Subgroups — C₆₇×#61178 #30740429

Order 17152.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3332	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3309	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3308	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	#554×C₆₇	—	2	1	no	—
32	#554×C₆₇	C₂²	1	2	yes	complemented
33	#553×C₆₇	—	2	1	no	—
34	#553×C₆₇	C₂²	1	2	yes	complemented
35	#552×C₆₇	—	2	1	no	—
36	#552×C₆₇	C₂²	1	2	yes	complemented
37	#550×C₆₇	—	2	1	no	—
38	#550×C₆₇	—	2	1	no	—
39	#550×C₆₇	C₂²	1	2	yes	—
40	#550×C₆₇	C₂²	1	2	yes	—
41	#548×C₆₇	—	2	1	no	—
42	#548×C₆₇	—	2	1	no	—
43	#548×C₆₇	C₂²	1	2	yes	—
44	#548×C₆₇	C₂²	1	2	yes	—
45	#547×C₆₇	—	2	1	no	—
46	#547×C₆₇	C₂²	1	2	yes	complemented
47	#544×C₆₇	C₂²	1	1	yes	characteristic
48	#539×C₆₇	—	2	2	no	—
49	#537×C₆₇	C₂²	1	1	yes	characteristic
50	#535×C₆₇	—	2	2	no	—
51	#535×C₆₇	C₂²	1	1	yes	characteristic
52	#535×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	—	2	2	no	—
54	#525×C₆₇	—	2	2	no	—
55	#525×C₆₇	C₂²	1	1	yes	characteristic
56	#525×C₆₇	C₂²	1	1	yes	characteristic
57	#525×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	C₂²	1	1	yes	characteristic
60	#519×C₆₇	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
62	#490×C₆₇	C₂²	1	2	yes	complemented
63	#489×C₆₇	C₂²	1	2	yes	complemented
64	#488×C₆₇	C₂²	1	2	yes	complemented
65	#486×C₆₇	C₂²	1	2	yes	complemented
66	#484×C₆₇	C₂²	1	2	yes	complemented
67	#483×C₆₇	C₂²	1	2	yes	complemented
68	#482×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	2	yes	complemented
70	#481×C₆₇	C₂²	1	2	yes	complemented
71	#481×C₆₇	C₂²	1	2	yes	complemented
72	#480×C₆₇	C₂²	1	2	yes	complemented
73	#480×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#479×C₆₇	C₂²	1	2	yes	complemented
76	#477×C₆₇	C₂²	1	2	yes	complemented
77	#475×C₆₇	C₂²	1	2	yes	complemented
78	#470×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#470×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#469×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#469×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#468×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#468×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#468×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#468×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#468×C₆₇	C₂²	1	2	yes	complemented
88	#466×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#463×C₆₇	C₂²	1	2	yes	complemented
92	#460×C₆₇	C₂²	1	2	yes	complemented
93	#459×C₆₇	C₂²	1	2	yes	complemented
94	#452×C₆₇	C₂²	1	2	yes	—
95	#452×C₆₇	C₂²	1	2	yes	—
96	#452×C₆₇	C₂²	1	2	yes	complemented
97	#451×C₆₇	C₂²	1	2	yes	complemented
98	#449×C₆₇	C₂²	1	2	yes	—
99	#449×C₆₇	C₂²	1	2	yes	—
100	#449×C₆₇	C₂²	1	2	yes	complemented
101	#448×C₆₇	C₂²	1	2	yes	complemented
102	#441×C₆₇	C₂²	1	2	yes	complemented
103	#440×C₆₇	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
106	#436×C₆₇	C₂²	1	2	yes	complemented
107	#436×C₆₇	C₂²	1	2	yes	complemented
108	#435×C₆₇	C₂²	1	2	yes	complemented
109	#435×C₆₇	C₂²	1	2	yes	complemented
110	#428×C₆₇	C₂²	1	1	yes	characteristic
111	#428×C₆₇	C₂²	1	1	yes	characteristic
112	#427×C₆₇	C₂²	1	1	yes	characteristic
113	#424×C₆₇	C₂²	1	1	yes	characteristic
114	#419×C₆₇	C₂²	1	1	yes	characteristic
115	#419×C₆₇	C₂²	1	2	yes	complemented
116	#418×C₆₇	C₂²	1	1	yes	characteristic
117	#417×C₆₇	C₂²	1	1	yes	characteristic
118	#417×C₆₇	C₂²	1	1	yes	characteristic
119	#417×C₆₇	C₂²	1	2	yes	—
120	#417×C₆₇	C₂²	1	2	yes	—
121	#417×C₆₇	C₂²	1	2	yes	—
122	#417×C₆₇	C₂²	1	2	yes	—
123	#417×C₆₇	C₂²	1	2	yes	complemented
124	#416×C₆₇	C₂²	1	1	yes	characteristic
125	#416×C₆₇	C₂²	1	1	yes	characteristic
126	#416×C₆₇	C₂²	1	2	yes	complemented
127	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
128	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	#407×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	—	2	2	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	1	no	—
142	C₂×#41×C₆₇	—	2	4	no	—
143	C₂×#41×C₆₇	—	4	2	no	—
144	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	2	yes	—
147	C₂×#41×C₆₇	C₂³	1	2	yes	—
148	C₂×#41×C₆₇	C₂³	1	2	yes	—
149	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₆₇	—	2	1	no	—
151	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₆₇	—	2	1	no	—
154	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₆₇	—	2	1	no	—
156	C₂³×C₄×C₆₇	—	2	1	no	—
157	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
158	#137×C₆₇	—	2	4	no	—
159	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
160	#135×C₆₇	—	4	2	no	—
161	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₆₇	C₂³	1	2	yes	—
168	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
169	#131×C₆₇	—	4	2	no	—
170	C₂×M₁₆×C₆₇	—	4	2	no	—
171	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
176	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
181	C₄⋊Q₈×C₆₇	—	2	1	no	—
182	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
183	#127×C₆₇	—	2	2	no	—
184	#127×C₆₇	—	2	2	no	—
185	#127×C₆₇	—	2	1	no	—
186	#127×C₆₇	C₂³	1	2	yes	—
187	#126×C₆₇	—	2	2	no	—
188	#126×C₆₇	—	2	2	no	—
189	#125×C₆₇	—	2	2	no	—
190	#125×C₆₇	—	2	2	no	—
191	#125×C₆₇	—	2	1	no	—
192	#125×C₆₇	C₂³	1	2	yes	—
193	#124×C₆₇	—	2	1	no	—
194	#124×C₆₇	—	2	2	no	—
195	#124×C₆₇	—	2	2	no	—
196	#124×C₆₇	C₂³	1	2	yes	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	1	no	—
199	#123×C₆₇	—	2	1	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₆₇	—	2	1	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
212	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
213	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	1	no	—
225	#121×C₆₇	—	2	2	no	—
226	#121×C₆₇	—	2	2	no	—
227	#121×C₆₇	—	2	2	no	—
228	#121×C₆₇	—	2	2	no	—
229	#121×C₆₇	D₄	1	1	yes	characteristic
230	#121×C₆₇	D₄	1	1	yes	characteristic
231	#121×C₆₇	C₂³	1	2	yes	—
232	#121×C₆₇	C₂³	1	1	yes	characteristic
233	#121×C₆₇	C₂³	1	1	yes	characteristic
234	#121×C₆₇	C₂³	1	2	yes	—
235	#121×C₆₇	C₂³	1	2	yes	—
236	#121×C₆₇	C₂³	1	1	yes	characteristic
237	#121×C₆₇	C₂³	1	1	yes	characteristic
238	#120×C₆₇	—	2	1	no	—
239	#120×C₆₇	—	2	1	no	—
240	#120×C₆₇	—	2	2	no	—
241	#120×C₆₇	—	2	2	no	—
242	#120×C₆₇	D₄	1	2	yes	—
243	C₄×Q₈×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	—	2	1	no	—
245	C₄×Q₈×C₆₇	—	2	1	no	—
246	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
248	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	2	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	—	2	1	no	—
254	C₄×D₄×C₆₇	—	2	1	no	—
255	C₄×D₄×C₆₇	—	2	1	no	—
256	C₄×D₄×C₆₇	—	2	2	no	—
257	C₄×D₄×C₆₇	—	2	2	no	—
258	C₄×D₄×C₆₇	—	2	2	no	—
259	C₄×D₄×C₆₇	—	2	2	no	—
260	C₄×D₄×C₆₇	—	2	2	no	—
261	C₄×D₄×C₆₇	—	2	2	no	—
262	C₄×D₄×C₆₇	C₂³	1	2	yes	—
263	C₄×D₄×C₆₇	C₂³	1	2	yes	—
264	C₄×D₄×C₆₇	C₂³	1	2	yes	—
265	#117×C₆₇	—	2	1	no	—
266	#117×C₆₇	—	2	2	no	—
267	#117×C₆₇	—	2	2	no	—
268	#117×C₆₇	C₂³	1	2	yes	—
269	#117×C₆₇	C₂³	1	1	yes	characteristic
270	#117×C₆₇	C₂³	1	1	yes	characteristic
271	#117×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
278	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
281	#107×C₆₇	C₂³	1	2	yes	—
282	#107×C₆₇	C₂³	1	1	yes	characteristic
283	#107×C₆₇	C₂³	1	1	yes	characteristic
284	#107×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	2	yes	—
286	#106×C₆₇	C₂³	1	1	yes	characteristic
287	#106×C₆₇	C₂³	1	1	yes	characteristic
288	#106×C₆₇	C₂³	1	2	yes	—
289	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
290	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	1	yes	characteristic
300	#103×C₆₇	C₂³	1	1	yes	characteristic
301	#103×C₆₇	C₂³	1	2	yes	—
302	#103×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	#102×C₆₇	C₂³	1	2	yes	—
309	#102×C₆₇	C₂³	1	2	yes	—
310	#102×C₆₇	C₂³	1	1	yes	characteristic
311	#102×C₆₇	C₂³	1	1	yes	characteristic
312	#102×C₆₇	C₂³	1	1	yes	characteristic
313	#102×C₆₇	C₂³	1	2	yes	—
314	#102×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
319	#97×C₆₇	C₂³	1	2	yes	—
320	C₄×C₈×C₆₇	C₂³	1	2	yes	—
321	C₂⁴×C₆₇	—	2	1	no	—
322	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	4	no	—
326	#41×C₆₇	—	2	4	no	—
327	#41×C₆₇	—	2	4	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	—	2	2	no	—
330	#41×C₆₇	—	2	2	no	—
331	#41×C₆₇	—	2	2	no	—
332	#41×C₆₇	—	4	2	no	—
333	#41×C₆₇	—	4	2	no	—
334	#41×C₆₇	—	4	2	no	—
335	#41×C₆₇	—	4	8	no	—
336	#41×C₆₇	—	4	4	no	—
337	#41×C₆₇	—	4	4	no	—
338	#41×C₆₇	—	4	4	no	—
339	#41×C₆₇	—	8	4	no	—
340	C₂×Q₈×C₆₇	—	2	1	no	—
341	C₂×Q₈×C₆₇	—	2	2	no	—
342	C₂×Q₈×C₆₇	—	2	2	no	—
343	C₂×Q₈×C₆₇	—	2	2	no	—
344	C₂×Q₈×C₆₇	—	2	4	no	—
345	C₂×Q₈×C₆₇	—	4	2	no	—
346	C₂×Q₈×C₆₇	—	4	4	no	—
347	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
349	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
352	C₂×D₄×C₆₇	—	2	1	no	—
353	C₂×D₄×C₆₇	—	2	1	no	—
354	C₂×D₄×C₆₇	—	2	1	no	—
355	C₂×D₄×C₆₇	—	2	1	no	—
356	C₂×D₄×C₆₇	—	2	2	no	—
357	C₂×D₄×C₆₇	—	2	2	no	—
358	C₂×D₄×C₆₇	—	2	2	no	—
359	C₂×D₄×C₆₇	—	2	2	no	—
360	C₂×D₄×C₆₇	—	2	2	no	—
361	C₂×D₄×C₆₇	—	2	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	2	no	—
364	C₂×D₄×C₆₇	—	2	1	no	—
365	C₂×D₄×C₆₇	—	2	2	no	—
366	C₂×D₄×C₆₇	—	2	2	no	—
367	C₂×D₄×C₆₇	—	2	2	no	—
368	C₂×D₄×C₆₇	—	2	2	no	—
369	C₂×D₄×C₆₇	—	4	4	no	—
370	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
375	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	2	no	—
380	C₂²×C₄×C₆₇	—	2	2	no	—
381	C₂²×C₄×C₆₇	—	2	2	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	2	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
387	C₂²×C₄×C₆₇	—	2	2	no	—
388	C₂²×C₄×C₆₇	—	2	1	no	—
389	C₂²×C₄×C₆₇	—	2	2	no	—
390	C₂²×C₄×C₆₇	—	2	2	no	—
391	C₂²×C₄×C₆₇	—	2	2	no	—
392	C₂²×C₄×C₆₇	—	4	4	no	—
393	C₂²×C₄×C₆₇	—	8	2	no	—
394	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
401	Q₁₆×C₆₇	—	2	4	no	—
402	Q₁₆×C₆₇	—	4	1	no	—
403	SD₁₆×C₆₇	—	2	4	no	—
404	SD₁₆×C₆₇	—	4	1	no	—
405	SD₁₆×C₆₇	—	4	1	no	—
406	SD₁₆×C₆₇	—	4	2	no	—
407	D₈×C₆₇	—	4	1	no	—
408	D₈×C₆₇	—	4	2	no	—
409	M₁₆×C₆₇	—	2	2	no	—
410	M₁₆×C₆₇	—	2	2	no	—
411	M₁₆×C₆₇	—	4	1	no	—
412	M₁₆×C₆₇	—	4	1	no	—
413	M₁₆×C₆₇	—	4	1	no	—
414	M₁₆×C₆₇	—	4	1	no	—
415	M₁₆×C₆₇	—	4	2	no	—
416	C₂×C₈×C₆₇	—	2	2	no	—
417	C₂×C₈×C₆₇	—	2	2	no	—
418	C₂×C₈×C₆₇	—	4	2	no	—
419	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
422	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	2	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	—	2	2	no	—
431	C₄⋊C₄×C₆₇	—	2	2	no	—
432	C₄⋊C₄×C₆₇	—	2	2	no	—
433	C₄⋊C₄×C₆₇	—	2	2	no	—
434	C₄⋊C₄×C₆₇	—	2	2	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	1	no	—
438	C₄⋊C₄×C₆₇	—	2	2	no	—
439	C₄⋊C₄×C₆₇	—	2	2	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	1	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	2	no	—
463	C₂²⋊C₄×C₆₇	—	2	2	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	no	—
465	C₂²⋊C₄×C₆₇	—	2	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	2	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
471	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
472	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
473	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
474	C₄²×C₆₇	—	2	2	no	—
475	C₄²×C₆₇	—	2	2	no	—
476	C₄²×C₆₇	—	2	2	no	—
477	C₄²×C₆₇	—	2	2	no	—
478	C₄²×C₆₇	—	2	1	no	—
479	C₄²×C₆₇	—	2	1	no	—
480	C₄²×C₆₇	C₂⁴	1	2	yes	—
481	C₂³×C₆₇	—	2	2	no	—
482	C₂³×C₆₇	—	2	1	no	—
483	C₂³×C₆₇	—	2	2	no	—
484	C₂³×C₆₇	—	2	1	no	—
485	C₂³×C₆₇	—	4	1	no	—
486	C₂³×C₆₇	—	4	1	no	—
487	C₂³×C₆₇	—	4	2	no	—
488	C₂³×C₆₇	—	8	1	no	—
489	C₂³×C₆₇	—	8	1	no	—
490	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
491	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
493	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
494	Q₈×C₆₇	—	2	4	no	—
495	Q₈×C₆₇	—	2	2	no	—
496	Q₈×C₆₇	—	2	2	no	—
497	Q₈×C₆₇	—	2	1	no	—
498	Q₈×C₆₇	—	2	1	no	—
499	Q₈×C₆₇	—	2	1	no	—
500	Q₈×C₆₇	—	2	1	no	—
501	Q₈×C₆₇	—	4	4	no	—
502	Q₈×C₆₇	—	8	2	no	—
503	Q₈×C₆₇	C₂×#41	1	4	yes	—
504	D₄×C₆₇	—	2	4	no	—
505	D₄×C₆₇	—	2	2	no	—
506	D₄×C₆₇	—	2	1	no	—
507	D₄×C₆₇	—	2	2	no	—
508	D₄×C₆₇	—	2	1	no	—
509	D₄×C₆₇	—	2	1	no	—
510	D₄×C₆₇	—	2	2	no	—
511	D₄×C₆₇	—	2	1	no	—
512	D₄×C₆₇	—	4	2	no	—
513	D₄×C₆₇	—	4	2	no	—
514	D₄×C₆₇	—	4	4	no	—
515	D₄×C₆₇	—	4	4	no	—
516	D₄×C₆₇	—	4	4	no	—
517	D₄×C₆₇	—	4	2	no	—
518	D₄×C₆₇	—	4	2	no	—
519	D₄×C₆₇	—	4	2	no	—
520	D₄×C₆₇	—	4	2	no	—
521	D₄×C₆₇	—	4	2	no	—
522	D₄×C₆₇	—	8	2	no	—
523	D₄×C₆₇	—	8	2	no	—
524	D₄×C₆₇	—	8	1	no	—
525	D₄×C₆₇	—	8	2	no	—
526	D₄×C₆₇	—	8	2	no	—
527	D₄×C₆₇	—	8	1	no	—
528	D₄×C₆₇	—	8	2	no	—
529	C₂×C₄×C₆₇	—	2	2	no	—
530	C₂×C₄×C₆₇	—	2	4	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	1	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	2	no	—
548	C₂×C₄×C₆₇	—	4	4	no	—
549	C₂×C₄×C₆₇	—	4	4	no	—
550	C₂×C₄×C₆₇	—	4	4	no	—
551	C₂×C₄×C₆₇	—	4	4	no	—
552	C₂×C₄×C₆₇	—	4	4	no	—
553	C₂×C₄×C₆₇	—	4	2	no	—
554	C₂×C₄×C₆₇	—	4	2	no	—
555	C₂×C₄×C₆₇	—	8	2	no	—
556	C₂×C₄×C₆₇	—	8	1	no	—
557	C₂×C₄×C₆₇	—	8	2	no	—
558	C₂×C₄×C₆₇	—	8	1	no	—
559	C₂×C₄×C₆₇	—	8	2	no	—
560	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
567	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
568	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
569	C₈×C₆₇	—	2	2	no	—
570	C₈×C₆₇	—	2	1	no	—
571	C₈×C₆₇	—	2	1	no	—
572	C₈×C₆₇	—	2	1	no	—
573	C₈×C₆₇	—	2	1	no	—
574	C₈×C₆₇	—	2	2	no	—
575	C₂²×C₆₇	—	2	1	no	—
576	C₂²×C₆₇	—	2	1	no	—
577	C₂²×C₆₇	—	2	1	no	—
578	C₂²×C₆₇	—	2	1	no	—
579	C₂²×C₆₇	—	2	2	no	—
580	C₂²×C₆₇	—	2	1	no	—
581	C₂²×C₆₇	—	2	2	no	—
582	C₂²×C₆₇	—	2	1	no	—
583	C₂²×C₆₇	—	2	1	no	—
584	C₂²×C₆₇	—	2	1	no	—
585	C₂²×C₆₇	—	2	2	no	—
586	C₂²×C₆₇	—	4	4	no	—
587	C₂²×C₆₇	—	4	1	no	—
588	C₂²×C₆₇	—	4	1	no	—
589	C₂²×C₆₇	—	4	2	no	—
590	C₂²×C₆₇	—	4	1	no	—
591	C₂²×C₆₇	—	4	1	no	—
592	C₂²×C₆₇	—	4	2	no	—
593	C₂²×C₆₇	—	4	1	no	—
594	C₂²×C₆₇	—	4	2	no	—
595	C₂²×C₆₇	—	4	1	no	—
596	C₂²×C₆₇	—	8	4	no	—
597	C₂²×C₆₇	#546	1	2	yes	—
598	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
599	C₄×C₆₇	—	2	2	no	—
600	C₄×C₆₇	—	2	2	no	—
601	C₄×C₆₇	—	2	1	no	—
602	C₄×C₆₇	—	2	1	no	—
603	C₄×C₆₇	—	2	4	no	—
604	C₄×C₆₇	—	2	2	no	—
605	C₄×C₆₇	—	4	2	no	—
606	C₄×C₆₇	—	4	2	no	—
607	C₄×C₆₇	—	4	1	no	—
608	C₄×C₆₇	—	4	1	no	—
609	C₄×C₆₇	—	4	1	no	—
610	C₄×C₆₇	—	4	1	no	—
611	C₄×C₆₇	—	4	1	no	—
612	C₄×C₆₇	—	4	1	no	—
613	C₄×C₆₇	#546	1	2	yes	—
614	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
615	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	#61178	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
617	C₂×C₆₇	—	2	2	no	—
618	C₂×C₆₇	—	4	2	no	—
619	C₂×C₆₇	—	4	1	no	—
620	C₂×C₆₇	—	4	1	no	—
621	C₂×C₆₇	—	8	1	no	—
622	C₂×C₆₇	—	8	1	no	—
623	C₂×C₆₇	—	8	2	no	—
624	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
625	C₂×C₆₇	#3585	1	1	yes	characteristic
626	C₂×C₆₇	#3586	1	1	yes	characteristic
627	#3492	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3487	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3333	C₂×C₆₇	1	2	yes	complemented
630	#3332	C₂×C₆₇	1	2	yes	complemented
631	#3327	C₂×C₆₇	1	2	yes	complemented
632	#3326	C₂×C₆₇	1	2	yes	complemented
633	#3317	C₂×C₆₇	1	2	yes	complemented
634	#3316	C₂×C₆₇	1	2	yes	complemented
635	#3309	C₂×C₆₇	1	2	yes	complemented
636	#3308	C₂×C₆₇	1	2	yes	complemented
637	#3136	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#3096	C₂×C₆₇	1	1	yes	characteristic, complemented
639	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
641	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
642	#3054	C₂×C₆₇	1	1	yes	characteristic, complemented
643	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
644	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#3005	C₂×C₆₇	1	1	yes	characteristic, complemented
646	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
647	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
648	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
649	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
650	C₆₇	#61178	1	1	yes	characteristic, direct product factor, Sylow
651	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
652	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
653	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
654	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
655	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
656	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
657	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
658	#554	—	2	1	no	—
659	#554	C₂²×C₆₇	1	2	yes	complemented
660	#553	—	2	1	no	—
661	#553	C₂²×C₆₇	1	2	yes	complemented
662	#552	—	2	1	no	—
663	#552	C₂²×C₆₇	1	2	yes	complemented
664	#550	—	2	1	no	—
665	#550	—	2	1	no	—
666	#550	C₂²×C₆₇	1	2	yes	—
667	#550	C₂²×C₆₇	1	2	yes	—
668	#548	—	2	1	no	—
669	#548	—	2	1	no	—
670	#548	C₂²×C₆₇	1	2	yes	—
671	#548	C₂²×C₆₇	1	2	yes	—
672	#547	—	2	1	no	—
673	#547	C₂²×C₆₇	1	2	yes	complemented
674	#544	C₂²×C₆₇	1	1	yes	characteristic
675	#539	—	2	2	no	—
676	#537	C₂²×C₆₇	1	1	yes	characteristic
677	#535	—	2	2	no	—
678	#535	C₂²×C₆₇	1	1	yes	characteristic
679	#535	C₂²×C₆₇	1	1	yes	characteristic
680	#525	—	2	2	no	—
681	#525	—	2	2	no	—
682	#525	C₂²×C₆₇	1	1	yes	characteristic
683	#525	C₂²×C₆₇	1	1	yes	characteristic
684	#525	C₂²×C₆₇	1	1	yes	characteristic
685	#520	C₂²×C₆₇	1	1	yes	characteristic
686	#520	C₂²×C₆₇	1	1	yes	characteristic
687	#519	C₂²×C₆₇	1	1	yes	characteristic
688	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
689	#490	C₂²×C₆₇	1	2	yes	complemented
690	#489	C₂²×C₆₇	1	2	yes	complemented
691	#488	C₂²×C₆₇	1	2	yes	complemented
692	#486	C₂²×C₆₇	1	2	yes	complemented
693	#484	C₂²×C₆₇	1	2	yes	complemented
694	#483	C₂²×C₆₇	1	2	yes	complemented
695	#482	C₂²×C₆₇	1	2	yes	complemented
696	#482	C₂²×C₆₇	1	2	yes	complemented
697	#481	C₂²×C₆₇	1	2	yes	complemented
698	#481	C₂²×C₆₇	1	2	yes	complemented
699	#480	C₂²×C₆₇	1	2	yes	complemented
700	#480	C₂²×C₆₇	1	2	yes	complemented
701	#479	C₂²×C₆₇	1	2	yes	complemented
702	#479	C₂²×C₆₇	1	2	yes	complemented
703	#477	C₂²×C₆₇	1	2	yes	complemented
704	#475	C₂²×C₆₇	1	2	yes	complemented
705	#470	C₂²×C₆₇	1	1	yes	characteristic, complemented
706	#470	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#469	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#469	C₂²×C₆₇	1	2	yes	complemented
709	#469	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#468	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#468	C₂²×C₆₇	1	2	yes	complemented
712	#468	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#468	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#468	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	#466	C₂²×C₆₇	1	2	yes	complemented
716	#465	C₂²×C₆₇	1	2	yes	complemented
717	#464	C₂²×C₆₇	1	2	yes	complemented
718	#463	C₂²×C₆₇	1	2	yes	complemented
719	#460	C₂²×C₆₇	1	2	yes	complemented
720	#459	C₂²×C₆₇	1	2	yes	complemented
721	#452	C₂²×C₆₇	1	2	yes	—
722	#452	C₂²×C₆₇	1	2	yes	—
723	#452	C₂²×C₆₇	1	2	yes	complemented
724	#451	C₂²×C₆₇	1	2	yes	complemented
725	#449	C₂²×C₆₇	1	2	yes	—
726	#449	C₂²×C₆₇	1	2	yes	—
727	#449	C₂²×C₆₇	1	2	yes	complemented
728	#448	C₂²×C₆₇	1	2	yes	complemented
729	#441	C₂²×C₆₇	1	2	yes	complemented
730	#440	C₂²×C₆₇	1	2	yes	complemented
731	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
732	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
733	#436	C₂²×C₆₇	1	2	yes	complemented
734	#436	C₂²×C₆₇	1	2	yes	complemented
735	#435	C₂²×C₆₇	1	2	yes	complemented
736	#435	C₂²×C₆₇	1	2	yes	complemented
737	#428	C₂²×C₆₇	1	1	yes	characteristic
738	#428	C₂²×C₆₇	1	1	yes	characteristic
739	#427	C₂²×C₆₇	1	1	yes	characteristic
740	#424	C₂²×C₆₇	1	1	yes	characteristic
741	#419	C₂²×C₆₇	1	1	yes	characteristic
742	#419	C₂²×C₆₇	1	2	yes	complemented
743	#418	C₂²×C₆₇	1	1	yes	characteristic
744	#417	C₂²×C₆₇	1	2	yes	—
745	#417	C₂²×C₆₇	1	2	yes	—
746	#417	C₂²×C₆₇	1	1	yes	characteristic
747	#417	C₂²×C₆₇	1	1	yes	characteristic
748	#417	C₂²×C₆₇	1	2	yes	—
749	#417	C₂²×C₆₇	1	2	yes	—
750	#417	C₂²×C₆₇	1	2	yes	complemented
751	#416	C₂²×C₆₇	1	1	yes	characteristic
752	#416	C₂²×C₆₇	1	1	yes	characteristic
753	#416	C₂²×C₆₇	1	2	yes	complemented
754	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
755	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
756	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
757	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
758	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
759	#408	C₂²×C₆₇	1	1	yes	characteristic
760	#407	C₂²×C₆₇	1	1	yes	characteristic
761	#405	C₂²×C₆₇	1	1	yes	characteristic
762	2₋¹⁺⁴	—	2	4	no	—
763	2₋¹⁺⁴	—	4	2	no	—
764	C₂×#41	—	2	2	no	—
765	C₂×#41	—	2	1	no	—
766	C₂×#41	—	2	2	no	—
767	C₂×#41	—	2	1	no	—
768	C₂×#41	—	2	1	no	—
769	C₂×#41	—	2	4	no	—
770	C₂×#41	—	4	2	no	—
771	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×#41	C₂³×C₆₇	1	2	yes	—
774	C₂×#41	C₂³×C₆₇	1	2	yes	—
775	C₂×#41	C₂³×C₆₇	1	2	yes	—
776	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
777	C₂²×Q₈	—	2	1	no	—
778	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
779	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
780	C₂²×D₄	—	2	1	no	—
781	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
782	C₂³×C₄	—	2	1	no	—
783	C₂³×C₄	—	2	1	no	—
784	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
785	#137	—	2	4	no	—
786	AGL(1,ℤ/8)	—	4	2	no	—
787	#135	—	4	2	no	—
788	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
789	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
792	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
793	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
794	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
795	C₂×D₈	C₂³×C₆₇	1	2	yes	—
796	#131	—	4	2	no	—
797	C₂×M₁₆	—	4	2	no	—
798	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
800	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
801	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
802	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
803	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
804	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
805	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
806	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
807	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
808	C₄⋊Q₈	—	2	1	no	—
809	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
810	#127	—	2	2	no	—
811	#127	—	2	2	no	—
812	#127	—	2	1	no	—
813	#127	C₂³×C₆₇	1	2	yes	—
814	#126	—	2	2	no	—
815	#126	—	2	2	no	—
816	#125	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	—	2	1	no	—
819	#125	C₂³×C₆₇	1	2	yes	—
820	#124	—	2	1	no	—
821	#124	—	2	2	no	—
822	#124	—	2	2	no	—
823	#124	C₂³×C₆₇	1	2	yes	—
824	#123	—	2	2	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	D₄×C₆₇	1	2	yes	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	2	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	—	2	2	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	—	2	2	no	—
837	C₂²⋊Q₈	—	2	2	no	—
838	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
839	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	—	2	1	no	—
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	2	no	—
853	#121	—	2	2	no	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	D₄×C₆₇	1	1	yes	characteristic
857	#121	D₄×C₆₇	1	1	yes	characteristic
858	#121	C₂³×C₆₇	1	1	yes	characteristic
859	#121	C₂³×C₆₇	1	1	yes	characteristic
860	#121	C₂³×C₆₇	1	1	yes	characteristic
861	#121	C₂³×C₆₇	1	1	yes	characteristic
862	#121	C₂³×C₆₇	1	2	yes	—
863	#121	C₂³×C₆₇	1	2	yes	—
864	#121	C₂³×C₆₇	1	2	yes	—
865	#120	—	2	1	no	—
866	#120	—	2	1	no	—
867	#120	—	2	2	no	—
868	#120	—	2	2	no	—
869	#120	D₄×C₆₇	1	2	yes	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
874	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
875	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	2	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	2	no	—
884	C₄×D₄	—	2	2	no	—
885	C₄×D₄	—	2	2	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	—	2	2	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	C₂³×C₆₇	1	2	yes	—
890	C₄×D₄	C₂³×C₆₇	1	2	yes	—
891	C₄×D₄	C₂³×C₆₇	1	2	yes	—
892	#117	—	2	1	no	—
893	#117	—	2	2	no	—
894	#117	—	2	2	no	—
895	#117	C₂³×C₆₇	1	1	yes	characteristic
896	#117	C₂³×C₆₇	1	1	yes	characteristic
897	#117	C₂³×C₆₇	1	2	yes	—
898	#117	C₂³×C₆₇	1	1	yes	characteristic
899	C₂×C₄⋊C₄	—	2	1	no	—
900	C₂×C₄⋊C₄	—	2	1	no	—
901	C₂×C₄⋊C₄	—	2	1	no	—
902	C₂×C₄⋊C₄	—	2	1	no	—
903	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
906	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
907	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
908	#107	C₂³×C₆₇	1	1	yes	characteristic
909	#107	C₂³×C₆₇	1	1	yes	characteristic
910	#107	C₂³×C₆₇	1	2	yes	—
911	#107	C₂³×C₆₇	1	2	yes	—
912	#106	C₂³×C₆₇	1	1	yes	characteristic
913	#106	C₂³×C₆₇	1	1	yes	characteristic
914	#106	C₂³×C₆₇	1	2	yes	—
915	#106	C₂³×C₆₇	1	2	yes	—
916	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
917	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
918	#103	C₂³×C₆₇	1	2	yes	—
919	#103	C₂³×C₆₇	1	2	yes	—
920	#103	C₂³×C₆₇	1	2	yes	—
921	#103	C₂³×C₆₇	1	2	yes	—
922	#103	C₂³×C₆₇	1	1	yes	characteristic
923	#103	C₂³×C₆₇	1	2	yes	—
924	#103	C₂³×C₆₇	1	2	yes	—
925	#103	C₂³×C₆₇	1	1	yes	characteristic
926	#103	C₂³×C₆₇	1	1	yes	characteristic
927	#103	C₂³×C₆₇	1	1	yes	characteristic
928	#103	C₂³×C₆₇	1	2	yes	—
929	#103	C₂³×C₆₇	1	2	yes	—
930	#102	C₂³×C₆₇	1	2	yes	—
931	#102	C₂³×C₆₇	1	2	yes	—
932	#102	C₂³×C₆₇	1	2	yes	—
933	#102	C₂³×C₆₇	1	2	yes	—
934	#102	C₂³×C₆₇	1	1	yes	characteristic
935	#102	C₂³×C₆₇	1	1	yes	characteristic
936	#102	C₂³×C₆₇	1	1	yes	characteristic
937	#102	C₂³×C₆₇	1	1	yes	characteristic
938	#102	C₂³×C₆₇	1	2	yes	—
939	#102	C₂³×C₆₇	1	2	yes	—
940	#102	C₂³×C₆₇	1	2	yes	—
941	#102	C₂³×C₆₇	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
943	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
945	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
946	#97	C₂³×C₆₇	1	2	yes	—
947	C₄×C₈	C₂³×C₆₇	1	2	yes	—
948	C₂⁴	—	2	1	no	—
949	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
950	#41	—	2	2	no	—
951	#41	—	2	2	no	—
952	#41	—	2	4	no	—
953	#41	—	2	4	no	—
954	#41	—	2	4	no	—
955	#41	—	2	2	no	—
956	#41	—	2	2	no	—
957	#41	—	2	2	no	—
958	#41	—	2	2	no	—
959	#41	—	4	2	no	—
960	#41	—	4	2	no	—
961	#41	—	4	2	no	—
962	#41	—	4	8	no	—
963	#41	—	4	4	no	—
964	#41	—	4	4	no	—
965	#41	—	4	4	no	—
966	#41	—	8	4	no	—
967	C₂×Q₈	—	2	1	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	—	2	2	no	—
970	C₂×Q₈	—	2	2	no	—
971	C₂×Q₈	—	2	4	no	—
972	C₂×Q₈	—	4	2	no	—
973	C₂×Q₈	—	4	4	no	—
974	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
976	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	4	4	no	—
997	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
998	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
999	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1000	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1001	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1003	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	4	4	no	—
1020	C₂²×C₄	—	8	2	no	—
1021	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1027	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1028	Q₁₆	—	2	4	no	—
1029	Q₁₆	—	4	1	no	—
1030	SD₁₆	—	2	4	no	—
1031	SD₁₆	—	4	1	no	—
1032	SD₁₆	—	4	1	no	—
1033	SD₁₆	—	4	2	no	—
1034	D₈	—	4	1	no	—
1035	D₈	—	4	2	no	—
1036	M₁₆	—	2	2	no	—
1037	M₁₆	—	2	2	no	—
1038	M₁₆	—	4	1	no	—
1039	M₁₆	—	4	1	no	—
1040	M₁₆	—	4	1	no	—
1041	M₁₆	—	4	1	no	—
1042	M₁₆	—	4	2	no	—
1043	C₂×C₈	—	2	2	no	—
1044	C₂×C₈	—	2	2	no	—
1045	C₂×C₈	—	4	2	no	—
1046	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1047	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1048	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1069	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1070	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1071	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1072	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1073	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1074	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1075	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1097	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1098	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1099	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1100	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1101	C₄²	—	2	2	no	—
1102	C₄²	—	2	2	no	—
1103	C₄²	—	2	2	no	—
1104	C₄²	—	2	2	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	C₂⁴×C₆₇	1	2	yes	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	1	no	—
1110	C₂³	—	2	2	no	—
1111	C₂³	—	2	1	no	—
1112	C₂³	—	4	1	no	—
1113	C₂³	—	4	1	no	—
1114	C₂³	—	4	2	no	—
1115	C₂³	—	8	1	no	—
1116	C₂³	—	8	1	no	—
1117	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1118	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1119	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1120	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1121	Q₈	—	2	4	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	2	2	no	—
1124	Q₈	—	2	1	no	—
1125	Q₈	—	2	1	no	—
1126	Q₈	—	2	1	no	—
1127	Q₈	—	2	1	no	—
1128	Q₈	—	4	4	no	—
1129	Q₈	—	8	2	no	—
1130	Q₈	C₂×#41×C₆₇	1	4	yes	—
1131	D₄	—	2	4	no	—
1132	D₄	—	2	2	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	2	1	no	—
1137	D₄	—	2	2	no	—
1138	D₄	—	2	1	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	2	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	4	2	no	—
1147	D₄	—	4	2	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	1	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	2	no	—
1155	D₄	—	8	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	4	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	4	4	no	—
1176	C₂×C₄	—	4	4	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	4	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	8	2	no	—
1187	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1188	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1189	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1190	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1191	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1192	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1193	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1194	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1195	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1196	C₈	—	2	2	no	—
1197	C₈	—	2	1	no	—
1198	C₈	—	2	1	no	—
1199	C₈	—	2	1	no	—
1200	C₈	—	2	1	no	—
1201	C₈	—	2	2	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	4	4	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	8	4	no	—
1224	C₂²	#546×C₆₇	1	2	yes	—
1225	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	4	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	2	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	#546×C₆₇	1	2	yes	—
1241	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1242	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1243	C₂	—	2	2	no	—
1244	C₂	—	4	1	no	—
1245	C₂	—	4	1	no	—
1246	C₂	—	4	2	no	—
1247	C₂	—	8	2	no	—
1248	C₂	—	8	1	no	—
1249	C₂	—	8	1	no	—
1250	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1251	C₂	C₆₇×#3585	1	1	yes	characteristic
1252	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3492	C₂	semidirect
2. C₆₇×#3487	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3332	C₂	semidirect
5. C₆₇×#3327	C₂	semidirect
6. C₆₇×#3326	C₂	semidirect
7. C₆₇×#3317	C₂	semidirect
8. C₆₇×#3316	C₂	semidirect
9. C₆₇×#3309	C₂	semidirect
10. C₆₇×#3308	C₂	semidirect
11. C₆₇×#3136	C₂	semidirect
12. C₆₇×#3096	C₂	semidirect
13. C₆₇×#3092	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3062	C₂	semidirect
16. C₆₇×#3054	C₂	semidirect
17. C₆₇×#3045	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3005	C₂	semidirect
20. C₆₇×#2947	C₂	semidirect
21. C₆₇×#2930	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₂×#417×C₆₇	C₂	semidirect
32. #554×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
36. #552×C₆₇	C₂²	semidirect
46. #547×C₆₇	C₂²	semidirect
62. #490×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #486×C₆₇	C₂²	semidirect
66. #484×C₆₇	C₂²	semidirect
67. #483×C₆₇	C₂²	semidirect
68. #482×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #481×C₆₇	C₂²	semidirect
71. #481×C₆₇	C₂²	semidirect
72. #480×C₆₇	C₂²	semidirect
73. #480×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #479×C₆₇	C₂²	semidirect
76. #477×C₆₇	C₂²	semidirect
77. #475×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #470×C₆₇	C₂²	semidirect
80. #469×C₆₇	C₂²	semidirect
81. #469×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
83. #468×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #468×C₆₇	C₂²	semidirect
87. #468×C₆₇	C₂²	semidirect
88. #466×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #463×C₆₇	C₂²	semidirect
92. #460×C₆₇	C₂²	semidirect
93. #459×C₆₇	C₂²	semidirect
96. #452×C₆₇	C₂²	semidirect
97. #451×C₆₇	C₂²	semidirect
100. #449×C₆₇	C₂²	semidirect
101. #448×C₆₇	C₂²	semidirect
102. #441×C₆₇	C₂²	semidirect
103. #440×C₆₇	C₂²	semidirect
104. C₄×Q₁₆×C₆₇	C₂²	semidirect
105. C₄×SD₁₆×C₆₇	C₂²	semidirect
106. #436×C₆₇	C₂²	semidirect
107. #436×C₆₇	C₂²	semidirect
108. #435×C₆₇	C₂²	semidirect
109. #435×C₆₇	C₂²	semidirect
115. #419×C₆₇	C₂²	semidirect
123. #417×C₆₇	C₂²	semidirect
126. #416×C₆₇	C₂²	semidirect
129. C₂×#103×C₆₇	C₂²	semidirect
348. C₂×Q₈×C₆₇	#41	semidirect
616. #61178	C₆₇	direct (N × H)
627. #3492	C₂×C₆₇	semidirect
628. #3487	C₂×C₆₇	semidirect
629. #3333	C₂×C₆₇	semidirect
630. #3332	C₂×C₆₇	semidirect
631. #3327	C₂×C₆₇	semidirect
632. #3326	C₂×C₆₇	semidirect
633. #3317	C₂×C₆₇	semidirect
634. #3316	C₂×C₆₇	semidirect
635. #3309	C₂×C₆₇	semidirect
636. #3308	C₂×C₆₇	semidirect
637. #3136	C₂×C₆₇	semidirect
638. #3096	C₂×C₆₇	semidirect
639. #3092	C₂×C₆₇	semidirect
640. #3082	C₂×C₆₇	semidirect
641. #3062	C₂×C₆₇	semidirect
642. #3054	C₂×C₆₇	semidirect
643. #3045	C₂×C₆₇	semidirect
644. #3013	C₂×C₆₇	semidirect
645. #3005	C₂×C₆₇	semidirect
646. #2947	C₂×C₆₇	semidirect
647. #2930	C₂×C₆₇	semidirect
648. #2898	C₂×C₆₇	semidirect
649. C₂×#417	C₂×C₆₇	semidirect
650. C₆₇	#61178	direct (N × H)
659. #554	C₂²×C₆₇	semidirect
661. #553	C₂²×C₆₇	semidirect
663. #552	C₂²×C₆₇	semidirect
673. #547	C₂²×C₆₇	semidirect
689. #490	C₂²×C₆₇	semidirect
690. #489	C₂²×C₆₇	semidirect
691. #488	C₂²×C₆₇	semidirect
692. #486	C₂²×C₆₇	semidirect
693. #484	C₂²×C₆₇	semidirect
694. #483	C₂²×C₆₇	semidirect
695. #482	C₂²×C₆₇	semidirect
696. #482	C₂²×C₆₇	semidirect
697. #481	C₂²×C₆₇	semidirect
698. #481	C₂²×C₆₇	semidirect
699. #480	C₂²×C₆₇	semidirect
700. #480	C₂²×C₆₇	semidirect
701. #479	C₂²×C₆₇	semidirect
702. #479	C₂²×C₆₇	semidirect
703. #477	C₂²×C₆₇	semidirect
704. #475	C₂²×C₆₇	semidirect
705. #470	C₂²×C₆₇	semidirect
706. #470	C₂²×C₆₇	semidirect
707. #469	C₂²×C₆₇	semidirect
708. #469	C₂²×C₆₇	semidirect
709. #469	C₂²×C₆₇	semidirect
710. #468	C₂²×C₆₇	semidirect
711. #468	C₂²×C₆₇	semidirect
712. #468	C₂²×C₆₇	semidirect
713. #468	C₂²×C₆₇	semidirect
714. #468	C₂²×C₆₇	semidirect
715. #466	C₂²×C₆₇	semidirect
716. #465	C₂²×C₆₇	semidirect
717. #464	C₂²×C₆₇	semidirect
718. #463	C₂²×C₆₇	semidirect
719. #460	C₂²×C₆₇	semidirect
720. #459	C₂²×C₆₇	semidirect
723. #452	C₂²×C₆₇	semidirect
724. #451	C₂²×C₆₇	semidirect
727. #449	C₂²×C₆₇	semidirect
728. #448	C₂²×C₆₇	semidirect
729. #441	C₂²×C₆₇	semidirect
730. #440	C₂²×C₆₇	semidirect
731. C₄×Q₁₆	C₂²×C₆₇	semidirect
732. C₄×SD₁₆	C₂²×C₆₇	semidirect
733. #436	C₂²×C₆₇	semidirect
734. #436	C₂²×C₆₇	semidirect
735. #435	C₂²×C₆₇	semidirect
736. #435	C₂²×C₆₇	semidirect
742. #419	C₂²×C₆₇	semidirect
750. #417	C₂²×C₆₇	semidirect
753. #416	C₂²×C₆₇	semidirect
756. C₂×#103	C₂²×C₆₇	semidirect
975. C₂×Q₈	#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×#3492	2
C₆₇×#3487	2
C₆₇×#3333	2
C₆₇×#3332	2
C₆₇×#3327	2
C₆₇×#3326	2
C₆₇×#3317	2
C₆₇×#3316	2
C₆₇×#3309	2
C₆₇×#3308	2
C₆₇×#3136	2
C₆₇×#3096	2
C₆₇×#3092	2
C₆₇×#3082	2
C₆₇×#3062	2
C₆₇×#3054	2
C₆₇×#3045	2
C₆₇×#3013	2
C₆₇×#3005	2
C₆₇×#2947	2
C₆₇×#2930	2
C₆₇×#2898	2
C₂×#417×C₆₇	2
#61178	67

Subgroups — C67×#61178 #30740429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61178 #30740429