Subgroups — C₆₇×#35091 #30714342

Order 17152.

2886 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2847	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2627	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2618	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2613	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2468	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2464	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2461	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2457	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2312	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
19	#538×C₆₇	—	2	8	no	—
20	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
21	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
24	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#120×C₆₇	C₂²	1	2	yes	—
31	C₂×#120×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	—	2	8	no	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
36	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
40	#400×C₆₇	C₂²	1	2	yes	complemented
41	#398×C₆₇	C₂²	1	2	yes	complemented
42	#398×C₆₇	C₂²	1	4	yes	complemented
43	#396×C₆₇	C₂²	1	4	yes	complemented
44	#395×C₆₇	C₂²	1	2	yes	complemented
45	#394×C₆₇	C₂²	1	4	yes	—
46	#394×C₆₇	C₂²	1	4	yes	—
47	#394×C₆₇	C₂²	1	2	yes	complemented
48	#392×C₆₇	C₂²	1	4	yes	—
49	#392×C₆₇	C₂²	1	4	yes	—
50	#390×C₆₇	C₂²	1	4	yes	complemented
51	#388×C₆₇	C₂²	1	4	yes	complemented
52	#388×C₆₇	C₂²	1	4	yes	complemented
53	#388×C₆₇	C₂²	1	4	yes	complemented
54	#388×C₆₇	C₂²	1	4	yes	complemented
55	#388×C₆₇	C₂²	1	4	yes	complemented
56	#387×C₆₇	C₂²	1	4	yes	complemented
57	#386×C₆₇	C₂²	1	2	yes	—
58	#386×C₆₇	C₂²	1	2	yes	—
59	#386×C₆₇	C₂²	1	4	yes	complemented
60	#386×C₆₇	C₂²	1	4	yes	complemented
61	#386×C₆₇	C₂²	1	4	yes	complemented
62	#385×C₆₇	C₂²	1	2	yes	—
63	#385×C₆₇	C₂²	1	2	yes	—
64	#385×C₆₇	C₂²	1	4	yes	complemented
65	#385×C₆₇	C₂²	1	4	yes	complemented
66	#381×C₆₇	C₂²	1	2	yes	—
67	#381×C₆₇	C₂²	1	4	yes	complemented
68	#380×C₆₇	C₂²	1	1	yes	characteristic
69	#380×C₆₇	C₂²	1	1	yes	characteristic
70	#380×C₆₇	C₂²	1	2	yes	complemented
71	#380×C₆₇	C₂²	1	2	yes	complemented
72	#379×C₆₇	C₂²	1	2	yes	—
73	#379×C₆₇	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
77	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
78	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₆₇	—	2	4	no	—
81	C₂²×D₄×C₆₇	—	2	4	no	—
82	C₂²×D₄×C₆₇	—	2	4	no	—
83	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
87	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	—	2	4	no	—
90	C₂³×C₄×C₆₇	—	2	4	no	—
91	C₂³×C₄×C₆₇	—	4	4	no	—
92	C₂³×C₄×C₆₇	—	4	4	no	—
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
96	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	#126×C₆₇	—	2	8	no	—
103	#124×C₆₇	—	2	8	no	—
104	#123×C₆₇	—	2	8	no	—
105	#123×C₆₇	—	2	8	no	—
106	#123×C₆₇	—	4	8	no	—
107	C₂²⋊Q₈×C₆₇	—	2	4	no	—
108	C₂²⋊Q₈×C₆₇	—	4	4	no	—
109	#121×C₆₇	—	2	4	no	—
110	#121×C₆₇	—	2	8	no	—
111	#121×C₆₇	—	4	4	no	—
112	#120×C₆₇	—	2	8	no	—
113	#120×C₆₇	—	2	8	no	—
114	C₄×D₄×C₆₇	—	2	8	no	—
115	C₄×D₄×C₆₇	—	2	16	no	—
116	C₄×D₄×C₆₇	—	2	16	no	—
117	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	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	4	yes	—
129	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₆₇	D₄	1	8	yes	complemented
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄²×C₆₇	—	2	4	no	—
150	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
151	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
153	#95×C₆₇	C₂³	1	4	yes	—
154	#95×C₆₇	C₂³	1	4	yes	—
155	#95×C₆₇	C₂³	1	4	yes	—
156	#95×C₆₇	C₂³	1	4	yes	—
157	#95×C₆₇	C₂³	1	4	yes	—
158	#95×C₆₇	C₂³	1	2	yes	—
159	#95×C₆₇	C₂³	1	2	yes	—
160	#95×C₆₇	C₂³	1	4	yes	—
161	#95×C₆₇	C₂³	1	4	yes	—
162	C₂⁴×C₆₇	—	2	2	no	—
163	C₂⁴×C₆₇	—	2	2	no	—
164	C₂⁴×C₆₇	—	2	2	no	—
165	C₂⁴×C₆₇	—	2	2	no	—
166	C₂⁴×C₆₇	—	4	2	no	—
167	C₂⁴×C₆₇	—	4	2	no	—
168	C₂⁴×C₆₇	—	4	2	no	—
169	C₂⁴×C₆₇	—	4	2	no	—
170	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
171	C₂⁴×C₆₇	#41	1	4	yes	—
172	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
173	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
174	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
175	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₆₇	—	2	2	no	—
177	C₂×Q₈×C₆₇	—	4	2	no	—
178	C₂×D₄×C₆₇	—	2	32	no	—
179	C₂×D₄×C₆₇	—	2	8	no	—
180	C₂×D₄×C₆₇	—	2	8	no	—
181	C₂×D₄×C₆₇	—	2	4	no	—
182	C₂×D₄×C₆₇	—	2	4	no	—
183	C₂×D₄×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	8	no	—
187	C₂×D₄×C₆₇	—	2	2	no	—
188	C₂×D₄×C₆₇	—	2	8	no	—
189	C₂×D₄×C₆₇	—	4	2	no	—
190	C₂×D₄×C₆₇	—	4	4	no	—
191	C₂×D₄×C₆₇	—	4	4	no	—
192	C₂×D₄×C₆₇	—	4	4	no	—
193	C₂×D₄×C₆₇	—	4	4	no	—
194	C₂²×C₄×C₆₇	—	2	2	no	—
195	C₂²×C₄×C₆₇	—	2	2	no	—
196	C₂²×C₄×C₆₇	—	2	2	no	—
197	C₂²×C₄×C₆₇	—	2	4	no	—
198	C₂²×C₄×C₆₇	—	2	2	no	—
199	C₂²×C₄×C₆₇	—	2	8	no	—
200	C₂²×C₄×C₆₇	—	2	4	no	—
201	C₂²×C₄×C₆₇	—	2	4	no	—
202	C₂²×C₄×C₆₇	—	2	4	no	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	2	8	no	—
205	C₂²×C₄×C₆₇	—	2	4	no	—
206	C₂²×C₄×C₆₇	—	4	2	no	—
207	C₂²×C₄×C₆₇	—	4	2	no	—
208	C₂²×C₄×C₆₇	—	4	2	no	—
209	C₂²×C₄×C₆₇	—	4	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	16	no	—
214	C₂²×C₄×C₆₇	—	4	16	no	—
215	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₆₇	#41	1	4	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	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	4	yes	—
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
229	C₄⋊C₄×C₆₇	—	2	4	no	—
230	C₄⋊C₄×C₆₇	—	2	4	no	—
231	C₄⋊C₄×C₆₇	—	2	4	no	—
232	C₄⋊C₄×C₆₇	—	2	4	no	—
233	C₄⋊C₄×C₆₇	—	2	2	no	—
234	C₄⋊C₄×C₆₇	—	2	2	no	—
235	C₄⋊C₄×C₆₇	—	2	8	no	—
236	C₄⋊C₄×C₆₇	—	2	8	no	—
237	C₄⋊C₄×C₆₇	—	4	2	no	—
238	C₄⋊C₄×C₆₇	—	4	2	no	—
239	C₄⋊C₄×C₆₇	—	4	4	no	—
240	C₂²⋊C₄×C₆₇	—	2	4	no	—
241	C₂²⋊C₄×C₆₇	—	2	4	no	—
242	C₂²⋊C₄×C₆₇	—	2	4	no	—
243	C₂²⋊C₄×C₆₇	—	2	8	no	—
244	C₂²⋊C₄×C₆₇	—	2	4	no	—
245	C₂²⋊C₄×C₆₇	—	2	4	no	—
246	C₂²⋊C₄×C₆₇	—	2	8	no	—
247	C₂²⋊C₄×C₆₇	—	2	4	no	—
248	C₂²⋊C₄×C₆₇	—	2	4	no	—
249	C₂²⋊C₄×C₆₇	—	2	8	no	—
250	C₂²⋊C₄×C₆₇	—	2	8	no	—
251	C₂²⋊C₄×C₆₇	—	4	4	no	—
252	C₂²⋊C₄×C₆₇	—	4	4	no	—
253	C₂²⋊C₄×C₆₇	—	4	4	no	—
254	C₂²⋊C₄×C₆₇	—	4	4	no	—
255	C₂²⋊C₄×C₆₇	—	4	4	no	—
256	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
257	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
258	C₄²×C₆₇	—	2	8	no	—
259	C₄²×C₆₇	—	2	4	no	—
260	C₄²×C₆₇	—	4	4	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	2	no	—
263	C₂³×C₆₇	—	2	8	no	—
264	C₂³×C₆₇	—	2	8	no	—
265	C₂³×C₆₇	—	2	2	no	—
266	C₂³×C₆₇	—	2	2	no	—
267	C₂³×C₆₇	—	2	2	no	—
268	C₂³×C₆₇	—	2	2	no	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	4	no	—
271	C₂³×C₆₇	—	2	2	no	—
272	C₂³×C₆₇	—	2	2	no	—
273	C₂³×C₆₇	—	2	4	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	4	no	—
279	C₂³×C₆₇	—	2	4	no	—
280	C₂³×C₆₇	—	4	4	no	—
281	C₂³×C₆₇	—	4	4	no	—
282	C₂³×C₆₇	—	4	8	no	—
283	C₂³×C₆₇	—	4	4	no	—
284	C₂³×C₆₇	—	4	8	no	—
285	C₂³×C₆₇	—	4	8	no	—
286	C₂³×C₆₇	—	4	4	no	—
287	C₂³×C₆₇	—	4	8	no	—
288	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
289	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
290	C₂³×C₆₇	C₂×#41	1	4	yes	—
291	C₂³×C₆₇	C₂×#41	1	2	yes	—
292	C₂³×C₆₇	C₂×#41	1	2	yes	—
293	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
294	Q₈×C₆₇	—	8	2	no	—
295	D₄×C₆₇	—	2	32	no	—
296	D₄×C₆₇	—	4	8	no	—
297	D₄×C₆₇	—	8	2	no	—
298	D₄×C₆₇	—	8	4	no	—
299	D₄×C₆₇	—	8	4	no	—
300	D₄×C₆₇	—	8	8	no	—
301	C₂×C₄×C₆₇	—	2	8	no	—
302	C₂×C₄×C₆₇	—	2	8	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	4	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	4	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	4	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	—	4	4	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	16	no	—
330	C₂×C₄×C₆₇	—	4	4	no	—
331	C₂×C₄×C₆₇	—	8	4	no	—
332	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
336	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
337	C₂²×C₆₇	—	2	4	no	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	2	2	no	—
340	C₂²×C₆₇	—	2	4	no	—
341	C₂²×C₆₇	—	2	4	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	16	no	—
348	C₂²×C₆₇	—	4	16	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	4	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	2	no	—
356	C₂²×C₆₇	—	4	4	no	—
357	C₂²×C₆₇	—	4	2	no	—
358	C₂²×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	4	4	no	—
360	C₂²×C₆₇	#525	1	4	yes	—
361	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
365	C₂²×C₆₇	#585	1	2	yes	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	2	4	no	—
368	C₄×C₆₇	—	2	2	no	—
369	C₄×C₆₇	—	2	2	no	—
370	C₄×C₆₇	—	2	4	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	4	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	4	no	—
377	#35091	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂×C₆₇	—	2	4	no	—
379	C₂×C₆₇	—	4	4	no	—
380	C₂×C₆₇	—	4	4	no	—
381	C₂×C₆₇	—	8	2	no	—
382	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
383	C₂×C₆₇	#3460	1	2	yes	—
384	C₂×C₆₇	#3484	1	1	yes	characteristic
385	C₂×C₆₇	#3485	1	1	yes	characteristic
386	C₂×C₆₇	#3505	1	2	yes	—
387	C₂×#538	C₂×C₆₇	1	1	yes	characteristic, complemented
388	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#2849	C₂×C₆₇	1	2	yes	complemented
390	#2848	C₂×C₆₇	1	1	yes	characteristic, complemented
391	#2847	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#2627	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#2618	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#2613	C₂×C₆₇	1	2	yes	complemented
395	#2468	C₂×C₆₇	1	4	yes	complemented
396	#2464	C₂×C₆₇	1	4	yes	complemented
397	#2461	C₂×C₆₇	1	4	yes	complemented
398	#2457	C₂×C₆₇	1	4	yes	complemented
399	#2321	C₂×C₆₇	1	2	yes	complemented
400	#2312	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₄×#123	C₂×C₆₇	1	2	yes	complemented
402	C₆₇	#35091	1	1	yes	characteristic, direct product factor, Sylow
403	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
404	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
405	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
406	#538	—	2	8	no	—
407	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
408	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
409	C₂×#123	C₂²×C₆₇	1	2	yes	—
410	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
411	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
412	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
414	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
416	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
417	C₂×#120	C₂²×C₆₇	1	2	yes	—
418	C₂×#120	C₂²×C₆₇	1	2	yes	—
419	C₂×C₄×D₄	—	2	8	no	—
420	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
422	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
423	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
424	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
425	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
426	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
427	#400	C₂²×C₆₇	1	2	yes	complemented
428	#398	C₂²×C₆₇	1	2	yes	complemented
429	#398	C₂²×C₆₇	1	4	yes	complemented
430	#396	C₂²×C₆₇	1	4	yes	complemented
431	#395	C₂²×C₆₇	1	2	yes	complemented
432	#394	C₂²×C₆₇	1	4	yes	—
433	#394	C₂²×C₆₇	1	4	yes	—
434	#394	C₂²×C₆₇	1	2	yes	complemented
435	#392	C₂²×C₆₇	1	4	yes	—
436	#392	C₂²×C₆₇	1	4	yes	—
437	#390	C₂²×C₆₇	1	4	yes	complemented
438	#388	C₂²×C₆₇	1	4	yes	complemented
439	#388	C₂²×C₆₇	1	4	yes	complemented
440	#388	C₂²×C₆₇	1	4	yes	complemented
441	#388	C₂²×C₆₇	1	4	yes	complemented
442	#388	C₂²×C₆₇	1	4	yes	complemented
443	#387	C₂²×C₆₇	1	4	yes	complemented
444	#386	C₂²×C₆₇	1	2	yes	—
445	#386	C₂²×C₆₇	1	2	yes	—
446	#386	C₂²×C₆₇	1	4	yes	complemented
447	#386	C₂²×C₆₇	1	4	yes	complemented
448	#386	C₂²×C₆₇	1	4	yes	complemented
449	#385	C₂²×C₆₇	1	2	yes	—
450	#385	C₂²×C₆₇	1	2	yes	—
451	#385	C₂²×C₆₇	1	4	yes	complemented
452	#385	C₂²×C₆₇	1	4	yes	complemented
453	#381	C₂²×C₆₇	1	2	yes	—
454	#381	C₂²×C₆₇	1	4	yes	complemented
455	#380	C₂²×C₆₇	1	1	yes	characteristic
456	#380	C₂²×C₆₇	1	1	yes	characteristic
457	#380	C₂²×C₆₇	1	2	yes	complemented
458	#380	C₂²×C₆₇	1	2	yes	complemented
459	#379	C₂²×C₆₇	1	2	yes	—
460	#379	C₂²×C₆₇	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
462	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
464	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
465	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	—	2	4	no	—
469	C₂²×D₄	—	2	4	no	—
470	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
471	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
472	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
473	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
474	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
475	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
476	C₂³×C₄	—	2	4	no	—
477	C₂³×C₄	—	2	4	no	—
478	C₂³×C₄	—	4	4	no	—
479	C₂³×C₄	—	4	4	no	—
480	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
482	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
483	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
484	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
487	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
489	#126	—	2	8	no	—
490	#124	—	2	8	no	—
491	#123	—	2	8	no	—
492	#123	—	2	8	no	—
493	#123	—	4	8	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	4	4	no	—
496	#121	—	2	4	no	—
497	#121	—	2	8	no	—
498	#121	—	4	4	no	—
499	#120	—	2	8	no	—
500	#120	—	2	8	no	—
501	C₄×D₄	—	2	8	no	—
502	C₄×D₄	—	2	16	no	—
503	C₄×D₄	—	2	16	no	—
504	C₂×C₄⋊C₄	—	2	4	no	—
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₂²⋊C₄	D₄×C₆₇	1	8	yes	complemented
518	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
536	C₂×C₄²	—	2	4	no	—
537	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
538	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
539	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
540	#95	C₂³×C₆₇	1	4	yes	—
541	#95	C₂³×C₆₇	1	4	yes	—
542	#95	C₂³×C₆₇	1	4	yes	—
543	#95	C₂³×C₆₇	1	4	yes	—
544	#95	C₂³×C₆₇	1	4	yes	—
545	#95	C₂³×C₆₇	1	2	yes	—
546	#95	C₂³×C₆₇	1	2	yes	—
547	#95	C₂³×C₆₇	1	4	yes	—
548	#95	C₂³×C₆₇	1	4	yes	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
558	C₂⁴	#41×C₆₇	1	4	yes	—
559	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
560	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
561	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
562	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	4	2	no	—
565	C₂×D₄	—	2	32	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	8	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	8	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	16	no	—
601	C₂²×C₄	—	4	16	no	—
602	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
603	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
604	C₂²×C₄	#41×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	4	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	2	yes	—
612	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
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	8	no	—
623	C₄⋊C₄	—	2	8	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	8	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
644	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
645	C₄²	—	2	8	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	4	4	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	8	no	—
651	C₂³	—	2	8	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	4	4	no	—
669	C₂³	—	4	8	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	4	8	no	—
675	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
676	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
677	C₂³	C₂×#41×C₆₇	1	4	yes	—
678	C₂³	C₂×#41×C₆₇	1	2	yes	—
679	C₂³	C₂×#41×C₆₇	1	2	yes	—
680	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
681	Q₈	—	8	2	no	—
682	D₄	—	2	32	no	—
683	D₄	—	4	8	no	—
684	D₄	—	8	2	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	8	no	—
688	C₂×C₄	—	2	8	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	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	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	16	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	4	no	—
719	C₂×C₄	C₂²×D₄×C₆₇	1	4	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	4	yes	—
724	C₂²	—	2	4	no	—
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	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	4	16	no	—
735	C₂²	—	4	16	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	4	no	—
747	C₂²	#525×C₆₇	1	4	yes	—
748	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
750	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
751	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
752	C₂²	#585×C₆₇	1	2	yes	—
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	4	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	4	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₂	—	2	4	no	—
765	C₂	—	4	4	no	—
766	C₂	—	4	4	no	—
767	C₂	—	8	2	no	—
768	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
769	C₂	C₆₇×#3460	1	2	yes	—
770	C₂	C₆₇×#3484	1	1	yes	characteristic
771	C₂	C₆₇×#3485	1	1	yes	characteristic
772	C₂	C₆₇×#3505	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×#538×C₆₇	C₂	semidirect
2. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2849	C₂	semidirect
4. C₆₇×#2848	C₂	semidirect
5. C₆₇×#2847	C₂	semidirect
6. C₆₇×#2627	C₂	semidirect
7. C₆₇×#2618	C₂	semidirect
8. C₆₇×#2613	C₂	semidirect
9. C₆₇×#2468	C₂	semidirect
10. C₆₇×#2464	C₂	semidirect
11. C₆₇×#2461	C₂	semidirect
12. C₆₇×#2457	C₂	semidirect
13. C₆₇×#2321	C₂	semidirect
14. C₆₇×#2312	C₂	semidirect
15. C₄×#123×C₆₇	C₂	semidirect
20. C₂×#126×C₆₇	C₂²	semidirect
21. C₂×#124×C₆₇	C₂²	semidirect
23. C₂×#123×C₆₇	C₂²	semidirect
24. C₂×#123×C₆₇	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
28. C₂×#121×C₆₇	C₂²	semidirect
29. C₂×#121×C₆₇	C₂²	semidirect
40. #400×C₆₇	C₂²	semidirect
41. #398×C₆₇	C₂²	semidirect
42. #398×C₆₇	C₂²	semidirect
43. #396×C₆₇	C₂²	semidirect
44. #395×C₆₇	C₂²	semidirect
47. #394×C₆₇	C₂²	semidirect
50. #390×C₆₇	C₂²	semidirect
51. #388×C₆₇	C₂²	semidirect
52. #388×C₆₇	C₂²	semidirect
53. #388×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #387×C₆₇	C₂²	semidirect
59. #386×C₆₇	C₂²	semidirect
60. #386×C₆₇	C₂²	semidirect
61. #386×C₆₇	C₂²	semidirect
64. #385×C₆₇	C₂²	semidirect
65. #385×C₆₇	C₂²	semidirect
67. #381×C₆₇	C₂²	semidirect
70. #380×C₆₇	C₂²	semidirect
71. #380×C₆₇	C₂²	semidirect
74. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
130. C₂×C₂²⋊C₄×C₆₇	D₄	semidirect
377. #35091	C₆₇	direct (N × H)
387. C₂×#538	C₂×C₆₇	semidirect
388. C₂²×C₄×D₄	C₂×C₆₇	semidirect
389. #2849	C₂×C₆₇	semidirect
390. #2848	C₂×C₆₇	semidirect
391. #2847	C₂×C₆₇	semidirect
392. #2627	C₂×C₆₇	semidirect
393. #2618	C₂×C₆₇	semidirect
394. #2613	C₂×C₆₇	semidirect
395. #2468	C₂×C₆₇	semidirect
396. #2464	C₂×C₆₇	semidirect
397. #2461	C₂×C₆₇	semidirect
398. #2457	C₂×C₆₇	semidirect
399. #2321	C₂×C₆₇	semidirect
400. #2312	C₂×C₆₇	semidirect
401. C₄×#123	C₂×C₆₇	semidirect
402. C₆₇	#35091	direct (N × H)
407. C₂×#126	C₂²×C₆₇	semidirect
408. C₂×#124	C₂²×C₆₇	semidirect
410. C₂×#123	C₂²×C₆₇	semidirect
411. C₂×#123	C₂²×C₆₇	semidirect
413. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
415. C₂×#121	C₂²×C₆₇	semidirect
416. C₂×#121	C₂²×C₆₇	semidirect
427. #400	C₂²×C₆₇	semidirect
428. #398	C₂²×C₆₇	semidirect
429. #398	C₂²×C₆₇	semidirect
430. #396	C₂²×C₆₇	semidirect
431. #395	C₂²×C₆₇	semidirect
434. #394	C₂²×C₆₇	semidirect
437. #390	C₂²×C₆₇	semidirect
438. #388	C₂²×C₆₇	semidirect
439. #388	C₂²×C₆₇	semidirect
440. #388	C₂²×C₆₇	semidirect
441. #388	C₂²×C₆₇	semidirect
442. #388	C₂²×C₆₇	semidirect
443. #387	C₂²×C₆₇	semidirect
446. #386	C₂²×C₆₇	semidirect
447. #386	C₂²×C₆₇	semidirect
448. #386	C₂²×C₆₇	semidirect
451. #385	C₂²×C₆₇	semidirect
452. #385	C₂²×C₆₇	semidirect
454. #381	C₂²×C₆₇	semidirect
457. #380	C₂²×C₆₇	semidirect
458. #380	C₂²×C₆₇	semidirect
461. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
463. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
517. C₂×C₂²⋊C₄	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×#538×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2849	2
C₆₇×#2848	2
C₆₇×#2847	2
C₆₇×#2627	2
C₆₇×#2618	2
C₆₇×#2613	2
C₆₇×#2468	2
C₆₇×#2464	2
C₆₇×#2461	2
C₆₇×#2457	2
C₆₇×#2321	2
C₆₇×#2312	2
C₄×#123×C₆₇	2
#35091	67

Subgroups — C67×#35091 #30714342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35091 #30714342