Subgroups — C₆₇×#60586 #30739837

Order 17152.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3123	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3116	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3107	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3102	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic
19	C₆₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	#556×C₆₇	—	2	1	no	—
30	#554×C₆₇	—	2	1	no	—
31	#552×C₆₇	—	2	2	no	—
32	#552×C₆₇	—	2	1	no	—
33	#552×C₆₇	—	2	1	no	—
34	#551×C₆₇	—	2	2	no	—
35	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#542×C₆₇	C₂²	1	2	yes	—
37	#541×C₆₇	C₂²	1	2	yes	—
38	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#533×C₆₇	C₂²	1	2	yes	complemented
40	#529×C₆₇	C₂²	1	2	yes	complemented
41	#525×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	#520×C₆₇	—	2	1	no	—
44	#520×C₆₇	—	2	1	no	—
45	#520×C₆₇	C₂²	1	1	yes	characteristic
46	#520×C₆₇	C₂²	1	1	yes	characteristic
47	#520×C₆₇	C₂²	1	1	yes	characteristic
48	#520×C₆₇	C₂²	1	1	yes	characteristic
49	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#519×C₆₇	C₂²	1	2	yes	—
51	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#518×C₆₇	—	2	2	no	—
53	#518×C₆₇	C₂²	1	2	yes	—
54	C₄×#41×C₆₇	—	2	2	no	—
55	C₄×#41×C₆₇	C₂²	1	2	yes	—
56	C₄×#41×C₆₇	C₂²	1	2	yes	—
57	C₂×#117×C₆₇	—	2	1	no	—
58	C₂×#117×C₆₇	—	2	1	no	—
59	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
61	#485×C₆₇	C₂²	1	2	yes	—
62	#485×C₆₇	C₂²	1	2	yes	—
63	#485×C₆₇	C₂²	1	2	yes	—
64	#485×C₆₇	C₂²	1	2	yes	complemented
65	#485×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#482×C₆₇	C₂²	1	2	yes	—
68	#482×C₆₇	C₂²	1	2	yes	complemented
69	#479×C₆₇	C₂²	1	2	yes	complemented
70	#479×C₆₇	C₂²	1	2	yes	complemented
71	#478×C₆₇	C₂²	1	2	yes	complemented
72	#478×C₆₇	C₂²	1	2	yes	complemented
73	#477×C₆₇	C₂²	1	2	yes	complemented
74	#476×C₆₇	C₂²	1	2	yes	complemented
75	#475×C₆₇	C₂²	1	2	yes	complemented
76	#474×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#464×C₆₇	C₂²	1	2	yes	complemented
79	#463×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#462×C₆₇	C₂²	1	2	yes	complemented
82	#462×C₆₇	C₂²	1	2	yes	complemented
83	#461×C₆₇	C₂²	1	2	yes	complemented
84	#461×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	—
86	#452×C₆₇	C₂²	1	1	yes	characteristic
87	#452×C₆₇	C₂²	1	2	yes	—
88	#452×C₆₇	C₂²	1	1	yes	characteristic
89	#451×C₆₇	C₂²	1	2	yes	—
90	#451×C₆₇	C₂²	1	1	yes	characteristic
91	#450×C₆₇	C₂²	1	2	yes	—
92	#450×C₆₇	C₂²	1	1	yes	characteristic
93	#449×C₆₇	C₂²	1	1	yes	characteristic
94	#449×C₆₇	C₂²	1	1	yes	characteristic
95	#448×C₆₇	C₂²	1	1	yes	characteristic
96	#447×C₆₇	C₂²	1	1	yes	characteristic
97	#442×C₆₇	C₂²	1	2	yes	complemented
98	#441×C₆₇	C₂²	1	2	yes	complemented
99	#441×C₆₇	C₂²	1	2	yes	complemented
100	#441×C₆₇	C₂²	1	2	yes	complemented
101	#440×C₆₇	C₂²	1	2	yes	complemented
102	#440×C₆₇	C₂²	1	2	yes	complemented
103	#440×C₆₇	C₂²	1	2	yes	complemented
104	#440×C₆₇	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
113	#433×C₆₇	C₂²	1	2	yes	—
114	#433×C₆₇	C₂²	1	2	yes	—
115	#432×C₆₇	C₂²	1	2	yes	complemented
116	#431×C₆₇	C₂²	1	2	yes	complemented
117	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#417×C₆₇	C₂²	1	1	yes	characteristic
124	#417×C₆₇	C₂²	1	1	yes	characteristic
125	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#416×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#407×C₆₇	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
133	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	—	2	4	no	—
136	C₂×#41×C₆₇	—	2	4	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₆₇	—	2	1	no	—
147	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	—	2	1	no	—
149	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
150	#137×C₆₇	—	2	4	no	—
151	#137×C₆₇	—	2	4	no	—
152	#135×C₆₇	—	2	4	no	—
153	#135×C₆₇	—	2	4	no	—
154	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₇	—	2	1	no	—
171	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
173	#126×C₆₇	—	2	2	no	—
174	#126×C₆₇	—	2	2	no	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	2	no	—
177	#125×C₆₇	—	2	2	no	—
178	#125×C₆₇	—	2	2	no	—
179	#125×C₆₇	—	2	1	no	—
180	#125×C₆₇	—	2	2	no	—
181	#125×C₆₇	C₂³	1	2	yes	—
182	#124×C₆₇	—	2	2	no	—
183	#124×C₆₇	C₂³	1	2	yes	—
184	#123×C₆₇	—	2	1	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	1	no	—
189	C₂²⋊Q₈×C₆₇	—	2	1	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	1	no	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	2	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
199	#121×C₆₇	C₂³	1	1	yes	characteristic
200	#121×C₆₇	C₂³	1	1	yes	characteristic
201	#120×C₆₇	—	2	1	no	—
202	C₄×Q₈×C₆₇	—	2	2	no	—
203	C₄×Q₈×C₆₇	—	2	2	no	—
204	C₄×Q₈×C₆₇	—	2	1	no	—
205	C₄×Q₈×C₆₇	—	2	1	no	—
206	C₄×Q₈×C₆₇	—	2	2	no	—
207	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
208	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
209	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
210	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
211	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
212	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
213	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
214	C₄×D₄×C₆₇	—	2	2	no	—
215	C₄×D₄×C₆₇	—	2	2	no	—
216	C₄×D₄×C₆₇	—	2	2	no	—
217	C₄×D₄×C₆₇	—	2	2	no	—
218	C₄×D₄×C₆₇	—	2	1	no	—
219	C₄×D₄×C₆₇	—	2	1	no	—
220	C₄×D₄×C₆₇	—	2	2	no	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	C₂³	1	2	yes	—
229	C₄×D₄×C₆₇	C₂³	1	2	yes	—
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	#117×C₆₇	—	2	1	no	—
234	#117×C₆₇	—	2	1	no	—
235	#117×C₆₇	—	2	2	no	—
236	#117×C₆₇	—	2	1	no	—
237	#117×C₆₇	—	2	1	no	—
238	#117×C₆₇	—	2	1	no	—
239	#117×C₆₇	—	2	1	no	—
240	#117×C₆₇	—	2	1	no	—
241	#117×C₆₇	—	2	2	no	—
242	#117×C₆₇	—	2	2	no	—
243	#117×C₆₇	—	2	2	no	—
244	#117×C₆₇	—	2	2	no	—
245	#117×C₆₇	—	2	2	no	—
246	#117×C₆₇	—	2	2	no	—
247	#117×C₆₇	D₄	1	1	yes	characteristic
248	#117×C₆₇	D₄	1	1	yes	characteristic
249	#117×C₆₇	D₄	1	2	yes	—
250	#117×C₆₇	C₂³	1	2	yes	—
251	#117×C₆₇	C₂³	1	2	yes	—
252	#117×C₆₇	C₂³	1	1	yes	characteristic
253	#117×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
268	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
269	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
272	C₂×C₄²×C₆₇	—	2	1	no	—
273	C₂×C₄²×C₆₇	—	2	2	no	—
274	C₂×C₄²×C₆₇	—	2	2	no	—
275	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	2	yes	—
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	2	yes	—
280	#106×C₆₇	C₂³	1	2	yes	—
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	2	yes	—
284	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	2	yes	—
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	#97×C₆₇	C₂³	1	2	yes	—
315	#97×C₆₇	C₂³	1	2	yes	—
316	C₄×C₈×C₆₇	C₂³	1	2	yes	—
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	C₂⁴×C₆₇	—	2	1	no	—
319	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
320	#41×C₆₇	—	2	8	no	—
321	#41×C₆₇	—	2	8	no	—
322	#41×C₆₇	—	2	2	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	—	2	2	no	—
330	#41×C₆₇	#41	1	4	yes	—
331	#41×C₆₇	#41	1	4	yes	—
332	C₂×Q₈×C₆₇	—	2	2	no	—
333	C₂×Q₈×C₆₇	—	2	2	no	—
334	C₂×Q₈×C₆₇	—	2	1	no	—
335	C₂×Q₈×C₆₇	—	2	1	no	—
336	C₂×Q₈×C₆₇	—	2	2	no	—
337	C₂×Q₈×C₆₇	—	2	2	no	—
338	C₂×Q₈×C₆₇	—	2	2	no	—
339	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
340	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₇	—	2	8	no	—
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	1	no	—
346	C₂×D₄×C₆₇	—	2	1	no	—
347	C₂×D₄×C₆₇	—	2	1	no	—
348	C₂×D₄×C₆₇	—	2	2	no	—
349	C₂×D₄×C₆₇	—	2	2	no	—
350	C₂×D₄×C₆₇	—	2	1	no	—
351	C₂×D₄×C₆₇	—	2	1	no	—
352	C₂×D₄×C₆₇	—	2	1	no	—
353	C₂×D₄×C₆₇	—	2	1	no	—
354	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	—	2	8	no	—
358	C₂²×C₄×C₆₇	—	2	1	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	1	no	—
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	2	no	—
372	C₂²×C₄×C₆₇	—	2	2	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
380	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
383	Q₁₆×C₆₇	—	2	2	no	—
384	Q₁₆×C₆₇	—	2	2	no	—
385	Q₁₆×C₆₇	—	2	4	no	—
386	Q₁₆×C₆₇	—	2	4	no	—
387	SD₁₆×C₆₇	—	2	2	no	—
388	SD₁₆×C₆₇	—	2	2	no	—
389	SD₁₆×C₆₇	—	2	2	no	—
390	SD₁₆×C₆₇	—	2	2	no	—
391	SD₁₆×C₆₇	—	2	4	no	—
392	SD₁₆×C₆₇	—	2	4	no	—
393	D₈×C₆₇	—	2	2	no	—
394	D₈×C₆₇	—	2	2	no	—
395	M₁₆×C₆₇	—	2	2	no	—
396	M₁₆×C₆₇	—	2	2	no	—
397	C₂×C₈×C₆₇	—	2	2	no	—
398	C₂×C₈×C₆₇	—	2	2	no	—
399	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
400	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
401	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	1	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
426	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
427	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
429	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
430	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
431	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	1	no	—
440	C₂²⋊C₄×C₆₇	—	2	1	no	—
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	1	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	1	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
455	C₄²×C₆₇	—	2	2	no	—
456	C₄²×C₆₇	—	2	2	no	—
457	C₄²×C₆₇	—	2	2	no	—
458	C₄²×C₆₇	—	2	2	no	—
459	C₄²×C₆₇	—	2	2	no	—
460	C₄²×C₆₇	—	2	2	no	—
461	C₄²×C₆₇	—	2	2	no	—
462	C₄²×C₆₇	—	2	2	no	—
463	C₄²×C₆₇	—	2	2	no	—
464	C₄²×C₆₇	—	2	1	no	—
465	C₄²×C₆₇	C₂×D₄	1	2	yes	—
466	C₄²×C₆₇	C₂×D₄	1	2	yes	—
467	C₄²×C₆₇	C₂⁴	1	2	yes	—
468	C₄²×C₆₇	C₂⁴	1	2	yes	—
469	C₂³×C₆₇	—	2	4	no	—
470	C₂³×C₆₇	—	2	1	no	—
471	C₂³×C₆₇	—	2	1	no	—
472	C₂³×C₆₇	—	2	2	no	—
473	C₂³×C₆₇	—	2	1	no	—
474	C₂³×C₆₇	—	4	1	no	—
475	C₂³×C₆₇	—	4	1	no	—
476	C₂³×C₆₇	—	8	1	no	—
477	C₂³×C₆₇	—	8	1	no	—
478	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
479	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
480	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
481	Q₈×C₆₇	—	2	4	no	—
482	Q₈×C₆₇	—	2	1	no	—
483	Q₈×C₆₇	—	2	1	no	—
484	Q₈×C₆₇	—	2	2	no	—
485	Q₈×C₆₇	—	2	2	no	—
486	Q₈×C₆₇	—	2	1	no	—
487	Q₈×C₆₇	—	2	1	no	—
488	Q₈×C₆₇	—	4	2	no	—
489	Q₈×C₆₇	—	8	2	no	—
490	Q₈×C₆₇	C₂×#41	1	2	yes	—
491	Q₈×C₆₇	C₂×#41	1	2	yes	—
492	D₄×C₆₇	—	2	4	no	—
493	D₄×C₆₇	—	2	4	no	—
494	D₄×C₆₇	—	2	4	no	—
495	D₄×C₆₇	—	2	4	no	—
496	D₄×C₆₇	—	2	4	no	—
497	D₄×C₆₇	—	2	1	no	—
498	D₄×C₆₇	—	2	1	no	—
499	D₄×C₆₇	—	2	1	no	—
500	D₄×C₆₇	—	2	1	no	—
501	D₄×C₆₇	—	4	2	no	—
502	D₄×C₆₇	—	4	2	no	—
503	D₄×C₆₇	—	8	1	no	—
504	D₄×C₆₇	C₂×#41	1	2	yes	—
505	D₄×C₆₇	C₂×#41	1	2	yes	—
506	C₂×C₄×C₆₇	—	2	4	no	—
507	C₂×C₄×C₆₇	—	2	4	no	—
508	C₂×C₄×C₆₇	—	2	4	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	2	no	—
513	C₂×C₄×C₆₇	—	2	4	no	—
514	C₂×C₄×C₆₇	—	2	4	no	—
515	C₂×C₄×C₆₇	—	2	2	no	—
516	C₂×C₄×C₆₇	—	2	1	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	2	1	no	—
519	C₂×C₄×C₆₇	—	2	1	no	—
520	C₂×C₄×C₆₇	—	2	2	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	4	2	no	—
528	C₂×C₄×C₆₇	—	4	2	no	—
529	C₂×C₄×C₆₇	—	4	2	no	—
530	C₂×C₄×C₆₇	—	4	2	no	—
531	C₂×C₄×C₆₇	—	8	2	no	—
532	C₂×C₄×C₆₇	—	8	2	no	—
533	C₂×C₄×C₆₇	—	8	2	no	—
534	C₂×C₄×C₆₇	—	8	2	no	—
535	C₂×C₄×C₆₇	—	8	2	no	—
536	C₂×C₄×C₆₇	—	8	1	no	—
537	C₂×C₄×C₆₇	—	8	1	no	—
538	C₂×C₄×C₆₇	—	8	1	no	—
539	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
547	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
548	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
549	C₈×C₆₇	—	2	1	no	—
550	C₈×C₆₇	—	2	1	no	—
551	C₈×C₆₇	—	2	1	no	—
552	C₈×C₆₇	—	2	1	no	—
553	C₈×C₆₇	—	2	2	no	—
554	C₈×C₆₇	—	2	2	no	—
555	C₂²×C₆₇	—	2	1	no	—
556	C₂²×C₆₇	—	2	1	no	—
557	C₂²×C₆₇	—	2	1	no	—
558	C₂²×C₆₇	—	2	1	no	—
559	C₂²×C₆₇	—	2	1	no	—
560	C₂²×C₆₇	—	2	1	no	—
561	C₂²×C₆₇	—	2	1	no	—
562	C₂²×C₆₇	—	2	1	no	—
563	C₂²×C₆₇	—	2	2	no	—
564	C₂²×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	4	1	no	—
566	C₂²×C₆₇	—	4	1	no	—
567	C₂²×C₆₇	—	4	1	no	—
568	C₂²×C₆₇	—	4	1	no	—
569	C₂²×C₆₇	—	4	1	no	—
570	C₂²×C₆₇	—	4	1	no	—
571	C₂²×C₆₇	—	4	1	no	—
572	C₂²×C₆₇	—	8	2	no	—
573	C₂²×C₆₇	—	8	4	no	—
574	C₂²×C₆₇	#525	1	2	yes	—
575	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₆₇	—	2	2	no	—
577	C₄×C₆₇	—	2	2	no	—
578	C₄×C₆₇	—	2	2	no	—
579	C₄×C₆₇	—	2	2	no	—
580	C₄×C₆₇	—	2	1	no	—
581	C₄×C₆₇	—	2	2	no	—
582	C₄×C₆₇	—	2	2	no	—
583	C₄×C₆₇	—	2	1	no	—
584	C₄×C₆₇	—	4	2	no	—
585	C₄×C₆₇	—	4	2	no	—
586	C₄×C₆₇	—	4	1	no	—
587	C₄×C₆₇	—	4	2	no	—
588	C₄×C₆₇	—	4	1	no	—
589	C₄×C₆₇	—	4	1	no	—
590	C₄×C₆₇	—	4	2	no	—
591	C₄×C₆₇	#525	1	2	yes	—
592	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
593	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
594	#60586	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
595	C₂×C₆₇	—	2	2	no	—
596	C₂×C₆₇	—	4	1	no	—
597	C₂×C₆₇	—	4	1	no	—
598	C₂×C₆₇	—	4	2	no	—
599	C₂×C₆₇	—	4	2	no	—
600	C₂×C₆₇	—	8	1	no	—
601	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
602	C₂×C₆₇	#3584	1	1	yes	characteristic
603	C₂×C₆₇	#3586	1	1	yes	characteristic
604	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#3127	C₂×C₆₇	1	2	yes	complemented
607	#3123	C₂×C₆₇	1	2	yes	complemented
608	#3121	C₂×C₆₇	1	2	yes	complemented
609	#3118	C₂×C₆₇	1	2	yes	complemented
610	#3116	C₂×C₆₇	1	2	yes	complemented
611	#3111	C₂×C₆₇	1	2	yes	complemented
612	#3107	C₂×C₆₇	1	2	yes	complemented
613	#3102	C₂×C₆₇	1	2	yes	complemented
614	#3093	C₂×C₆₇	1	1	yes	characteristic, complemented
615	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3084	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#3002	C₂×C₆₇	1	1	yes	characteristic
622	#2952	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#2951	C₂×C₆₇	1	1	yes	characteristic, complemented
624	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
625	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
627	C₆₇	#60586	1	1	yes	characteristic, direct product factor, Sylow
628	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
629	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
630	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
631	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
632	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
633	#556	—	2	1	no	—
634	#554	—	2	1	no	—
635	#552	—	2	2	no	—
636	#552	—	2	1	no	—
637	#552	—	2	1	no	—
638	#551	—	2	2	no	—
639	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	#542	C₂²×C₆₇	1	2	yes	—
641	#541	C₂²×C₆₇	1	2	yes	—
642	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#533	C₂²×C₆₇	1	2	yes	complemented
644	#529	C₂²×C₆₇	1	2	yes	complemented
645	#525	C₂²×C₆₇	1	1	yes	characteristic
646	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
647	#520	—	2	1	no	—
648	#520	—	2	1	no	—
649	#520	C₂²×C₆₇	1	1	yes	characteristic
650	#520	C₂²×C₆₇	1	1	yes	characteristic
651	#520	C₂²×C₆₇	1	1	yes	characteristic
652	#520	C₂²×C₆₇	1	1	yes	characteristic
653	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#519	C₂²×C₆₇	1	2	yes	—
655	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#518	—	2	2	no	—
657	#518	C₂²×C₆₇	1	2	yes	—
658	C₄×#41	—	2	2	no	—
659	C₄×#41	C₂²×C₆₇	1	2	yes	—
660	C₄×#41	C₂²×C₆₇	1	2	yes	—
661	C₂×#117	—	2	1	no	—
662	C₂×#117	—	2	1	no	—
663	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
664	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
665	#485	C₂²×C₆₇	1	2	yes	—
666	#485	C₂²×C₆₇	1	2	yes	—
667	#485	C₂²×C₆₇	1	2	yes	—
668	#485	C₂²×C₆₇	1	2	yes	complemented
669	#485	C₂²×C₆₇	1	2	yes	complemented
670	#485	C₂²×C₆₇	1	2	yes	complemented
671	#482	C₂²×C₆₇	1	2	yes	—
672	#482	C₂²×C₆₇	1	2	yes	complemented
673	#479	C₂²×C₆₇	1	2	yes	complemented
674	#479	C₂²×C₆₇	1	2	yes	complemented
675	#478	C₂²×C₆₇	1	2	yes	complemented
676	#478	C₂²×C₆₇	1	2	yes	complemented
677	#477	C₂²×C₆₇	1	2	yes	complemented
678	#476	C₂²×C₆₇	1	2	yes	complemented
679	#475	C₂²×C₆₇	1	2	yes	complemented
680	#474	C₂²×C₆₇	1	2	yes	complemented
681	#464	C₂²×C₆₇	1	2	yes	complemented
682	#464	C₂²×C₆₇	1	2	yes	complemented
683	#463	C₂²×C₆₇	1	2	yes	complemented
684	#463	C₂²×C₆₇	1	2	yes	complemented
685	#462	C₂²×C₆₇	1	2	yes	complemented
686	#462	C₂²×C₆₇	1	2	yes	complemented
687	#461	C₂²×C₆₇	1	2	yes	complemented
688	#461	C₂²×C₆₇	1	2	yes	complemented
689	#452	C₂²×C₆₇	1	2	yes	—
690	#452	C₂²×C₆₇	1	1	yes	characteristic
691	#452	C₂²×C₆₇	1	2	yes	—
692	#452	C₂²×C₆₇	1	1	yes	characteristic
693	#451	C₂²×C₆₇	1	2	yes	—
694	#451	C₂²×C₆₇	1	1	yes	characteristic
695	#450	C₂²×C₆₇	1	2	yes	—
696	#450	C₂²×C₆₇	1	1	yes	characteristic
697	#449	C₂²×C₆₇	1	1	yes	characteristic
698	#449	C₂²×C₆₇	1	1	yes	characteristic
699	#448	C₂²×C₆₇	1	1	yes	characteristic
700	#447	C₂²×C₆₇	1	1	yes	characteristic
701	#442	C₂²×C₆₇	1	2	yes	complemented
702	#441	C₂²×C₆₇	1	2	yes	complemented
703	#441	C₂²×C₆₇	1	2	yes	complemented
704	#441	C₂²×C₆₇	1	2	yes	complemented
705	#440	C₂²×C₆₇	1	2	yes	complemented
706	#440	C₂²×C₆₇	1	2	yes	complemented
707	#440	C₂²×C₆₇	1	2	yes	complemented
708	#440	C₂²×C₆₇	1	2	yes	complemented
709	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
710	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
711	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
712	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
713	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
714	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
715	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
716	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
717	#433	C₂²×C₆₇	1	2	yes	—
718	#433	C₂²×C₆₇	1	2	yes	—
719	#432	C₂²×C₆₇	1	2	yes	complemented
720	#431	C₂²×C₆₇	1	2	yes	complemented
721	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
722	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
723	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	#417	C₂²×C₆₇	1	1	yes	characteristic
728	#417	C₂²×C₆₇	1	1	yes	characteristic
729	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
730	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	#416	C₂²×C₆₇	1	1	yes	characteristic
732	#416	C₂²×C₆₇	1	1	yes	characteristic
733	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
734	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	#407	C₂²×C₆₇	1	1	yes	characteristic
736	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
737	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	C₂×#41	—	2	4	no	—
740	C₂×#41	—	2	4	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	—	2	1	no	—
743	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
748	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
749	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
750	C₂²×D₄	—	2	1	no	—
751	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
752	C₂³×C₄	—	2	1	no	—
753	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
754	#137	—	2	4	no	—
755	#137	—	2	4	no	—
756	#135	—	2	4	no	—
757	#135	—	2	4	no	—
758	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
761	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
764	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
765	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
766	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
767	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
768	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
772	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
776	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#125	—	2	2	no	—
782	#125	—	2	2	no	—
783	#125	—	2	1	no	—
784	#125	—	2	2	no	—
785	#125	C₂³×C₆₇	1	2	yes	—
786	#124	—	2	2	no	—
787	#124	C₂³×C₆₇	1	2	yes	—
788	#123	—	2	1	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
802	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
803	#121	C₂³×C₆₇	1	1	yes	characteristic
804	#121	C₂³×C₆₇	1	1	yes	characteristic
805	#120	—	2	1	no	—
806	C₄×Q₈	—	2	2	no	—
807	C₄×Q₈	—	2	2	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	2	2	no	—
811	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
812	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
813	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
814	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
815	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
816	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
817	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	C₂³×C₆₇	1	2	yes	—
833	C₄×D₄	C₂³×C₆₇	1	2	yes	—
834	C₄×D₄	C₂³×C₆₇	1	2	yes	—
835	C₄×D₄	C₂³×C₆₇	1	2	yes	—
836	C₄×D₄	C₂³×C₆₇	1	2	yes	—
837	#117	—	2	1	no	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	—	2	2	no	—
848	#117	—	2	2	no	—
849	#117	—	2	2	no	—
850	#117	—	2	2	no	—
851	#117	D₄×C₆₇	1	1	yes	characteristic
852	#117	D₄×C₆₇	1	1	yes	characteristic
853	#117	D₄×C₆₇	1	2	yes	—
854	#117	C₂³×C₆₇	1	2	yes	—
855	#117	C₂³×C₆₇	1	2	yes	—
856	#117	C₂³×C₆₇	1	1	yes	characteristic
857	#117	C₂³×C₆₇	1	2	yes	—
858	#117	C₂³×C₆₇	1	1	yes	characteristic
859	#117	C₂³×C₆₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	—	2	1	no	—
866	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
867	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
871	C₂×C₂²⋊C₄	—	2	1	no	—
872	C₂×C₂²⋊C₄	—	2	1	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₂²⋊C₄	—	2	2	no	—
875	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
876	C₂×C₄²	—	2	1	no	—
877	C₂×C₄²	—	2	2	no	—
878	C₂×C₄²	—	2	2	no	—
879	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
880	#107	C₂³×C₆₇	1	2	yes	—
881	#107	C₂³×C₆₇	1	2	yes	—
882	#107	C₂³×C₆₇	1	2	yes	—
883	#107	C₂³×C₆₇	1	2	yes	—
884	#106	C₂³×C₆₇	1	2	yes	—
885	#106	C₂³×C₆₇	1	2	yes	—
886	#106	C₂³×C₆₇	1	2	yes	—
887	#106	C₂³×C₆₇	1	2	yes	—
888	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
889	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
890	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
891	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
892	#103	C₂³×C₆₇	1	2	yes	—
893	#103	C₂³×C₆₇	1	2	yes	—
894	#103	C₂³×C₆₇	1	2	yes	—
895	#103	C₂³×C₆₇	1	2	yes	—
896	#103	C₂³×C₆₇	1	1	yes	characteristic
897	#103	C₂³×C₆₇	1	1	yes	characteristic
898	#103	C₂³×C₆₇	1	1	yes	characteristic
899	#103	C₂³×C₆₇	1	1	yes	characteristic
900	#103	C₂³×C₆₇	1	2	yes	—
901	#103	C₂³×C₆₇	1	2	yes	—
902	#103	C₂³×C₆₇	1	2	yes	—
903	#103	C₂³×C₆₇	1	2	yes	—
904	#102	C₂³×C₆₇	1	1	yes	characteristic
905	#102	C₂³×C₆₇	1	1	yes	characteristic
906	#102	C₂³×C₆₇	1	1	yes	characteristic
907	#102	C₂³×C₆₇	1	1	yes	characteristic
908	#102	C₂³×C₆₇	1	2	yes	—
909	#102	C₂³×C₆₇	1	2	yes	—
910	#102	C₂³×C₆₇	1	2	yes	—
911	#102	C₂³×C₆₇	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
913	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
914	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
915	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
916	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
918	#97	C₂³×C₆₇	1	2	yes	—
919	#97	C₂³×C₆₇	1	2	yes	—
920	C₄×C₈	C₂³×C₆₇	1	2	yes	—
921	C₄×C₈	C₂³×C₆₇	1	2	yes	—
922	C₂⁴	—	2	1	no	—
923	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
924	#41	—	2	8	no	—
925	#41	—	2	8	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	#41×C₆₇	1	4	yes	—
935	#41	#41×C₆₇	1	4	yes	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	1	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
944	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
946	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
947	C₂×D₄	—	2	8	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
961	C₂²×C₄	—	2	8	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
980	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
981	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
982	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
983	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
984	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
986	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
987	Q₁₆	—	2	2	no	—
988	Q₁₆	—	2	2	no	—
989	Q₁₆	—	2	4	no	—
990	Q₁₆	—	2	4	no	—
991	SD₁₆	—	2	2	no	—
992	SD₁₆	—	2	2	no	—
993	SD₁₆	—	2	2	no	—
994	SD₁₆	—	2	2	no	—
995	SD₁₆	—	2	4	no	—
996	SD₁₆	—	2	4	no	—
997	D₈	—	2	2	no	—
998	D₈	—	2	2	no	—
999	M₁₆	—	2	2	no	—
1000	M₁₆	—	2	2	no	—
1001	C₂×C₈	—	2	2	no	—
1002	C₂×C₈	—	2	2	no	—
1003	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1006	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1007	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1029	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1030	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1031	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1033	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1034	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1056	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	2	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	2	no	—
1067	C₄²	—	2	2	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1070	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1071	C₄²	C₂⁴×C₆₇	1	2	yes	—
1072	C₄²	C₂⁴×C₆₇	1	2	yes	—
1073	C₂³	—	2	4	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	1	no	—
1082	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1083	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1084	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1085	Q₈	—	2	4	no	—
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	1	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	4	2	no	—
1093	Q₈	—	8	2	no	—
1094	Q₈	C₂×#41×C₆₇	1	2	yes	—
1095	Q₈	C₂×#41×C₆₇	1	2	yes	—
1096	D₄	—	2	4	no	—
1097	D₄	—	2	4	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	4	no	—
1100	D₄	—	2	4	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	2	no	—
1107	D₄	—	8	1	no	—
1108	D₄	C₂×#41×C₆₇	1	2	yes	—
1109	D₄	C₂×#41×C₆₇	1	2	yes	—
1110	C₂×C₄	—	2	4	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	4	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	4	no	—
1118	C₂×C₄	—	2	4	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	2	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	4	2	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	2	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1146	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1147	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1148	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1149	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1150	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1151	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1152	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1153	C₈	—	2	1	no	—
1154	C₈	—	2	1	no	—
1155	C₈	—	2	1	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	2	no	—
1158	C₈	—	2	2	no	—
1159	C₂²	—	2	1	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	1	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	1	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	8	2	no	—
1177	C₂²	—	8	4	no	—
1178	C₂²	#525×C₆₇	1	2	yes	—
1179	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	2	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	#525×C₆₇	1	2	yes	—
1196	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1197	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1198	C₂	—	2	2	no	—
1199	C₂	—	4	1	no	—
1200	C₂	—	4	1	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	8	1	no	—
1204	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1205	C₂	C₆₇×#3584	1	1	yes	characteristic
1206	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3495	C₂	semidirect
2. C₆₇×#3428	C₂	semidirect
3. C₆₇×#3127	C₂	semidirect
4. C₆₇×#3123	C₂	semidirect
5. C₆₇×#3121	C₂	semidirect
6. C₆₇×#3118	C₂	semidirect
7. C₆₇×#3116	C₂	semidirect
8. C₆₇×#3111	C₂	semidirect
9. C₆₇×#3107	C₂	semidirect
10. C₆₇×#3102	C₂	semidirect
11. C₆₇×#3093	C₂	semidirect
12. C₂×#485×C₆₇	C₂	semidirect
13. C₆₇×#3084	C₂	semidirect
14. C₆₇×#3083	C₂	semidirect
15. C₆₇×#3046	C₂	semidirect
16. C₆₇×#3046	C₂	semidirect
17. C₆₇×#3007	C₂	semidirect
19. C₆₇×#2952	C₂	semidirect
20. C₆₇×#2951	C₂	semidirect
21. C₆₇×#2947	C₂	semidirect
22. C₆₇×#2947	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
35. #544×C₆₇	C₂²	semidirect
38. #536×C₆₇	C₂²	semidirect
39. #533×C₆₇	C₂²	semidirect
40. #529×C₆₇	C₂²	semidirect
49. #520×C₆₇	C₂²	semidirect
51. #519×C₆₇	C₂²	semidirect
64. #485×C₆₇	C₂²	semidirect
65. #485×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
68. #482×C₆₇	C₂²	semidirect
69. #479×C₆₇	C₂²	semidirect
70. #479×C₆₇	C₂²	semidirect
71. #478×C₆₇	C₂²	semidirect
72. #478×C₆₇	C₂²	semidirect
73. #477×C₆₇	C₂²	semidirect
74. #476×C₆₇	C₂²	semidirect
75. #475×C₆₇	C₂²	semidirect
76. #474×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #463×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #462×C₆₇	C₂²	semidirect
82. #462×C₆₇	C₂²	semidirect
83. #461×C₆₇	C₂²	semidirect
84. #461×C₆₇	C₂²	semidirect
97. #442×C₆₇	C₂²	semidirect
98. #441×C₆₇	C₂²	semidirect
99. #441×C₆₇	C₂²	semidirect
100. #441×C₆₇	C₂²	semidirect
101. #440×C₆₇	C₂²	semidirect
102. #440×C₆₇	C₂²	semidirect
103. #440×C₆₇	C₂²	semidirect
104. #440×C₆₇	C₂²	semidirect
105. C₄×Q₁₆×C₆₇	C₂²	semidirect
106. C₄×Q₁₆×C₆₇	C₂²	semidirect
107. C₄×Q₁₆×C₆₇	C₂²	semidirect
108. C₄×SD₁₆×C₆₇	C₂²	semidirect
109. C₄×SD₁₆×C₆₇	C₂²	semidirect
110. C₄×SD₁₆×C₆₇	C₂²	semidirect
111. C₄×SD₁₆×C₆₇	C₂²	semidirect
112. C₄×D₈×C₆₇	C₂²	semidirect
115. #432×C₆₇	C₂²	semidirect
116. #431×C₆₇	C₂²	semidirect
117. #428×C₆₇	C₂²	semidirect
118. #428×C₆₇	C₂²	semidirect
119. C₂×#107×C₆₇	C₂²	semidirect
120. C₂×#106×C₆₇	C₂²	semidirect
121. #424×C₆₇	C₂²	semidirect
122. #424×C₆₇	C₂²	semidirect
125. #417×C₆₇	C₂²	semidirect
126. #417×C₆₇	C₂²	semidirect
129. C₂×#103×C₆₇	C₂²	semidirect
130. C₂×#103×C₆₇	C₂²	semidirect
133. #405×C₆₇	C₂²	semidirect
134. #405×C₆₇	C₂²	semidirect
594. #60586	C₆₇	direct (N × H)
604. #3495	C₂×C₆₇	semidirect
605. #3428	C₂×C₆₇	semidirect
606. #3127	C₂×C₆₇	semidirect
607. #3123	C₂×C₆₇	semidirect
608. #3121	C₂×C₆₇	semidirect
609. #3118	C₂×C₆₇	semidirect
610. #3116	C₂×C₆₇	semidirect
611. #3111	C₂×C₆₇	semidirect
612. #3107	C₂×C₆₇	semidirect
613. #3102	C₂×C₆₇	semidirect
614. #3093	C₂×C₆₇	semidirect
615. C₂×#485	C₂×C₆₇	semidirect
616. #3084	C₂×C₆₇	semidirect
617. #3083	C₂×C₆₇	semidirect
618. #3046	C₂×C₆₇	semidirect
619. #3046	C₂×C₆₇	semidirect
620. #3007	C₂×C₆₇	semidirect
622. #2952	C₂×C₆₇	semidirect
623. #2951	C₂×C₆₇	semidirect
624. #2947	C₂×C₆₇	semidirect
625. #2947	C₂×C₆₇	semidirect
626. #2924	C₂×C₆₇	semidirect
627. C₆₇	#60586	direct (N × H)
639. #544	C₂²×C₆₇	semidirect
642. #536	C₂²×C₆₇	semidirect
643. #533	C₂²×C₆₇	semidirect
644. #529	C₂²×C₆₇	semidirect
653. #520	C₂²×C₆₇	semidirect
655. #519	C₂²×C₆₇	semidirect
668. #485	C₂²×C₆₇	semidirect
669. #485	C₂²×C₆₇	semidirect
670. #485	C₂²×C₆₇	semidirect
672. #482	C₂²×C₆₇	semidirect
673. #479	C₂²×C₆₇	semidirect
674. #479	C₂²×C₆₇	semidirect
675. #478	C₂²×C₆₇	semidirect
676. #478	C₂²×C₆₇	semidirect
677. #477	C₂²×C₆₇	semidirect
678. #476	C₂²×C₆₇	semidirect
679. #475	C₂²×C₆₇	semidirect
680. #474	C₂²×C₆₇	semidirect
681. #464	C₂²×C₆₇	semidirect
682. #464	C₂²×C₆₇	semidirect
683. #463	C₂²×C₆₇	semidirect
684. #463	C₂²×C₆₇	semidirect
685. #462	C₂²×C₆₇	semidirect
686. #462	C₂²×C₆₇	semidirect
687. #461	C₂²×C₆₇	semidirect
688. #461	C₂²×C₆₇	semidirect
701. #442	C₂²×C₆₇	semidirect
702. #441	C₂²×C₆₇	semidirect
703. #441	C₂²×C₆₇	semidirect
704. #441	C₂²×C₆₇	semidirect
705. #440	C₂²×C₆₇	semidirect
706. #440	C₂²×C₆₇	semidirect
707. #440	C₂²×C₆₇	semidirect
708. #440	C₂²×C₆₇	semidirect
709. C₄×Q₁₆	C₂²×C₆₇	semidirect
710. C₄×Q₁₆	C₂²×C₆₇	semidirect
711. C₄×Q₁₆	C₂²×C₆₇	semidirect
712. C₄×SD₁₆	C₂²×C₆₇	semidirect
713. C₄×SD₁₆	C₂²×C₆₇	semidirect
714. C₄×SD₁₆	C₂²×C₆₇	semidirect
715. C₄×SD₁₆	C₂²×C₆₇	semidirect
716. C₄×D₈	C₂²×C₆₇	semidirect
719. #432	C₂²×C₆₇	semidirect
720. #431	C₂²×C₆₇	semidirect
721. #428	C₂²×C₆₇	semidirect
722. #428	C₂²×C₆₇	semidirect
723. C₂×#107	C₂²×C₆₇	semidirect
724. C₂×#106	C₂²×C₆₇	semidirect
725. #424	C₂²×C₆₇	semidirect
726. #424	C₂²×C₆₇	semidirect
729. #417	C₂²×C₆₇	semidirect
730. #417	C₂²×C₆₇	semidirect
733. C₂×#103	C₂²×C₆₇	semidirect
734. C₂×#103	C₂²×C₆₇	semidirect
737. #405	C₂²×C₆₇	semidirect
738. #405	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×#3495	2
C₆₇×#3428	2
C₆₇×#3127	2
C₆₇×#3123	2
C₆₇×#3121	2
C₆₇×#3118	2
C₆₇×#3116	2
C₆₇×#3111	2
C₆₇×#3107	2
C₆₇×#3102	2
C₆₇×#3093	2
C₂×#485×C₆₇	2
C₆₇×#3084	2
C₆₇×#3083	2
C₆₇×#3046	2
C₆₇×#3007	2
C₆₇×#3002	2
C₆₇×#2952	2
C₆₇×#2951	2
C₆₇×#2947	2
C₆₇×#2924	2
#60586	67

Subgroups — C67×#60586 #30739837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60586 #30739837