Subgroups — C₆₇×#61010 #30740261

Order 17152.

1700 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3258	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3233	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3232	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3212	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3211	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3183	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3168	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3127	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3126	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3123	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3122	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	#559×C₆₇	—	2	2	no	—
21	#556×C₆₇	—	2	2	no	—
22	#553×C₆₇	—	2	2	no	—
23	#553×C₆₇	—	2	2	no	—
24	#553×C₆₇	—	2	2	no	—
25	#552×C₆₇	—	2	2	no	—
26	#551×C₆₇	—	2	2	no	—
27	#551×C₆₇	—	2	2	no	—
28	#542×C₆₇	C₂²	1	2	yes	—
29	#542×C₆₇	C₂²	1	2	yes	—
30	#541×C₆₇	C₂²	1	1	yes	characteristic
31	#541×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#540×C₆₇	C₂²	1	1	yes	characteristic
33	#540×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#537×C₆₇	C₂²	1	2	yes	—
35	#536×C₆₇	C₂²	1	1	yes	characteristic
36	#535×C₆₇	C₂²	1	1	yes	characteristic
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#529×C₆₇	C₂²	1	2	yes	—
40	#529×C₆₇	C₂²	1	2	yes	—
41	#529×C₆₇	C₂²	1	2	yes	—
42	#529×C₆₇	C₂²	1	2	yes	complemented
43	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
45	#520×C₆₇	C₂²	1	2	yes	complemented
46	#519×C₆₇	C₂²	1	1	yes	characteristic
47	#518×C₆₇	C₂²	1	1	yes	characteristic
48	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
49	#499×C₆₇	C₂²	1	2	yes	complemented
50	#499×C₆₇	C₂²	1	2	yes	complemented
51	#495×C₆₇	C₂²	1	2	yes	—
52	#495×C₆₇	C₂²	1	2	yes	—
53	#488×C₆₇	C₂²	1	2	yes	—
54	#488×C₆₇	C₂²	1	2	yes	—
55	#488×C₆₇	C₂²	1	2	yes	complemented
56	#488×C₆₇	C₂²	1	2	yes	complemented
57	#485×C₆₇	C₂²	1	2	yes	—
58	#485×C₆₇	C₂²	1	2	yes	—
59	#484×C₆₇	C₂²	1	2	yes	complemented
60	#483×C₆₇	C₂²	1	2	yes	complemented
61	#482×C₆₇	C₂²	1	2	yes	—
62	#482×C₆₇	C₂²	1	2	yes	—
63	#481×C₆₇	C₂²	1	2	yes	—
64	#480×C₆₇	C₂²	1	2	yes	—
65	#479×C₆₇	C₂²	1	2	yes	complemented
66	#479×C₆₇	C₂²	1	2	yes	complemented
67	#478×C₆₇	C₂²	1	2	yes	—
68	#478×C₆₇	C₂²	1	2	yes	—
69	#477×C₆₇	C₂²	1	2	yes	complemented
70	#476×C₆₇	C₂²	1	2	yes	complemented
71	#475×C₆₇	C₂²	1	2	yes	complemented
72	#474×C₆₇	C₂²	1	2	yes	complemented
73	#470×C₆₇	C₂²	1	2	yes	complemented
74	#469×C₆₇	C₂²	1	2	yes	—
75	#468×C₆₇	C₂²	1	2	yes	—
76	#468×C₆₇	C₂²	1	2	yes	complemented
77	#467×C₆₇	C₂²	1	2	yes	complemented
78	#466×C₆₇	C₂²	1	2	yes	—
79	#465×C₆₇	C₂²	1	2	yes	—
80	#465×C₆₇	C₂²	1	2	yes	complemented
81	#464×C₆₇	C₂²	1	2	yes	—
82	#464×C₆₇	C₂²	1	2	yes	—
83	#463×C₆₇	C₂²	1	2	yes	—
84	#463×C₆₇	C₂²	1	2	yes	—
85	#462×C₆₇	C₂²	1	2	yes	complemented
86	#461×C₆₇	C₂²	1	2	yes	—
87	#460×C₆₇	C₂²	1	2	yes	complemented
88	#459×C₆₇	C₂²	1	2	yes	—
89	#452×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	2	yes	complemented
91	#451×C₆₇	C₂²	1	2	yes	—
92	#450×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	—
95	#448×C₆₇	C₂²	1	2	yes	—
96	#447×C₆₇	C₂²	1	2	yes	—
97	#442×C₆₇	C₂²	1	2	yes	—
98	#441×C₆₇	C₂²	1	2	yes	complemented
99	#440×C₆₇	C₂²	1	2	yes	—
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
104	C₄×D₈×C₆₇	C₂²	1	2	yes	—
105	#433×C₆₇	C₂²	1	1	yes	characteristic
106	#433×C₆₇	C₂²	1	1	yes	characteristic
107	#433×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#433×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#431×C₆₇	C₂²	1	2	yes	—
110	#431×C₆₇	C₂²	1	2	yes	complemented
111	#424×C₆₇	C₂²	1	2	yes	complemented
112	#408×C₆₇	C₂²	1	2	yes	—
113	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₆₇	C₂³	1	2	yes	—
116	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×D₈×C₆₇	C₂³	1	2	yes	—
126	C₂×D₈×C₆₇	C₂³	1	2	yes	—
127	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₇	—	2	1	no	—
130	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
132	#127×C₆₇	—	2	1	no	—
133	#127×C₆₇	C₂³	1	1	yes	characteristic
134	#126×C₆₇	—	2	2	no	—
135	#126×C₆₇	—	2	2	no	—
136	#126×C₆₇	—	2	2	no	—
137	#126×C₆₇	—	2	2	no	—
138	#126×C₆₇	—	2	2	no	—
139	#126×C₆₇	—	2	2	no	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#125×C₆₇	—	2	2	no	—
143	#125×C₆₇	—	2	2	no	—
144	#125×C₆₇	—	2	2	no	—
145	#125×C₆₇	C₂³	1	1	yes	characteristic
146	#125×C₆₇	C₂³	1	1	yes	characteristic
147	#125×C₆₇	C₂³	1	2	yes	—
148	#125×C₆₇	C₂³	1	2	yes	—
149	#124×C₆₇	—	2	1	no	—
150	#124×C₆₇	—	2	1	no	—
151	#124×C₆₇	—	2	2	no	—
152	#124×C₆₇	—	2	2	no	—
153	#124×C₆₇	—	2	2	no	—
154	#124×C₆₇	C₂³	1	2	yes	—
155	#124×C₆₇	C₂³	1	2	yes	—
156	#124×C₆₇	C₂³	1	2	yes	—
157	#123×C₆₇	—	2	1	no	—
158	#123×C₆₇	—	2	1	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	#123×C₆₇	—	2	2	no	—
163	#123×C₆₇	—	2	2	no	—
164	#123×C₆₇	—	2	2	no	—
165	#123×C₆₇	—	2	2	no	—
166	#123×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	—	2	2	no	—
169	C₂²⋊Q₈×C₆₇	—	2	2	no	—
170	C₂²⋊Q₈×C₆₇	—	2	2	no	—
171	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
172	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
173	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
174	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
175	#121×C₆₇	—	2	2	no	—
176	#121×C₆₇	—	2	2	no	—
177	#121×C₆₇	—	2	2	no	—
178	#121×C₆₇	—	2	2	no	—
179	#121×C₆₇	—	2	2	no	—
180	#121×C₆₇	—	2	2	no	—
181	#121×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#121×C₆₇	C₂³	1	2	yes	—
184	#121×C₆₇	C₂³	1	2	yes	—
185	#120×C₆₇	—	2	1	no	—
186	#120×C₆₇	—	2	1	no	—
187	C₄×Q₈×C₆₇	—	2	2	no	—
188	C₄×Q₈×C₆₇	—	2	2	no	—
189	C₄×Q₈×C₆₇	D₄	1	2	yes	—
190	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
191	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
192	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
193	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	2	no	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	—	2	2	no	—
201	C₄×D₄×C₆₇	—	2	2	no	—
202	C₄×D₄×C₆₇	D₄	1	2	yes	—
203	C₄×D₄×C₆₇	D₄	1	2	yes	—
204	C₄×D₄×C₆₇	D₄	1	2	yes	—
205	C₄×D₄×C₆₇	C₂³	1	2	yes	—
206	C₄×D₄×C₆₇	C₂³	1	2	yes	—
207	C₄×D₄×C₆₇	C₂³	1	2	yes	—
208	C₄×D₄×C₆₇	C₂³	1	2	yes	—
209	#117×C₆₇	—	2	2	no	—
210	#117×C₆₇	—	2	2	no	—
211	#117×C₆₇	—	2	2	no	—
212	#117×C₆₇	—	2	2	no	—
213	#117×C₆₇	—	2	2	no	—
214	#117×C₆₇	—	2	2	no	—
215	#117×C₆₇	C₂³	1	1	yes	characteristic
216	#117×C₆₇	C₂³	1	1	yes	characteristic
217	#117×C₆₇	C₂³	1	1	yes	characteristic
218	#117×C₆₇	C₂³	1	1	yes	characteristic
219	#117×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
221	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
224	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	#107×C₆₇	C₂³	1	2	yes	—
229	#107×C₆₇	C₂³	1	2	yes	—
230	#107×C₆₇	C₂³	1	2	yes	—
231	#107×C₆₇	C₂³	1	2	yes	—
232	#106×C₆₇	C₂³	1	2	yes	—
233	#106×C₆₇	C₂³	1	2	yes	—
234	#106×C₆₇	C₂³	1	2	yes	—
235	#106×C₆₇	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
238	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
239	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
240	#103×C₆₇	C₂³	1	2	yes	—
241	#103×C₆₇	C₂³	1	2	yes	—
242	#103×C₆₇	C₂³	1	2	yes	—
243	#103×C₆₇	C₂³	1	2	yes	—
244	#103×C₆₇	C₂³	1	2	yes	—
245	#103×C₆₇	C₂³	1	2	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	2	yes	—
248	#102×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	#102×C₆₇	C₂³	1	2	yes	—
253	#102×C₆₇	C₂³	1	2	yes	—
254	#102×C₆₇	C₂³	1	2	yes	—
255	#102×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
260	#97×C₆₇	C₂³	1	1	yes	characteristic
261	#97×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₆₇	C₂³	1	2	yes	—
263	C₄×C₈×C₆₇	C₂³	1	2	yes	—
264	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
266	C₂⁴×C₆₇	—	2	1	no	—
267	#41×C₆₇	—	4	2	no	—
268	#41×C₆₇	—	4	2	no	—
269	#41×C₆₇	—	4	2	no	—
270	C₂×Q₈×C₆₇	—	2	1	no	—
271	C₂×Q₈×C₆₇	—	2	2	no	—
272	C₂×Q₈×C₆₇	—	4	2	no	—
273	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
275	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	2	1	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	4	2	no	—
284	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	—	2	1	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	2	no	—
292	C₂²×C₄×C₆₇	—	2	2	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	2	2	no	—
296	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	Q₁₆×C₆₇	—	4	2	no	—
303	Q₁₆×C₆₇	—	4	2	no	—
304	SD₁₆×C₆₇	—	4	2	no	—
305	SD₁₆×C₆₇	—	4	2	no	—
306	SD₁₆×C₆₇	—	4	2	no	—
307	SD₁₆×C₆₇	—	4	2	no	—
308	D₈×C₆₇	—	4	2	no	—
309	D₈×C₆₇	—	4	2	no	—
310	M₁₆×C₆₇	—	4	2	no	—
311	C₂×C₈×C₆₇	—	4	2	no	—
312	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
313	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
314	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
315	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂²⋊C₄×C₆₇	—	2	1	no	—
341	C₂²⋊C₄×C₆₇	—	2	1	no	—
342	C₂²⋊C₄×C₆₇	—	2	2	no	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	2	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	2	no	—
359	C₂²⋊C₄×C₆₇	—	2	2	no	—
360	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
361	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
362	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
363	C₄²×C₆₇	—	2	2	no	—
364	C₄²×C₆₇	—	2	2	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	2	1	no	—
368	C₄²×C₆₇	—	2	1	no	—
369	C₄²×C₆₇	C₂×D₄	1	2	yes	—
370	C₄²×C₆₇	C₂×D₄	1	2	yes	—
371	C₄²×C₆₇	C₂×D₄	1	2	yes	—
372	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂³×C₆₇	—	2	2	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	4	2	no	—
379	C₂³×C₆₇	—	8	2	no	—
380	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
381	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₆₇	—	2	2	no	—
384	Q₈×C₆₇	—	2	2	no	—
385	Q₈×C₆₇	—	2	2	no	—
386	Q₈×C₆₇	—	2	2	no	—
387	Q₈×C₆₇	—	4	1	no	—
388	Q₈×C₆₇	—	4	2	no	—
389	Q₈×C₆₇	—	8	2	no	—
390	D₄×C₆₇	—	2	2	no	—
391	D₄×C₆₇	—	2	2	no	—
392	D₄×C₆₇	—	2	2	no	—
393	D₄×C₆₇	—	2	2	no	—
394	D₄×C₆₇	—	4	1	no	—
395	D₄×C₆₇	—	4	1	no	—
396	D₄×C₆₇	—	4	1	no	—
397	D₄×C₆₇	—	4	2	no	—
398	D₄×C₆₇	—	4	4	no	—
399	D₄×C₆₇	—	8	2	no	—
400	D₄×C₆₇	—	8	2	no	—
401	D₄×C₆₇	—	8	2	no	—
402	D₄×C₆₇	—	8	2	no	—
403	D₄×C₆₇	—	8	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	4	2	no	—
414	C₂×C₄×C₆₇	—	4	2	no	—
415	C₂×C₄×C₆₇	—	4	2	no	—
416	C₂×C₄×C₆₇	—	4	4	no	—
417	C₂×C₄×C₆₇	—	4	2	no	—
418	C₂×C₄×C₆₇	—	8	2	no	—
419	C₂×C₄×C₆₇	—	8	2	no	—
420	C₂×C₄×C₆₇	—	8	2	no	—
421	C₂×C₄×C₆₇	—	8	2	no	—
422	C₂×C₄×C₆₇	—	8	2	no	—
423	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
431	C₈×C₆₇	—	2	2	no	—
432	C₈×C₆₇	—	2	2	no	—
433	C₈×C₆₇	—	2	2	no	—
434	C₈×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	2	1	no	—
439	C₂²×C₆₇	—	2	1	no	—
440	C₂²×C₆₇	—	2	1	no	—
441	C₂²×C₆₇	—	4	2	no	—
442	C₂²×C₆₇	—	4	2	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	4	2	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	16	2	no	—
448	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	2	no	—
451	C₄×C₆₇	—	2	2	no	—
452	C₄×C₆₇	—	2	2	no	—
453	C₄×C₆₇	—	2	1	no	—
454	C₄×C₆₇	—	2	1	no	—
455	C₄×C₆₇	—	2	1	no	—
456	C₄×C₆₇	—	4	2	no	—
457	C₄×C₆₇	—	4	2	no	—
458	C₄×C₆₇	—	4	2	no	—
459	C₄×C₆₇	—	4	2	no	—
460	C₄×C₆₇	—	4	2	no	—
461	C₄×C₆₇	—	4	2	no	—
462	C₄×C₆₇	#585	1	2	yes	—
463	#61010	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₂×C₆₇	—	4	1	no	—
465	C₂×C₆₇	—	4	1	no	—
466	C₂×C₆₇	—	4	1	no	—
467	C₂×C₆₇	—	8	2	no	—
468	C₂×C₆₇	—	8	2	no	—
469	C₂×C₆₇	#3449	1	1	yes	characteristic
470	C₂×C₆₇	#3584	1	2	yes	—
471	#3512	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#3510	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#3258	C₂×C₆₇	1	2	yes	complemented
474	#3257	C₂×C₆₇	1	2	yes	complemented
475	#3233	C₂×C₆₇	1	2	yes	complemented
476	#3232	C₂×C₆₇	1	2	yes	complemented
477	#3212	C₂×C₆₇	1	2	yes	complemented
478	#3211	C₂×C₆₇	1	2	yes	complemented
479	#3201	C₂×C₆₇	1	2	yes	complemented
480	#3198	C₂×C₆₇	1	2	yes	complemented
481	#3183	C₂×C₆₇	1	2	yes	complemented
482	#3168	C₂×C₆₇	1	2	yes	complemented
483	#3127	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#3126	C₂×C₆₇	1	1	yes	characteristic, complemented
485	#3125	C₂×C₆₇	1	2	yes	complemented
486	#3124	C₂×C₆₇	1	2	yes	complemented
487	#3123	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#3122	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#2922	C₂×C₆₇	1	1	yes	characteristic, complemented
490	C₆₇	#61010	1	1	yes	characteristic, direct product factor, Sylow
491	#559	—	2	2	no	—
492	#556	—	2	2	no	—
493	#553	—	2	2	no	—
494	#553	—	2	2	no	—
495	#553	—	2	2	no	—
496	#552	—	2	2	no	—
497	#551	—	2	2	no	—
498	#551	—	2	2	no	—
499	#542	C₂²×C₆₇	1	2	yes	—
500	#542	C₂²×C₆₇	1	2	yes	—
501	#541	C₂²×C₆₇	1	1	yes	characteristic
502	#541	C₂²×C₆₇	1	1	yes	characteristic, complemented
503	#540	C₂²×C₆₇	1	1	yes	characteristic
504	#540	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	#537	C₂²×C₆₇	1	2	yes	—
506	#536	C₂²×C₆₇	1	1	yes	characteristic
507	#535	C₂²×C₆₇	1	1	yes	characteristic
508	#533	C₂²×C₆₇	1	1	yes	characteristic
509	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
510	#529	C₂²×C₆₇	1	2	yes	—
511	#529	C₂²×C₆₇	1	2	yes	—
512	#529	C₂²×C₆₇	1	2	yes	—
513	#529	C₂²×C₆₇	1	2	yes	complemented
514	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
515	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
516	#520	C₂²×C₆₇	1	2	yes	complemented
517	#519	C₂²×C₆₇	1	1	yes	characteristic
518	#518	C₂²×C₆₇	1	1	yes	characteristic
519	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
520	#499	C₂²×C₆₇	1	2	yes	complemented
521	#499	C₂²×C₆₇	1	2	yes	complemented
522	#495	C₂²×C₆₇	1	2	yes	—
523	#495	C₂²×C₆₇	1	2	yes	—
524	#488	C₂²×C₆₇	1	2	yes	—
525	#488	C₂²×C₆₇	1	2	yes	—
526	#488	C₂²×C₆₇	1	2	yes	complemented
527	#488	C₂²×C₆₇	1	2	yes	complemented
528	#485	C₂²×C₆₇	1	2	yes	—
529	#485	C₂²×C₆₇	1	2	yes	—
530	#484	C₂²×C₆₇	1	2	yes	complemented
531	#483	C₂²×C₆₇	1	2	yes	complemented
532	#482	C₂²×C₆₇	1	2	yes	—
533	#482	C₂²×C₆₇	1	2	yes	—
534	#481	C₂²×C₆₇	1	2	yes	—
535	#480	C₂²×C₆₇	1	2	yes	—
536	#479	C₂²×C₆₇	1	2	yes	complemented
537	#479	C₂²×C₆₇	1	2	yes	complemented
538	#478	C₂²×C₆₇	1	2	yes	—
539	#478	C₂²×C₆₇	1	2	yes	—
540	#477	C₂²×C₆₇	1	2	yes	complemented
541	#476	C₂²×C₆₇	1	2	yes	complemented
542	#475	C₂²×C₆₇	1	2	yes	complemented
543	#474	C₂²×C₆₇	1	2	yes	complemented
544	#470	C₂²×C₆₇	1	2	yes	complemented
545	#469	C₂²×C₆₇	1	2	yes	—
546	#468	C₂²×C₆₇	1	2	yes	—
547	#468	C₂²×C₆₇	1	2	yes	complemented
548	#467	C₂²×C₆₇	1	2	yes	complemented
549	#466	C₂²×C₆₇	1	2	yes	—
550	#465	C₂²×C₆₇	1	2	yes	—
551	#465	C₂²×C₆₇	1	2	yes	complemented
552	#464	C₂²×C₆₇	1	2	yes	—
553	#464	C₂²×C₆₇	1	2	yes	—
554	#463	C₂²×C₆₇	1	2	yes	—
555	#463	C₂²×C₆₇	1	2	yes	—
556	#462	C₂²×C₆₇	1	2	yes	complemented
557	#461	C₂²×C₆₇	1	2	yes	—
558	#460	C₂²×C₆₇	1	2	yes	complemented
559	#459	C₂²×C₆₇	1	2	yes	—
560	#452	C₂²×C₆₇	1	2	yes	complemented
561	#452	C₂²×C₆₇	1	2	yes	complemented
562	#451	C₂²×C₆₇	1	2	yes	—
563	#450	C₂²×C₆₇	1	2	yes	—
564	#449	C₂²×C₆₇	1	2	yes	—
565	#449	C₂²×C₆₇	1	2	yes	—
566	#448	C₂²×C₆₇	1	2	yes	—
567	#447	C₂²×C₆₇	1	2	yes	—
568	#442	C₂²×C₆₇	1	2	yes	—
569	#441	C₂²×C₆₇	1	2	yes	complemented
570	#440	C₂²×C₆₇	1	2	yes	—
571	#440	C₂²×C₆₇	1	2	yes	complemented
572	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
573	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
574	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
575	C₄×D₈	C₂²×C₆₇	1	2	yes	—
576	#433	C₂²×C₆₇	1	1	yes	characteristic
577	#433	C₂²×C₆₇	1	1	yes	characteristic
578	#433	C₂²×C₆₇	1	1	yes	characteristic, complemented
579	#433	C₂²×C₆₇	1	1	yes	characteristic, complemented
580	#431	C₂²×C₆₇	1	2	yes	—
581	#431	C₂²×C₆₇	1	2	yes	complemented
582	#424	C₂²×C₆₇	1	2	yes	complemented
583	#408	C₂²×C₆₇	1	2	yes	—
584	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
585	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	C₂×#41	C₂³×C₆₇	1	2	yes	—
587	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
588	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
590	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
591	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
592	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
596	C₂×D₈	C₂³×C₆₇	1	2	yes	—
597	C₂×D₈	C₂³×C₆₇	1	2	yes	—
598	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
599	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
600	C₄⋊Q₈	—	2	1	no	—
601	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
602	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
603	#127	—	2	1	no	—
604	#127	C₂³×C₆₇	1	1	yes	characteristic
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	—	2	2	no	—
616	#125	C₂³×C₆₇	1	2	yes	—
617	#125	C₂³×C₆₇	1	1	yes	characteristic
618	#125	C₂³×C₆₇	1	1	yes	characteristic
619	#125	C₂³×C₆₇	1	2	yes	—
620	#124	—	2	1	no	—
621	#124	—	2	1	no	—
622	#124	—	2	2	no	—
623	#124	—	2	2	no	—
624	#124	—	2	2	no	—
625	#124	C₂³×C₆₇	1	2	yes	—
626	#124	C₂³×C₆₇	1	2	yes	—
627	#124	C₂³×C₆₇	1	2	yes	—
628	#123	—	2	1	no	—
629	#123	—	2	1	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	C₂³×C₆₇	1	2	yes	—
653	#121	C₂³×C₆₇	1	2	yes	—
654	#121	C₂³×C₆₇	1	2	yes	—
655	#121	C₂³×C₆₇	1	2	yes	—
656	#120	—	2	1	no	—
657	#120	—	2	1	no	—
658	C₄×Q₈	—	2	2	no	—
659	C₄×Q₈	—	2	2	no	—
660	C₄×Q₈	D₄×C₆₇	1	2	yes	—
661	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
662	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
663	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
664	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	D₄×C₆₇	1	2	yes	—
674	C₄×D₄	D₄×C₆₇	1	2	yes	—
675	C₄×D₄	D₄×C₆₇	1	2	yes	—
676	C₄×D₄	C₂³×C₆₇	1	2	yes	—
677	C₄×D₄	C₂³×C₆₇	1	2	yes	—
678	C₄×D₄	C₂³×C₆₇	1	2	yes	—
679	C₄×D₄	C₂³×C₆₇	1	2	yes	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	2	no	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	—	2	2	no	—
686	#117	C₂³×C₆₇	1	1	yes	characteristic
687	#117	C₂³×C₆₇	1	1	yes	characteristic
688	#117	C₂³×C₆₇	1	1	yes	characteristic
689	#117	C₂³×C₆₇	1	1	yes	characteristic
690	#117	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	—	2	2	no	—
692	C₂×C₄⋊C₄	—	2	2	no	—
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₂²⋊C₄	—	2	2	no	—
696	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
699	#107	C₂³×C₆₇	1	2	yes	—
700	#107	C₂³×C₆₇	1	2	yes	—
701	#107	C₂³×C₆₇	1	2	yes	—
702	#107	C₂³×C₆₇	1	2	yes	—
703	#106	C₂³×C₆₇	1	2	yes	—
704	#106	C₂³×C₆₇	1	2	yes	—
705	#106	C₂³×C₆₇	1	2	yes	—
706	#106	C₂³×C₆₇	1	2	yes	—
707	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
708	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
709	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
710	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
711	#103	C₂³×C₆₇	1	2	yes	—
712	#103	C₂³×C₆₇	1	2	yes	—
713	#103	C₂³×C₆₇	1	2	yes	—
714	#103	C₂³×C₆₇	1	2	yes	—
715	#103	C₂³×C₆₇	1	2	yes	—
716	#103	C₂³×C₆₇	1	2	yes	—
717	#103	C₂³×C₆₇	1	2	yes	—
718	#103	C₂³×C₆₇	1	2	yes	—
719	#102	C₂³×C₆₇	1	2	yes	—
720	#102	C₂³×C₆₇	1	2	yes	—
721	#102	C₂³×C₆₇	1	2	yes	—
722	#102	C₂³×C₆₇	1	2	yes	—
723	#102	C₂³×C₆₇	1	2	yes	—
724	#102	C₂³×C₆₇	1	2	yes	—
725	#102	C₂³×C₆₇	1	2	yes	—
726	#102	C₂³×C₆₇	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
731	#97	C₂³×C₆₇	1	1	yes	characteristic
732	#97	C₂³×C₆₇	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₆₇	1	2	yes	—
734	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
735	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
736	C₄×C₈	C₂³×C₆₇	1	2	yes	—
737	C₂⁴	—	2	1	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	C₂×Q₈	—	2	1	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	4	2	no	—
744	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
745	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
746	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
756	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
757	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
758	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
759	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
769	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	Q₁₆	—	4	2	no	—
774	Q₁₆	—	4	2	no	—
775	SD₁₆	—	4	2	no	—
776	SD₁₆	—	4	2	no	—
777	SD₁₆	—	4	2	no	—
778	SD₁₆	—	4	2	no	—
779	D₈	—	4	2	no	—
780	D₈	—	4	2	no	—
781	M₁₆	—	4	2	no	—
782	C₂×C₈	—	4	2	no	—
783	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
784	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
785	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
786	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
805	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
806	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
808	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	1	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
832	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
833	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	1	no	—
839	C₄²	—	2	1	no	—
840	C₄²	C₂×D₄×C₆₇	1	2	yes	—
841	C₄²	C₂×D₄×C₆₇	1	2	yes	—
842	C₄²	C₂×D₄×C₆₇	1	2	yes	—
843	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
844	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
845	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
846	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	4	2	no	—
850	C₂³	—	8	2	no	—
851	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
852	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
853	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	1	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	8	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	2	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	1	no	—
868	D₄	—	4	2	no	—
869	D₄	—	4	4	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	2	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	—	8	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	8	2	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
901	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	16	2	no	—
919	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	#585×C₆₇	1	2	yes	—
934	C₂	—	4	1	no	—
935	C₂	—	4	1	no	—
936	C₂	—	4	1	no	—
937	C₂	—	8	2	no	—
938	C₂	—	8	2	no	—
939	C₂	C₆₇×#3449	1	1	yes	characteristic
940	C₂	C₆₇×#3584	1	2	yes	—

	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 ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3512	C₂	semidirect
2. C₆₇×#3510	C₂	semidirect
3. C₆₇×#3258	C₂	semidirect
4. C₆₇×#3257	C₂	semidirect
5. C₆₇×#3233	C₂	semidirect
6. C₆₇×#3232	C₂	semidirect
7. C₆₇×#3212	C₂	semidirect
8. C₆₇×#3211	C₂	semidirect
9. C₆₇×#3201	C₂	semidirect
10. C₆₇×#3198	C₂	semidirect
11. C₆₇×#3183	C₂	semidirect
12. C₆₇×#3168	C₂	semidirect
13. C₆₇×#3127	C₂	semidirect
14. C₆₇×#3126	C₂	semidirect
15. C₆₇×#3125	C₂	semidirect
16. C₆₇×#3124	C₂	semidirect
17. C₆₇×#3123	C₂	semidirect
18. C₆₇×#3122	C₂	semidirect
19. C₆₇×#2922	C₂	semidirect
31. #541×C₆₇	C₂²	semidirect
33. #540×C₆₇	C₂²	semidirect
38. #532×C₆₇	C₂²	semidirect
42. #529×C₆₇	C₂²	semidirect
43. C₂×#125×C₆₇	C₂²	semidirect
45. #520×C₆₇	C₂²	semidirect
49. #499×C₆₇	C₂²	semidirect
50. #499×C₆₇	C₂²	semidirect
55. #488×C₆₇	C₂²	semidirect
56. #488×C₆₇	C₂²	semidirect
59. #484×C₆₇	C₂²	semidirect
60. #483×C₆₇	C₂²	semidirect
65. #479×C₆₇	C₂²	semidirect
66. #479×C₆₇	C₂²	semidirect
69. #477×C₆₇	C₂²	semidirect
70. #476×C₆₇	C₂²	semidirect
71. #475×C₆₇	C₂²	semidirect
72. #474×C₆₇	C₂²	semidirect
73. #470×C₆₇	C₂²	semidirect
76. #468×C₆₇	C₂²	semidirect
77. #467×C₆₇	C₂²	semidirect
80. #465×C₆₇	C₂²	semidirect
85. #462×C₆₇	C₂²	semidirect
87. #460×C₆₇	C₂²	semidirect
89. #452×C₆₇	C₂²	semidirect
90. #452×C₆₇	C₂²	semidirect
98. #441×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. C₄×Q₁₆×C₆₇	C₂²	semidirect
103. C₄×SD₁₆×C₆₇	C₂²	semidirect
107. #433×C₆₇	C₂²	semidirect
108. #433×C₆₇	C₂²	semidirect
110. #431×C₆₇	C₂²	semidirect
111. #424×C₆₇	C₂²	semidirect
113. C₄×M₁₆×C₆₇	C₂²	semidirect
114. C₂×C₄×C₈×C₆₇	C₂²	semidirect
463. #61010	C₆₇	direct (N × H)
471. #3512	C₂×C₆₇	semidirect
472. #3510	C₂×C₆₇	semidirect
473. #3258	C₂×C₆₇	semidirect
474. #3257	C₂×C₆₇	semidirect
475. #3233	C₂×C₆₇	semidirect
476. #3232	C₂×C₆₇	semidirect
477. #3212	C₂×C₆₇	semidirect
478. #3211	C₂×C₆₇	semidirect
479. #3201	C₂×C₆₇	semidirect
480. #3198	C₂×C₆₇	semidirect
481. #3183	C₂×C₆₇	semidirect
482. #3168	C₂×C₆₇	semidirect
483. #3127	C₂×C₆₇	semidirect
484. #3126	C₂×C₆₇	semidirect
485. #3125	C₂×C₆₇	semidirect
486. #3124	C₂×C₆₇	semidirect
487. #3123	C₂×C₆₇	semidirect
488. #3122	C₂×C₆₇	semidirect
489. #2922	C₂×C₆₇	semidirect
490. C₆₇	#61010	direct (N × H)
502. #541	C₂²×C₆₇	semidirect
504. #540	C₂²×C₆₇	semidirect
509. #532	C₂²×C₆₇	semidirect
513. #529	C₂²×C₆₇	semidirect
514. C₂×#125	C₂²×C₆₇	semidirect
516. #520	C₂²×C₆₇	semidirect
520. #499	C₂²×C₆₇	semidirect
521. #499	C₂²×C₆₇	semidirect
526. #488	C₂²×C₆₇	semidirect
527. #488	C₂²×C₆₇	semidirect
530. #484	C₂²×C₆₇	semidirect
531. #483	C₂²×C₆₇	semidirect
536. #479	C₂²×C₆₇	semidirect
537. #479	C₂²×C₆₇	semidirect
540. #477	C₂²×C₆₇	semidirect
541. #476	C₂²×C₆₇	semidirect
542. #475	C₂²×C₆₇	semidirect
543. #474	C₂²×C₆₇	semidirect
544. #470	C₂²×C₆₇	semidirect
547. #468	C₂²×C₆₇	semidirect
548. #467	C₂²×C₆₇	semidirect
551. #465	C₂²×C₆₇	semidirect
556. #462	C₂²×C₆₇	semidirect
558. #460	C₂²×C₆₇	semidirect
560. #452	C₂²×C₆₇	semidirect
561. #452	C₂²×C₆₇	semidirect
569. #441	C₂²×C₆₇	semidirect
571. #440	C₂²×C₆₇	semidirect
572. C₄×Q₁₆	C₂²×C₆₇	semidirect
574. C₄×SD₁₆	C₂²×C₆₇	semidirect
578. #433	C₂²×C₆₇	semidirect
579. #433	C₂²×C₆₇	semidirect
581. #431	C₂²×C₆₇	semidirect
582. #424	C₂²×C₆₇	semidirect
584. C₄×M₁₆	C₂²×C₆₇	semidirect
585. C₂×C₄×C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3512	2
C₆₇×#3510	2
C₆₇×#3258	2
C₆₇×#3257	2
C₆₇×#3233	2
C₆₇×#3232	2
C₆₇×#3212	2
C₆₇×#3211	2
C₆₇×#3201	2
C₆₇×#3198	2
C₆₇×#3183	2
C₆₇×#3168	2
C₆₇×#3127	2
C₆₇×#3126	2
C₆₇×#3125	2
C₆₇×#3124	2
C₆₇×#3123	2
C₆₇×#3122	2
C₆₇×#2922	2
#61010	67

Subgroups — C67×#61010 #30740261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61010 #30740261