Subgroups — C₆₇×#59818 #30739069

Order 17152.

3276 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2680	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2669	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2555	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2536	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2535	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2472	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2464	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2409	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2407	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
14	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#124×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂²×#41×C₆₇	C₂²	1	2	yes	—
17	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
19	#548×C₆₇	—	2	16	no	—
20	#546×C₆₇	—	2	16	no	—
21	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₂²	1	2	yes	—
23	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
24	C₂×#123×C₆₇	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₂×#121×C₆₇	C₂²	1	2	yes	—
30	C₂×#121×C₆₇	C₂²	1	4	yes	—
31	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#120×C₆₇	C₂²	1	2	yes	—
33	C₂×#120×C₆₇	C₂²	1	4	yes	—
34	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
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	complemented
39	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
42	#398×C₆₇	C₂²	1	4	yes	complemented
43	#397×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	2	yes	—
47	#394×C₆₇	C₂²	1	4	yes	complemented
48	#393×C₆₇	C₂²	1	2	yes	—
49	#392×C₆₇	C₂²	1	2	yes	—
50	#392×C₆₇	C₂²	1	4	yes	complemented
51	#392×C₆₇	C₂²	1	4	yes	complemented
52	#391×C₆₇	C₂²	1	2	yes	complemented
53	#390×C₆₇	C₂²	1	2	yes	—
54	#390×C₆₇	C₂²	1	1	yes	characteristic
55	#390×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#390×C₆₇	C₂²	1	2	yes	complemented
58	#388×C₆₇	C₂²	1	4	yes	—
59	#388×C₆₇	C₂²	1	4	yes	complemented
60	#388×C₆₇	C₂²	1	4	yes	complemented
61	#388×C₆₇	C₂²	1	4	yes	complemented
62	#386×C₆₇	C₂²	1	2	yes	—
63	#386×C₆₇	C₂²	1	4	yes	complemented
64	#386×C₆₇	C₂²	1	4	yes	complemented
65	#386×C₆₇	C₂²	1	4	yes	complemented
66	#385×C₆₇	C₂²	1	4	yes	complemented
67	#385×C₆₇	C₂²	1	2	yes	complemented
68	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#382×C₆₇	C₂²	1	2	yes	complemented
70	#380×C₆₇	C₂²	1	1	yes	characteristic
71	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#380×C₆₇	C₂²	1	2	yes	complemented
73	#379×C₆₇	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
76	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₆₇	C₂³	1	2	yes	—
78	C₂×#41×C₆₇	—	2	8	no	—
79	C₂×#41×C₆₇	—	2	8	no	—
80	C₂×#41×C₆₇	—	4	4	no	—
81	C₂²×Q₈×C₆₇	—	2	8	no	—
82	C₂²×Q₈×C₆₇	—	4	2	no	—
83	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
84	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
85	C₂²×D₄×C₆₇	—	2	8	no	—
86	C₂²×D₄×C₆₇	—	4	2	no	—
87	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
89	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
91	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
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	4	yes	—
102	#127×C₆₇	—	2	4	no	—
103	#124×C₆₇	—	2	16	no	—
104	#124×C₆₇	D₄	1	16	yes	complemented
105	#123×C₆₇	—	2	16	no	—
106	C₂²⋊Q₈×C₆₇	—	2	8	no	—
107	C₂²⋊Q₈×C₆₇	—	2	8	no	—
108	C₂²⋊Q₈×C₆₇	—	2	16	no	—
109	#121×C₆₇	—	2	8	no	—
110	#121×C₆₇	—	2	8	no	—
111	#121×C₆₇	—	2	16	no	—
112	#121×C₆₇	—	2	16	no	—
113	#120×C₆₇	—	2	8	no	—
114	#120×C₆₇	—	2	16	no	—
115	C₄×Q₈×C₆₇	—	2	8	no	—
116	C₄×D₄×C₆₇	—	2	16	no	—
117	C₄×D₄×C₆₇	—	2	8	no	—
118	C₄×D₄×C₆₇	—	2	8	no	—
119	C₄×D₄×C₆₇	—	2	8	no	—
120	C₄×D₄×C₆₇	—	4	2	no	—
121	C₄×D₄×C₆₇	—	4	2	no	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	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	4	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
153	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
157	#95×C₆₇	C₂³	1	4	yes	—
158	#95×C₆₇	C₂³	1	4	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	4	yes	—
161	#95×C₆₇	C₂³	1	2	yes	—
162	#95×C₆₇	C₂³	1	4	yes	—
163	#95×C₆₇	C₂³	1	2	yes	—
164	C₂⁴×C₆₇	—	2	8	no	—
165	C₂⁴×C₆₇	—	2	4	no	—
166	C₂⁴×C₆₇	—	4	2	no	—
167	C₂⁴×C₆₇	—	4	4	no	—
168	C₂⁴×C₆₇	—	4	2	no	—
169	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
170	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
171	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
172	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
173	#41×C₆₇	—	4	32	no	—
174	C₂×Q₈×C₆₇	—	2	4	no	—
175	C₂×Q₈×C₆₇	—	2	8	no	—
176	C₂×Q₈×C₆₇	—	2	4	no	—
177	C₂×Q₈×C₆₇	—	4	2	no	—
178	C₂×Q₈×C₆₇	—	4	16	no	—
179	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
180	C₂×D₄×C₆₇	—	2	8	no	—
181	C₂×D₄×C₆₇	—	2	8	no	—
182	C₂×D₄×C₆₇	—	2	8	no	—
183	C₂×D₄×C₆₇	—	2	8	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	4	no	—
188	C₂×D₄×C₆₇	—	2	4	no	—
189	C₂×D₄×C₆₇	—	2	4	no	—
190	C₂×D₄×C₆₇	—	2	8	no	—
191	C₂×D₄×C₆₇	—	2	2	no	—
192	C₂×D₄×C₆₇	—	2	4	no	—
193	C₂×D₄×C₆₇	—	4	1	no	—
194	C₂×D₄×C₆₇	—	4	1	no	—
195	C₂×D₄×C₆₇	—	4	2	no	—
196	C₂×D₄×C₆₇	—	4	1	no	—
197	C₂×D₄×C₆₇	—	4	2	no	—
198	C₂×D₄×C₆₇	—	4	2	no	—
199	C₂×D₄×C₆₇	—	4	1	no	—
200	C₂×D₄×C₆₇	—	4	4	no	—
201	C₂×D₄×C₆₇	—	4	4	no	—
202	C₂×D₄×C₆₇	—	4	4	no	—
203	C₂×D₄×C₆₇	—	4	4	no	—
204	C₂×D₄×C₆₇	—	4	16	no	—
205	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
206	C₂×D₄×C₆₇	#41	1	4	yes	complemented
207	C₂²×C₄×C₆₇	—	2	8	no	—
208	C₂²×C₄×C₆₇	—	2	8	no	—
209	C₂²×C₄×C₆₇	—	2	8	no	—
210	C₂²×C₄×C₆₇	—	2	4	no	—
211	C₂²×C₄×C₆₇	—	2	4	no	—
212	C₂²×C₄×C₆₇	—	2	4	no	—
213	C₂²×C₄×C₆₇	—	2	4	no	—
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	2	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	8	no	—
218	C₂²×C₄×C₆₇	—	4	2	no	—
219	C₂²×C₄×C₆₇	—	4	4	no	—
220	C₂²×C₄×C₆₇	—	4	4	no	—
221	C₂²×C₄×C₆₇	—	4	4	no	—
222	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
231	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	8	no	—
235	C₄⋊C₄×C₆₇	—	2	4	no	—
236	C₄⋊C₄×C₆₇	—	2	4	no	—
237	C₄⋊C₄×C₆₇	—	2	8	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	8	no	—
240	C₄⋊C₄×C₆₇	—	4	1	no	—
241	C₄⋊C₄×C₆₇	—	4	1	no	—
242	C₂²⋊C₄×C₆₇	—	2	8	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	8	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	8	no	—
253	C₂²⋊C₄×C₆₇	—	4	4	no	—
254	C₂²⋊C₄×C₆₇	—	4	4	no	—
255	C₂²⋊C₄×C₆₇	—	4	2	no	—
256	C₂²⋊C₄×C₆₇	—	4	2	no	—
257	C₂²⋊C₄×C₆₇	—	4	1	no	—
258	C₂²⋊C₄×C₆₇	—	4	1	no	—
259	C₂²⋊C₄×C₆₇	C₂×D₄	1	16	yes	—
260	C₂²⋊C₄×C₆₇	C₂×D₄	1	16	yes	—
261	C₄²×C₆₇	—	2	8	no	—
262	C₄²×C₆₇	—	2	2	no	—
263	C₄²×C₆₇	—	2	2	no	—
264	C₄²×C₆₇	—	4	1	no	—
265	C₄²×C₆₇	—	4	2	no	—
266	C₄²×C₆₇	C₂×D₄	1	8	yes	—
267	C₂³×C₆₇	—	2	2	no	—
268	C₂³×C₆₇	—	2	2	no	—
269	C₂³×C₆₇	—	2	4	no	—
270	C₂³×C₆₇	—	2	4	no	—
271	C₂³×C₆₇	—	2	1	no	—
272	C₂³×C₆₇	—	2	1	no	—
273	C₂³×C₆₇	—	2	4	no	—
274	C₂³×C₆₇	—	2	1	no	—
275	C₂³×C₆₇	—	2	4	no	—
276	C₂³×C₆₇	—	2	4	no	—
277	C₂³×C₆₇	—	2	4	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	2	1	no	—
281	C₂³×C₆₇	—	2	2	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	4	8	no	—
289	C₂³×C₆₇	—	4	16	no	—
290	C₂³×C₆₇	—	8	8	no	—
291	C₂³×C₆₇	—	8	4	no	—
292	C₂³×C₆₇	—	8	4	no	—
293	C₂³×C₆₇	C₂²×D₄	1	8	yes	—
294	C₂³×C₆₇	C₂×#41	1	2	yes	—
295	C₂³×C₆₇	C₂×#41	1	2	yes	—
296	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
297	Q₈×C₆₇	—	2	16	no	—
298	Q₈×C₆₇	—	4	8	no	—
299	D₄×C₆₇	—	2	16	no	—
300	D₄×C₆₇	—	4	4	no	—
301	D₄×C₆₇	—	4	8	no	—
302	D₄×C₆₇	—	4	8	no	—
303	D₄×C₆₇	—	4	16	no	—
304	D₄×C₆₇	—	4	4	no	—
305	D₄×C₆₇	—	4	16	no	—
306	D₄×C₆₇	—	4	8	no	—
307	D₄×C₆₇	—	8	8	no	—
308	C₂×C₄×C₆₇	—	2	4	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	4	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	4	no	—
318	C₂×C₄×C₆₇	—	2	2	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	1	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	4	no	—
329	C₂×C₄×C₆₇	—	2	4	no	—
330	C₂×C₄×C₆₇	—	2	4	no	—
331	C₂×C₄×C₆₇	—	4	8	no	—
332	C₂×C₄×C₆₇	—	4	16	no	—
333	C₂×C₄×C₆₇	—	4	4	no	—
334	C₂×C₄×C₆₇	—	4	4	no	—
335	C₂×C₄×C₆₇	—	4	8	no	—
336	C₂×C₄×C₆₇	—	8	8	no	—
337	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
340	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
341	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
342	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
343	C₂²×C₆₇	—	2	8	no	—
344	C₂²×C₆₇	—	2	4	no	—
345	C₂²×C₆₇	—	2	4	no	—
346	C₂²×C₆₇	—	2	8	no	—
347	C₂²×C₆₇	—	2	8	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	4	1	no	—
351	C₂²×C₆₇	—	4	1	no	—
352	C₂²×C₆₇	—	4	4	no	—
353	C₂²×C₆₇	—	4	4	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	2	no	—
356	C₂²×C₆₇	—	4	4	no	—
357	C₂²×C₆₇	—	4	1	no	—
358	C₂²×C₆₇	—	4	4	no	—
359	C₂²×C₆₇	—	4	1	no	—
360	C₂²×C₆₇	—	4	2	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	—	4	2	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	8	16	no	—
368	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
369	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
370	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂²×C₆₇	#585	1	2	yes	—
372	C₂²×C₆₇	#585	1	1	yes	characteristic
373	C₄×C₆₇	—	2	8	no	—
374	C₄×C₆₇	—	2	4	no	—
375	C₄×C₆₇	—	2	4	no	—
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	1	no	—
379	C₄×C₆₇	—	4	1	no	—
380	C₄×C₆₇	—	4	4	no	—
381	C₄×C₆₇	—	4	4	no	—
382	C₄×C₆₇	—	4	1	no	—
383	C₄×C₆₇	D₄²	1	4	yes	—
384	#59818	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
385	C₂×C₆₇	—	4	2	no	—
386	C₂×C₆₇	—	4	8	no	—
387	C₂×C₆₇	—	4	2	no	—
388	C₂×C₆₇	—	8	2	no	—
389	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
390	C₂×C₆₇	D₄×#41	1	2	yes	—
391	C₂×C₆₇	#3500	1	2	yes	—
392	C₂×C₆₇	#3505	1	1	yes	characteristic
393	C₂×C₆₇	#3551	1	1	yes	characteristic
394	C₂×#548	C₂×C₆₇	1	2	yes	complemented
395	C₂×#546	C₂×C₆₇	1	2	yes	complemented
396	#2680	C₂×C₆₇	1	2	yes	complemented
397	#2669	C₂×C₆₇	1	2	yes	complemented
398	#2555	C₂×C₆₇	1	2	yes	complemented
399	#2536	C₂×C₆₇	1	2	yes	complemented
400	#2535	C₂×C₆₇	1	2	yes	complemented
401	#2472	C₂×C₆₇	1	4	yes	complemented
402	#2464	C₂×C₆₇	1	4	yes	complemented
403	#2409	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#2408	C₂×C₆₇	1	1	yes	characteristic, complemented
405	#2407	C₂×C₆₇	1	2	yes	complemented
406	#2358	C₂×C₆₇	1	2	yes	complemented
407	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
408	C₄×#124	C₂×C₆₇	1	2	yes	complemented
409	C₆₇	#59818	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²×#41	C₂²×C₆₇	1	2	yes	—
411	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
412	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
413	#548	—	2	16	no	—
414	#546	—	2	16	no	—
415	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×#124	C₂²×C₆₇	1	2	yes	—
417	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
418	C₂×#123	C₂²×C₆₇	1	4	yes	—
419	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
420	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
421	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
422	C₂×#121	C₂²×C₆₇	1	2	yes	—
423	C₂×#121	C₂²×C₆₇	1	2	yes	—
424	C₂×#121	C₂²×C₆₇	1	4	yes	—
425	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
426	C₂×#120	C₂²×C₆₇	1	2	yes	—
427	C₂×#120	C₂²×C₆₇	1	4	yes	—
428	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
429	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
433	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
434	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
435	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
436	#398	C₂²×C₆₇	1	4	yes	complemented
437	#397	C₂²×C₆₇	1	4	yes	complemented
438	#395	C₂²×C₆₇	1	2	yes	complemented
439	#394	C₂²×C₆₇	1	2	yes	—
440	#394	C₂²×C₆₇	1	4	yes	—
441	#394	C₂²×C₆₇	1	4	yes	complemented
442	#393	C₂²×C₆₇	1	2	yes	—
443	#392	C₂²×C₆₇	1	2	yes	—
444	#392	C₂²×C₆₇	1	4	yes	complemented
445	#392	C₂²×C₆₇	1	4	yes	complemented
446	#391	C₂²×C₆₇	1	2	yes	complemented
447	#390	C₂²×C₆₇	1	1	yes	characteristic
448	#390	C₂²×C₆₇	1	2	yes	—
449	#390	C₂²×C₆₇	1	2	yes	—
450	#390	C₂²×C₆₇	1	2	yes	complemented
451	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
452	#388	C₂²×C₆₇	1	4	yes	—
453	#388	C₂²×C₆₇	1	4	yes	complemented
454	#388	C₂²×C₆₇	1	4	yes	complemented
455	#388	C₂²×C₆₇	1	4	yes	complemented
456	#386	C₂²×C₆₇	1	2	yes	—
457	#386	C₂²×C₆₇	1	4	yes	complemented
458	#386	C₂²×C₆₇	1	4	yes	complemented
459	#386	C₂²×C₆₇	1	4	yes	complemented
460	#385	C₂²×C₆₇	1	4	yes	complemented
461	#385	C₂²×C₆₇	1	2	yes	complemented
462	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	#382	C₂²×C₆₇	1	2	yes	complemented
464	#380	C₂²×C₆₇	1	1	yes	characteristic
465	#380	C₂²×C₆₇	1	2	yes	complemented
466	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
467	#379	C₂²×C₆₇	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
469	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
470	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	C₂⁵	C₂³×C₆₇	1	2	yes	—
472	C₂×#41	—	2	8	no	—
473	C₂×#41	—	2	8	no	—
474	C₂×#41	—	4	4	no	—
475	C₂²×Q₈	—	2	8	no	—
476	C₂²×Q₈	—	4	2	no	—
477	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
478	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
479	C₂²×D₄	—	2	8	no	—
480	C₂²×D₄	—	4	2	no	—
481	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
482	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
483	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
484	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
485	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
486	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
487	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
489	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
493	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
494	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
495	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
496	#127	—	2	4	no	—
497	#124	—	2	16	no	—
498	#124	D₄×C₆₇	1	16	yes	complemented
499	#123	—	2	16	no	—
500	C₂²⋊Q₈	—	2	8	no	—
501	C₂²⋊Q₈	—	2	8	no	—
502	C₂²⋊Q₈	—	2	16	no	—
503	#121	—	2	8	no	—
504	#121	—	2	8	no	—
505	#121	—	2	16	no	—
506	#121	—	2	16	no	—
507	#120	—	2	8	no	—
508	#120	—	2	16	no	—
509	C₄×Q₈	—	2	8	no	—
510	C₄×D₄	—	2	16	no	—
511	C₄×D₄	—	2	8	no	—
512	C₄×D₄	—	2	8	no	—
513	C₄×D₄	—	2	8	no	—
514	C₄×D₄	—	4	2	no	—
515	C₄×D₄	—	4	2	no	—
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
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	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	—	2	16	no	—
526	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	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	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	2	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	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
545	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
547	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
551	#95	C₂³×C₆₇	1	4	yes	—
552	#95	C₂³×C₆₇	1	4	yes	—
553	#95	C₂³×C₆₇	1	4	yes	—
554	#95	C₂³×C₆₇	1	4	yes	—
555	#95	C₂³×C₆₇	1	2	yes	—
556	#95	C₂³×C₆₇	1	4	yes	—
557	#95	C₂³×C₆₇	1	2	yes	—
558	C₂⁴	—	2	8	no	—
559	C₂⁴	—	2	4	no	—
560	C₂⁴	—	4	2	no	—
561	C₂⁴	—	4	4	no	—
562	C₂⁴	—	4	2	no	—
563	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
564	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
565	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
566	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
567	#41	—	4	32	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	8	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	16	no	—
573	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
574	C₂×D₄	—	2	8	no	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	4	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	1	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	16	no	—
599	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
600	C₂×D₄	#41×C₆₇	1	4	yes	complemented
601	C₂²×C₄	—	2	8	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	4	no	—
614	C₂²×C₄	—	4	4	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
619	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
625	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
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	—	2	8	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	8	no	—
634	C₄⋊C₄	—	4	1	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	1	no	—
649	C₂²⋊C₄	—	4	1	no	—
650	C₂²⋊C₄	—	4	4	no	—
651	C₂²⋊C₄	—	4	4	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	C₂×D₄×C₆₇	1	16	yes	—
654	C₂²⋊C₄	C₂×D₄×C₆₇	1	16	yes	—
655	C₄²	—	2	8	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	4	1	no	—
659	C₄²	—	4	2	no	—
660	C₄²	C₂×D₄×C₆₇	1	8	yes	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	4	8	no	—
683	C₂³	—	4	16	no	—
684	C₂³	—	8	8	no	—
685	C₂³	—	8	4	no	—
686	C₂³	—	8	4	no	—
687	C₂³	C₂²×D₄×C₆₇	1	8	yes	—
688	C₂³	C₂×#41×C₆₇	1	2	yes	—
689	C₂³	C₂×#41×C₆₇	1	2	yes	—
690	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
691	Q₈	—	2	16	no	—
692	Q₈	—	4	8	no	—
693	D₄	—	2	16	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	16	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	8	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	8	no	—
700	D₄	—	4	16	no	—
701	D₄	—	8	8	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	4	8	no	—
726	C₂×C₄	—	4	16	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	8	8	no	—
731	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
732	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
733	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
734	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
735	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
736	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	8	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	8	16	no	—
762	C₂²	C₂³×D₄×C₆₇	1	2	yes	—
763	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
764	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
765	C₂²	#585×C₆₇	1	2	yes	—
766	C₂²	#585×C₆₇	1	1	yes	characteristic
767	C₄	—	2	8	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	4	no	—
770	C₄	—	2	2	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	4	no	—
776	C₄	—	4	4	no	—
777	C₄	D₄²×C₆₇	1	4	yes	—
778	C₂	—	4	2	no	—
779	C₂	—	4	8	no	—
780	C₂	—	4	2	no	—
781	C₂	—	8	2	no	—
782	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
783	C₂	D₄×#41×C₆₇	1	2	yes	—
784	C₂	C₆₇×#3500	1	2	yes	—
785	C₂	C₆₇×#3505	1	1	yes	characteristic
786	C₂	C₆₇×#3551	1	1	yes	characteristic

	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×#548×C₆₇	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#2680	C₂	semidirect
4. C₆₇×#2669	C₂	semidirect
5. C₆₇×#2555	C₂	semidirect
6. C₆₇×#2536	C₂	semidirect
7. C₆₇×#2535	C₂	semidirect
8. C₆₇×#2472	C₂	semidirect
9. C₆₇×#2464	C₂	semidirect
10. C₆₇×#2409	C₂	semidirect
11. C₆₇×#2408	C₂	semidirect
12. C₆₇×#2407	C₂	semidirect
13. C₆₇×#2358	C₂	semidirect
14. C₄×#127×C₆₇	C₂	semidirect
15. C₄×#124×C₆₇	C₂	semidirect
17. C₂³×Q₈×C₆₇	C₂²	semidirect
23. C₂×#124×C₆₇	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
31. C₂×#121×C₆₇	C₂²	semidirect
34. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
38. C₂×C₄×D₄×C₆₇	C₂²	semidirect
39. C₂×C₄×D₄×C₆₇	C₂²	semidirect
40. C₂×C₄×D₄×C₆₇	C₂²	semidirect
42. #398×C₆₇	C₂²	semidirect
43. #397×C₆₇	C₂²	semidirect
44. #395×C₆₇	C₂²	semidirect
47. #394×C₆₇	C₂²	semidirect
50. #392×C₆₇	C₂²	semidirect
51. #392×C₆₇	C₂²	semidirect
52. #391×C₆₇	C₂²	semidirect
56. #390×C₆₇	C₂²	semidirect
57. #390×C₆₇	C₂²	semidirect
59. #388×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
63. #386×C₆₇	C₂²	semidirect
64. #386×C₆₇	C₂²	semidirect
65. #386×C₆₇	C₂²	semidirect
66. #385×C₆₇	C₂²	semidirect
67. #385×C₆₇	C₂²	semidirect
68. #384×C₆₇	C₂²	semidirect
69. #382×C₆₇	C₂²	semidirect
71. #380×C₆₇	C₂²	semidirect
72. #380×C₆₇	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
76. C₄³×C₆₇	C₂²	semidirect
104. #124×C₆₇	D₄	semidirect
206. C₂×D₄×C₆₇	#41	semidirect
384. #59818	C₆₇	direct (N × H)
394. C₂×#548	C₂×C₆₇	semidirect
395. C₂×#546	C₂×C₆₇	semidirect
396. #2680	C₂×C₆₇	semidirect
397. #2669	C₂×C₆₇	semidirect
398. #2555	C₂×C₆₇	semidirect
399. #2536	C₂×C₆₇	semidirect
400. #2535	C₂×C₆₇	semidirect
401. #2472	C₂×C₆₇	semidirect
402. #2464	C₂×C₆₇	semidirect
403. #2409	C₂×C₆₇	semidirect
404. #2408	C₂×C₆₇	semidirect
405. #2407	C₂×C₆₇	semidirect
406. #2358	C₂×C₆₇	semidirect
407. C₄×#127	C₂×C₆₇	semidirect
408. C₄×#124	C₂×C₆₇	semidirect
409. C₆₇	#59818	direct (N × H)
411. C₂³×Q₈	C₂²×C₆₇	semidirect
417. C₂×#124	C₂²×C₆₇	semidirect
420. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
421. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
425. C₂×#121	C₂²×C₆₇	semidirect
428. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
432. C₂×C₄×D₄	C₂²×C₆₇	semidirect
433. C₂×C₄×D₄	C₂²×C₆₇	semidirect
434. C₂×C₄×D₄	C₂²×C₆₇	semidirect
436. #398	C₂²×C₆₇	semidirect
437. #397	C₂²×C₆₇	semidirect
438. #395	C₂²×C₆₇	semidirect
441. #394	C₂²×C₆₇	semidirect
444. #392	C₂²×C₆₇	semidirect
445. #392	C₂²×C₆₇	semidirect
446. #391	C₂²×C₆₇	semidirect
450. #390	C₂²×C₆₇	semidirect
451. #390	C₂²×C₆₇	semidirect
453. #388	C₂²×C₆₇	semidirect
454. #388	C₂²×C₆₇	semidirect
455. #388	C₂²×C₆₇	semidirect
457. #386	C₂²×C₆₇	semidirect
458. #386	C₂²×C₆₇	semidirect
459. #386	C₂²×C₆₇	semidirect
460. #385	C₂²×C₆₇	semidirect
461. #385	C₂²×C₆₇	semidirect
462. #384	C₂²×C₆₇	semidirect
463. #382	C₂²×C₆₇	semidirect
465. #380	C₂²×C₆₇	semidirect
466. #380	C₂²×C₆₇	semidirect
468. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
469. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
470. C₄³	C₂²×C₆₇	semidirect
498. #124	D₄×C₆₇	semidirect
600. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#548×C₆₇	2
C₂×#546×C₆₇	2
C₆₇×#2680	2
C₆₇×#2669	2
C₆₇×#2555	2
C₆₇×#2536	2
C₆₇×#2535	2
C₆₇×#2472	2
C₆₇×#2464	2
C₆₇×#2409	2
C₆₇×#2408	2
C₆₇×#2407	2
C₆₇×#2358	2
C₄×#127×C₆₇	2
C₄×#124×C₆₇	2
#59818	67

Subgroups — C67×#59818 #30739069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59818 #30739069