2	yes	complemented
435	#446	C₂²×C₆₇	1	2	yes	complemented
436	#446	C₂²×C₆₇	1	4	yes	complemented
437	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
438	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
439	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
440	#436	C₂²×C₆₇	1	2	yes	—
441	#436	C₂²×C₆₇	1	4	yes	complemented
442	#435	C₂²×C₆₇	1	4	yes	—
443	#435	C₂²×C₆₇	1	4	yes	complemented
444	#435	C₂²×C₆₇	1	4	yes	complemented
445	#435	C₂²×C₆₇	1	4	yes	complemented
446	#435	C₂²×C₆₇	1	4	yes	complemented
447	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
448	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
449	C₈×D₄	C₂²×C₆₇	1	2	yes	—
450	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
451	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
452	C₈×D₄	C₂²×C₆₇	1	2	yes	—
453	C₈×D₄	C₂²×C₆₇	1	2	yes	—
454	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
455	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
456	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
457	#433	C₂²×C₆₇	1	2	yes	complemented
458	#433	C₂²×C₆₇	1	2	yes	complemented
459	#433	C₂²×C₆₇	1	4	yes	complemented
460	#433	C₂²×C₆₇	1	4	yes	complemented
461	#432	C₂²×C₆₇	1	4	yes	complemented
462	#431	C₂²×C₆₇	1	2	yes	complemented
463	#431	C₂²×C₆₇	1	2	yes	complemented
464	#431	C₂²×C₆₇	1	4	yes	complemented
465	#424	C₂²×C₆₇	1	1	yes	characteristic
466	#424	C₂²×C₆₇	1	2	yes	—
467	#424	C₂²×C₆₇	1	2	yes	—
468	#424	C₂²×C₆₇	1	2	yes	—
469	#424	C₂²×C₆₇	1	1	yes	characteristic
470	#424	C₂²×C₆₇	1	4	yes	complemented
471	#424	C₂²×C₆₇	1	4	yes	complemented
472	#424	C₂²×C₆₇	1	4	yes	complemented
473	#423	C₂²×C₆₇	1	1	yes	characteristic
474	#423	C₂²×C₆₇	1	2	yes	complemented
475	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
477	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
478	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
479	#408	C₂²×C₆₇	1	1	yes	characteristic
480	#408	C₂²×C₆₇	1	1	yes	characteristic
481	#407	C₂²×C₆₇	1	2	yes	—
482	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
483	#405	C₂²×C₆₇	1	2	yes	—
484	#405	C₂²×C₆₇	1	2	yes	—
485	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
486	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
487	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
488	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
489	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
491	#131	—	4	4	no	—
492	C₂×M₁₆	—	4	4	no	—
493	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
495	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
497	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
498	C₂²×C₈	—	4	4	no	—
499	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
501	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
503	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
504	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
505	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
506	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
507	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
508	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
509	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
510	#126	C₂×C₄×C₆₇	1	4	yes	—
511	#126	C₂×C₄×C₆₇	1	4	yes	—
512	#126	C₂×C₄×C₆₇	1	4	yes	—
513	#125	C₂×C₄×C₆₇	1	4	yes	—
514	#125	C₂×C₄×C₆₇	1	2	yes	—
515	#125	C₂×C₄×C₆₇	1	2	yes	—
516	#124	C₂×C₄×C₆₇	1	2	yes	—
517	#124	C₂×C₄×C₆₇	1	4	yes	—
518	#123	C₂×C₄×C₆₇	1	4	yes	—
519	#123	C₂×C₄×C₆₇	1	4	yes	—
520	#123	C₂×C₄×C₆₇	1	4	yes	—
521	#123	C₂×C₄×C₆₇	1	4	yes	—
522	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
523	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
524	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
525	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
526	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
527	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
528	#121	C₂×C₄×C₆₇	1	2	yes	—
529	#121	C₂×C₄×C₆₇	1	2	yes	—
530	#121	C₂×C₄×C₆₇	1	4	yes	—
531	#121	C₂×C₄×C₆₇	1	2	yes	—
532	#120	C₂×C₄×C₆₇	1	4	yes	—
533	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
534	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
535	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
536	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
537	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
538	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
539	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
540	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
541	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
542	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
543	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
544	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
545	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
546	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
547	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
548	C₄×D₄	C₂³×C₆₇	1	2	yes	—
549	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
550	C₄×D₄	C₂³×C₆₇	1	4	yes	—
551	C₄×D₄	C₂³×C₆₇	1	4	yes	—
552	#117	C₂×C₄×C₆₇	1	4	yes	—
553	#117	C₂×C₄×C₆₇	1	2	yes	—
554	#117	C₂×C₄×C₆₇	1	2	yes	—
555	#117	C₂×C₄×C₆₇	1	4	yes	—
556	#117	C₂×C₄×C₆₇	1	2	yes	—
557	#117	C₂³×C₆₇	1	1	yes	characteristic
558	#117	C₂³×C₆₇	1	2	yes	—
559	#117	C₂³×C₆₇	1	4	yes	—
560	#117	C₂³×C₆₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
562	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
566	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
567	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
569	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
570	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
571	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
572	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
573	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
574	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
575	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
576	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
577	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
578	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
579	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
580	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
581	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
582	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
583	C₄⋊C₈	C₂³×C₆₇	1	2	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	2	yes	—
591	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
592	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
593	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
594	#97	C₂³×C₆₇	1	2	yes	—
595	#97	C₂³×C₆₇	1	4	yes	—
596	#97	C₂³×C₆₇	1	4	yes	—
597	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
602	C₄×C₈	C₂³×C₆₇	1	4	yes	—
603	C₄×C₈	C₂³×C₆₇	1	4	yes	—
604	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
605	#41	—	2	8	no	—
606	#41	—	2	2	no	—
607	#41	—	2	2	no	—
608	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
609	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
610	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
613	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
614	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
615	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
616	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
617	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
618	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
622	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
623	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
624	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
625	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
626	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
627	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
628	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
629	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
634	M₁₆	—	2	2	no	—
635	M₁₆	—	2	4	no	—
636	M₁₆	—	2	2	no	—
637	M₁₆	—	4	4	no	—
638	M₁₆	—	4	4	no	—
639	C₂×C₈	—	2	2	no	—
640	C₂×C₈	—	2	4	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	4	2	no	—
643	C₂×C₈	—	4	2	no	—
644	C₂×C₈	—	4	2	no	—
645	C₂×C₈	—	4	2	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	—	4	4	no	—
648	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
649	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
650	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
654	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
655	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
656	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
657	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
658	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
659	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
660	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
661	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
662	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
663	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
664	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
666	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
667	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
668	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
669	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
670	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
671	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
672	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
673	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
674	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
675	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
676	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
679	C₂²⋊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	2	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
688	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
689	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
690	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
691	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
692	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
693	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
694	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
695	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
696	C₄²	C₂⁴×C₆₇	1	4	yes	—
697	C₄²	C₂⁴×C₆₇	1	2	yes	—
698	C₂³	—	2	4	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	4	2	no	—
701	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
702	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
703	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
704	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	4	2	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	8	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	4	4	no	—
714	D₄	#131×C₆₇	1	4	yes	complemented
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	8	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
731	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
732	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
733	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
734	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
735	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
736	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
737	C₂×C₄	C₂³×C₄×C₆₇	1	4	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	1	yes	characteristic
741	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
742	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
743	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
744	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
745	C₈	—	2	1	no	—
746	C₈	—	2	1	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	4	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	2	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	8	no	—
765	C₂²	#520×C₆₇	1	2	yes	—
766	C₂²	C₂×#131×C₆₇	1	4	yes	—
767	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
768	C₄	—	2	2	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	4	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	2	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	#520×C₆₇	1	2	yes	—
779	C₄	C₂×#131×C₆₇	1	2	yes	—
780	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
781	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
782	C₂	—	2	2	no	—
783	C₂	—	2	4	no	—
784	C₂	—	4	2	no	—
785	C₂	—	4	2	no	—
786	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
787	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
788	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×#3475	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×#2994	C₂	semidirect
3. C₆₇×#2994	C₂	semidirect
4. C₆₇×#2993	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2990	C₂	semidirect
7. C₆₇×#2988	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×#2924	C₂	semidirect
15. C₆₇×#2922	C₂	semidirect
16. C₆₇×#2906	C₂	semidirect
17. C₂×#424×C₆₇	C₂	semidirect
38. #446×C₆₇	C₂²	semidirect
39. #446×C₆₇	C₂²	semidirect
40. #446×C₆₇	C₂²	semidirect
41. #446×C₆₇	C₂²	semidirect
42. C₈×Q₈×C₆₇	C₂²	semidirect
43. C₈×Q₈×C₆₇	C₂²	semidirect
44. C₈×Q₈×C₆₇	C₂²	semidirect
46. #436×C₆₇	C₂²	semidirect
48. #435×C₆₇	C₂²	semidirect
49. #435×C₆₇	C₂²	semidirect
50. #435×C₆₇	C₂²	semidirect
51. #435×C₆₇	C₂²	semidirect
59. C₈×D₄×C₆₇	C₂²	semidirect
60. C₈×D₄×C₆₇	C₂²	semidirect
61. C₈×D₄×C₆₇	C₂²	semidirect
62. #433×C₆₇	C₂²	semidirect
63. #433×C₆₇	C₂²	semidirect
64. #433×C₆₇	C₂²	semidirect
65. #433×C₆₇	C₂²	semidirect
66. #432×C₆₇	C₂²	semidirect
67. #431×C₆₇	C₂²	semidirect
68. #431×C₆₇	C₂²	semidirect
69. #431×C₆₇	C₂²	semidirect
75. #424×C₆₇	C₂²	semidirect
76. #424×C₆₇	C₂²	semidirect
77. #424×C₆₇	C₂²	semidirect
79. #423×C₆₇	C₂²	semidirect
81. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
82. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
83. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
319. D₄×C₆₇	#131	semidirect
387. #60271	C₆₇	direct (N × H)
396. #2994	C₂×C₆₇	semidirect
397. #2994	C₂×C₆₇	semidirect
398. #2993	C₂×C₆₇	semidirect
399. #2992	C₂×C₆₇	semidirect
400. #2990	C₂×C₆₇	semidirect
401. #2988	C₂×C₆₇	semidirect
402. #2962	C₂×C₆₇	semidirect
403. #2960	C₂×C₆₇	semidirect
404. D₄×M₁₆	C₂×C₆₇	semidirect
405. #2933	C₂×C₆₇	semidirect
406. #2929	C₂×C₆₇	semidirect
407. C₂×C₈×D₄	C₂×C₆₇	semidirect
408. #2924	C₂×C₆₇	semidirect
409. #2922	C₂×C₆₇	semidirect
410. #2906	C₂×C₆₇	semidirect
411. C₂×#424	C₂×C₆₇	semidirect
412. C₆₇	#60271	direct (N × H)
433. #446	C₂²×C₆₇	semidirect
434. #446	C₂²×C₆₇	semidirect
435. #446	C₂²×C₆₇	semidirect
436. #446	C₂²×C₆₇	semidirect
437. C₈×Q₈	C₂²×C₆₇	semidirect
438. C₈×Q₈	C₂²×C₆₇	semidirect
439. C₈×Q₈	C₂²×C₆₇	semidirect
441. #436	C₂²×C₆₇	semidirect
443. #435	C₂²×C₆₇	semidirect
444. #435	C₂²×C₆₇	semidirect
445. #435	C₂²×C₆₇	semidirect
446. #435	C₂²×C₆₇	semidirect
454. C₈×D₄	C₂²×C₆₇	semidirect
455. C₈×D₄	C₂²×C₆₇	semidirect
456. C₈×D₄	C₂²×C₆₇	semidirect
457. #433	C₂²×C₆₇	semidirect
458. #433	C₂²×C₆₇	semidirect
459. #433	C₂²×C₆₇	semidirect
460. #433	C₂²×C₆₇	semidirect
461. #432	C₂²×C₆₇	semidirect
462. #431	C₂²×C₆₇	semidirect
463. #431	C₂²×C₆₇	semidirect
464. #431	C₂²×C₆₇	semidirect
470. #424	C₂²×C₆₇	semidirect
471. #424	C₂²×C₆₇	semidirect
472. #424	C₂²×C₆₇	semidirect
474. #423	C₂²×C₆₇	semidirect
476. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
477. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
478. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
714. 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×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2990	2
C₆₇×#2988	2
C₆₇×#2962	2
C₆₇×#2960	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2929	2
C₂×C₈×D₄×C₆₇	2
C₆₇×#2924	2
C₆₇×#2922	2
C₆₇×#2906	2
C₂×#424×C₆₇	2
#60271	67

Subgroups — C67×#60271 #30739522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60271 #30739522