Subgroups — C₆₇×#35130 #30714381

Order 17152.

2486 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2851	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2850	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2637	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2636	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2609	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2580	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2535	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2498	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2430	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2417	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2416	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2325	C₂	1	4	yes	maximal, complemented
17	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	#529×C₆₇	—	2	8	no	—
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×#121×C₆₇	C₂²	1	4	yes	—
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₄×#41×C₆₇	—	2	8	no	—
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₇	C₂²	1	2	yes	—
41	C₂×#117×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
44	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
45	#400×C₆₇	C₂²	1	2	yes	—
46	#399×C₆₇	C₂²	1	2	yes	—
47	#398×C₆₇	C₂²	1	2	yes	—
48	#398×C₆₇	C₂²	1	4	yes	—
49	#397×C₆₇	C₂²	1	2	yes	—
50	#396×C₆₇	C₂²	1	4	yes	—
51	#396×C₆₇	C₂²	1	4	yes	—
52	#395×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#394×C₆₇	C₂²	1	4	yes	—
55	#393×C₆₇	C₂²	1	2	yes	—
56	#392×C₆₇	C₂²	1	2	yes	—
57	#391×C₆₇	C₂²	1	2	yes	—
58	#390×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	2	yes	—
61	#388×C₆₇	C₂²	1	4	yes	—
62	#388×C₆₇	C₂²	1	4	yes	—
63	#388×C₆₇	C₂²	1	4	yes	—
64	#387×C₆₇	C₂²	1	4	yes	—
65	#387×C₆₇	C₂²	1	4	yes	—
66	#387×C₆₇	C₂²	1	4	yes	—
67	#386×C₆₇	C₂²	1	4	yes	—
68	#386×C₆₇	C₂²	1	4	yes	—
69	#386×C₆₇	C₂²	1	4	yes	—
70	#386×C₆₇	C₂²	1	4	yes	—
71	#386×C₆₇	C₂²	1	4	yes	—
72	#385×C₆₇	C₂²	1	4	yes	—
73	#385×C₆₇	C₂²	1	4	yes	—
74	#385×C₆₇	C₂²	1	4	yes	—
75	#382×C₆₇	C₂²	1	1	yes	characteristic
76	#382×C₆₇	C₂²	1	1	yes	characteristic
77	#382×C₆₇	C₂²	1	2	yes	—
78	#382×C₆₇	C₂²	1	2	yes	—
79	#382×C₆₇	C₂²	1	2	yes	—
80	#380×C₆₇	C₂²	1	4	yes	—
81	#380×C₆₇	C₂²	1	2	yes	—
82	#380×C₆₇	C₂²	1	2	yes	—
83	C₂×#95×C₆₇	C₂²	1	2	yes	—
84	C₂×#95×C₆₇	C₂²	1	2	yes	—
85	C₂×#41×C₆₇	—	2	8	no	—
86	C₂×#41×C₆₇	—	2	4	no	—
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
94	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	#126×C₆₇	—	2	8	no	—
103	#125×C₆₇	—	2	4	no	—
104	#124×C₆₇	—	2	4	no	—
105	#123×C₆₇	—	2	8	no	—
106	C₂²⋊Q₈×C₆₇	—	2	4	no	—
107	C₂²⋊Q₈×C₆₇	—	4	4	no	—
108	#121×C₆₇	—	2	16	no	—
109	#121×C₆₇	—	2	4	no	—
110	#121×C₆₇	—	4	4	no	—
111	C₄×Q₈×C₆₇	—	2	4	no	—
112	C₄×Q₈×C₆₇	—	2	4	no	—
113	C₄×Q₈×C₆₇	—	2	4	no	—
114	C₄×D₄×C₆₇	—	2	8	no	—
115	C₄×D₄×C₆₇	—	2	8	no	—
116	C₄×D₄×C₆₇	—	2	8	no	—
117	C₄×D₄×C₆₇	—	2	4	no	—
118	C₄×D₄×C₆₇	—	2	4	no	—
119	C₄×D₄×C₆₇	—	2	4	no	—
120	#117×C₆₇	—	2	4	no	—
121	#117×C₆₇	—	2	8	no	—
122	#117×C₆₇	—	2	8	no	—
123	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
154	C₂×C₄²×C₆₇	—	2	8	no	—
155	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
156	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	#95×C₆₇	C₂³	1	2	yes	—
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	4	yes	—
167	#95×C₆₇	C₂³	1	2	yes	—
168	#95×C₆₇	C₂³	1	2	yes	—
169	#95×C₆₇	C₂³	1	2	yes	—
170	#95×C₆₇	C₂³	1	4	yes	—
171	#95×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	#95×C₆₇	C₂³	1	4	yes	—
175	#95×C₆₇	C₂³	1	4	yes	—
176	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
177	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
178	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
179	#41×C₆₇	—	2	32	no	—
180	C₂×Q₈×C₆₇	—	2	2	no	—
181	C₂×Q₈×C₆₇	—	2	2	no	—
182	C₂×Q₈×C₆₇	—	2	4	no	—
183	C₂×Q₈×C₆₇	—	2	2	no	—
184	C₂×Q₈×C₆₇	—	2	2	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	4	no	—
187	C₂×D₄×C₆₇	—	2	4	no	—
188	C₂×D₄×C₆₇	—	2	4	no	—
189	C₂×D₄×C₆₇	—	2	8	no	—
190	C₂×D₄×C₆₇	—	2	8	no	—
191	C₂×D₄×C₆₇	—	2	2	no	—
192	C₂×D₄×C₆₇	—	2	2	no	—
193	C₂×D₄×C₆₇	—	2	2	no	—
194	C₂×D₄×C₆₇	—	2	2	no	—
195	C₂×D₄×C₆₇	—	4	4	no	—
196	C₂×D₄×C₆₇	—	4	4	no	—
197	C₂×D₄×C₆₇	#41	1	8	yes	—
198	C₂²×C₄×C₆₇	—	2	4	no	—
199	C₂²×C₄×C₆₇	—	2	4	no	—
200	C₂²×C₄×C₆₇	—	2	4	no	—
201	C₂²×C₄×C₆₇	—	2	4	no	—
202	C₂²×C₄×C₆₇	—	2	2	no	—
203	C₂²×C₄×C₆₇	—	2	2	no	—
204	C₂²×C₄×C₆₇	—	2	8	no	—
205	C₂²×C₄×C₆₇	—	2	4	no	—
206	C₂²×C₄×C₆₇	—	2	4	no	—
207	C₂²×C₄×C₆₇	—	2	4	no	—
208	C₂²×C₄×C₆₇	—	2	4	no	—
209	C₂²×C₄×C₆₇	—	2	4	no	—
210	C₂²×C₄×C₆₇	—	4	2	no	—
211	C₂²×C₄×C₆₇	—	4	2	no	—
212	C₂²×C₄×C₆₇	—	4	4	no	—
213	C₂²×C₄×C₆₇	—	4	2	no	—
214	C₂²×C₄×C₆₇	—	4	4	no	—
215	C₂²×C₄×C₆₇	—	4	4	no	—
216	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	2	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	2	no	—
242	C₄⋊C₄×C₆₇	—	2	4	no	—
243	C₄⋊C₄×C₆₇	—	2	8	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	4	no	—
246	C₄⋊C₄×C₆₇	—	4	4	no	—
247	C₄⋊C₄×C₆₇	—	4	4	no	—
248	C₄⋊C₄×C₆₇	—	4	4	no	—
249	C₂²⋊C₄×C₆₇	—	2	4	no	—
250	C₂²⋊C₄×C₆₇	—	2	4	no	—
251	C₂²⋊C₄×C₆₇	—	2	8	no	—
252	C₂²⋊C₄×C₆₇	—	2	4	no	—
253	C₂²⋊C₄×C₆₇	—	2	4	no	—
254	C₂²⋊C₄×C₆₇	—	2	4	no	—
255	C₂²⋊C₄×C₆₇	—	2	4	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	8	no	—
259	C₂²⋊C₄×C₆₇	—	4	4	no	—
260	C₂²⋊C₄×C₆₇	—	4	4	no	—
261	C₂²⋊C₄×C₆₇	—	4	4	no	—
262	C₂²⋊C₄×C₆₇	—	4	4	no	—
263	C₄²×C₆₇	—	2	4	no	—
264	C₄²×C₆₇	—	2	4	no	—
265	C₄²×C₆₇	—	2	4	no	—
266	C₄²×C₆₇	—	2	4	no	—
267	C₄²×C₆₇	C₂×D₄	1	4	yes	—
268	C₄²×C₆₇	C₂×D₄	1	4	yes	—
269	C₄²×C₆₇	C₂×D₄	1	4	yes	—
270	C₄²×C₆₇	C₂×D₄	1	4	yes	—
271	C₂³×C₆₇	—	2	1	no	—
272	C₂³×C₆₇	—	2	1	no	—
273	C₂³×C₆₇	—	2	2	no	—
274	C₂³×C₆₇	—	2	2	no	—
275	C₂³×C₆₇	—	2	2	no	—
276	C₂³×C₆₇	—	2	2	no	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	2	4	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	4	no	—
285	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
286	C₂³×C₆₇	C₂×#41	1	4	yes	—
287	C₂³×C₆₇	C₂×#41	1	4	yes	—
288	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
289	Q₈×C₆₇	—	2	8	no	—
290	Q₈×C₆₇	—	4	4	no	—
291	D₄×C₆₇	—	2	8	no	—
292	D₄×C₆₇	—	2	16	no	—
293	D₄×C₆₇	—	4	8	no	—
294	D₄×C₆₇	—	4	4	no	—
295	D₄×C₆₇	—	8	8	no	—
296	C₂×C₄×C₆₇	—	2	16	no	—
297	C₂×C₄×C₆₇	—	2	8	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	8	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	4	no	—
313	C₂×C₄×C₆₇	—	2	4	no	—
314	C₂×C₄×C₆₇	—	2	4	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	4	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	4	no	—
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	4	4	no	—
327	C₂×C₄×C₆₇	—	4	8	no	—
328	C₂×C₄×C₆₇	—	4	8	no	—
329	C₂×C₄×C₆₇	—	4	8	no	—
330	C₂×C₄×C₆₇	—	8	8	no	—
331	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
338	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
339	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
340	C₂²×C₆₇	—	2	2	no	—
341	C₂²×C₆₇	—	2	2	no	—
342	C₂²×C₆₇	—	2	4	no	—
343	C₂²×C₆₇	—	2	4	no	—
344	C₂²×C₆₇	—	2	4	no	—
345	C₂²×C₆₇	—	2	4	no	—
346	C₂²×C₆₇	—	2	4	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	2	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	4	no	—
355	C₂²×C₆₇	—	4	4	no	—
356	C₂²×C₆₇	#525	1	4	yes	—
357	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
358	C₂²×C₆₇	C₂²×#41	1	2	yes	—
359	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₂²×C₆₇	#585	1	2	yes	—
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	2	2	no	—
364	C₄×C₆₇	—	2	4	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	2	2	no	—
367	C₄×C₆₇	—	2	2	no	—
368	C₄×C₆₇	—	4	2	no	—
369	C₄×C₆₇	—	4	2	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	4	no	—
374	C₄×C₆₇	—	4	4	no	—
375	C₄×C₆₇	#537	1	4	yes	—
376	#35130	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂×C₆₇	—	2	4	no	—
378	C₂×C₆₇	—	4	4	no	—
379	C₂×C₆₇	—	8	2	no	—
380	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
381	C₂×C₆₇	C₂×#537	1	1	yes	characteristic
382	C₂×C₆₇	#3449	1	1	yes	characteristic
383	C₂×C₆₇	#3514	1	2	yes	—
384	C₂×C₆₇	#3515	1	2	yes	—
385	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
387	#2851	C₂×C₆₇	1	2	yes	complemented
388	#2850	C₂×C₆₇	1	2	yes	complemented
389	#2637	C₂×C₆₇	1	2	yes	complemented
390	#2636	C₂×C₆₇	1	2	yes	complemented
391	#2609	C₂×C₆₇	1	4	yes	complemented
392	#2581	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#2580	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#2536	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#2535	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#2498	C₂×C₆₇	1	2	yes	complemented
397	#2430	C₂×C₆₇	1	2	yes	complemented
398	#2417	C₂×C₆₇	1	2	yes	complemented
399	#2416	C₂×C₆₇	1	2	yes	complemented
400	#2325	C₂×C₆₇	1	4	yes	complemented
401	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₆₇	#35130	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
404	#529	—	2	8	no	—
405	C₂×#126	C₂²×C₆₇	1	2	yes	—
406	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
408	C₂×#123	C₂²×C₆₇	1	2	yes	—
409	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
410	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
411	C₂×#121	C₂²×C₆₇	1	4	yes	—
412	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
413	C₂×#121	C₂²×C₆₇	1	2	yes	—
414	C₄×#41	—	2	8	no	—
415	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
423	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×#117	C₂²×C₆₇	1	2	yes	—
425	C₂×#117	C₂²×C₆₇	1	2	yes	—
426	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
427	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
428	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
429	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
430	#400	C₂²×C₆₇	1	2	yes	—
431	#399	C₂²×C₆₇	1	2	yes	—
432	#398	C₂²×C₆₇	1	4	yes	—
433	#398	C₂²×C₆₇	1	2	yes	—
434	#397	C₂²×C₆₇	1	2	yes	—
435	#396	C₂²×C₆₇	1	4	yes	—
436	#396	C₂²×C₆₇	1	4	yes	—
437	#395	C₂²×C₆₇	1	2	yes	—
438	#394	C₂²×C₆₇	1	4	yes	—
439	#394	C₂²×C₆₇	1	2	yes	—
440	#393	C₂²×C₆₇	1	2	yes	—
441	#392	C₂²×C₆₇	1	2	yes	—
442	#391	C₂²×C₆₇	1	2	yes	—
443	#390	C₂²×C₆₇	1	2	yes	—
444	#389	C₂²×C₆₇	1	2	yes	—
445	#389	C₂²×C₆₇	1	2	yes	—
446	#388	C₂²×C₆₇	1	4	yes	—
447	#388	C₂²×C₆₇	1	4	yes	—
448	#388	C₂²×C₆₇	1	4	yes	—
449	#387	C₂²×C₆₇	1	4	yes	—
450	#387	C₂²×C₆₇	1	4	yes	—
451	#387	C₂²×C₆₇	1	4	yes	—
452	#386	C₂²×C₆₇	1	4	yes	—
453	#386	C₂²×C₆₇	1	4	yes	—
454	#386	C₂²×C₆₇	1	4	yes	—
455	#386	C₂²×C₆₇	1	4	yes	—
456	#386	C₂²×C₆₇	1	4	yes	—
457	#385	C₂²×C₆₇	1	4	yes	—
458	#385	C₂²×C₆₇	1	4	yes	—
459	#385	C₂²×C₆₇	1	4	yes	—
460	#382	C₂²×C₆₇	1	1	yes	characteristic
461	#382	C₂²×C₆₇	1	1	yes	characteristic
462	#382	C₂²×C₆₇	1	2	yes	—
463	#382	C₂²×C₆₇	1	2	yes	—
464	#382	C₂²×C₆₇	1	2	yes	—
465	#380	C₂²×C₆₇	1	4	yes	—
466	#380	C₂²×C₆₇	1	2	yes	—
467	#380	C₂²×C₆₇	1	2	yes	—
468	C₂×#95	C₂²×C₆₇	1	2	yes	—
469	C₂×#95	C₂²×C₆₇	1	2	yes	—
470	C₂×#41	—	2	8	no	—
471	C₂×#41	—	2	4	no	—
472	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
476	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
478	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
479	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
480	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
481	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
484	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
485	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
486	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
487	#126	—	2	8	no	—
488	#125	—	2	4	no	—
489	#124	—	2	4	no	—
490	#123	—	2	8	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	4	4	no	—
493	#121	—	2	16	no	—
494	#121	—	2	4	no	—
495	#121	—	4	4	no	—
496	C₄×Q₈	—	2	4	no	—
497	C₄×Q₈	—	2	4	no	—
498	C₄×Q₈	—	2	4	no	—
499	C₄×D₄	—	2	8	no	—
500	C₄×D₄	—	2	8	no	—
501	C₄×D₄	—	2	8	no	—
502	C₄×D₄	—	2	4	no	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	4	no	—
505	#117	—	2	4	no	—
506	#117	—	2	8	no	—
507	#117	—	2	8	no	—
508	C₂×C₄⋊C₄	—	4	4	no	—
509	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
539	C₂×C₄²	—	2	8	no	—
540	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
541	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
543	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
544	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
545	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
549	#95	C₂³×C₆₇	1	2	yes	—
550	#95	C₂³×C₆₇	1	4	yes	—
551	#95	C₂³×C₆₇	1	4	yes	—
552	#95	C₂³×C₆₇	1	2	yes	—
553	#95	C₂³×C₆₇	1	2	yes	—
554	#95	C₂³×C₆₇	1	2	yes	—
555	#95	C₂³×C₆₇	1	4	yes	—
556	#95	C₂³×C₆₇	1	4	yes	—
557	#95	C₂³×C₆₇	1	4	yes	—
558	#95	C₂³×C₆₇	1	4	yes	—
559	#95	C₂³×C₆₇	1	4	yes	—
560	#95	C₂³×C₆₇	1	4	yes	—
561	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
562	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
563	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
564	#41	—	2	32	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	8	no	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂×D₄	—	4	4	no	—
582	C₂×D₄	#41×C₆₇	1	8	yes	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	8	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
602	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
603	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
604	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
606	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	8	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	—	4	4	no	—
633	C₄⋊C₄	—	4	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₂²⋊C₄	—	4	4	no	—
647	C₂²⋊C₄	—	4	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	4	no	—
652	C₄²	C₂×D₄×C₆₇	1	4	yes	—
653	C₄²	C₂×D₄×C₆₇	1	4	yes	—
654	C₄²	C₂×D₄×C₆₇	1	4	yes	—
655	C₄²	C₂×D₄×C₆₇	1	4	yes	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
671	C₂³	C₂×#41×C₆₇	1	4	yes	—
672	C₂³	C₂×#41×C₆₇	1	4	yes	—
673	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
674	Q₈	—	2	8	no	—
675	Q₈	—	4	4	no	—
676	D₄	—	2	8	no	—
677	D₄	—	2	16	no	—
678	D₄	—	4	8	no	—
679	D₄	—	4	4	no	—
680	D₄	—	8	8	no	—
681	C₂×C₄	—	2	16	no	—
682	C₂×C₄	—	2	8	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	8	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	8	8	no	—
716	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
722	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
723	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
724	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	#525×C₆₇	1	4	yes	—
742	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
743	C₂²	C₂²×#41×C₆₇	1	2	yes	—
744	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
745	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
746	C₂²	#585×C₆₇	1	2	yes	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	4	no	—
759	C₄	—	4	4	no	—
760	C₄	#537×C₆₇	1	4	yes	—
761	C₂	—	2	4	no	—
762	C₂	—	4	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
765	C₂	C₂×#537×C₆₇	1	1	yes	characteristic
766	C₂	C₆₇×#3449	1	1	yes	characteristic
767	C₂	C₆₇×#3514	1	2	yes	—
768	C₂	C₆₇×#3515	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₆₇	C₂	semidirect
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#2851	C₂	semidirect
4. C₆₇×#2850	C₂	semidirect
5. C₆₇×#2637	C₂	semidirect
6. C₆₇×#2636	C₂	semidirect
7. C₆₇×#2609	C₂	semidirect
8. C₆₇×#2581	C₂	semidirect
9. C₆₇×#2580	C₂	semidirect
10. C₆₇×#2536	C₂	semidirect
11. C₆₇×#2535	C₂	semidirect
12. C₆₇×#2498	C₂	semidirect
13. C₆₇×#2430	C₂	semidirect
14. C₆₇×#2417	C₂	semidirect
15. C₆₇×#2416	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₂×#382×C₆₇	C₂	semidirect
155. C₂×C₄²×C₆₇	D₄	semidirect
376. #35130	C₆₇	direct (N × H)
385. C₂×#529	C₂×C₆₇	semidirect
386. C₂×C₄×#41	C₂×C₆₇	semidirect
387. #2851	C₂×C₆₇	semidirect
388. #2850	C₂×C₆₇	semidirect
389. #2637	C₂×C₆₇	semidirect
390. #2636	C₂×C₆₇	semidirect
391. #2609	C₂×C₆₇	semidirect
392. #2581	C₂×C₆₇	semidirect
393. #2580	C₂×C₆₇	semidirect
394. #2536	C₂×C₆₇	semidirect
395. #2535	C₂×C₆₇	semidirect
396. #2498	C₂×C₆₇	semidirect
397. #2430	C₂×C₆₇	semidirect
398. #2417	C₂×C₆₇	semidirect
399. #2416	C₂×C₆₇	semidirect
400. #2325	C₂×C₆₇	semidirect
401. C₂×#382	C₂×C₆₇	semidirect
402. C₆₇	#35130	direct (N × H)
540. C₂×C₄²	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#2851	2
C₆₇×#2850	2
C₆₇×#2637	2
C₆₇×#2636	2
C₆₇×#2609	2
C₆₇×#2581	2
C₆₇×#2580	2
C₆₇×#2536	2
C₆₇×#2535	2
C₆₇×#2498	2
C₆₇×#2430	2
C₆₇×#2417	2
C₆₇×#2416	2
C₆₇×#2325	2
C₂×#382×C₆₇	2
#35130	67

Subgroups — C67×#35130 #30714381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35130 #30714381