Subgroups — C₆₇×#60580 #30739831

Order 17152.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3494	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×#3119	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3115	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3106	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3102	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3094	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×#3043	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2948	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×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
29	#555×C₆₇	—	2	1	no	—
30	#553×C₆₇	—	2	1	no	—
31	#553×C₆₇	—	2	1	no	—
32	#551×C₆₇	—	2	2	no	—
33	#547×C₆₇	—	2	1	no	—
34	#546×C₆₇	—	2	2	no	—
35	#544×C₆₇	C₂²	1	1	yes	characteristic
36	#542×C₆₇	C₂²	1	2	yes	complemented
37	#540×C₆₇	C₂²	1	2	yes	complemented
38	#535×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	2	yes	complemented
40	#529×C₆₇	C₂²	1	2	yes	complemented
41	#525×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#121×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	2	yes	complemented
47	#520×C₆₇	C₂²	1	2	yes	complemented
48	#519×C₆₇	C₂²	1	1	yes	characteristic
49	#519×C₆₇	C₂²	1	1	yes	characteristic
50	#518×C₆₇	—	2	2	no	—
51	#518×C₆₇	C₂²	1	1	yes	characteristic
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	complemented
57	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
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	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#482×C₆₇	C₂²	1	2	yes	complemented
68	#482×C₆₇	C₂²	1	2	yes	complemented
69	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#481×C₆₇	C₂²	1	2	yes	complemented
71	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#480×C₆₇	C₂²	1	2	yes	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	#460×C₆₇	C₂²	1	2	yes	complemented
86	#460×C₆₇	C₂²	1	2	yes	complemented
87	#459×C₆₇	C₂²	1	2	yes	complemented
88	#459×C₆₇	C₂²	1	2	yes	complemented
89	#452×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	2	yes	complemented
91	#449×C₆₇	C₂²	1	2	yes	—
92	#449×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	—
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#442×C₆₇	C₂²	1	2	yes	complemented
98	#442×C₆₇	C₂²	1	2	yes	complemented
99	#442×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×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×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×D₈×C₆₇	C₂²	1	2	yes	complemented
111	C₄×D₈×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	#418×C₆₇	C₂²	1	1	yes	characteristic
125	#418×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	—	2	2	no	—
140	C₂×#41×C₆₇	C₂³	1	2	yes	—
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	C₂×#41×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	—	2	1	no	—
146	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
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	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	—	2	4	no	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
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×D₈×C₆₇	—	2	4	no	—
159	C₂×D₈×C₆₇	C₂³	1	2	yes	—
160	C₂×D₈×C₆₇	C₂³	1	2	yes	—
161	C₂×D₈×C₆₇	C₂³	1	2	yes	—
162	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	—	2	1	no	—
167	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
168	#127×C₆₇	C₂³	1	2	yes	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	1	no	—
172	#125×C₆₇	C₂³	1	2	yes	—
173	#124×C₆₇	—	2	2	no	—
174	#124×C₆₇	—	2	2	no	—
175	#124×C₆₇	C₂³	1	2	yes	—
176	#123×C₆₇	—	2	1	no	—
177	#123×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	C₂²⋊Q₈×C₆₇	—	2	2	no	—
182	C₂²⋊Q₈×C₆₇	—	2	2	no	—
183	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
185	#121×C₆₇	—	2	1	no	—
186	#121×C₆₇	—	2	1	no	—
187	#121×C₆₇	—	2	2	no	—
188	#121×C₆₇	—	2	1	no	—
189	#121×C₆₇	—	2	1	no	—
190	#121×C₆₇	—	2	2	no	—
191	#121×C₆₇	—	2	2	no	—
192	#121×C₆₇	C₂³	1	2	yes	—
193	#121×C₆₇	C₂³	1	2	yes	—
194	#121×C₆₇	C₂³	1	1	yes	characteristic
195	#121×C₆₇	C₂³	1	1	yes	characteristic
196	#120×C₆₇	—	2	1	no	—
197	#120×C₆₇	—	2	2	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	C₂³	1	2	yes	—
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×D₄×C₆₇	—	2	2	no	—
208	C₄×D₄×C₆₇	—	2	2	no	—
209	C₄×D₄×C₆₇	—	2	2	no	—
210	C₄×D₄×C₆₇	—	2	2	no	—
211	C₄×D₄×C₆₇	—	2	1	no	—
212	C₄×D₄×C₆₇	—	2	1	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	1	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	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	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	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	2	no	—
237	#117×C₆₇	—	2	1	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	2	no	—
255	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
256	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₆₇	C₂³	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×C₂²⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	2	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	1	yes	characteristic
295	#103×C₆₇	C₂³	1	1	yes	characteristic
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×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	1	yes	characteristic
312	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	—	2	1	no	—
320	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
321	#41×C₆₇	—	2	8	no	—
322	#41×C₆₇	—	2	8	no	—
323	#41×C₆₇	—	2	4	no	—
324	#41×C₆₇	—	2	4	no	—
325	#41×C₆₇	—	2	4	no	—
326	#41×C₆₇	—	2	4	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	—	8	4	no	—
330	C₂×Q₈×C₆₇	—	2	1	no	—
331	C₂×Q₈×C₆₇	—	2	2	no	—
332	C₂×Q₈×C₆₇	—	2	2	no	—
333	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
334	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
336	C₂×D₄×C₆₇	—	2	8	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	2	no	—
339	C₂×D₄×C₆₇	—	2	1	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	2	2	no	—
342	C₂×D₄×C₆₇	—	2	1	no	—
343	C₂×D₄×C₆₇	—	2	2	no	—
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	1	no	—
346	C₂×D₄×C₆₇	—	2	2	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	—	2	2	no	—
349	C₂×D₄×C₆₇	—	2	2	no	—
350	C₂×D₄×C₆₇	—	2	2	no	—
351	C₂×D₄×C₆₇	—	8	2	no	—
352	C₂×D₄×C₆₇	#41	1	4	yes	complemented
353	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
354	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₆₇	—	2	8	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	—	2	2	no	—
361	C₂²×C₄×C₆₇	—	2	2	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	1	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	2	no	—
367	C₂²×C₄×C₆₇	—	2	2	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
377	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
378	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	Q₁₆×C₆₇	—	2	4	no	—
382	SD₁₆×C₆₇	—	2	4	no	—
383	SD₁₆×C₆₇	—	2	4	no	—
384	SD₁₆×C₆₇	—	2	4	no	—
385	SD₁₆×C₆₇	—	2	4	no	—
386	D₈×C₆₇	—	2	4	no	—
387	D₈×C₆₇	—	2	4	no	—
388	D₈×C₆₇	—	2	4	no	—
389	M₁₆×C₆₇	—	2	2	no	—
390	M₁₆×C₆₇	—	2	2	no	—
391	C₂×C₈×C₆₇	—	2	2	no	—
392	C₂×C₈×C₆₇	—	2	2	no	—
393	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
394	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
397	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	—	2	1	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	2	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	1	no	—
412	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₆₇	C₂×D₄	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	2	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	—	2	1	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	—	2	1	no	—
445	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₄²×C₆₇	—	2	1	no	—
451	C₄²×C₆₇	—	2	2	no	—
452	C₄²×C₆₇	—	2	2	no	—
453	C₄²×C₆₇	—	2	2	no	—
454	C₄²×C₆₇	—	2	2	no	—
455	C₄²×C₆₇	—	2	1	no	—
456	C₄²×C₆₇	—	2	1	no	—
457	C₄²×C₆₇	—	2	2	no	—
458	C₄²×C₆₇	—	2	1	no	—
459	C₄²×C₆₇	C₂×D₄	1	2	yes	—
460	C₄²×C₆₇	C₂×D₄	1	2	yes	—
461	C₄²×C₆₇	C₂⁴	1	2	yes	—
462	C₄²×C₆₇	C₂⁴	1	2	yes	—
463	C₂³×C₆₇	—	2	2	no	—
464	C₂³×C₆₇	—	2	2	no	—
465	C₂³×C₆₇	—	2	4	no	—
466	C₂³×C₆₇	—	2	2	no	—
467	C₂³×C₆₇	—	2	1	no	—
468	C₂³×C₆₇	—	4	1	no	—
469	C₂³×C₆₇	—	4	1	no	—
470	C₂³×C₆₇	—	4	2	no	—
471	C₂³×C₆₇	—	8	1	no	—
472	C₂³×C₆₇	—	8	1	no	—
473	C₂³×C₆₇	—	8	1	no	—
474	C₂³×C₆₇	—	8	1	no	—
475	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
476	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
477	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
478	Q₈×C₆₇	—	2	4	no	—
479	Q₈×C₆₇	—	2	2	no	—
480	Q₈×C₆₇	—	2	1	no	—
481	Q₈×C₆₇	—	2	1	no	—
482	Q₈×C₆₇	—	8	2	no	—
483	Q₈×C₆₇	C₂×#41	1	4	yes	—
484	D₄×C₆₇	—	2	8	no	—
485	D₄×C₆₇	—	2	8	no	—
486	D₄×C₆₇	—	2	4	no	—
487	D₄×C₆₇	—	2	2	no	—
488	D₄×C₆₇	—	2	2	no	—
489	D₄×C₆₇	—	2	1	no	—
490	D₄×C₆₇	—	2	2	no	—
491	D₄×C₆₇	—	2	1	no	—
492	D₄×C₆₇	—	4	4	no	—
493	D₄×C₆₇	—	4	2	no	—
494	D₄×C₆₇	—	4	2	no	—
495	D₄×C₆₇	—	4	2	no	—
496	D₄×C₆₇	—	8	2	no	—
497	D₄×C₆₇	—	8	2	no	—
498	D₄×C₆₇	—	8	1	no	—
499	D₄×C₆₇	—	8	2	no	—
500	D₄×C₆₇	C₂×#41	1	4	yes	—
501	C₂×C₄×C₆₇	—	2	8	no	—
502	C₂×C₄×C₆₇	—	2	8	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	4	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	2	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	1	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	2	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	4	2	no	—
522	C₂×C₄×C₆₇	—	4	2	no	—
523	C₂×C₄×C₆₇	—	8	2	no	—
524	C₂×C₄×C₆₇	—	8	2	no	—
525	C₂×C₄×C₆₇	—	8	2	no	—
526	C₂×C₄×C₆₇	—	8	2	no	—
527	C₂×C₄×C₆₇	—	8	2	no	—
528	C₂×C₄×C₆₇	—	8	2	no	—
529	C₂×C₄×C₆₇	—	8	2	no	—
530	C₂×C₄×C₆₇	—	8	1	no	—
531	C₂×C₄×C₆₇	—	8	1	no	—
532	C₂×C₄×C₆₇	—	8	1	no	—
533	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
541	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
542	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
543	C₈×C₆₇	—	2	1	no	—
544	C₈×C₆₇	—	2	1	no	—
545	C₈×C₆₇	—	2	1	no	—
546	C₈×C₆₇	—	2	1	no	—
547	C₈×C₆₇	—	2	2	no	—
548	C₈×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	1	no	—
552	C₂²×C₆₇	—	2	1	no	—
553	C₂²×C₆₇	—	2	1	no	—
554	C₂²×C₆₇	—	2	1	no	—
555	C₂²×C₆₇	—	2	1	no	—
556	C₂²×C₆₇	—	2	1	no	—
557	C₂²×C₆₇	—	2	4	no	—
558	C₂²×C₆₇	—	4	2	no	—
559	C₂²×C₆₇	—	4	2	no	—
560	C₂²×C₆₇	—	4	2	no	—
561	C₂²×C₆₇	—	4	1	no	—
562	C₂²×C₆₇	—	4	1	no	—
563	C₂²×C₆₇	—	4	2	no	—
564	C₂²×C₆₇	—	4	1	no	—
565	C₂²×C₆₇	—	4	2	no	—
566	C₂²×C₆₇	—	8	2	no	—
567	C₂²×C₆₇	—	8	4	no	—
568	C₂²×C₆₇	—	16	2	no	—
569	C₂²×C₆₇	#525	1	2	yes	—
570	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	2	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	1	no	—
577	C₄×C₆₇	—	2	4	no	—
578	C₄×C₆₇	—	4	1	no	—
579	C₄×C₆₇	—	4	1	no	—
580	C₄×C₆₇	—	4	1	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	2	no	—
584	C₄×C₆₇	—	4	1	no	—
585	C₄×C₆₇	—	4	1	no	—
586	C₄×C₆₇	#525	1	2	yes	—
587	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
588	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
589	#60580	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
590	C₂×C₆₇	—	2	2	no	—
591	C₂×C₆₇	—	4	1	no	—
592	C₂×C₆₇	—	4	1	no	—
593	C₂×C₆₇	—	4	4	no	—
594	C₂×C₆₇	—	8	1	no	—
595	C₂×C₆₇	—	8	2	no	—
596	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
597	C₂×C₆₇	#3584	1	1	yes	characteristic
598	C₂×C₆₇	#3585	1	1	yes	characteristic
599	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3125	C₂×C₆₇	1	2	yes	complemented
602	#3124	C₂×C₆₇	1	2	yes	complemented
603	#3119	C₂×C₆₇	1	2	yes	complemented
604	#3119	C₂×C₆₇	1	2	yes	complemented
605	#3115	C₂×C₆₇	1	2	yes	complemented
606	#3111	C₂×C₆₇	1	2	yes	complemented
607	#3106	C₂×C₆₇	1	2	yes	complemented
608	#3102	C₂×C₆₇	1	2	yes	complemented
609	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#3043	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3041	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3005	C₂×C₆₇	1	1	yes	characteristic, complemented
616	C₂×#449	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#2948	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#2946	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
622	C₆₇	#60580	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
624	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
625	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
626	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
627	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
628	#555	—	2	1	no	—
629	#553	—	2	1	no	—
630	#553	—	2	1	no	—
631	#551	—	2	2	no	—
632	#547	—	2	1	no	—
633	#546	—	2	2	no	—
634	#544	C₂²×C₆₇	1	1	yes	characteristic
635	#542	C₂²×C₆₇	1	2	yes	complemented
636	#540	C₂²×C₆₇	1	2	yes	complemented
637	#535	C₂²×C₆₇	1	1	yes	characteristic
638	#532	C₂²×C₆₇	1	2	yes	complemented
639	#529	C₂²×C₆₇	1	2	yes	complemented
640	#525	C₂²×C₆₇	1	1	yes	characteristic
641	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
642	#520	—	2	1	no	—
643	#520	—	2	1	no	—
644	#520	C₂²×C₆₇	1	1	yes	characteristic
645	#520	C₂²×C₆₇	1	2	yes	complemented
646	#520	C₂²×C₆₇	1	2	yes	complemented
647	#519	C₂²×C₆₇	1	1	yes	characteristic
648	#519	C₂²×C₆₇	1	1	yes	characteristic
649	#518	—	2	2	no	—
650	#518	C₂²×C₆₇	1	1	yes	characteristic
651	#518	C₂²×C₆₇	1	1	yes	characteristic
652	#518	C₂²×C₆₇	1	1	yes	characteristic
653	C₄×#41	—	2	1	no	—
654	C₄×#41	—	2	1	no	—
655	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
656	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
657	C₂×#117	—	2	2	no	—
658	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
659	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
660	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	#482	C₂²×C₆₇	1	2	yes	complemented
667	#482	C₂²×C₆₇	1	2	yes	complemented
668	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
669	#481	C₂²×C₆₇	1	2	yes	complemented
670	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
671	#480	C₂²×C₆₇	1	2	yes	complemented
672	#479	C₂²×C₆₇	1	2	yes	complemented
673	#479	C₂²×C₆₇	1	2	yes	complemented
674	#478	C₂²×C₆₇	1	2	yes	complemented
675	#478	C₂²×C₆₇	1	2	yes	complemented
676	#477	C₂²×C₆₇	1	2	yes	complemented
677	#476	C₂²×C₆₇	1	2	yes	complemented
678	#475	C₂²×C₆₇	1	2	yes	complemented
679	#474	C₂²×C₆₇	1	2	yes	complemented
680	#464	C₂²×C₆₇	1	2	yes	complemented
681	#464	C₂²×C₆₇	1	2	yes	complemented
682	#463	C₂²×C₆₇	1	2	yes	complemented
683	#463	C₂²×C₆₇	1	2	yes	complemented
684	#460	C₂²×C₆₇	1	2	yes	complemented
685	#460	C₂²×C₆₇	1	2	yes	complemented
686	#459	C₂²×C₆₇	1	2	yes	complemented
687	#459	C₂²×C₆₇	1	2	yes	complemented
688	#452	C₂²×C₆₇	1	2	yes	complemented
689	#452	C₂²×C₆₇	1	2	yes	complemented
690	#449	C₂²×C₆₇	1	2	yes	—
691	#449	C₂²×C₆₇	1	2	yes	—
692	#449	C₂²×C₆₇	1	2	yes	—
693	#449	C₂²×C₆₇	1	2	yes	—
694	#449	C₂²×C₆₇	1	2	yes	complemented
695	#449	C₂²×C₆₇	1	2	yes	complemented
696	#442	C₂²×C₆₇	1	2	yes	complemented
697	#442	C₂²×C₆₇	1	2	yes	complemented
698	#442	C₂²×C₆₇	1	2	yes	complemented
699	#441	C₂²×C₆₇	1	2	yes	complemented
700	#440	C₂²×C₆₇	1	2	yes	complemented
701	#440	C₂²×C₆₇	1	2	yes	complemented
702	#440	C₂²×C₆₇	1	2	yes	complemented
703	#440	C₂²×C₆₇	1	2	yes	complemented
704	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
707	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
708	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
709	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
710	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
711	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
712	#433	C₂²×C₆₇	1	2	yes	complemented
713	#433	C₂²×C₆₇	1	2	yes	complemented
714	#432	C₂²×C₆₇	1	2	yes	complemented
715	#431	C₂²×C₆₇	1	2	yes	complemented
716	#428	C₂²×C₆₇	1	1	yes	characteristic
717	#428	C₂²×C₆₇	1	1	yes	characteristic
718	#427	C₂²×C₆₇	1	1	yes	characteristic
719	#427	C₂²×C₆₇	1	1	yes	characteristic
720	#424	C₂²×C₆₇	1	1	yes	characteristic
721	#424	C₂²×C₆₇	1	1	yes	characteristic
722	#419	C₂²×C₆₇	1	1	yes	characteristic
723	#418	C₂²×C₆₇	1	1	yes	characteristic
724	#418	C₂²×C₆₇	1	1	yes	characteristic
725	#418	C₂²×C₆₇	1	1	yes	characteristic
726	#416	C₂²×C₆₇	1	1	yes	characteristic
727	#416	C₂²×C₆₇	1	1	yes	characteristic
728	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
729	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
730	#407	C₂²×C₆₇	1	1	yes	characteristic
731	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
732	#405	C₂²×C₆₇	1	1	yes	characteristic
733	#405	C₂²×C₆₇	1	1	yes	characteristic
734	C₂×#41	—	2	4	no	—
735	C₂×#41	—	2	4	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	2	no	—
739	C₂×#41	C₂³×C₆₇	1	2	yes	—
740	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×#41	C₂³×C₆₇	1	2	yes	—
742	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
747	C₂³×C₄	—	2	1	no	—
748	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
749	#137	—	2	4	no	—
750	AGL(1,ℤ/8)	—	2	4	no	—
751	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
752	C₂×SD₁₆	—	2	4	no	—
753	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
757	C₂×D₈	—	2	4	no	—
758	C₂×D₈	C₂³×C₆₇	1	2	yes	—
759	C₂×D₈	C₂³×C₆₇	1	2	yes	—
760	C₂×D₈	C₂³×C₆₇	1	2	yes	—
761	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
763	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
764	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
765	C₄⋊Q₈	—	2	1	no	—
766	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
767	#127	C₂³×C₆₇	1	2	yes	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#125	—	2	1	no	—
771	#125	C₂³×C₆₇	1	2	yes	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₆₇	1	2	yes	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	C₂³×C₆₇	1	2	yes	—
792	#121	C₂³×C₆₇	1	2	yes	—
793	#121	C₂³×C₆₇	1	1	yes	characteristic
794	#121	C₂³×C₆₇	1	1	yes	characteristic
795	#120	—	2	1	no	—
796	#120	—	2	2	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
804	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
805	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
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	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	C₂³×C₆₇	1	2	yes	—
826	C₄×D₄	C₂³×C₆₇	1	2	yes	—
827	C₄×D₄	C₂³×C₆₇	1	2	yes	—
828	C₄×D₄	C₂³×C₆₇	1	2	yes	—
829	C₄×D₄	C₂³×C₆₇	1	2	yes	—
830	C₄×D₄	C₂³×C₆₇	1	2	yes	—
831	C₄×D₄	C₂³×C₆₇	1	2	yes	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	2	no	—
839	#117	—	2	2	no	—
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	D₄×C₆₇	1	2	yes	—
843	#117	D₄×C₆₇	1	1	yes	characteristic
844	#117	D₄×C₆₇	1	1	yes	characteristic
845	#117	C₂³×C₆₇	1	1	yes	characteristic
846	#117	C₂³×C₆₇	1	1	yes	characteristic
847	#117	C₂³×C₆₇	1	1	yes	characteristic
848	#117	C₂³×C₆₇	1	1	yes	characteristic
849	#117	C₂³×C₆₇	1	1	yes	characteristic
850	#117	C₂³×C₆₇	1	1	yes	characteristic
851	#117	C₂³×C₆₇	1	1	yes	characteristic
852	#117	C₂³×C₆₇	1	2	yes	—
853	C₂×C₄⋊C₄	—	2	2	no	—
854	C₂×C₄⋊C₄	—	2	2	no	—
855	C₂×C₄⋊C₄	—	2	1	no	—
856	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
857	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
858	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
859	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
861	C₂×C₂²⋊C₄	—	2	1	no	—
862	C₂×C₂²⋊C₄	—	2	1	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
867	C₂×C₄²	—	2	1	no	—
868	C₂×C₄²	—	2	2	no	—
869	C₂×C₄²	—	2	2	no	—
870	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
871	#107	C₂³×C₆₇	1	1	yes	characteristic
872	#107	C₂³×C₆₇	1	1	yes	characteristic
873	#107	C₂³×C₆₇	1	1	yes	characteristic
874	#107	C₂³×C₆₇	1	1	yes	characteristic
875	#107	C₂³×C₆₇	1	2	yes	—
876	#107	C₂³×C₆₇	1	2	yes	—
877	#106	C₂³×C₆₇	1	1	yes	characteristic
878	#106	C₂³×C₆₇	1	1	yes	characteristic
879	#106	C₂³×C₆₇	1	1	yes	characteristic
880	#106	C₂³×C₆₇	1	1	yes	characteristic
881	#106	C₂³×C₆₇	1	2	yes	—
882	#106	C₂³×C₆₇	1	2	yes	—
883	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
884	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
885	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
886	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
887	#103	C₂³×C₆₇	1	2	yes	—
888	#103	C₂³×C₆₇	1	2	yes	—
889	#103	C₂³×C₆₇	1	1	yes	characteristic
890	#103	C₂³×C₆₇	1	1	yes	characteristic
891	#103	C₂³×C₆₇	1	1	yes	characteristic
892	#103	C₂³×C₆₇	1	1	yes	characteristic
893	#103	C₂³×C₆₇	1	2	yes	—
894	#103	C₂³×C₆₇	1	2	yes	—
895	#102	C₂³×C₆₇	1	2	yes	—
896	#102	C₂³×C₆₇	1	2	yes	—
897	#102	C₂³×C₆₇	1	1	yes	characteristic
898	#102	C₂³×C₆₇	1	1	yes	characteristic
899	#102	C₂³×C₆₇	1	1	yes	characteristic
900	#102	C₂³×C₆₇	1	1	yes	characteristic
901	#102	C₂³×C₆₇	1	2	yes	—
902	#102	C₂³×C₆₇	1	2	yes	—
903	#102	C₂³×C₆₇	1	2	yes	—
904	#102	C₂³×C₆₇	1	2	yes	—
905	#102	C₂³×C₆₇	1	2	yes	—
906	#102	C₂³×C₆₇	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
908	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
911	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
913	#97	C₂³×C₆₇	1	2	yes	—
914	#97	C₂³×C₆₇	1	2	yes	—
915	C₄×C₈	C₂³×C₆₇	1	2	yes	—
916	C₄×C₈	C₂³×C₆₇	1	2	yes	—
917	C₂⁴	—	2	1	no	—
918	C₂⁴	—	2	1	no	—
919	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
920	#41	—	2	8	no	—
921	#41	—	2	8	no	—
922	#41	—	2	4	no	—
923	#41	—	2	4	no	—
924	#41	—	2	4	no	—
925	#41	—	2	4	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	8	4	no	—
929	C₂×Q₈	—	2	1	no	—
930	C₂×Q₈	—	2	2	no	—
931	C₂×Q₈	—	2	2	no	—
932	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
933	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
935	C₂×D₄	—	2	8	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	8	2	no	—
951	C₂×D₄	#41×C₆₇	1	4	yes	complemented
952	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
953	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
955	C₂²×C₄	—	2	8	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
973	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
976	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
977	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
980	Q₁₆	—	2	4	no	—
981	SD₁₆	—	2	4	no	—
982	SD₁₆	—	2	4	no	—
983	SD₁₆	—	2	4	no	—
984	SD₁₆	—	2	4	no	—
985	D₈	—	2	4	no	—
986	D₈	—	2	4	no	—
987	D₈	—	2	4	no	—
988	M₁₆	—	2	2	no	—
989	M₁₆	—	2	2	no	—
990	C₂×C₈	—	2	2	no	—
991	C₂×C₈	—	2	2	no	—
992	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
993	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
995	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
996	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1012	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1015	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1016	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1022	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1023	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1047	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	2	no	—
1053	C₄²	—	2	2	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1059	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1060	C₄²	C₂⁴×C₆₇	1	2	yes	—
1061	C₄²	C₂⁴×C₆₇	1	2	yes	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	4	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	4	1	no	—
1069	C₂³	—	4	2	no	—
1070	C₂³	—	8	1	no	—
1071	C₂³	—	8	1	no	—
1072	C₂³	—	8	1	no	—
1073	C₂³	—	8	1	no	—
1074	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1075	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1076	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1077	Q₈	—	2	4	no	—
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	1	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	8	2	no	—
1082	Q₈	C₂×#41×C₆₇	1	4	yes	—
1083	D₄	—	2	8	no	—
1084	D₄	—	2	8	no	—
1085	D₄	—	2	4	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	1	no	—
1099	D₄	C₂×#41×C₆₇	1	4	yes	—
1100	C₂×C₄	—	2	8	no	—
1101	C₂×C₄	—	2	8	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	4	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	—	8	2	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1136	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1139	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1140	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1141	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1142	C₈	—	2	1	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	1	no	—
1146	C₈	—	2	2	no	—
1147	C₈	—	2	2	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	4	2	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	8	2	no	—
1166	C₂²	—	8	4	no	—
1167	C₂²	—	16	2	no	—
1168	C₂²	#525×C₆₇	1	2	yes	—
1169	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1170	C₄	—	2	2	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	2	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	4	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	2	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	#525×C₆₇	1	2	yes	—
1186	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1187	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1188	C₂	—	2	2	no	—
1189	C₂	—	4	1	no	—
1190	C₂	—	4	1	no	—
1191	C₂	—	4	4	no	—
1192	C₂	—	8	2	no	—
1193	C₂	—	8	1	no	—
1194	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1195	C₂	C₆₇×#3584	1	1	yes	characteristic
1196	C₂	C₆₇×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3494	C₂	semidirect
2. C₆₇×#3428	C₂	semidirect
3. C₆₇×#3125	C₂	semidirect
4. C₆₇×#3124	C₂	semidirect
5. C₆₇×#3119	C₂	semidirect
6. C₆₇×#3119	C₂	semidirect
7. C₆₇×#3115	C₂	semidirect
8. C₆₇×#3111	C₂	semidirect
9. C₆₇×#3106	C₂	semidirect
10. C₆₇×#3102	C₂	semidirect
11. C₆₇×#3094	C₂	semidirect
12. C₆₇×#3091	C₂	semidirect
13. C₆₇×#3082	C₂	semidirect
14. C₆₇×#3081	C₂	semidirect
15. C₆₇×#3043	C₂	semidirect
16. C₆₇×#3041	C₂	semidirect
17. C₆₇×#3005	C₂	semidirect
18. C₂×#449×C₆₇	C₂	semidirect
19. C₆₇×#2949	C₂	semidirect
20. C₆₇×#2948	C₂	semidirect
21. C₆₇×#2947	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
36. #542×C₆₇	C₂²	semidirect
37. #540×C₆₇	C₂²	semidirect
39. #532×C₆₇	C₂²	semidirect
40. #529×C₆₇	C₂²	semidirect
46. #520×C₆₇	C₂²	semidirect
47. #520×C₆₇	C₂²	semidirect
56. C₄×#41×C₆₇	C₂²	semidirect
57. C₄×#41×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #485×C₆₇	C₂²	semidirect
63. #484×C₆₇	C₂²	semidirect
64. #483×C₆₇	C₂²	semidirect
65. #482×C₆₇	C₂²	semidirect
66. #482×C₆₇	C₂²	semidirect
67. #482×C₆₇	C₂²	semidirect
68. #482×C₆₇	C₂²	semidirect
69. #481×C₆₇	C₂²	semidirect
70. #481×C₆₇	C₂²	semidirect
71. #480×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. #460×C₆₇	C₂²	semidirect
86. #460×C₆₇	C₂²	semidirect
87. #459×C₆₇	C₂²	semidirect
88. #459×C₆₇	C₂²	semidirect
89. #452×C₆₇	C₂²	semidirect
90. #452×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
97. #442×C₆₇	C₂²	semidirect
98. #442×C₆₇	C₂²	semidirect
99. #442×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×SD₁₆×C₆₇	C₂²	semidirect
107. C₄×SD₁₆×C₆₇	C₂²	semidirect
108. C₄×SD₁₆×C₆₇	C₂²	semidirect
109. C₄×SD₁₆×C₆₇	C₂²	semidirect
110. C₄×D₈×C₆₇	C₂²	semidirect
111. C₄×D₈×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
333. C₂×Q₈×C₆₇	#41	semidirect
352. C₂×D₄×C₆₇	#41	semidirect
589. #60580	C₆₇	direct (N × H)
599. #3494	C₂×C₆₇	semidirect
600. #3428	C₂×C₆₇	semidirect
601. #3125	C₂×C₆₇	semidirect
602. #3124	C₂×C₆₇	semidirect
603. #3119	C₂×C₆₇	semidirect
604. #3119	C₂×C₆₇	semidirect
605. #3115	C₂×C₆₇	semidirect
606. #3111	C₂×C₆₇	semidirect
607. #3106	C₂×C₆₇	semidirect
608. #3102	C₂×C₆₇	semidirect
609. #3094	C₂×C₆₇	semidirect
610. #3091	C₂×C₆₇	semidirect
611. #3082	C₂×C₆₇	semidirect
612. #3081	C₂×C₆₇	semidirect
613. #3043	C₂×C₆₇	semidirect
614. #3041	C₂×C₆₇	semidirect
615. #3005	C₂×C₆₇	semidirect
616. C₂×#449	C₂×C₆₇	semidirect
617. #2949	C₂×C₆₇	semidirect
618. #2948	C₂×C₆₇	semidirect
619. #2947	C₂×C₆₇	semidirect
620. #2946	C₂×C₆₇	semidirect
621. #2924	C₂×C₆₇	semidirect
622. C₆₇	#60580	direct (N × H)
635. #542	C₂²×C₆₇	semidirect
636. #540	C₂²×C₆₇	semidirect
638. #532	C₂²×C₆₇	semidirect
639. #529	C₂²×C₆₇	semidirect
645. #520	C₂²×C₆₇	semidirect
646. #520	C₂²×C₆₇	semidirect
655. C₄×#41	C₂²×C₆₇	semidirect
656. C₄×#41	C₂²×C₆₇	semidirect
660. #485	C₂²×C₆₇	semidirect
661. #485	C₂²×C₆₇	semidirect
662. #484	C₂²×C₆₇	semidirect
663. #483	C₂²×C₆₇	semidirect
664. #482	C₂²×C₆₇	semidirect
665. #482	C₂²×C₆₇	semidirect
666. #482	C₂²×C₆₇	semidirect
667. #482	C₂²×C₆₇	semidirect
668. #481	C₂²×C₆₇	semidirect
669. #481	C₂²×C₆₇	semidirect
670. #480	C₂²×C₆₇	semidirect
671. #480	C₂²×C₆₇	semidirect
672. #479	C₂²×C₆₇	semidirect
673. #479	C₂²×C₆₇	semidirect
674. #478	C₂²×C₆₇	semidirect
675. #478	C₂²×C₆₇	semidirect
676. #477	C₂²×C₆₇	semidirect
677. #476	C₂²×C₆₇	semidirect
678. #475	C₂²×C₆₇	semidirect
679. #474	C₂²×C₆₇	semidirect
680. #464	C₂²×C₆₇	semidirect
681. #464	C₂²×C₆₇	semidirect
682. #463	C₂²×C₆₇	semidirect
683. #463	C₂²×C₆₇	semidirect
684. #460	C₂²×C₆₇	semidirect
685. #460	C₂²×C₆₇	semidirect
686. #459	C₂²×C₆₇	semidirect
687. #459	C₂²×C₆₇	semidirect
688. #452	C₂²×C₆₇	semidirect
689. #452	C₂²×C₆₇	semidirect
694. #449	C₂²×C₆₇	semidirect
695. #449	C₂²×C₆₇	semidirect
696. #442	C₂²×C₆₇	semidirect
697. #442	C₂²×C₆₇	semidirect
698. #442	C₂²×C₆₇	semidirect
699. #441	C₂²×C₆₇	semidirect
700. #440	C₂²×C₆₇	semidirect
701. #440	C₂²×C₆₇	semidirect
702. #440	C₂²×C₆₇	semidirect
703. #440	C₂²×C₆₇	semidirect
704. C₄×Q₁₆	C₂²×C₆₇	semidirect
705. C₄×SD₁₆	C₂²×C₆₇	semidirect
706. C₄×SD₁₆	C₂²×C₆₇	semidirect
707. C₄×SD₁₆	C₂²×C₆₇	semidirect
708. C₄×SD₁₆	C₂²×C₆₇	semidirect
709. C₄×D₈	C₂²×C₆₇	semidirect
710. C₄×D₈	C₂²×C₆₇	semidirect
711. C₄×D₈	C₂²×C₆₇	semidirect
712. #433	C₂²×C₆₇	semidirect
713. #433	C₂²×C₆₇	semidirect
714. #432	C₂²×C₆₇	semidirect
715. #431	C₂²×C₆₇	semidirect
932. C₂×Q₈	#41×C₆₇	semidirect
951. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3494	2
C₆₇×#3428	2
C₆₇×#3125	2
C₆₇×#3124	2
C₆₇×#3119	2
C₆₇×#3115	2
C₆₇×#3111	2
C₆₇×#3106	2
C₆₇×#3102	2
C₆₇×#3094	2
C₆₇×#3091	2
C₆₇×#3082	2
C₆₇×#3081	2
C₆₇×#3043	2
C₆₇×#3041	2
C₆₇×#3005	2
C₂×#449×C₆₇	2
C₆₇×#2949	2
C₆₇×#2948	2
C₆₇×#2947	2
C₆₇×#2946	2
C₆₇×#2924	2
#60580	67

Subgroups — C67×#60580 #30739831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60580 #30739831