Subgroups — C₆₇×#60581 #30739832

Order 17152.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1170 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×#3125	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3120	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×#3095	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic
18	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2946	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×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×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
36	#542×C₆₇	C₂²	1	2	yes	complemented
37	#541×C₆₇	C₂²	1	2	yes	complemented
38	#536×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
46	#520×C₆₇	C₂²	1	2	yes	—
47	#520×C₆₇	C₂²	1	1	yes	characteristic
48	#519×C₆₇	C₂²	1	1	yes	characteristic
49	#519×C₆₇	C₂²	1	1	yes	characteristic
50	#519×C₆₇	C₂²	1	1	yes	characteristic
51	#518×C₆₇	—	2	2	no	—
52	#518×C₆₇	C₂²	1	1	yes	characteristic
53	#518×C₆₇	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₇	—	2	1	no	—
55	C₄×#41×C₆₇	—	2	1	no	—
56	C₄×#41×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	2	yes	—
58	C₂×#117×C₆₇	—	2	2	no	—
59	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
61	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#485×C₆₇	C₂²	1	2	yes	complemented
64	#485×C₆₇	C₂²	1	2	yes	complemented
65	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#484×C₆₇	C₂²	1	2	yes	complemented
67	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#483×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#479×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#478×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	2	yes	complemented
77	#477×C₆₇	C₂²	1	2	yes	complemented
78	#476×C₆₇	C₂²	1	2	yes	complemented
79	#475×C₆₇	C₂²	1	2	yes	complemented
80	#474×C₆₇	C₂²	1	2	yes	complemented
81	#464×C₆₇	C₂²	1	2	yes	complemented
82	#464×C₆₇	C₂²	1	2	yes	complemented
83	#463×C₆₇	C₂²	1	2	yes	complemented
84	#463×C₆₇	C₂²	1	2	yes	complemented
85	#462×C₆₇	C₂²	1	2	yes	complemented
86	#462×C₆₇	C₂²	1	2	yes	complemented
87	#461×C₆₇	C₂²	1	2	yes	complemented
88	#461×C₆₇	C₂²	1	2	yes	complemented
89	#452×C₆₇	C₂²	1	2	yes	—
90	#452×C₆₇	C₂²	1	2	yes	—
91	#452×C₆₇	C₂²	1	2	yes	—
92	#452×C₆₇	C₂²	1	2	yes	—
93	#452×C₆₇	C₂²	1	2	yes	—
94	#452×C₆₇	C₂²	1	2	yes	—
95	#449×C₆₇	C₂²	1	2	yes	—
96	#449×C₆₇	C₂²	1	2	yes	—
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	complemented
114	#433×C₆₇	C₂²	1	2	yes	complemented
115	#432×C₆₇	C₂²	1	2	yes	complemented
116	#431×C₆₇	C₂²	1	2	yes	complemented
117	#428×C₆₇	C₂²	1	1	yes	characteristic
118	#428×C₆₇	C₂²	1	1	yes	characteristic
119	#427×C₆₇	C₂²	1	1	yes	characteristic
120	#427×C₆₇	C₂²	1	1	yes	characteristic
121	#424×C₆₇	C₂²	1	1	yes	characteristic
122	#424×C₆₇	C₂²	1	1	yes	characteristic
123	#419×C₆₇	C₂²	1	1	yes	characteristic
124	#419×C₆₇	C₂²	1	1	yes	characteristic
125	#419×C₆₇	C₂²	1	1	yes	characteristic
126	#418×C₆₇	C₂²	1	1	yes	characteristic
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
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
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
134	#405×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
140	C₂×#41×C₆₇	C₂³	1	2	yes	—
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₇	—	2	1	no	—
147	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
148	#137×C₆₇	—	2	4	no	—
149	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
150	C₂×Q₁₆×C₆₇	—	2	4	no	—
151	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	—	2	4	no	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×D₈×C₆₇	C₂³	1	2	yes	—
160	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	—	2	1	no	—
165	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	1	no	—
174	#125×C₆₇	—	2	2	no	—
175	#125×C₆₇	C₂³	1	2	yes	—
176	#124×C₆₇	—	2	2	no	—
177	#124×C₆₇	C₂³	1	2	yes	—
178	#123×C₆₇	—	2	1	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	C₂²⋊Q₈×C₆₇	—	2	1	no	—
183	C₂²⋊Q₈×C₆₇	—	2	1	no	—
184	C₂²⋊Q₈×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	1	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
191	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
193	#121×C₆₇	C₂³	1	1	yes	characteristic
194	#121×C₆₇	C₂³	1	1	yes	characteristic
195	#120×C₆₇	—	2	1	no	—
196	C₄×Q₈×C₆₇	—	2	1	no	—
197	C₄×Q₈×C₆₇	—	2	1	no	—
198	C₄×Q₈×C₆₇	—	2	1	no	—
199	C₄×Q₈×C₆₇	—	2	1	no	—
200	C₄×Q₈×C₆₇	—	2	1	no	—
201	C₄×Q₈×C₆₇	—	2	1	no	—
202	C₄×Q₈×C₆₇	—	2	2	no	—
203	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
204	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
205	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
206	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
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×D₄×C₆₇	—	2	2	no	—
211	C₄×D₄×C₆₇	—	2	2	no	—
212	C₄×D₄×C₆₇	—	2	2	no	—
213	C₄×D₄×C₆₇	—	2	2	no	—
214	C₄×D₄×C₆₇	—	2	1	no	—
215	C₄×D₄×C₆₇	—	2	1	no	—
216	C₄×D₄×C₆₇	—	2	2	no	—
217	C₄×D₄×C₆₇	—	2	1	no	—
218	C₄×D₄×C₆₇	—	2	1	no	—
219	C₄×D₄×C₆₇	—	2	1	no	—
220	C₄×D₄×C₆₇	—	2	1	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	C₂³	1	2	yes	—
227	C₄×D₄×C₆₇	C₂³	1	2	yes	—
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	#117×C₆₇	—	2	1	no	—
232	#117×C₆₇	—	2	1	no	—
233	#117×C₆₇	—	2	2	no	—
234	#117×C₆₇	—	2	2	no	—
235	#117×C₆₇	—	2	2	no	—
236	#117×C₆₇	—	2	1	no	—
237	#117×C₆₇	—	2	2	no	—
238	#117×C₆₇	—	2	2	no	—
239	#117×C₆₇	—	2	2	no	—
240	#117×C₆₇	—	2	2	no	—
241	#117×C₆₇	—	2	2	no	—
242	#117×C₆₇	—	2	2	no	—
243	#117×C₆₇	D₄	1	2	yes	—
244	#117×C₆₇	D₄	1	1	yes	characteristic
245	#117×C₆₇	D₄	1	1	yes	characteristic
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	#117×C₆₇	C₂³	1	1	yes	characteristic
248	#117×C₆₇	C₂³	1	1	yes	characteristic
249	#117×C₆₇	C₂³	1	1	yes	characteristic
250	#117×C₆₇	C₂³	1	1	yes	characteristic
251	#117×C₆₇	C₂³	1	1	yes	characteristic
252	#117×C₆₇	C₂³	1	1	yes	characteristic
253	#117×C₆₇	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
255	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
256	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
257	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	—	2	2	no	—
270	C₂×C₄²×C₆₇	—	2	2	no	—
271	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	1	yes	characteristic
273	#107×C₆₇	C₂³	1	2	yes	—
274	#107×C₆₇	C₂³	1	1	yes	characteristic
275	#107×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	1	yes	characteristic
277	#107×C₆₇	C₂³	1	1	yes	characteristic
278	#106×C₆₇	C₂³	1	1	yes	characteristic
279	#106×C₆₇	C₂³	1	2	yes	—
280	#106×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	1	yes	characteristic
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
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	4	no	—
323	#41×C₆₇	—	2	4	no	—
324	#41×C₆₇	—	2	4	no	—
325	#41×C₆₇	—	2	4	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	C₂×Q₈×C₆₇	—	2	1	no	—
329	C₂×Q₈×C₆₇	—	2	1	no	—
330	C₂×Q₈×C₆₇	—	2	2	no	—
331	C₂×Q₈×C₆₇	—	2	2	no	—
332	C₂×Q₈×C₆₇	—	2	2	no	—
333	C₂×Q₈×C₆₇	—	2	2	no	—
334	C₂×Q₈×C₆₇	#41	1	4	yes	—
335	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
336	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
338	C₂×D₄×C₆₇	—	2	8	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	2	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
342	C₂×D₄×C₆₇	—	2	1	no	—
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	2	no	—
346	C₂×D₄×C₆₇	#41	1	4	yes	—
347	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₆₇	—	2	8	no	—
350	C₂²×C₄×C₆₇	—	2	1	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	1	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	1	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	2	no	—
361	C₂²×C₄×C₆₇	—	2	2	no	—
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	Q₁₆×C₆₇	—	2	4	no	—
374	Q₁₆×C₆₇	—	2	4	no	—
375	Q₁₆×C₆₇	—	2	4	no	—
376	SD₁₆×C₆₇	—	2	4	no	—
377	SD₁₆×C₆₇	—	2	4	no	—
378	SD₁₆×C₆₇	—	2	4	no	—
379	SD₁₆×C₆₇	—	2	4	no	—
380	D₈×C₆₇	—	2	4	no	—
381	M₁₆×C₆₇	—	2	2	no	—
382	M₁₆×C₆₇	—	2	2	no	—
383	C₂×C₈×C₆₇	—	2	2	no	—
384	C₂×C₈×C₆₇	—	2	2	no	—
385	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₆₇	—	2	1	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	1	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	1	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	1	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	1	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
441	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₄²×C₆₇	—	2	1	no	—
446	C₄²×C₆₇	—	2	1	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	—	2	2	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	1	no	—
452	C₄²×C₆₇	—	2	1	no	—
453	C₄²×C₆₇	—	2	2	no	—
454	C₄²×C₆₇	—	2	2	no	—
455	C₄²×C₆₇	—	2	2	no	—
456	C₄²×C₆₇	—	2	1	no	—
457	C₄²×C₆₇	C₂×D₄	1	2	yes	—
458	C₄²×C₆₇	C₂×D₄	1	2	yes	—
459	C₄²×C₆₇	C₂⁴	1	2	yes	—
460	C₄²×C₆₇	C₂⁴	1	2	yes	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	2	2	no	—
463	C₂³×C₆₇	—	2	4	no	—
464	C₂³×C₆₇	—	2	1	no	—
465	C₂³×C₆₇	—	4	1	no	—
466	C₂³×C₆₇	—	4	1	no	—
467	C₂³×C₆₇	—	8	1	no	—
468	C₂³×C₆₇	—	8	1	no	—
469	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
470	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₆₇	—	2	4	no	—
473	Q₈×C₆₇	—	2	2	no	—
474	Q₈×C₆₇	—	2	2	no	—
475	Q₈×C₆₇	—	2	1	no	—
476	Q₈×C₆₇	—	2	2	no	—
477	Q₈×C₆₇	—	2	1	no	—
478	Q₈×C₆₇	—	4	2	no	—
479	Q₈×C₆₇	—	8	2	no	—
480	Q₈×C₆₇	C₂×#41	1	4	yes	—
481	D₄×C₆₇	—	2	8	no	—
482	D₄×C₆₇	—	2	8	no	—
483	D₄×C₆₇	—	2	4	no	—
484	D₄×C₆₇	—	2	2	no	—
485	D₄×C₆₇	—	2	1	no	—
486	D₄×C₆₇	—	2	1	no	—
487	D₄×C₆₇	—	4	2	no	—
488	D₄×C₆₇	—	4	2	no	—
489	D₄×C₆₇	—	8	1	no	—
490	D₄×C₆₇	C₂×#41	1	4	yes	—
491	C₂×C₄×C₆₇	—	2	8	no	—
492	C₂×C₄×C₆₇	—	2	8	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	4	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	2	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	2	no	—
511	C₂×C₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	4	2	no	—
514	C₂×C₄×C₆₇	—	4	2	no	—
515	C₂×C₄×C₆₇	—	8	2	no	—
516	C₂×C₄×C₆₇	—	8	2	no	—
517	C₂×C₄×C₆₇	—	8	2	no	—
518	C₂×C₄×C₆₇	—	8	2	no	—
519	C₂×C₄×C₆₇	—	8	2	no	—
520	C₂×C₄×C₆₇	—	8	1	no	—
521	C₂×C₄×C₆₇	—	8	1	no	—
522	C₂×C₄×C₆₇	—	8	1	no	—
523	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
531	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
532	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	—	2	1	no	—
535	C₈×C₆₇	—	2	1	no	—
536	C₈×C₆₇	—	2	1	no	—
537	C₈×C₆₇	—	2	2	no	—
538	C₈×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	1	no	—
542	C₂²×C₆₇	—	2	1	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	1	no	—
545	C₂²×C₆₇	—	2	1	no	—
546	C₂²×C₆₇	—	2	1	no	—
547	C₂²×C₆₇	—	2	4	no	—
548	C₂²×C₆₇	—	4	2	no	—
549	C₂²×C₆₇	—	4	2	no	—
550	C₂²×C₆₇	—	4	1	no	—
551	C₂²×C₆₇	—	4	1	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	8	2	no	—
554	C₂²×C₆₇	—	8	4	no	—
555	C₂²×C₆₇	#525	1	2	yes	—
556	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₆₇	—	2	2	no	—
558	C₄×C₆₇	—	2	2	no	—
559	C₄×C₆₇	—	2	2	no	—
560	C₄×C₆₇	—	2	2	no	—
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	4	no	—
564	C₄×C₆₇	—	4	1	no	—
565	C₄×C₆₇	—	4	1	no	—
566	C₄×C₆₇	—	4	2	no	—
567	C₄×C₆₇	—	4	1	no	—
568	C₄×C₆₇	—	4	1	no	—
569	C₄×C₆₇	—	4	1	no	—
570	C₄×C₆₇	—	4	1	no	—
571	C₄×C₆₇	—	4	1	no	—
572	C₄×C₆₇	—	4	2	no	—
573	C₄×C₆₇	#525	1	2	yes	—
574	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
575	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
576	#60581	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
577	C₂×C₆₇	—	2	2	no	—
578	C₂×C₆₇	—	4	1	no	—
579	C₂×C₆₇	—	4	1	no	—
580	C₂×C₆₇	—	4	4	no	—
581	C₂×C₆₇	—	8	1	no	—
582	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
583	C₂×C₆₇	#3584	1	1	yes	characteristic
584	C₂×C₆₇	#3586	1	1	yes	characteristic
585	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3125	C₂×C₆₇	1	2	yes	complemented
588	#3124	C₂×C₆₇	1	2	yes	complemented
589	#3120	C₂×C₆₇	1	2	yes	complemented
590	#3120	C₂×C₆₇	1	2	yes	complemented
591	#3116	C₂×C₆₇	1	2	yes	complemented
592	#3111	C₂×C₆₇	1	2	yes	complemented
593	#3107	C₂×C₆₇	1	2	yes	complemented
594	#3102	C₂×C₆₇	1	2	yes	complemented
595	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
596	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3044	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3005	C₂×C₆₇	1	1	yes	characteristic
602	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#2950	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2946	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
608	C₆₇	#60581	1	1	yes	characteristic, direct product factor, Sylow
609	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
610	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
611	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
612	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
613	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
614	#556	—	2	1	no	—
615	#554	—	2	1	no	—
616	#552	—	2	2	no	—
617	#552	—	2	1	no	—
618	#552	—	2	1	no	—
619	#551	—	2	2	no	—
620	#544	C₂²×C₆₇	1	1	yes	characteristic
621	#542	C₂²×C₆₇	1	2	yes	complemented
622	#541	C₂²×C₆₇	1	2	yes	complemented
623	#536	C₂²×C₆₇	1	1	yes	characteristic
624	#533	C₂²×C₆₇	1	2	yes	complemented
625	#529	C₂²×C₆₇	1	2	yes	complemented
626	#525	C₂²×C₆₇	1	1	yes	characteristic
627	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
628	#520	—	2	1	no	—
629	#520	—	2	1	no	—
630	#520	C₂²×C₆₇	1	2	yes	—
631	#520	C₂²×C₆₇	1	2	yes	—
632	#520	C₂²×C₆₇	1	1	yes	characteristic
633	#519	C₂²×C₆₇	1	1	yes	characteristic
634	#519	C₂²×C₆₇	1	1	yes	characteristic
635	#519	C₂²×C₆₇	1	1	yes	characteristic
636	#518	—	2	2	no	—
637	#518	C₂²×C₆₇	1	1	yes	characteristic
638	#518	C₂²×C₆₇	1	1	yes	characteristic
639	C₄×#41	—	2	1	no	—
640	C₄×#41	—	2	1	no	—
641	C₄×#41	C₂²×C₆₇	1	2	yes	—
642	C₄×#41	C₂²×C₆₇	1	2	yes	—
643	C₂×#117	—	2	2	no	—
644	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
645	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
646	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#485	C₂²×C₆₇	1	2	yes	complemented
649	#485	C₂²×C₆₇	1	2	yes	complemented
650	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#484	C₂²×C₆₇	1	2	yes	complemented
652	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#483	C₂²×C₆₇	1	2	yes	complemented
654	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#479	C₂²×C₆₇	1	2	yes	complemented
659	#479	C₂²×C₆₇	1	2	yes	complemented
660	#478	C₂²×C₆₇	1	2	yes	complemented
661	#478	C₂²×C₆₇	1	2	yes	complemented
662	#477	C₂²×C₆₇	1	2	yes	complemented
663	#476	C₂²×C₆₇	1	2	yes	complemented
664	#475	C₂²×C₆₇	1	2	yes	complemented
665	#474	C₂²×C₆₇	1	2	yes	complemented
666	#464	C₂²×C₆₇	1	2	yes	complemented
667	#464	C₂²×C₆₇	1	2	yes	complemented
668	#463	C₂²×C₆₇	1	2	yes	complemented
669	#463	C₂²×C₆₇	1	2	yes	complemented
670	#462	C₂²×C₆₇	1	2	yes	complemented
671	#462	C₂²×C₆₇	1	2	yes	complemented
672	#461	C₂²×C₆₇	1	2	yes	complemented
673	#461	C₂²×C₆₇	1	2	yes	complemented
674	#452	C₂²×C₆₇	1	2	yes	—
675	#452	C₂²×C₆₇	1	2	yes	—
676	#452	C₂²×C₆₇	1	2	yes	—
677	#452	C₂²×C₆₇	1	2	yes	—
678	#452	C₂²×C₆₇	1	2	yes	—
679	#452	C₂²×C₆₇	1	2	yes	—
680	#449	C₂²×C₆₇	1	2	yes	—
681	#449	C₂²×C₆₇	1	2	yes	—
682	#442	C₂²×C₆₇	1	2	yes	complemented
683	#441	C₂²×C₆₇	1	2	yes	complemented
684	#441	C₂²×C₆₇	1	2	yes	complemented
685	#441	C₂²×C₆₇	1	2	yes	complemented
686	#440	C₂²×C₆₇	1	2	yes	complemented
687	#440	C₂²×C₆₇	1	2	yes	complemented
688	#440	C₂²×C₆₇	1	2	yes	complemented
689	#440	C₂²×C₆₇	1	2	yes	complemented
690	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
691	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
692	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
694	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
695	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
696	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
697	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
698	#433	C₂²×C₆₇	1	2	yes	complemented
699	#433	C₂²×C₆₇	1	2	yes	complemented
700	#432	C₂²×C₆₇	1	2	yes	complemented
701	#431	C₂²×C₆₇	1	2	yes	complemented
702	#428	C₂²×C₆₇	1	1	yes	characteristic
703	#428	C₂²×C₆₇	1	1	yes	characteristic
704	#427	C₂²×C₆₇	1	1	yes	characteristic
705	#427	C₂²×C₆₇	1	1	yes	characteristic
706	#424	C₂²×C₆₇	1	1	yes	characteristic
707	#424	C₂²×C₆₇	1	1	yes	characteristic
708	#419	C₂²×C₆₇	1	1	yes	characteristic
709	#419	C₂²×C₆₇	1	1	yes	characteristic
710	#419	C₂²×C₆₇	1	1	yes	characteristic
711	#418	C₂²×C₆₇	1	1	yes	characteristic
712	#416	C₂²×C₆₇	1	1	yes	characteristic
713	#416	C₂²×C₆₇	1	1	yes	characteristic
714	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
715	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
716	#407	C₂²×C₆₇	1	1	yes	characteristic
717	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
718	#405	C₂²×C₆₇	1	1	yes	characteristic
719	#405	C₂²×C₆₇	1	1	yes	characteristic
720	C₂×#41	—	2	4	no	—
721	C₂×#41	—	2	4	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	C₂³×C₆₇	1	2	yes	—
725	C₂×#41	C₂³×C₆₇	1	2	yes	—
726	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
727	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
728	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
731	C₂³×C₄	—	2	1	no	—
732	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
733	#137	—	2	4	no	—
734	AGL(1,ℤ/8)	—	2	4	no	—
735	C₂×Q₁₆	—	2	4	no	—
736	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
738	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
739	C₂×SD₁₆	—	2	4	no	—
740	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
744	C₂×D₈	C₂³×C₆₇	1	2	yes	—
745	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
748	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
749	C₄⋊Q₈	—	2	1	no	—
750	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	1	no	—
759	#125	—	2	2	no	—
760	#125	C₂³×C₆₇	1	2	yes	—
761	#124	—	2	2	no	—
762	#124	C₂³×C₆₇	1	2	yes	—
763	#123	—	2	1	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	#121	C₂³×C₆₇	1	1	yes	characteristic
779	#121	C₂³×C₆₇	1	1	yes	characteristic
780	#120	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	2	no	—
788	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
789	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
790	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
791	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
792	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
793	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
794	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	C₂³×C₆₇	1	2	yes	—
812	C₄×D₄	C₂³×C₆₇	1	2	yes	—
813	C₄×D₄	C₂³×C₆₇	1	2	yes	—
814	C₄×D₄	C₂³×C₆₇	1	2	yes	—
815	C₄×D₄	C₂³×C₆₇	1	2	yes	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	2	2	no	—
819	#117	—	2	2	no	—
820	#117	—	2	2	no	—
821	#117	—	2	1	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	D₄×C₆₇	1	2	yes	—
829	#117	D₄×C₆₇	1	1	yes	characteristic
830	#117	D₄×C₆₇	1	1	yes	characteristic
831	#117	C₂³×C₆₇	1	1	yes	characteristic
832	#117	C₂³×C₆₇	1	1	yes	characteristic
833	#117	C₂³×C₆₇	1	1	yes	characteristic
834	#117	C₂³×C₆₇	1	1	yes	characteristic
835	#117	C₂³×C₆₇	1	1	yes	characteristic
836	#117	C₂³×C₆₇	1	1	yes	characteristic
837	#117	C₂³×C₆₇	1	1	yes	characteristic
838	#117	C₂³×C₆₇	1	2	yes	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	—	2	2	no	—
841	C₂×C₄⋊C₄	—	2	2	no	—
842	C₂×C₄⋊C₄	—	2	1	no	—
843	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
844	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
848	C₂×C₂²⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	2	1	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	—	2	2	no	—
855	C₂×C₄²	—	2	2	no	—
856	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
857	#107	C₂³×C₆₇	1	1	yes	characteristic
858	#107	C₂³×C₆₇	1	1	yes	characteristic
859	#107	C₂³×C₆₇	1	1	yes	characteristic
860	#107	C₂³×C₆₇	1	1	yes	characteristic
861	#107	C₂³×C₆₇	1	2	yes	—
862	#107	C₂³×C₆₇	1	2	yes	—
863	#106	C₂³×C₆₇	1	1	yes	characteristic
864	#106	C₂³×C₆₇	1	1	yes	characteristic
865	#106	C₂³×C₆₇	1	1	yes	characteristic
866	#106	C₂³×C₆₇	1	1	yes	characteristic
867	#106	C₂³×C₆₇	1	2	yes	—
868	#106	C₂³×C₆₇	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
872	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
873	#103	C₂³×C₆₇	1	2	yes	—
874	#103	C₂³×C₆₇	1	2	yes	—
875	#103	C₂³×C₆₇	1	1	yes	characteristic
876	#103	C₂³×C₆₇	1	1	yes	characteristic
877	#103	C₂³×C₆₇	1	1	yes	characteristic
878	#103	C₂³×C₆₇	1	1	yes	characteristic
879	#103	C₂³×C₆₇	1	2	yes	—
880	#103	C₂³×C₆₇	1	2	yes	—
881	#103	C₂³×C₆₇	1	2	yes	—
882	#103	C₂³×C₆₇	1	2	yes	—
883	#103	C₂³×C₆₇	1	2	yes	—
884	#103	C₂³×C₆₇	1	2	yes	—
885	#102	C₂³×C₆₇	1	2	yes	—
886	#102	C₂³×C₆₇	1	2	yes	—
887	#102	C₂³×C₆₇	1	1	yes	characteristic
888	#102	C₂³×C₆₇	1	1	yes	characteristic
889	#102	C₂³×C₆₇	1	1	yes	characteristic
890	#102	C₂³×C₆₇	1	1	yes	characteristic
891	#102	C₂³×C₆₇	1	2	yes	—
892	#102	C₂³×C₆₇	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
894	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
895	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
897	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
899	#97	C₂³×C₆₇	1	2	yes	—
900	#97	C₂³×C₆₇	1	2	yes	—
901	C₄×C₈	C₂³×C₆₇	1	2	yes	—
902	C₄×C₈	C₂³×C₆₇	1	2	yes	—
903	C₂⁴	—	2	1	no	—
904	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
905	#41	—	2	8	no	—
906	#41	—	2	8	no	—
907	#41	—	2	4	no	—
908	#41	—	2	4	no	—
909	#41	—	2	4	no	—
910	#41	—	2	4	no	—
911	#41	—	2	2	no	—
912	#41	—	2	2	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	—	2	2	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	#41×C₆₇	1	4	yes	—
920	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
921	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
923	C₂×D₄	—	2	8	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	#41×C₆₇	1	4	yes	—
932	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
934	C₂²×C₄	—	2	8	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
951	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
954	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
955	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
958	Q₁₆	—	2	4	no	—
959	Q₁₆	—	2	4	no	—
960	Q₁₆	—	2	4	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	2	4	no	—
964	SD₁₆	—	2	4	no	—
965	D₈	—	2	4	no	—
966	M₁₆	—	2	2	no	—
967	M₁₆	—	2	2	no	—
968	C₂×C₈	—	2	2	no	—
969	C₂×C₈	—	2	2	no	—
970	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
973	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
974	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1043	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1044	C₄²	C₂⁴×C₆₇	1	2	yes	—
1045	C₄²	C₂⁴×C₆₇	1	2	yes	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	4	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	—	8	1	no	—
1054	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1055	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1056	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1057	Q₈	—	2	4	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	4	2	no	—
1064	Q₈	—	8	2	no	—
1065	Q₈	C₂×#41×C₆₇	1	4	yes	—
1066	D₄	—	2	8	no	—
1067	D₄	—	2	8	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	C₂×#41×C₆₇	1	4	yes	—
1076	C₂×C₄	—	2	8	no	—
1077	C₂×C₄	—	2	8	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	4	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	1	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1115	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1116	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1117	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	1	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	4	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	8	2	no	—
1139	C₂²	—	8	4	no	—
1140	C₂²	#525×C₆₇	1	2	yes	—
1141	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	4	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	#525×C₆₇	1	2	yes	—
1159	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1160	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1161	C₂	—	2	2	no	—
1162	C₂	—	4	1	no	—
1163	C₂	—	4	1	no	—
1164	C₂	—	4	4	no	—
1165	C₂	—	8	1	no	—
1166	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1167	C₂	C₆₇×#3584	1	1	yes	characteristic
1168	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×#3005	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×#3125	C₂	semidirect
4. C₆₇×#3124	C₂	semidirect
5. C₆₇×#3120	C₂	semidirect
6. C₆₇×#3120	C₂	semidirect
7. C₆₇×#3116	C₂	semidirect
8. C₆₇×#3111	C₂	semidirect
9. C₆₇×#3107	C₂	semidirect
10. C₆₇×#3102	C₂	semidirect
11. C₆₇×#3095	C₂	semidirect
12. C₆₇×#3091	C₂	semidirect
13. C₆₇×#3082	C₂	semidirect
14. C₆₇×#3081	C₂	semidirect
15. C₆₇×#3044	C₂	semidirect
16. C₆₇×#3042	C₂	semidirect
18. C₂×#452×C₆₇	C₂	semidirect
19. C₆₇×#2950	C₂	semidirect
20. C₆₇×#2949	C₂	semidirect
21. C₆₇×#2947	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
36. #542×C₆₇	C₂²	semidirect
37. #541×C₆₇	C₂²	semidirect
39. #533×C₆₇	C₂²	semidirect
40. #529×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #485×C₆₇	C₂²	semidirect
63. #485×C₆₇	C₂²	semidirect
64. #485×C₆₇	C₂²	semidirect
65. #484×C₆₇	C₂²	semidirect
66. #484×C₆₇	C₂²	semidirect
67. #483×C₆₇	C₂²	semidirect
68. #483×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #481×C₆₇	C₂²	semidirect
72. #480×C₆₇	C₂²	semidirect
73. #479×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #478×C₆₇	C₂²	semidirect
76. #478×C₆₇	C₂²	semidirect
77. #477×C₆₇	C₂²	semidirect
78. #476×C₆₇	C₂²	semidirect
79. #475×C₆₇	C₂²	semidirect
80. #474×C₆₇	C₂²	semidirect
81. #464×C₆₇	C₂²	semidirect
82. #464×C₆₇	C₂²	semidirect
83. #463×C₆₇	C₂²	semidirect
84. #463×C₆₇	C₂²	semidirect
85. #462×C₆₇	C₂²	semidirect
86. #462×C₆₇	C₂²	semidirect
87. #461×C₆₇	C₂²	semidirect
88. #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
113. #433×C₆₇	C₂²	semidirect
114. #433×C₆₇	C₂²	semidirect
115. #432×C₆₇	C₂²	semidirect
116. #431×C₆₇	C₂²	semidirect
576. #60581	C₆₇	direct (N × H)
585. #3495	C₂×C₆₇	semidirect
586. #3428	C₂×C₆₇	semidirect
587. #3125	C₂×C₆₇	semidirect
588. #3124	C₂×C₆₇	semidirect
589. #3120	C₂×C₆₇	semidirect
590. #3120	C₂×C₆₇	semidirect
591. #3116	C₂×C₆₇	semidirect
592. #3111	C₂×C₆₇	semidirect
593. #3107	C₂×C₆₇	semidirect
594. #3102	C₂×C₆₇	semidirect
595. #3095	C₂×C₆₇	semidirect
596. #3091	C₂×C₆₇	semidirect
597. #3082	C₂×C₆₇	semidirect
598. #3081	C₂×C₆₇	semidirect
599. #3044	C₂×C₆₇	semidirect
600. #3042	C₂×C₆₇	semidirect
602. C₂×#452	C₂×C₆₇	semidirect
603. #2950	C₂×C₆₇	semidirect
604. #2949	C₂×C₆₇	semidirect
605. #2947	C₂×C₆₇	semidirect
606. #2946	C₂×C₆₇	semidirect
607. #2924	C₂×C₆₇	semidirect
608. C₆₇	#60581	direct (N × H)
621. #542	C₂²×C₆₇	semidirect
622. #541	C₂²×C₆₇	semidirect
624. #533	C₂²×C₆₇	semidirect
625. #529	C₂²×C₆₇	semidirect
646. #485	C₂²×C₆₇	semidirect
647. #485	C₂²×C₆₇	semidirect
648. #485	C₂²×C₆₇	semidirect
649. #485	C₂²×C₆₇	semidirect
650. #484	C₂²×C₆₇	semidirect
651. #484	C₂²×C₆₇	semidirect
652. #483	C₂²×C₆₇	semidirect
653. #483	C₂²×C₆₇	semidirect
654. #482	C₂²×C₆₇	semidirect
655. #482	C₂²×C₆₇	semidirect
656. #481	C₂²×C₆₇	semidirect
657. #480	C₂²×C₆₇	semidirect
658. #479	C₂²×C₆₇	semidirect
659. #479	C₂²×C₆₇	semidirect
660. #478	C₂²×C₆₇	semidirect
661. #478	C₂²×C₆₇	semidirect
662. #477	C₂²×C₆₇	semidirect
663. #476	C₂²×C₆₇	semidirect
664. #475	C₂²×C₆₇	semidirect
665. #474	C₂²×C₆₇	semidirect
666. #464	C₂²×C₆₇	semidirect
667. #464	C₂²×C₆₇	semidirect
668. #463	C₂²×C₆₇	semidirect
669. #463	C₂²×C₆₇	semidirect
670. #462	C₂²×C₆₇	semidirect
671. #462	C₂²×C₆₇	semidirect
672. #461	C₂²×C₆₇	semidirect
673. #461	C₂²×C₆₇	semidirect
682. #442	C₂²×C₆₇	semidirect
683. #441	C₂²×C₆₇	semidirect
684. #441	C₂²×C₆₇	semidirect
685. #441	C₂²×C₆₇	semidirect
686. #440	C₂²×C₆₇	semidirect
687. #440	C₂²×C₆₇	semidirect
688. #440	C₂²×C₆₇	semidirect
689. #440	C₂²×C₆₇	semidirect
690. C₄×Q₁₆	C₂²×C₆₇	semidirect
691. C₄×Q₁₆	C₂²×C₆₇	semidirect
692. C₄×Q₁₆	C₂²×C₆₇	semidirect
693. C₄×SD₁₆	C₂²×C₆₇	semidirect
694. C₄×SD₁₆	C₂²×C₆₇	semidirect
695. C₄×SD₁₆	C₂²×C₆₇	semidirect
696. C₄×SD₁₆	C₂²×C₆₇	semidirect
697. C₄×D₈	C₂²×C₆₇	semidirect
698. #433	C₂²×C₆₇	semidirect
699. #433	C₂²×C₆₇	semidirect
700. #432	C₂²×C₆₇	semidirect
701. #431	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×#3125	2
C₆₇×#3124	2
C₆₇×#3120	2
C₆₇×#3116	2
C₆₇×#3111	2
C₆₇×#3107	2
C₆₇×#3102	2
C₆₇×#3095	2
C₆₇×#3091	2
C₆₇×#3082	2
C₆₇×#3081	2
C₆₇×#3044	2
C₆₇×#3042	2
C₆₇×#3005	2
C₂×#452×C₆₇	2
C₆₇×#2950	2
C₆₇×#2949	2
C₆₇×#2947	2
C₆₇×#2946	2
C₆₇×#2924	2
#60581	67

Subgroups — C67×#60581 #30739832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60581 #30739832