Subgroups — C₆₇×#60292 #30739543

Order 17152.

1806 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2991	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2990	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2989	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2988	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2986	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2979	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2976	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2969	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2966	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2925	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#533×C₆₇	C₄	1	1	yes	characteristic
15	#533×C₆₇	C₄	1	1	yes	characteristic
16	#533×C₆₇	C₂²	1	1	yes	characteristic
17	#532×C₆₇	C₄	1	1	yes	characteristic
18	#532×C₆₇	C₄	1	1	yes	characteristic
19	#532×C₆₇	C₂²	1	1	yes	characteristic
20	#529×C₆₇	C₄	1	2	yes	—
21	#529×C₆₇	C₄	1	2	yes	—
22	#529×C₆₇	C₄	1	2	yes	—
23	#529×C₆₇	C₄	1	2	yes	—
24	#529×C₆₇	C₂²	1	2	yes	—
25	#529×C₆₇	C₂²	1	2	yes	—
26	#525×C₆₇	C₄	1	2	yes	—
27	#525×C₆₇	C₄	1	2	yes	—
28	#525×C₆₇	C₂²	1	2	yes	—
29	C₄×#41×C₆₇	C₂²	1	2	yes	—
30	C₄×#41×C₆₇	C₂²	1	2	yes	—
31	C₄×#41×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#446×C₆₇	C₂²	1	4	yes	complemented
34	#446×C₆₇	C₂²	1	4	yes	complemented
35	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
36	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
37	#436×C₆₇	C₂²	1	8	yes	—
38	#436×C₆₇	C₂²	1	4	yes	complemented
39	#436×C₆₇	C₂²	1	4	yes	complemented
40	#435×C₆₇	C₂²	1	8	yes	—
41	#435×C₆₇	C₂²	1	8	yes	—
42	C₈×D₄×C₆₇	C₂²	1	8	yes	—
43	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
44	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
45	#433×C₆₇	C₂²	1	8	yes	—
46	#433×C₆₇	C₂²	1	8	yes	complemented
47	#432×C₆₇	C₂²	1	2	yes	—
48	#432×C₆₇	C₂²	1	2	yes	—
49	#432×C₆₇	C₂²	1	4	yes	complemented
50	#431×C₆₇	C₂²	1	2	yes	—
51	#431×C₆₇	C₂²	1	2	yes	—
52	#431×C₆₇	C₂²	1	2	yes	—
53	#431×C₆₇	C₂²	1	2	yes	—
54	#431×C₆₇	C₂²	1	2	yes	—
55	#431×C₆₇	C₂²	1	2	yes	—
56	#431×C₆₇	C₂²	1	4	yes	complemented
57	#423×C₆₇	C₂²	1	1	yes	characteristic
58	#423×C₆₇	C₂²	1	1	yes	characteristic
59	#423×C₆₇	C₂²	1	4	yes	complemented
60	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
63	#408×C₆₇	C₂²	1	8	yes	—
64	#407×C₆₇	C₂²	1	2	yes	—
65	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
66	#405×C₆₇	C₂²	1	8	yes	complemented
67	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
68	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
69	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
70	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
71	C₂×#41×C₆₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
76	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
77	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
78	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
79	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
81	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
84	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
85	#126×C₆₇	C₂×C₄	1	4	yes	—
86	#126×C₆₇	C₂×C₄	1	4	yes	—
87	#125×C₆₇	C₂×C₄	1	2	yes	—
88	#125×C₆₇	C₂×C₄	1	2	yes	—
89	#125×C₆₇	C₂×C₄	1	2	yes	—
90	#124×C₆₇	C₂×C₄	1	2	yes	—
91	#124×C₆₇	C₂×C₄	1	2	yes	—
92	#124×C₆₇	C₂×C₄	1	2	yes	—
93	#123×C₆₇	C₂×C₄	1	4	yes	—
94	#123×C₆₇	C₂×C₄	1	4	yes	—
95	#123×C₆₇	C₂×C₄	1	4	yes	—
96	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
97	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
98	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
99	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
100	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
101	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
102	#121×C₆₇	C₂×C₄	1	2	yes	—
103	#121×C₆₇	C₂×C₄	1	2	yes	—
104	#121×C₆₇	C₂×C₄	1	2	yes	—
105	#121×C₆₇	C₂×C₄	1	2	yes	—
106	#121×C₆₇	C₂×C₄	1	2	yes	—
107	#121×C₆₇	C₂×C₄	1	2	yes	—
108	#120×C₆₇	C₂×C₄	1	4	yes	—
109	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
110	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
111	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
112	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
113	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
114	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
115	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
116	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
117	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
118	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
119	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
120	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
121	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
122	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
123	C₄×D₄×C₆₇	C₂³	1	4	yes	—
124	C₄×D₄×C₆₇	C₂³	1	4	yes	—
125	C₄×D₄×C₆₇	C₂³	1	2	yes	—
126	C₄×D₄×C₆₇	C₂³	1	2	yes	—
127	#117×C₆₇	C₂×C₄	1	2	yes	—
128	#117×C₆₇	C₂×C₄	1	2	yes	—
129	#117×C₆₇	C₂×C₄	1	4	yes	—
130	#117×C₆₇	C₂×C₄	1	4	yes	—
131	#117×C₆₇	C₂³	1	2	yes	—
132	#117×C₆₇	C₂³	1	4	yes	—
133	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
146	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
147	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
148	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
149	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
150	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
151	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
152	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
153	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
155	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
156	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
157	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
158	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
160	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
161	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
162	#97×C₆₇	C₂³	1	4	yes	—
163	#97×C₆₇	C₂³	1	8	yes	—
164	C₄×C₈×C₆₇	C₂³	1	4	yes	—
165	C₄×C₈×C₆₇	C₂³	1	4	yes	—
166	C₄×C₈×C₆₇	C₂³	1	4	yes	—
167	C₄×C₈×C₆₇	C₂³	1	8	yes	—
168	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	#41×C₆₇	—	2	8	no	—
170	#41×C₆₇	—	4	2	no	—
171	#41×C₆₇	—	4	2	no	—
172	#41×C₆₇	—	4	4	no	—
173	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
174	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
175	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
176	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
177	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
178	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
179	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
181	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₆₇	—	2	4	no	—
183	C₂²×C₄×C₆₇	—	4	2	no	—
184	C₂²×C₄×C₆₇	—	4	1	no	—
185	C₂²×C₄×C₆₇	—	4	1	no	—
186	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
207	M₁₆×C₆₇	—	4	2	no	—
208	M₁₆×C₆₇	—	4	8	no	—
209	M₁₆×C₆₇	—	4	2	no	—
210	C₂×C₈×C₆₇	—	4	2	no	—
211	C₂×C₈×C₆₇	—	4	8	no	—
212	C₂×C₈×C₆₇	—	4	2	no	—
213	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
214	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
215	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
216	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
217	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
224	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
225	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
226	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
227	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
228	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
229	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
230	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
233	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
234	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
235	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
236	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
238	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
250	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
251	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
252	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₄²×C₆₇	C₂⁴	1	4	yes	—
256	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	—	4	1	no	—
259	C₂³×C₆₇	—	4	1	no	—
260	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
261	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
262	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
263	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
264	Q₈×C₆₇	—	2	4	no	—
265	Q₈×C₆₇	—	2	4	no	—
266	Q₈×C₆₇	—	4	2	no	—
267	D₄×C₆₇	—	2	8	no	—
268	D₄×C₆₇	—	2	4	no	—
269	D₄×C₆₇	—	2	4	no	—
270	D₄×C₆₇	—	4	2	no	—
271	D₄×C₆₇	—	4	4	no	—
272	D₄×C₆₇	—	4	4	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	8	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	1	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	2	1	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	1	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	4	1	no	—
291	C₂×C₄×C₆₇	—	4	1	no	—
292	C₂×C₄×C₆₇	—	4	1	no	—
293	C₂×C₄×C₆₇	—	4	1	no	—
294	C₂×C₄×C₆₇	—	4	1	no	—
295	C₂×C₄×C₆₇	—	4	1	no	—
296	C₂×C₄×C₆₇	—	4	4	no	—
297	C₂×C₄×C₆₇	#131	1	4	yes	—
298	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
303	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
309	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
310	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
311	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
312	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
313	C₈×C₆₇	—	2	4	no	—
314	C₈×C₆₇	—	2	4	no	—
315	C₈×C₆₇	—	2	4	no	—
316	C₈×C₆₇	—	2	4	no	—
317	C₂²×C₆₇	—	2	1	no	—
318	C₂²×C₆₇	—	2	1	no	—
319	C₂²×C₆₇	—	2	1	no	—
320	C₂²×C₆₇	—	2	1	no	—
321	C₂²×C₆₇	—	2	4	no	—
322	C₂²×C₆₇	—	2	1	no	—
323	C₂²×C₆₇	—	2	1	no	—
324	C₂²×C₆₇	—	2	4	no	—
325	C₂²×C₆₇	—	2	1	no	—
326	C₂²×C₆₇	—	2	1	no	—
327	C₂²×C₆₇	—	2	4	no	—
328	C₂²×C₆₇	—	4	4	no	—
329	C₂²×C₆₇	C₂×#131	1	2	yes	—
330	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
331	C₄×C₆₇	—	2	1	no	—
332	C₄×C₆₇	—	2	1	no	—
333	C₄×C₆₇	—	2	1	no	—
334	C₄×C₆₇	—	2	4	no	—
335	C₄×C₆₇	—	2	1	no	—
336	C₄×C₆₇	—	2	1	no	—
337	C₄×C₆₇	—	2	4	no	—
338	C₄×C₆₇	—	2	1	no	—
339	C₄×C₆₇	—	2	1	no	—
340	C₄×C₆₇	—	2	1	no	—
341	C₄×C₆₇	—	2	4	no	—
342	C₄×C₆₇	C₂×#131	1	2	yes	—
343	C₄×C₆₇	C₂×#131	1	2	yes	—
344	C₄×C₆₇	#568	1	2	yes	—
345	C₄×C₆₇	#585	1	1	yes	characteristic
346	C₄×C₆₇	#585	1	1	yes	characteristic
347	#60292	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂×C₆₇	—	2	2	no	—
349	C₂×C₆₇	—	4	4	no	—
350	C₂×C₆₇	—	4	1	no	—
351	C₂×C₆₇	—	4	1	no	—
352	C₂×C₆₇	#3428	1	1	yes	characteristic
353	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
354	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
355	#3444	C₂×C₆₇	1	1	yes	characteristic
356	#2991	C₂×C₆₇	1	2	yes	complemented
357	#2990	C₂×C₆₇	1	2	yes	complemented
358	#2989	C₂×C₆₇	1	2	yes	complemented
359	#2988	C₂×C₆₇	1	2	yes	complemented
360	#2986	C₂×C₆₇	1	2	yes	complemented
361	#2979	C₂×C₆₇	1	2	yes	complemented
362	#2976	C₂×C₆₇	1	4	yes	complemented
363	#2969	C₂×C₆₇	1	4	yes	complemented
364	#2966	C₂×C₆₇	1	4	yes	complemented
365	#2925	C₂×C₆₇	1	4	yes	complemented
366	#2920	C₂×C₆₇	1	1	yes	characteristic, complemented
367	C₂×#431	C₂×C₆₇	1	1	yes	characteristic, complemented
368	C₆₇	#60292	1	1	yes	characteristic, direct product factor, Sylow
369	#533	C₄×C₆₇	1	1	yes	characteristic
370	#533	C₄×C₆₇	1	1	yes	characteristic
371	#533	C₂²×C₆₇	1	1	yes	characteristic
372	#532	C₄×C₆₇	1	1	yes	characteristic
373	#532	C₄×C₆₇	1	1	yes	characteristic
374	#532	C₂²×C₆₇	1	1	yes	characteristic
375	#529	C₄×C₆₇	1	2	yes	—
376	#529	C₄×C₆₇	1	2	yes	—
377	#529	C₄×C₆₇	1	2	yes	—
378	#529	C₄×C₆₇	1	2	yes	—
379	#529	C₂²×C₆₇	1	2	yes	—
380	#529	C₂²×C₆₇	1	2	yes	—
381	#525	C₄×C₆₇	1	2	yes	—
382	#525	C₄×C₆₇	1	2	yes	—
383	#525	C₂²×C₆₇	1	2	yes	—
384	C₄×#41	C₂²×C₆₇	1	2	yes	—
385	C₄×#41	C₂²×C₆₇	1	2	yes	—
386	C₄×#41	C₂²×C₆₇	1	2	yes	—
387	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
388	#446	C₂²×C₆₇	1	4	yes	complemented
389	#446	C₂²×C₆₇	1	4	yes	complemented
390	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
391	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
392	#436	C₂²×C₆₇	1	8	yes	—
393	#436	C₂²×C₆₇	1	4	yes	complemented
394	#436	C₂²×C₆₇	1	4	yes	complemented
395	#435	C₂²×C₆₇	1	8	yes	—
396	#435	C₂²×C₆₇	1	8	yes	—
397	C₈×D₄	C₂²×C₆₇	1	8	yes	—
398	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
399	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
400	#433	C₂²×C₆₇	1	8	yes	—
401	#433	C₂²×C₆₇	1	8	yes	complemented
402	#432	C₂²×C₆₇	1	2	yes	—
403	#432	C₂²×C₆₇	1	2	yes	—
404	#432	C₂²×C₆₇	1	4	yes	complemented
405	#431	C₂²×C₆₇	1	2	yes	—
406	#431	C₂²×C₆₇	1	2	yes	—
407	#431	C₂²×C₆₇	1	2	yes	—
408	#431	C₂²×C₆₇	1	2	yes	—
409	#431	C₂²×C₆₇	1	2	yes	—
410	#431	C₂²×C₆₇	1	2	yes	—
411	#431	C₂²×C₆₇	1	4	yes	complemented
412	#423	C₂²×C₆₇	1	1	yes	characteristic
413	#423	C₂²×C₆₇	1	1	yes	characteristic
414	#423	C₂²×C₆₇	1	4	yes	complemented
415	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
418	#408	C₂²×C₆₇	1	8	yes	—
419	#407	C₂²×C₆₇	1	2	yes	—
420	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
421	#405	C₂²×C₆₇	1	8	yes	complemented
422	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
423	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
424	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
425	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
426	C₂×#41	C₂³×C₆₇	1	2	yes	—
427	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
428	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
430	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
431	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
432	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
433	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
434	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
435	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
436	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
437	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
438	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
439	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
440	#126	C₂×C₄×C₆₇	1	4	yes	—
441	#126	C₂×C₄×C₆₇	1	4	yes	—
442	#125	C₂×C₄×C₆₇	1	2	yes	—
443	#125	C₂×C₄×C₆₇	1	2	yes	—
444	#125	C₂×C₄×C₆₇	1	2	yes	—
445	#124	C₂×C₄×C₆₇	1	2	yes	—
446	#124	C₂×C₄×C₆₇	1	2	yes	—
447	#124	C₂×C₄×C₆₇	1	2	yes	—
448	#123	C₂×C₄×C₆₇	1	4	yes	—
449	#123	C₂×C₄×C₆₇	1	4	yes	—
450	#123	C₂×C₄×C₆₇	1	4	yes	—
451	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
452	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
455	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
456	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
457	#121	C₂×C₄×C₆₇	1	2	yes	—
458	#121	C₂×C₄×C₆₇	1	2	yes	—
459	#121	C₂×C₄×C₆₇	1	2	yes	—
460	#121	C₂×C₄×C₆₇	1	2	yes	—
461	#121	C₂×C₄×C₆₇	1	2	yes	—
462	#121	C₂×C₄×C₆₇	1	2	yes	—
463	#120	C₂×C₄×C₆₇	1	4	yes	—
464	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
465	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
466	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
467	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
468	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
469	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
470	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
471	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
472	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
473	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
474	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
475	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
476	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
477	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
478	C₄×D₄	C₂³×C₆₇	1	4	yes	—
479	C₄×D₄	C₂³×C₆₇	1	4	yes	—
480	C₄×D₄	C₂³×C₆₇	1	2	yes	—
481	C₄×D₄	C₂³×C₆₇	1	2	yes	—
482	#117	C₂×C₄×C₆₇	1	2	yes	—
483	#117	C₂×C₄×C₆₇	1	2	yes	—
484	#117	C₂×C₄×C₆₇	1	4	yes	—
485	#117	C₂×C₄×C₆₇	1	4	yes	—
486	#117	C₂³×C₆₇	1	2	yes	—
487	#117	C₂³×C₆₇	1	4	yes	—
488	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
489	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
490	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
491	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
492	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
493	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
495	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
501	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
502	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
503	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
504	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
505	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
506	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
507	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
508	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
509	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
510	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
511	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
512	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
513	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
514	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
515	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
516	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
517	#97	C₂³×C₆₇	1	4	yes	—
518	#97	C₂³×C₆₇	1	8	yes	—
519	C₄×C₈	C₂³×C₆₇	1	4	yes	—
520	C₄×C₈	C₂³×C₆₇	1	4	yes	—
521	C₄×C₈	C₂³×C₆₇	1	4	yes	—
522	C₄×C₈	C₂³×C₆₇	1	8	yes	—
523	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
524	#41	—	2	8	no	—
525	#41	—	4	2	no	—
526	#41	—	4	2	no	—
527	#41	—	4	4	no	—
528	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
529	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
530	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
531	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
532	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
533	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
534	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
535	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
536	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
550	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
554	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
555	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
556	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
557	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
562	M₁₆	—	4	2	no	—
563	M₁₆	—	4	8	no	—
564	M₁₆	—	4	2	no	—
565	C₂×C₈	—	4	2	no	—
566	C₂×C₈	—	4	8	no	—
567	C₂×C₈	—	4	2	no	—
568	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
569	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
570	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
571	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
573	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
574	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
577	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
578	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
579	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
580	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
581	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
582	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
583	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
590	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
591	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
592	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
593	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
595	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
596	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
597	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
598	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
599	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
600	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
601	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
602	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
603	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
604	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
605	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
606	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
607	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
608	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
609	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
610	C₄²	C₂⁴×C₆₇	1	4	yes	—
611	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
612	C₂³	—	2	2	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
616	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
617	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
618	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
619	Q₈	—	2	4	no	—
620	Q₈	—	2	4	no	—
621	Q₈	—	4	2	no	—
622	D₄	—	2	8	no	—
623	D₄	—	2	4	no	—
624	D₄	—	2	4	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	#131×C₆₇	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
654	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
655	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
657	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
658	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
659	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
660	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
661	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
662	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
663	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
664	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
665	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
666	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
667	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
668	C₈	—	2	4	no	—
669	C₈	—	2	4	no	—
670	C₈	—	2	4	no	—
671	C₈	—	2	4	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	C₂×#131×C₆₇	1	2	yes	—
685	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	4	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	4	no	—
697	C₄	C₂×#131×C₆₇	1	2	yes	—
698	C₄	C₂×#131×C₆₇	1	2	yes	—
699	C₄	#568×C₆₇	1	2	yes	—
700	C₄	#585×C₆₇	1	1	yes	characteristic
701	C₄	#585×C₆₇	1	1	yes	characteristic
702	C₂	—	2	2	no	—
703	C₂	—	4	1	no	—
704	C₂	—	4	1	no	—
705	C₂	—	4	4	no	—
706	C₂	C₆₇×#3428	1	1	yes	characteristic
707	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
708	C₂	C₂×#568×C₆₇	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×#3444	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×#2991	C₂	semidirect
3. C₆₇×#2990	C₂	semidirect
4. C₆₇×#2989	C₂	semidirect
5. C₆₇×#2988	C₂	semidirect
6. C₆₇×#2986	C₂	semidirect
7. C₆₇×#2979	C₂	semidirect
8. C₆₇×#2976	C₂	semidirect
9. C₆₇×#2969	C₂	semidirect
10. C₆₇×#2966	C₂	semidirect
11. C₆₇×#2925	C₂	semidirect
12. C₆₇×#2920	C₂	semidirect
13. C₂×#431×C₆₇	C₂	semidirect
33. #446×C₆₇	C₂²	semidirect
34. #446×C₆₇	C₂²	semidirect
35. C₈×Q₈×C₆₇	C₂²	semidirect
36. C₈×Q₈×C₆₇	C₂²	semidirect
38. #436×C₆₇	C₂²	semidirect
39. #436×C₆₇	C₂²	semidirect
43. C₈×D₄×C₆₇	C₂²	semidirect
44. C₈×D₄×C₆₇	C₂²	semidirect
46. #433×C₆₇	C₂²	semidirect
49. #432×C₆₇	C₂²	semidirect
56. #431×C₆₇	C₂²	semidirect
59. #423×C₆₇	C₂²	semidirect
62. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
66. #405×C₆₇	C₂²	semidirect
347. #60292	C₆₇	direct (N × H)
356. #2991	C₂×C₆₇	semidirect
357. #2990	C₂×C₆₇	semidirect
358. #2989	C₂×C₆₇	semidirect
359. #2988	C₂×C₆₇	semidirect
360. #2986	C₂×C₆₇	semidirect
361. #2979	C₂×C₆₇	semidirect
362. #2976	C₂×C₆₇	semidirect
363. #2969	C₂×C₆₇	semidirect
364. #2966	C₂×C₆₇	semidirect
365. #2925	C₂×C₆₇	semidirect
366. #2920	C₂×C₆₇	semidirect
367. C₂×#431	C₂×C₆₇	semidirect
368. C₆₇	#60292	direct (N × H)
388. #446	C₂²×C₆₇	semidirect
389. #446	C₂²×C₆₇	semidirect
390. C₈×Q₈	C₂²×C₆₇	semidirect
391. C₈×Q₈	C₂²×C₆₇	semidirect
393. #436	C₂²×C₆₇	semidirect
394. #436	C₂²×C₆₇	semidirect
398. C₈×D₄	C₂²×C₆₇	semidirect
399. C₈×D₄	C₂²×C₆₇	semidirect
401. #433	C₂²×C₆₇	semidirect
404. #432	C₂²×C₆₇	semidirect
411. #431	C₂²×C₆₇	semidirect
414. #423	C₂²×C₆₇	semidirect
417. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
421. #405	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×#3444	2
C₆₇×#2991	2
C₆₇×#2990	2
C₆₇×#2989	2
C₆₇×#2988	2
C₆₇×#2986	2
C₆₇×#2979	2
C₆₇×#2976	2
C₆₇×#2969	2
C₆₇×#2966	2
C₆₇×#2925	2
C₆₇×#2920	2
C₂×#431×C₆₇	2
#60292	67

Subgroups — C67×#60292 #30739543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60292 #30739543