Subgroups — C₆₇×#61564 #30740815

Order 17152.

2142 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#548×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3301	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3300	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3285	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3282	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3211	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3190	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3108	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
13	C₂×#451×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#448×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
17	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
19	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
21	#553×C₆₇	—	2	2	no	—
22	#553×C₆₇	C₂²	1	2	yes	complemented
23	#552×C₆₇	C₂²	1	2	yes	complemented
24	#551×C₆₇	—	2	2	no	—
25	#548×C₆₇	—	2	2	no	—
26	#548×C₆₇	—	2	2	no	—
27	#548×C₆₇	C₂²	1	4	yes	—
28	#548×C₆₇	C₂²	1	2	yes	complemented
29	#548×C₆₇	C₂²	1	4	yes	complemented
30	#546×C₆₇	C₂²	1	2	yes	complemented
31	#539×C₆₇	—	2	1	no	—
32	#538×C₆₇	—	2	1	no	—
33	#534×C₆₇	—	2	1	no	—
34	#529×C₆₇	C₂²	1	2	yes	—
35	C₂×#124×C₆₇	—	2	1	no	—
36	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#525×C₆₇	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#121×C₆₇	—	2	1	no	—
42	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
44	#518×C₆₇	—	2	1	no	—
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₆₇	—	2	1	no	—
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	#495×C₆₇	C₂²	1	4	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	complemented
50	#485×C₆₇	C₂²	1	4	yes	complemented
51	#483×C₆₇	C₂²	1	2	yes	complemented
52	#481×C₆₇	C₂²	1	2	yes	complemented
53	#480×C₆₇	C₂²	1	2	yes	—
54	#480×C₆₇	C₂²	1	2	yes	complemented
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#467×C₆₇	C₂²	1	4	yes	complemented
57	#466×C₆₇	C₂²	1	4	yes	complemented
58	#465×C₆₇	C₂²	1	4	yes	complemented
59	#465×C₆₇	C₂²	1	4	yes	complemented
60	#464×C₆₇	C₂²	1	4	yes	complemented
61	#464×C₆₇	C₂²	1	4	yes	complemented
62	#463×C₆₇	C₂²	1	4	yes	complemented
63	#452×C₆₇	C₂²	1	4	yes	complemented
64	#452×C₆₇	C₂²	1	4	yes	complemented
65	#451×C₆₇	C₂²	1	4	yes	complemented
66	#451×C₆₇	C₂²	1	2	yes	complemented
67	#451×C₆₇	C₂²	1	2	yes	complemented
68	#450×C₆₇	C₂²	1	2	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#448×C₆₇	C₂²	1	2	yes	—
71	#448×C₆₇	C₂²	1	2	yes	—
72	#448×C₆₇	C₂²	1	2	yes	complemented
73	#448×C₆₇	C₂²	1	4	yes	complemented
74	#447×C₆₇	C₂²	1	2	yes	—
75	#447×C₆₇	C₂²	1	2	yes	complemented
76	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
77	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
78	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
80	#431×C₆₇	C₂²	1	2	yes	complemented
81	#416×C₆₇	C₂²	1	4	yes	complemented
82	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
83	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
84	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#41×C₆₇	—	2	2	no	—
88	C₂×#41×C₆₇	—	4	4	no	—
89	C₂×#41×C₆₇	C₂³	1	4	yes	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂²×Q₈×C₆₇	—	2	1	no	—
92	C₂²×Q₈×C₆₇	—	2	1	no	—
93	C₂²×Q₈×C₆₇	—	2	1	no	—
94	C₂²×Q₈×C₆₇	—	4	4	no	—
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
98	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	—	2	1	no	—
102	C₂²×D₄×C₆₇	—	2	1	no	—
103	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	—	2	1	no	—
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	#135×C₆₇	—	4	8	no	—
111	C₂×Q₁₆×C₆₇	—	4	4	no	—
112	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₇	—	4	4	no	—
115	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
118	C₂×D₈×C₆₇	C₂³	1	4	yes	—
119	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
120	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
121	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
122	#126×C₆₇	—	2	2	no	—
123	#126×C₆₇	—	2	2	no	—
124	#126×C₆₇	—	2	2	no	—
125	#125×C₆₇	—	2	2	no	—
126	#125×C₆₇	C₂³	1	2	yes	—
127	#124×C₆₇	—	2	4	no	—
128	#124×C₆₇	—	2	4	no	—
129	#124×C₆₇	—	2	2	no	—
130	#124×C₆₇	—	2	2	no	—
131	#124×C₆₇	C₂³	1	4	yes	—
132	#124×C₆₇	C₂³	1	2	yes	—
133	#123×C₆₇	—	2	2	no	—
134	#123×C₆₇	—	2	2	no	—
135	#123×C₆₇	—	2	2	no	—
136	#123×C₆₇	—	2	2	no	—
137	#123×C₆₇	—	2	2	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	1	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	—	2	2	no	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
148	#121×C₆₇	—	2	4	no	—
149	#121×C₆₇	—	2	4	no	—
150	#121×C₆₇	—	2	2	no	—
151	#121×C₆₇	—	2	2	no	—
152	#121×C₆₇	—	2	1	no	—
153	#121×C₆₇	—	2	1	no	—
154	#121×C₆₇	—	2	1	no	—
155	#121×C₆₇	—	2	1	no	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	C₂³	1	2	yes	—
158	#121×C₆₇	C₂³	1	2	yes	—
159	#121×C₆₇	C₂³	1	2	yes	—
160	#121×C₆₇	C₂³	1	2	yes	—
161	#121×C₆₇	C₂³	1	2	yes	—
162	#120×C₆₇	—	2	2	no	—
163	#120×C₆₇	—	2	2	no	—
164	C₄×Q₈×C₆₇	—	2	2	no	—
165	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	4	no	—
171	C₄×D₄×C₆₇	—	2	4	no	—
172	C₄×D₄×C₆₇	—	2	2	no	—
173	C₄×D₄×C₆₇	—	2	2	no	—
174	C₄×D₄×C₆₇	D₄	1	2	yes	—
175	C₄×D₄×C₆₇	D₄	1	2	yes	—
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	2	yes	—
178	C₄×D₄×C₆₇	C₂³	1	2	yes	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	—	2	1	no	—
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	#107×C₆₇	C₂³	1	4	yes	—
201	#106×C₆₇	C₂³	1	4	yes	—
202	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	4	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#103×C₆₇	C₂³	1	4	yes	—
206	#103×C₆₇	C₂³	1	4	yes	—
207	#103×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	4	yes	—
210	#102×C₆₇	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
216	C₄×C₈×C₆₇	C₂³	1	4	yes	—
217	C₂⁴×C₆₇	—	2	1	no	—
218	C₂⁴×C₆₇	—	2	1	no	—
219	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
221	#41×C₆₇	—	2	8	no	—
222	#41×C₆₇	—	4	4	no	—
223	#41×C₆₇	—	4	4	no	—
224	#41×C₆₇	—	4	8	no	—
225	C₂×Q₈×C₆₇	—	2	4	no	—
226	C₂×Q₈×C₆₇	—	2	1	no	—
227	C₂×Q₈×C₆₇	—	2	2	no	—
228	C₂×Q₈×C₆₇	—	2	2	no	—
229	C₂×Q₈×C₆₇	—	2	1	no	—
230	C₂×Q₈×C₆₇	—	2	1	no	—
231	C₂×Q₈×C₆₇	—	2	4	no	—
232	C₂×Q₈×C₆₇	—	2	4	no	—
233	C₂×Q₈×C₆₇	—	4	2	no	—
234	C₂×Q₈×C₆₇	—	4	2	no	—
235	C₂×Q₈×C₆₇	—	4	2	no	—
236	C₂×Q₈×C₆₇	—	4	4	no	—
237	C₂×Q₈×C₆₇	—	4	2	no	—
238	C₂×Q₈×C₆₇	—	4	4	no	—
239	C₂×Q₈×C₆₇	—	4	4	no	—
240	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
243	C₂×D₄×C₆₇	—	2	4	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	1	no	—
252	C₂×D₄×C₆₇	—	2	1	no	—
253	C₂×D₄×C₆₇	—	4	2	no	—
254	C₂×D₄×C₆₇	—	4	2	no	—
255	C₂×D₄×C₆₇	—	4	4	no	—
256	C₂×D₄×C₆₇	—	4	4	no	—
257	C₂×D₄×C₆₇	—	4	4	no	—
258	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	—	2	1	no	—
263	C₂²×C₄×C₆₇	—	2	1	no	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	1	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	1	no	—
269	C₂²×C₄×C₆₇	—	2	1	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	4	no	—
276	C₂²×C₄×C₆₇	—	4	4	no	—
277	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	Q₁₆×C₆₇	—	2	8	no	—
289	Q₁₆×C₆₇	—	4	4	no	—
290	SD₁₆×C₆₇	—	2	8	no	—
291	SD₁₆×C₆₇	—	4	4	no	—
292	SD₁₆×C₆₇	—	4	4	no	—
293	D₈×C₆₇	—	4	4	no	—
294	C₂×C₈×C₆₇	—	4	2	no	—
295	C₂×C₈×C₆₇	—	4	2	no	—
296	C₂×C₈×C₆₇	—	4	4	no	—
297	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
298	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	2	4	no	—
301	C₄⋊C₄×C₆₇	—	2	4	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	1	no	—
304	C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₄⋊C₄×C₆₇	—	2	1	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₆₇	—	2	2	no	—
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	2	no	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₄²×C₆₇	—	2	4	no	—
335	C₄²×C₆₇	—	2	2	no	—
336	C₄²×C₆₇	—	2	2	no	—
337	C₄²×C₆₇	C₂×D₄	1	2	yes	—
338	C₄²×C₆₇	C₂⁴	1	2	yes	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	4	1	no	—
343	C₂³×C₆₇	—	4	1	no	—
344	C₂³×C₆₇	—	4	1	no	—
345	C₂³×C₆₇	—	4	1	no	—
346	C₂³×C₆₇	—	4	2	no	—
347	C₂³×C₆₇	—	4	2	no	—
348	C₂³×C₆₇	—	4	2	no	—
349	C₂³×C₆₇	—	4	2	no	—
350	C₂³×C₆₇	—	8	1	no	—
351	C₂³×C₆₇	—	8	1	no	—
352	C₂³×C₆₇	#135	1	4	yes	complemented
353	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
354	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
355	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₆₇	—	2	4	no	—
358	Q₈×C₆₇	—	2	2	no	—
359	Q₈×C₆₇	—	2	2	no	—
360	Q₈×C₆₇	—	2	4	no	—
361	Q₈×C₆₇	—	2	2	no	—
362	Q₈×C₆₇	—	4	4	no	—
363	Q₈×C₆₇	—	4	4	no	—
364	Q₈×C₆₇	—	4	2	no	—
365	Q₈×C₆₇	—	8	1	no	—
366	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
367	D₄×C₆₇	—	2	4	no	—
368	D₄×C₆₇	—	2	4	no	—
369	D₄×C₆₇	—	2	4	no	—
370	D₄×C₆₇	—	2	4	no	—
371	D₄×C₆₇	—	4	8	no	—
372	D₄×C₆₇	—	4	2	no	—
373	D₄×C₆₇	—	4	4	no	—
374	D₄×C₆₇	—	4	4	no	—
375	D₄×C₆₇	—	4	4	no	—
376	D₄×C₆₇	—	4	4	no	—
377	D₄×C₆₇	—	8	1	no	—
378	D₄×C₆₇	—	8	2	no	—
379	D₄×C₆₇	—	8	2	no	—
380	C₂×C₄×C₆₇	—	2	4	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	4	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	4	1	no	—
393	C₂×C₄×C₆₇	—	4	1	no	—
394	C₂×C₄×C₆₇	—	4	1	no	—
395	C₂×C₄×C₆₇	—	4	1	no	—
396	C₂×C₄×C₆₇	—	4	2	no	—
397	C₂×C₄×C₆₇	—	4	1	no	—
398	C₂×C₄×C₆₇	—	4	8	no	—
399	C₂×C₄×C₆₇	—	4	4	no	—
400	C₂×C₄×C₆₇	—	4	4	no	—
401	C₂×C₄×C₆₇	—	4	2	no	—
402	C₂×C₄×C₆₇	—	4	2	no	—
403	C₂×C₄×C₆₇	—	4	2	no	—
404	C₂×C₄×C₆₇	—	8	2	no	—
405	C₂×C₄×C₆₇	—	8	2	no	—
406	C₂×C₄×C₆₇	—	8	1	no	—
407	C₂×C₄×C₆₇	—	8	1	no	—
408	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
415	C₈×C₆₇	—	2	4	no	—
416	C₈×C₆₇	—	2	4	no	—
417	C₂²×C₆₇	—	2	1	no	—
418	C₂²×C₆₇	—	2	1	no	—
419	C₂²×C₆₇	—	2	1	no	—
420	C₂²×C₆₇	—	2	1	no	—
421	C₂²×C₆₇	—	2	1	no	—
422	C₂²×C₆₇	—	2	1	no	—
423	C₂²×C₆₇	—	2	2	no	—
424	C₂²×C₆₇	—	2	2	no	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	4	4	no	—
427	C₂²×C₆₇	—	4	2	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	2	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	8	2	no	—
434	C₂²×C₆₇	—	8	4	no	—
435	C₂²×C₆₇	—	16	2	no	—
436	C₂²×C₆₇	C₂×#135	1	2	yes	—
437	C₂²×C₆₇	C₂×#135	1	2	yes	—
438	C₂²×C₆₇	C₂×#135	1	2	yes	—
439	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₆₇	—	2	2	no	—
441	C₄×C₆₇	—	2	4	no	—
442	C₄×C₆₇	—	2	2	no	—
443	C₄×C₆₇	—	2	1	no	—
444	C₄×C₆₇	—	2	1	no	—
445	C₄×C₆₇	—	2	1	no	—
446	C₄×C₆₇	—	2	2	no	—
447	C₄×C₆₇	—	4	2	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	2	no	—
451	C₄×C₆₇	—	4	2	no	—
452	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
453	#61564	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂×C₆₇	—	2	2	no	—
455	C₂×C₆₇	—	2	2	no	—
456	C₂×C₆₇	—	2	2	no	—
457	C₂×C₆₇	—	4	2	no	—
458	C₂×C₆₇	—	8	2	no	—
459	C₂×C₆₇	—	8	2	no	—
460	C₂×C₆₇	#3484	1	1	yes	characteristic
461	C₂×C₆₇	C₂²×#135	1	1	yes	characteristic
462	C₂×C₆₇	#3586	1	1	yes	characteristic
463	#3505	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₂×#548	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#3301	C₂×C₆₇	1	4	yes	complemented
466	#3300	C₂×C₆₇	1	4	yes	complemented
467	#3285	C₂×C₆₇	1	4	yes	complemented
468	#3282	C₂×C₆₇	1	4	yes	complemented
469	#3211	C₂×C₆₇	1	2	yes	complemented
470	#3190	C₂×C₆₇	1	2	yes	complemented
471	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#3108	C₂×C₆₇	1	2	yes	complemented
474	#3002	C₂×C₆₇	1	2	yes	complemented
475	C₂×#451	C₂×C₆₇	1	1	yes	characteristic, complemented
476	C₂×#448	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#2972	C₂×C₆₇	1	1	yes	characteristic, complemented
478	C₆₇	#61564	1	1	yes	characteristic, direct product factor, Sylow
479	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
482	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
483	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
484	#553	—	2	2	no	—
485	#553	C₂²×C₆₇	1	2	yes	complemented
486	#552	C₂²×C₆₇	1	2	yes	complemented
487	#551	—	2	2	no	—
488	#548	—	2	2	no	—
489	#548	—	2	2	no	—
490	#548	C₂²×C₆₇	1	4	yes	—
491	#548	C₂²×C₆₇	1	4	yes	complemented
492	#548	C₂²×C₆₇	1	2	yes	complemented
493	#546	C₂²×C₆₇	1	2	yes	complemented
494	#539	—	2	1	no	—
495	#538	—	2	1	no	—
496	#534	—	2	1	no	—
497	#529	C₂²×C₆₇	1	2	yes	—
498	C₂×#124	—	2	1	no	—
499	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	#525	C₂²×C₆₇	1	2	yes	—
501	C₂×C₂²⋊Q₈	—	2	1	no	—
502	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
503	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
504	C₂×#121	—	2	1	no	—
505	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
506	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
507	#518	—	2	1	no	—
508	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
509	C₂×C₄×D₄	—	2	1	no	—
510	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
511	#495	C₂²×C₆₇	1	4	yes	complemented
512	#488	C₂²×C₆₇	1	4	yes	complemented
513	#485	C₂²×C₆₇	1	4	yes	complemented
514	#483	C₂²×C₆₇	1	2	yes	complemented
515	#481	C₂²×C₆₇	1	2	yes	complemented
516	#480	C₂²×C₆₇	1	2	yes	—
517	#480	C₂²×C₆₇	1	2	yes	complemented
518	#479	C₂²×C₆₇	1	4	yes	complemented
519	#467	C₂²×C₆₇	1	4	yes	complemented
520	#466	C₂²×C₆₇	1	4	yes	complemented
521	#465	C₂²×C₆₇	1	4	yes	complemented
522	#465	C₂²×C₆₇	1	4	yes	complemented
523	#464	C₂²×C₆₇	1	4	yes	complemented
524	#464	C₂²×C₆₇	1	4	yes	complemented
525	#463	C₂²×C₆₇	1	4	yes	complemented
526	#452	C₂²×C₆₇	1	4	yes	complemented
527	#452	C₂²×C₆₇	1	4	yes	complemented
528	#451	C₂²×C₆₇	1	2	yes	complemented
529	#451	C₂²×C₆₇	1	2	yes	complemented
530	#451	C₂²×C₆₇	1	4	yes	complemented
531	#450	C₂²×C₆₇	1	2	yes	complemented
532	#449	C₂²×C₆₇	1	4	yes	complemented
533	#448	C₂²×C₆₇	1	2	yes	—
534	#448	C₂²×C₆₇	1	2	yes	—
535	#448	C₂²×C₆₇	1	2	yes	complemented
536	#448	C₂²×C₆₇	1	4	yes	complemented
537	#447	C₂²×C₆₇	1	2	yes	—
538	#447	C₂²×C₆₇	1	2	yes	complemented
539	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
540	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
541	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
542	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
543	#431	C₂²×C₆₇	1	2	yes	complemented
544	#416	C₂²×C₆₇	1	4	yes	complemented
545	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
546	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
547	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
548	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
549	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
550	C₂×#41	—	2	2	no	—
551	C₂×#41	—	4	4	no	—
552	C₂×#41	C₂³×C₆₇	1	4	yes	—
553	C₂×#41	C₂³×C₆₇	1	2	yes	—
554	C₂²×Q₈	—	2	1	no	—
555	C₂²×Q₈	—	2	1	no	—
556	C₂²×Q₈	—	2	1	no	—
557	C₂²×Q₈	—	4	4	no	—
558	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
560	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
561	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
573	#135	—	4	8	no	—
574	C₂×Q₁₆	—	4	4	no	—
575	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
576	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
577	C₂×SD₁₆	—	4	4	no	—
578	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
581	C₂×D₈	C₂³×C₆₇	1	4	yes	—
582	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
583	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
584	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#126	—	2	2	no	—
588	#125	—	2	2	no	—
589	#125	C₂³×C₆₇	1	2	yes	—
590	#124	—	2	4	no	—
591	#124	—	2	4	no	—
592	#124	—	2	2	no	—
593	#124	—	2	2	no	—
594	#124	C₂³×C₆₇	1	4	yes	—
595	#124	C₂³×C₆₇	1	2	yes	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	4	no	—
605	C₂²⋊Q₈	—	2	4	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
608	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
609	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
610	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
611	#121	—	2	4	no	—
612	#121	—	2	4	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	—	2	1	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	1	no	—
619	#121	—	2	2	no	—
620	#121	C₂³×C₆₇	1	2	yes	—
621	#121	C₂³×C₆₇	1	2	yes	—
622	#121	C₂³×C₆₇	1	2	yes	—
623	#121	C₂³×C₆₇	1	2	yes	—
624	#121	C₂³×C₆₇	1	2	yes	—
625	#120	—	2	2	no	—
626	#120	—	2	2	no	—
627	C₄×Q₈	—	2	2	no	—
628	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
629	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	4	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	D₄×C₆₇	1	2	yes	—
638	C₄×D₄	D₄×C₆₇	1	2	yes	—
639	C₄×D₄	C₂³×C₆₇	1	2	yes	—
640	C₄×D₄	C₂³×C₆₇	1	2	yes	—
641	C₄×D₄	C₂³×C₆₇	1	2	yes	—
642	#117	—	2	2	no	—
643	#117	—	2	2	no	—
644	#117	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
663	#107	C₂³×C₆₇	1	4	yes	—
664	#106	C₂³×C₆₇	1	4	yes	—
665	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
666	#103	C₂³×C₆₇	1	4	yes	—
667	#103	C₂³×C₆₇	1	4	yes	—
668	#103	C₂³×C₆₇	1	4	yes	—
669	#103	C₂³×C₆₇	1	4	yes	—
670	#103	C₂³×C₆₇	1	4	yes	—
671	#102	C₂³×C₆₇	1	4	yes	—
672	#102	C₂³×C₆₇	1	4	yes	—
673	#102	C₂³×C₆₇	1	4	yes	—
674	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
679	C₄×C₈	C₂³×C₆₇	1	4	yes	—
680	C₂⁴	—	2	1	no	—
681	C₂⁴	—	2	1	no	—
682	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
683	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
684	#41	—	2	8	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	4	8	no	—
688	C₂×Q₈	—	2	4	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	4	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	4	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	—	4	4	no	—
702	C₂×Q₈	—	4	4	no	—
703	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
704	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
705	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
722	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
723	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
751	Q₁₆	—	2	8	no	—
752	Q₁₆	—	4	4	no	—
753	SD₁₆	—	2	8	no	—
754	SD₁₆	—	4	4	no	—
755	SD₁₆	—	4	4	no	—
756	D₈	—	4	4	no	—
757	C₂×C₈	—	4	2	no	—
758	C₂×C₈	—	4	2	no	—
759	C₂×C₈	—	4	4	no	—
760	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
761	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
775	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
797	C₄²	—	2	4	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	C₂×D₄×C₆₇	1	2	yes	—
801	C₄²	C₂⁴×C₆₇	1	2	yes	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	#135×C₆₇	1	4	yes	complemented
816	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
817	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
818	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
819	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
820	Q₈	—	2	4	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	4	4	no	—
826	Q₈	—	4	4	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
830	D₄	—	2	4	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	4	no	—
834	D₄	—	4	8	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	8	1	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	1	no	—
870	C₂×C₄	—	8	1	no	—
871	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
877	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
878	C₈	—	2	4	no	—
879	C₈	—	2	4	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	8	4	no	—
898	C₂²	—	16	2	no	—
899	C₂²	C₂×#135×C₆₇	1	2	yes	—
900	C₂²	C₂×#135×C₆₇	1	2	yes	—
901	C₂²	C₂×#135×C₆₇	1	2	yes	—
902	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
916	C₂	—	2	2	no	—
917	C₂	—	2	2	no	—
918	C₂	—	2	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	8	2	no	—
921	C₂	—	8	2	no	—
922	C₂	C₆₇×#3484	1	1	yes	characteristic
923	C₂	C₂²×#135×C₆₇	1	1	yes	characteristic
924	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3505	C₂	semidirect
2. C₂×#548×C₆₇	C₂	semidirect
3. C₆₇×#3301	C₂	semidirect
4. C₆₇×#3300	C₂	semidirect
5. C₆₇×#3285	C₂	semidirect
6. C₆₇×#3282	C₂	semidirect
7. C₆₇×#3211	C₂	semidirect
8. C₆₇×#3190	C₂	semidirect
9. C₆₇×#3187	C₂	semidirect
10. C₆₇×#3186	C₂	semidirect
11. C₆₇×#3108	C₂	semidirect
12. C₆₇×#3002	C₂	semidirect
13. C₂×#451×C₆₇	C₂	semidirect
14. C₂×#448×C₆₇	C₂	semidirect
15. C₆₇×#2972	C₂	semidirect
16. C₂²×#41×C₆₇	C₂²	semidirect
18. C₂×#135×C₆₇	C₂²	semidirect
19. C₂²×Q₁₆×C₆₇	C₂²	semidirect
20. C₂²×SD₁₆×C₆₇	C₂²	semidirect
22. #553×C₆₇	C₂²	semidirect
23. #552×C₆₇	C₂²	semidirect
28. #548×C₆₇	C₂²	semidirect
29. #548×C₆₇	C₂²	semidirect
30. #546×C₆₇	C₂²	semidirect
36. C₂×#124×C₆₇	C₂²	semidirect
40. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
45. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
48. #495×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #485×C₆₇	C₂²	semidirect
51. #483×C₆₇	C₂²	semidirect
52. #481×C₆₇	C₂²	semidirect
54. #480×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #467×C₆₇	C₂²	semidirect
57. #466×C₆₇	C₂²	semidirect
58. #465×C₆₇	C₂²	semidirect
59. #465×C₆₇	C₂²	semidirect
60. #464×C₆₇	C₂²	semidirect
61. #464×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #452×C₆₇	C₂²	semidirect
64. #452×C₆₇	C₂²	semidirect
65. #451×C₆₇	C₂²	semidirect
66. #451×C₆₇	C₂²	semidirect
67. #451×C₆₇	C₂²	semidirect
68. #450×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
72. #448×C₆₇	C₂²	semidirect
73. #448×C₆₇	C₂²	semidirect
75. #447×C₆₇	C₂²	semidirect
76. C₄×Q₁₆×C₆₇	C₂²	semidirect
77. C₄×SD₁₆×C₆₇	C₂²	semidirect
78. C₈×D₄×C₆₇	C₂²	semidirect
79. C₈×D₄×C₆₇	C₂²	semidirect
80. #431×C₆₇	C₂²	semidirect
81. #416×C₆₇	C₂²	semidirect
82. C₂×#103×C₆₇	C₂²	semidirect
83. C₂×#103×C₆₇	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
352. C₂³×C₆₇	#135	semidirect
453. #61564	C₆₇	direct (N × H)
463. #3505	C₂×C₆₇	semidirect
464. C₂×#548	C₂×C₆₇	semidirect
465. #3301	C₂×C₆₇	semidirect
466. #3300	C₂×C₆₇	semidirect
467. #3285	C₂×C₆₇	semidirect
468. #3282	C₂×C₆₇	semidirect
469. #3211	C₂×C₆₇	semidirect
470. #3190	C₂×C₆₇	semidirect
471. #3187	C₂×C₆₇	semidirect
472. #3186	C₂×C₆₇	semidirect
473. #3108	C₂×C₆₇	semidirect
474. #3002	C₂×C₆₇	semidirect
475. C₂×#451	C₂×C₆₇	semidirect
476. C₂×#448	C₂×C₆₇	semidirect
477. #2972	C₂×C₆₇	semidirect
478. C₆₇	#61564	direct (N × H)
479. C₂²×#41	C₂²×C₆₇	semidirect
481. C₂×#135	C₂²×C₆₇	semidirect
482. C₂²×Q₁₆	C₂²×C₆₇	semidirect
483. C₂²×SD₁₆	C₂²×C₆₇	semidirect
485. #553	C₂²×C₆₇	semidirect
486. #552	C₂²×C₆₇	semidirect
491. #548	C₂²×C₆₇	semidirect
492. #548	C₂²×C₆₇	semidirect
493. #546	C₂²×C₆₇	semidirect
499. C₂×#124	C₂²×C₆₇	semidirect
503. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
508. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
511. #495	C₂²×C₆₇	semidirect
512. #488	C₂²×C₆₇	semidirect
513. #485	C₂²×C₆₇	semidirect
514. #483	C₂²×C₆₇	semidirect
515. #481	C₂²×C₆₇	semidirect
517. #480	C₂²×C₆₇	semidirect
518. #479	C₂²×C₆₇	semidirect
519. #467	C₂²×C₆₇	semidirect
520. #466	C₂²×C₆₇	semidirect
521. #465	C₂²×C₆₇	semidirect
522. #465	C₂²×C₆₇	semidirect
523. #464	C₂²×C₆₇	semidirect
524. #464	C₂²×C₆₇	semidirect
525. #463	C₂²×C₆₇	semidirect
526. #452	C₂²×C₆₇	semidirect
527. #452	C₂²×C₆₇	semidirect
528. #451	C₂²×C₆₇	semidirect
529. #451	C₂²×C₆₇	semidirect
530. #451	C₂²×C₆₇	semidirect
531. #450	C₂²×C₆₇	semidirect
532. #449	C₂²×C₆₇	semidirect
535. #448	C₂²×C₆₇	semidirect
536. #448	C₂²×C₆₇	semidirect
538. #447	C₂²×C₆₇	semidirect
539. C₄×Q₁₆	C₂²×C₆₇	semidirect
540. C₄×SD₁₆	C₂²×C₆₇	semidirect
541. C₈×D₄	C₂²×C₆₇	semidirect
542. C₈×D₄	C₂²×C₆₇	semidirect
543. #431	C₂²×C₆₇	semidirect
544. #416	C₂²×C₆₇	semidirect
545. C₂×#103	C₂²×C₆₇	semidirect
546. C₂×#103	C₂²×C₆₇	semidirect
549. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
815. C₂³	#135×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3505	2
C₂×#548×C₆₇	2
C₆₇×#3301	2
C₆₇×#3300	2
C₆₇×#3285	2
C₆₇×#3282	2
C₆₇×#3211	2
C₆₇×#3190	2
C₆₇×#3187	2
C₆₇×#3186	2
C₆₇×#3108	2
C₆₇×#3002	2
C₂×#451×C₆₇	2
C₂×#448×C₆₇	2
C₆₇×#2972	2
#61564	67

Subgroups — C67×#61564 #30740815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61564 #30740815