Subgroups — C₆₇×#61190 #30740441

Order 17152.

2044 conjugacy classes of subgroups.

The subgroup lattice has 1222 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×#3487	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3313	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3304	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3300	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×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2896	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	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×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	#556×C₆₇	C₂²	1	2	yes	complemented
32	#554×C₆₇	C₂²	1	2	yes	complemented
33	#552×C₆₇	—	2	2	no	—
34	#552×C₆₇	C₂²	1	2	yes	complemented
35	#552×C₆₇	C₂²	1	2	yes	complemented
36	#551×C₆₇	—	2	2	no	—
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	#544×C₆₇	C₂²	1	1	yes	characteristic
46	#542×C₆₇	—	2	1	no	—
47	#541×C₆₇	—	2	1	no	—
48	#536×C₆₇	C₂²	1	1	yes	characteristic
49	#535×C₆₇	—	2	2	no	—
50	#535×C₆₇	C₂²	1	1	yes	characteristic
51	#535×C₆₇	C₂²	1	1	yes	characteristic
52	#533×C₆₇	—	2	1	no	—
53	#529×C₆₇	—	2	1	no	—
54	#525×C₆₇	—	2	2	no	—
55	#525×C₆₇	C₂²	1	1	yes	characteristic
56	#525×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#519×C₆₇	C₂²	1	1	yes	characteristic
60	#519×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#117×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	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	2	yes	complemented
73	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#481×C₆₇	C₂²	1	2	yes	complemented
75	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#480×C₆₇	C₂²	1	2	yes	complemented
77	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#479×C₆₇	C₂²	1	2	yes	complemented
79	#479×C₆₇	C₂²	1	2	yes	complemented
80	#477×C₆₇	C₂²	1	2	yes	complemented
81	#475×C₆₇	C₂²	1	2	yes	complemented
82	#470×C₆₇	C₂²	1	2	yes	complemented
83	#468×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#467×C₆₇	C₂²	1	2	yes	complemented
87	#465×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#464×C₆₇	C₂²	1	2	yes	complemented
92	#460×C₆₇	C₂²	1	2	yes	complemented
93	#460×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	—
97	#452×C₆₇	C₂²	1	2	yes	—
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#452×C₆₇	C₂²	1	2	yes	complemented
100	#451×C₆₇	C₂²	1	2	yes	complemented
101	#451×C₆₇	C₂²	1	2	yes	complemented
102	#441×C₆₇	C₂²	1	2	yes	complemented
103	#441×C₆₇	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
106	#436×C₆₇	C₂²	1	2	yes	complemented
107	#435×C₆₇	C₂²	1	2	yes	complemented
108	#435×C₆₇	C₂²	1	2	yes	complemented
109	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
110	#428×C₆₇	C₂²	1	1	yes	characteristic
111	#427×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	1	yes	characteristic
116	#419×C₆₇	C₂²	1	1	yes	characteristic
117	#419×C₆₇	C₂²	1	2	yes	complemented
118	#418×C₆₇	C₂²	1	1	yes	characteristic
119	#418×C₆₇	C₂²	1	1	yes	characteristic
120	#417×C₆₇	C₂²	1	1	yes	characteristic
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	—
127	#416×C₆₇	C₂²	1	2	yes	—
128	#416×C₆₇	C₂²	1	2	yes	complemented
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
131	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×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	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	4	no	—
142	C₂×#41×C₆₇	—	4	2	no	—
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂×#41×C₆₇	C₂³	1	2	yes	—
146	C₂×#41×C₆₇	C₂³	1	2	yes	—
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₆₇	—	2	1	no	—
149	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₆₇	—	2	1	no	—
153	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₆₇	—	2	1	no	—
155	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
156	#137×C₆₇	—	4	2	no	—
157	C₂×Q₁₆×C₆₇	—	2	4	no	—
158	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₇	—	4	2	no	—
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	#131×C₆₇	—	4	2	no	—
166	C₂×M₁₆×C₆₇	—	4	2	no	—
167	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
170	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
171	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
174	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₆₇	—	2	1	no	—
176	C₄⋊Q₈×C₆₇	—	2	1	no	—
177	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
178	#127×C₆₇	—	2	2	no	—
179	#127×C₆₇	—	2	2	no	—
180	#127×C₆₇	—	2	1	no	—
181	#127×C₆₇	C₂³	1	2	yes	—
182	#126×C₆₇	—	2	2	no	—
183	#126×C₆₇	—	2	2	no	—
184	#126×C₆₇	—	2	2	no	—
185	#126×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	1	no	—
187	#125×C₆₇	—	2	2	no	—
188	#125×C₆₇	—	2	2	no	—
189	#125×C₆₇	—	2	2	no	—
190	#125×C₆₇	C₂³	1	2	yes	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	—	2	1	no	—
193	#124×C₆₇	—	2	2	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	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	#123×C₆₇	—	2	1	no	—
201	#123×C₆₇	D₄	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	—	2	1	no	—
203	C₂²⋊Q₈×C₆₇	—	2	1	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	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	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	#121×C₆₇	—	2	2	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	1	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	—	2	2	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	D₄	1	1	yes	characteristic
226	#121×C₆₇	D₄	1	1	yes	characteristic
227	#121×C₆₇	C₂³	1	1	yes	characteristic
228	#121×C₆₇	C₂³	1	2	yes	—
229	#121×C₆₇	C₂³	1	2	yes	—
230	#121×C₆₇	C₂³	1	1	yes	characteristic
231	#120×C₆₇	—	2	1	no	—
232	#120×C₆₇	—	2	2	no	—
233	#120×C₆₇	—	2	2	no	—
234	#120×C₆₇	D₄	1	2	yes	—
235	C₄×Q₈×C₆₇	—	2	1	no	—
236	C₄×Q₈×C₆₇	—	2	1	no	—
237	C₄×Q₈×C₆₇	—	2	1	no	—
238	C₄×Q₈×C₆₇	—	2	1	no	—
239	C₄×Q₈×C₆₇	—	2	1	no	—
240	C₄×Q₈×C₆₇	—	2	2	no	—
241	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
243	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
244	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	2	no	—
247	C₄×D₄×C₆₇	—	2	2	no	—
248	C₄×D₄×C₆₇	—	2	1	no	—
249	C₄×D₄×C₆₇	—	2	1	no	—
250	C₄×D₄×C₆₇	—	2	2	no	—
251	C₄×D₄×C₆₇	—	2	2	no	—
252	C₄×D₄×C₆₇	—	2	2	no	—
253	C₄×D₄×C₆₇	—	2	2	no	—
254	C₄×D₄×C₆₇	C₂³	1	2	yes	—
255	C₄×D₄×C₆₇	C₂³	1	2	yes	—
256	#117×C₆₇	—	2	1	no	—
257	#117×C₆₇	—	2	1	no	—
258	#117×C₆₇	—	2	2	no	—
259	#117×C₆₇	—	2	2	no	—
260	#117×C₆₇	—	2	2	no	—
261	#117×C₆₇	—	2	2	no	—
262	#117×C₆₇	C₂³	1	2	yes	—
263	#117×C₆₇	C₂³	1	1	yes	characteristic
264	#117×C₆₇	C₂³	1	1	yes	characteristic
265	#117×C₆₇	C₂³	1	1	yes	characteristic
266	#117×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	C₂³	1	1	yes	characteristic
268	#117×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	1	yes	characteristic
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#107×C₆₇	C₂³	1	1	yes	characteristic
282	#106×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	#106×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	1	yes	characteristic
286	#106×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
296	#103×C₆₇	C₂³	1	1	yes	characteristic
297	#103×C₆₇	C₂³	1	2	yes	—
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×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	#102×C₆₇	C₂³	1	2	yes	—
309	#102×C₆₇	C₂³	1	2	yes	—
310	#102×C₆₇	C₂³	1	2	yes	—
311	#102×C₆₇	C₂³	1	2	yes	—
312	#102×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
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	—	4	2	no	—
331	#41×C₆₇	—	4	2	no	—
332	#41×C₆₇	—	4	2	no	—
333	#41×C₆₇	—	4	8	no	—
334	#41×C₆₇	—	4	4	no	—
335	#41×C₆₇	—	4	4	no	—
336	#41×C₆₇	—	4	4	no	—
337	C₂×Q₈×C₆₇	—	2	1	no	—
338	C₂×Q₈×C₆₇	—	2	1	no	—
339	C₂×Q₈×C₆₇	—	2	2	no	—
340	C₂×Q₈×C₆₇	—	2	2	no	—
341	C₂×Q₈×C₆₇	—	2	2	no	—
342	C₂×Q₈×C₆₇	—	2	4	no	—
343	C₂×Q₈×C₆₇	—	2	2	no	—
344	C₂×Q₈×C₆₇	—	2	2	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	—
349	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
351	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
352	C₂×D₄×C₆₇	—	2	1	no	—
353	C₂×D₄×C₆₇	—	2	2	no	—
354	C₂×D₄×C₆₇	—	2	2	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	2	no	—
357	C₂×D₄×C₆₇	—	2	2	no	—
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	2	no	—
362	C₂×D₄×C₆₇	—	2	2	no	—
363	C₂×D₄×C₆₇	—	2	2	no	—
364	C₂×D₄×C₆₇	—	2	2	no	—
365	C₂×D₄×C₆₇	—	4	4	no	—
366	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
371	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	—	2	1	no	—
376	C₂²×C₄×C₆₇	—	2	1	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	2	1	no	—
379	C₂²×C₄×C₆₇	—	2	1	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	2	no	—
385	C₂²×C₄×C₆₇	—	4	4	no	—
386	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
393	Q₁₆×C₆₇	—	2	4	no	—
394	Q₁₆×C₆₇	—	2	4	no	—
395	Q₁₆×C₆₇	—	4	2	no	—
396	SD₁₆×C₆₇	—	4	2	no	—
397	SD₁₆×C₆₇	—	4	2	no	—
398	SD₁₆×C₆₇	—	4	2	no	—
399	M₁₆×C₆₇	—	2	2	no	—
400	M₁₆×C₆₇	—	2	2	no	—
401	M₁₆×C₆₇	—	4	2	no	—
402	M₁₆×C₆₇	—	4	2	no	—
403	C₂×C₈×C₆₇	—	2	2	no	—
404	C₂×C₈×C₆₇	—	2	2	no	—
405	C₂×C₈×C₆₇	—	4	2	no	—
406	C₂×C₈×C₆₇	—	4	2	no	—
407	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
411	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	1	no	—
416	C₄⋊C₄×C₆₇	—	2	1	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
425	C₄⋊C₄×C₆₇	—	2	2	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
432	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₂²⋊C₄×C₆₇	—	2	1	no	—
443	C₂²⋊C₄×C₆₇	—	2	1	no	—
444	C₂²⋊C₄×C₆₇	—	2	1	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	1	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	1	no	—
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	no	—
455	C₂²⋊C₄×C₆₇	—	2	2	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₄²×C₆₇	—	2	1	no	—
465	C₄²×C₆₇	—	2	1	no	—
466	C₄²×C₆₇	—	2	1	no	—
467	C₄²×C₆₇	—	2	1	no	—
468	C₄²×C₆₇	—	2	2	no	—
469	C₄²×C₆₇	—	2	2	no	—
470	C₄²×C₆₇	—	2	2	no	—
471	C₄²×C₆₇	—	2	2	no	—
472	C₄²×C₆₇	—	2	2	no	—
473	C₄²×C₆₇	—	2	1	no	—
474	C₄²×C₆₇	C₂⁴	1	2	yes	—
475	C₂³×C₆₇	—	2	2	no	—
476	C₂³×C₆₇	—	2	2	no	—
477	C₂³×C₆₇	—	2	1	no	—
478	C₂³×C₆₇	—	4	1	no	—
479	C₂³×C₆₇	—	4	1	no	—
480	C₂³×C₆₇	—	4	2	no	—
481	C₂³×C₆₇	—	8	1	no	—
482	C₂³×C₆₇	—	8	1	no	—
483	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
484	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
485	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
486	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
487	Q₈×C₆₇	—	2	4	no	—
488	Q₈×C₆₇	—	2	2	no	—
489	Q₈×C₆₇	—	2	2	no	—
490	Q₈×C₆₇	—	2	2	no	—
491	Q₈×C₆₇	—	2	1	no	—
492	Q₈×C₆₇	—	2	2	no	—
493	Q₈×C₆₇	—	2	1	no	—
494	Q₈×C₆₇	—	4	4	no	—
495	Q₈×C₆₇	—	4	2	no	—
496	Q₈×C₆₇	—	8	2	no	—
497	Q₈×C₆₇	C₂×#41	1	4	yes	—
498	D₄×C₆₇	—	2	4	no	—
499	D₄×C₆₇	—	2	2	no	—
500	D₄×C₆₇	—	2	2	no	—
501	D₄×C₆₇	—	2	1	no	—
502	D₄×C₆₇	—	2	2	no	—
503	D₄×C₆₇	—	2	1	no	—
504	D₄×C₆₇	—	4	2	no	—
505	D₄×C₆₇	—	4	2	no	—
506	D₄×C₆₇	—	4	4	no	—
507	D₄×C₆₇	—	4	4	no	—
508	D₄×C₆₇	—	4	4	no	—
509	D₄×C₆₇	—	4	2	no	—
510	D₄×C₆₇	—	4	2	no	—
511	D₄×C₆₇	—	8	2	no	—
512	D₄×C₆₇	—	8	2	no	—
513	D₄×C₆₇	—	8	2	no	—
514	D₄×C₆₇	—	8	1	no	—
515	D₄×C₆₇	—	8	2	no	—
516	D₄×C₆₇	—	8	1	no	—
517	C₂×C₄×C₆₇	—	2	2	no	—
518	C₂×C₄×C₆₇	—	2	4	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	2	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	4	4	no	—
538	C₂×C₄×C₆₇	—	4	4	no	—
539	C₂×C₄×C₆₇	—	4	4	no	—
540	C₂×C₄×C₆₇	—	4	4	no	—
541	C₂×C₄×C₆₇	—	4	2	no	—
542	C₂×C₄×C₆₇	—	4	2	no	—
543	C₂×C₄×C₆₇	—	4	2	no	—
544	C₂×C₄×C₆₇	—	8	2	no	—
545	C₂×C₄×C₆₇	—	8	1	no	—
546	C₂×C₄×C₆₇	—	8	1	no	—
547	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
554	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
555	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
556	C₈×C₆₇	—	2	1	no	—
557	C₈×C₆₇	—	2	1	no	—
558	C₈×C₆₇	—	2	1	no	—
559	C₈×C₆₇	—	2	1	no	—
560	C₈×C₆₇	—	2	2	no	—
561	C₈×C₆₇	—	2	2	no	—
562	C₂²×C₆₇	—	2	1	no	—
563	C₂²×C₆₇	—	2	1	no	—
564	C₂²×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	1	no	—
566	C₂²×C₆₇	—	2	1	no	—
567	C₂²×C₆₇	—	2	1	no	—
568	C₂²×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	1	no	—
570	C₂²×C₆₇	—	2	1	no	—
571	C₂²×C₆₇	—	2	1	no	—
572	C₂²×C₆₇	—	2	2	no	—
573	C₂²×C₆₇	—	4	1	no	—
574	C₂²×C₆₇	—	4	2	no	—
575	C₂²×C₆₇	—	4	1	no	—
576	C₂²×C₆₇	—	4	2	no	—
577	C₂²×C₆₇	—	4	1	no	—
578	C₂²×C₆₇	—	4	2	no	—
579	C₂²×C₆₇	—	8	2	no	—
580	C₂²×C₆₇	—	8	4	no	—
581	C₂²×C₆₇	#546	1	2	yes	—
582	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
583	C₄×C₆₇	—	2	2	no	—
584	C₄×C₆₇	—	2	2	no	—
585	C₄×C₆₇	—	2	1	no	—
586	C₄×C₆₇	—	2	1	no	—
587	C₄×C₆₇	—	2	4	no	—
588	C₄×C₆₇	—	2	2	no	—
589	C₄×C₆₇	—	4	1	no	—
590	C₄×C₆₇	—	4	2	no	—
591	C₄×C₆₇	—	4	1	no	—
592	C₄×C₆₇	—	4	1	no	—
593	C₄×C₆₇	—	4	1	no	—
594	C₄×C₆₇	—	4	1	no	—
595	C₄×C₆₇	—	4	1	no	—
596	C₄×C₆₇	—	4	1	no	—
597	C₄×C₆₇	—	4	2	no	—
598	C₄×C₆₇	#546	1	2	yes	—
599	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
600	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	#61190	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
602	C₂×C₆₇	—	2	2	no	—
603	C₂×C₆₇	—	4	2	no	—
604	C₂×C₆₇	—	4	1	no	—
605	C₂×C₆₇	—	4	1	no	—
606	C₂×C₆₇	—	8	1	no	—
607	C₂×C₆₇	—	8	2	no	—
608	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
609	C₂×C₆₇	#3584	1	1	yes	characteristic
610	C₂×C₆₇	#3586	1	1	yes	characteristic
611	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3487	C₂×C₆₇	1	1	yes	characteristic
613	#3333	C₂×C₆₇	1	2	yes	complemented
614	#3327	C₂×C₆₇	1	2	yes	complemented
615	#3317	C₂×C₆₇	1	2	yes	complemented
616	#3317	C₂×C₆₇	1	2	yes	complemented
617	#3316	C₂×C₆₇	1	2	yes	complemented
618	#3313	C₂×C₆₇	1	2	yes	complemented
619	#3304	C₂×C₆₇	1	2	yes	complemented
620	#3300	C₂×C₆₇	1	2	yes	complemented
621	#3136	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#3096	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
624	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
625	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#3056	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3043	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
629	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#2950	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
633	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
634	C₆₇	#61190	1	1	yes	characteristic, direct product factor, Sylow
635	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
636	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
637	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
638	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
639	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
640	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
641	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
642	#556	C₂²×C₆₇	1	2	yes	complemented
643	#554	C₂²×C₆₇	1	2	yes	complemented
644	#552	—	2	2	no	—
645	#552	C₂²×C₆₇	1	2	yes	complemented
646	#552	C₂²×C₆₇	1	2	yes	complemented
647	#551	—	2	2	no	—
648	#550	—	2	1	no	—
649	#550	—	2	1	no	—
650	#550	C₂²×C₆₇	1	2	yes	—
651	#550	C₂²×C₆₇	1	2	yes	—
652	#548	—	2	1	no	—
653	#548	—	2	1	no	—
654	#548	C₂²×C₆₇	1	2	yes	—
655	#548	C₂²×C₆₇	1	2	yes	—
656	#544	C₂²×C₆₇	1	1	yes	characteristic
657	#542	—	2	1	no	—
658	#541	—	2	1	no	—
659	#536	C₂²×C₆₇	1	1	yes	characteristic
660	#535	—	2	2	no	—
661	#535	C₂²×C₆₇	1	1	yes	characteristic
662	#535	C₂²×C₆₇	1	1	yes	characteristic
663	#533	—	2	1	no	—
664	#529	—	2	1	no	—
665	#525	—	2	2	no	—
666	#525	C₂²×C₆₇	1	1	yes	characteristic
667	#525	C₂²×C₆₇	1	1	yes	characteristic
668	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
669	#520	C₂²×C₆₇	1	1	yes	characteristic
670	#519	C₂²×C₆₇	1	1	yes	characteristic
671	#519	C₂²×C₆₇	1	1	yes	characteristic
672	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
673	#490	C₂²×C₆₇	1	2	yes	complemented
674	#489	C₂²×C₆₇	1	2	yes	complemented
675	#488	C₂²×C₆₇	1	2	yes	complemented
676	#486	C₂²×C₆₇	1	2	yes	complemented
677	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
679	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#482	C₂²×C₆₇	1	2	yes	complemented
684	#482	C₂²×C₆₇	1	2	yes	complemented
685	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#481	C₂²×C₆₇	1	2	yes	complemented
687	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#480	C₂²×C₆₇	1	2	yes	complemented
689	#479	C₂²×C₆₇	1	2	yes	complemented
690	#479	C₂²×C₆₇	1	2	yes	complemented
691	#477	C₂²×C₆₇	1	2	yes	complemented
692	#475	C₂²×C₆₇	1	2	yes	complemented
693	#470	C₂²×C₆₇	1	2	yes	complemented
694	#468	C₂²×C₆₇	1	2	yes	complemented
695	#468	C₂²×C₆₇	1	2	yes	complemented
696	#468	C₂²×C₆₇	1	2	yes	complemented
697	#467	C₂²×C₆₇	1	2	yes	complemented
698	#465	C₂²×C₆₇	1	2	yes	complemented
699	#465	C₂²×C₆₇	1	2	yes	complemented
700	#465	C₂²×C₆₇	1	2	yes	complemented
701	#464	C₂²×C₆₇	1	2	yes	complemented
702	#464	C₂²×C₆₇	1	2	yes	complemented
703	#460	C₂²×C₆₇	1	2	yes	complemented
704	#460	C₂²×C₆₇	1	2	yes	complemented
705	#452	C₂²×C₆₇	1	2	yes	—
706	#452	C₂²×C₆₇	1	2	yes	—
707	#452	C₂²×C₆₇	1	2	yes	—
708	#452	C₂²×C₆₇	1	2	yes	—
709	#452	C₂²×C₆₇	1	2	yes	complemented
710	#452	C₂²×C₆₇	1	2	yes	complemented
711	#451	C₂²×C₆₇	1	2	yes	complemented
712	#451	C₂²×C₆₇	1	2	yes	complemented
713	#441	C₂²×C₆₇	1	2	yes	complemented
714	#441	C₂²×C₆₇	1	2	yes	complemented
715	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
716	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
717	#436	C₂²×C₆₇	1	2	yes	complemented
718	#435	C₂²×C₆₇	1	2	yes	complemented
719	#435	C₂²×C₆₇	1	2	yes	complemented
720	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
721	#428	C₂²×C₆₇	1	1	yes	characteristic
722	#427	C₂²×C₆₇	1	1	yes	characteristic
723	#427	C₂²×C₆₇	1	1	yes	characteristic
724	#424	C₂²×C₆₇	1	1	yes	characteristic
725	#419	C₂²×C₆₇	1	1	yes	characteristic
726	#419	C₂²×C₆₇	1	1	yes	characteristic
727	#419	C₂²×C₆₇	1	1	yes	characteristic
728	#419	C₂²×C₆₇	1	2	yes	complemented
729	#418	C₂²×C₆₇	1	1	yes	characteristic
730	#418	C₂²×C₆₇	1	1	yes	characteristic
731	#417	C₂²×C₆₇	1	2	yes	—
732	#417	C₂²×C₆₇	1	1	yes	characteristic
733	#417	C₂²×C₆₇	1	2	yes	—
734	#417	C₂²×C₆₇	1	2	yes	complemented
735	#416	C₂²×C₆₇	1	1	yes	characteristic
736	#416	C₂²×C₆₇	1	1	yes	characteristic
737	#416	C₂²×C₆₇	1	2	yes	—
738	#416	C₂²×C₆₇	1	2	yes	—
739	#416	C₂²×C₆₇	1	2	yes	complemented
740	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
741	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
742	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
743	#408	C₂²×C₆₇	1	1	yes	characteristic
744	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
745	#405	C₂²×C₆₇	1	1	yes	characteristic
746	2₋¹⁺⁴	—	2	4	no	—
747	2₋¹⁺⁴	—	4	2	no	—
748	C₂×#41	—	2	2	no	—
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	4	no	—
753	C₂×#41	—	4	2	no	—
754	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×#41	C₂³×C₆₇	1	2	yes	—
756	C₂×#41	C₂³×C₆₇	1	2	yes	—
757	C₂×#41	C₂³×C₆₇	1	2	yes	—
758	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
759	C₂²×Q₈	—	2	1	no	—
760	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
761	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
762	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
765	C₂³×C₄	—	2	1	no	—
766	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
767	#137	—	4	2	no	—
768	C₂×Q₁₆	—	2	4	no	—
769	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
770	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
771	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
772	C₂×SD₁₆	—	4	2	no	—
773	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
776	#131	—	4	2	no	—
777	C₂×M₁₆	—	4	2	no	—
778	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
781	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
782	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
783	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
784	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
785	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
789	#127	—	2	2	no	—
790	#127	—	2	2	no	—
791	#127	—	2	1	no	—
792	#127	C₂³×C₆₇	1	2	yes	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	2	no	—
797	#125	—	2	1	no	—
798	#125	—	2	2	no	—
799	#125	—	2	2	no	—
800	#125	—	2	2	no	—
801	#125	C₂³×C₆₇	1	2	yes	—
802	#124	—	2	1	no	—
803	#124	—	2	1	no	—
804	#124	—	2	2	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	C₂³×C₆₇	1	2	yes	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	1	no	—
812	#123	D₄×C₆₇	1	2	yes	—
813	C₂²⋊Q₈	—	2	1	no	—
814	C₂²⋊Q₈	—	2	1	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
821	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
822	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
825	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
826	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	D₄×C₆₇	1	1	yes	characteristic
837	#121	D₄×C₆₇	1	1	yes	characteristic
838	#121	C₂³×C₆₇	1	1	yes	characteristic
839	#121	C₂³×C₆₇	1	1	yes	characteristic
840	#121	C₂³×C₆₇	1	2	yes	—
841	#121	C₂³×C₆₇	1	2	yes	—
842	#120	—	2	1	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	D₄×C₆₇	1	2	yes	—
846	C₄×Q₈	—	2	1	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	—	2	2	no	—
852	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
853	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
854	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
855	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	C₂³×C₆₇	1	2	yes	—
866	C₄×D₄	C₂³×C₆₇	1	2	yes	—
867	#117	—	2	1	no	—
868	#117	—	2	1	no	—
869	#117	—	2	2	no	—
870	#117	—	2	2	no	—
871	#117	—	2	2	no	—
872	#117	—	2	2	no	—
873	#117	C₂³×C₆₇	1	1	yes	characteristic
874	#117	C₂³×C₆₇	1	1	yes	characteristic
875	#117	C₂³×C₆₇	1	1	yes	characteristic
876	#117	C₂³×C₆₇	1	1	yes	characteristic
877	#117	C₂³×C₆₇	1	1	yes	characteristic
878	#117	C₂³×C₆₇	1	2	yes	—
879	#117	C₂³×C₆₇	1	1	yes	characteristic
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	1	no	—
887	C₂×C₄²	—	2	1	no	—
888	#107	C₂³×C₆₇	1	1	yes	characteristic
889	#107	C₂³×C₆₇	1	1	yes	characteristic
890	#107	C₂³×C₆₇	1	1	yes	characteristic
891	#107	C₂³×C₆₇	1	1	yes	characteristic
892	#107	C₂³×C₆₇	1	2	yes	—
893	#106	C₂³×C₆₇	1	1	yes	characteristic
894	#106	C₂³×C₆₇	1	1	yes	characteristic
895	#106	C₂³×C₆₇	1	1	yes	characteristic
896	#106	C₂³×C₆₇	1	1	yes	characteristic
897	#106	C₂³×C₆₇	1	2	yes	—
898	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
899	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
900	#103	C₂³×C₆₇	1	2	yes	—
901	#103	C₂³×C₆₇	1	2	yes	—
902	#103	C₂³×C₆₇	1	1	yes	characteristic
903	#103	C₂³×C₆₇	1	2	yes	—
904	#103	C₂³×C₆₇	1	2	yes	—
905	#103	C₂³×C₆₇	1	2	yes	—
906	#103	C₂³×C₆₇	1	2	yes	—
907	#103	C₂³×C₆₇	1	2	yes	—
908	#103	C₂³×C₆₇	1	1	yes	characteristic
909	#103	C₂³×C₆₇	1	1	yes	characteristic
910	#103	C₂³×C₆₇	1	1	yes	characteristic
911	#103	C₂³×C₆₇	1	2	yes	—
912	#103	C₂³×C₆₇	1	2	yes	—
913	#102	C₂³×C₆₇	1	2	yes	—
914	#102	C₂³×C₆₇	1	2	yes	—
915	#102	C₂³×C₆₇	1	1	yes	characteristic
916	#102	C₂³×C₆₇	1	2	yes	—
917	#102	C₂³×C₆₇	1	2	yes	—
918	#102	C₂³×C₆₇	1	2	yes	—
919	#102	C₂³×C₆₇	1	2	yes	—
920	#102	C₂³×C₆₇	1	1	yes	characteristic
921	#102	C₂³×C₆₇	1	1	yes	characteristic
922	#102	C₂³×C₆₇	1	1	yes	characteristic
923	#102	C₂³×C₆₇	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
925	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
926	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
930	#97	C₂³×C₆₇	1	2	yes	—
931	C₄×C₈	C₂³×C₆₇	1	2	yes	—
932	C₂⁴	—	2	1	no	—
933	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	4	no	—
937	#41	—	2	4	no	—
938	#41	—	2	4	no	—
939	#41	—	2	2	no	—
940	#41	—	2	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	4	2	no	—
944	#41	—	4	8	no	—
945	#41	—	4	4	no	—
946	#41	—	4	4	no	—
947	#41	—	4	4	no	—
948	C₂×Q₈	—	2	1	no	—
949	C₂×Q₈	—	2	1	no	—
950	C₂×Q₈	—	2	2	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	4	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	4	2	no	—
957	C₂×Q₈	—	4	4	no	—
958	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
959	C₂×Q₈	#41×C₆₇	1	4	yes	—
960	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
961	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
962	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	4	4	no	—
977	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
978	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
979	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
981	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
982	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	4	4	no	—
997	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
999	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1003	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1004	Q₁₆	—	2	4	no	—
1005	Q₁₆	—	2	4	no	—
1006	Q₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	SD₁₆	—	4	2	no	—
1009	SD₁₆	—	4	2	no	—
1010	M₁₆	—	2	2	no	—
1011	M₁₆	—	2	2	no	—
1012	M₁₆	—	4	2	no	—
1013	M₁₆	—	4	2	no	—
1014	C₂×C₈	—	2	2	no	—
1015	C₂×C₈	—	2	2	no	—
1016	C₂×C₈	—	4	2	no	—
1017	C₂×C₈	—	4	2	no	—
1018	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1019	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1020	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1022	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1042	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1043	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1044	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1046	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1047	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1048	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1071	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1072	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1075	C₄²	—	2	1	no	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	C₂⁴×C₆₇	1	2	yes	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	4	1	no	—
1090	C₂³	—	4	1	no	—
1091	C₂³	—	4	2	no	—
1092	C₂³	—	8	1	no	—
1093	C₂³	—	8	1	no	—
1094	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1095	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1096	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1097	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1098	Q₈	—	2	4	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	2	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	4	4	no	—
1106	Q₈	—	4	2	no	—
1107	Q₈	—	8	2	no	—
1108	Q₈	C₂×#41×C₆₇	1	4	yes	—
1109	D₄	—	2	4	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	4	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	1	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	4	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	4	4	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1159	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1161	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1162	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1163	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1164	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1165	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1166	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1167	C₈	—	2	1	no	—
1168	C₈	—	2	1	no	—
1169	C₈	—	2	1	no	—
1170	C₈	—	2	1	no	—
1171	C₈	—	2	2	no	—
1172	C₈	—	2	2	no	—
1173	C₂²	—	2	1	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	8	2	no	—
1191	C₂²	—	8	4	no	—
1192	C₂²	#546×C₆₇	1	2	yes	—
1193	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	4	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	#546×C₆₇	1	2	yes	—
1210	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1211	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1212	C₂	—	2	2	no	—
1213	C₂	—	4	1	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	8	2	no	—
1217	C₂	—	8	1	no	—
1218	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1219	C₂	C₆₇×#3584	1	1	yes	characteristic
1220	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×#3487	C₂
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×#3495	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3327	C₂	semidirect
5. C₆₇×#3317	C₂	semidirect
6. C₆₇×#3317	C₂	semidirect
7. C₆₇×#3316	C₂	semidirect
8. C₆₇×#3313	C₂	semidirect
9. C₆₇×#3304	C₂	semidirect
10. C₆₇×#3300	C₂	semidirect
11. C₆₇×#3136	C₂	semidirect
12. C₆₇×#3096	C₂	semidirect
13. C₆₇×#3091	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3057	C₂	semidirect
16. C₆₇×#3056	C₂	semidirect
17. C₆₇×#3043	C₂	semidirect
18. C₆₇×#3011	C₂	semidirect
19. C₂×#452×C₆₇	C₂	semidirect
20. C₆₇×#2950	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₆₇×#2896	C₂	semidirect
31. #556×C₆₇	C₂²	semidirect
32. #554×C₆₇	C₂²	semidirect
34. #552×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
62. #490×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #486×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #484×C₆₇	C₂²	semidirect
69. #483×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #482×C₆₇	C₂²	semidirect
74. #481×C₆₇	C₂²	semidirect
75. #481×C₆₇	C₂²	semidirect
76. #480×C₆₇	C₂²	semidirect
77. #480×C₆₇	C₂²	semidirect
78. #479×C₆₇	C₂²	semidirect
79. #479×C₆₇	C₂²	semidirect
80. #477×C₆₇	C₂²	semidirect
81. #475×C₆₇	C₂²	semidirect
82. #470×C₆₇	C₂²	semidirect
83. #468×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #467×C₆₇	C₂²	semidirect
87. #465×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #464×C₆₇	C₂²	semidirect
92. #460×C₆₇	C₂²	semidirect
93. #460×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #451×C₆₇	C₂²	semidirect
101. #451×C₆₇	C₂²	semidirect
102. #441×C₆₇	C₂²	semidirect
103. #441×C₆₇	C₂²	semidirect
104. C₄×Q₁₆×C₆₇	C₂²	semidirect
105. C₄×Q₁₆×C₆₇	C₂²	semidirect
106. #436×C₆₇	C₂²	semidirect
107. #435×C₆₇	C₂²	semidirect
108. #435×C₆₇	C₂²	semidirect
109. C₈×D₄×C₆₇	C₂²	semidirect
117. #419×C₆₇	C₂²	semidirect
123. #417×C₆₇	C₂²	semidirect
128. #416×C₆₇	C₂²	semidirect
130. C₂×#103×C₆₇	C₂²	semidirect
601. #61190	C₆₇	direct (N × H)
611. #3495	C₂×C₆₇	semidirect
613. #3333	C₂×C₆₇	semidirect
614. #3327	C₂×C₆₇	semidirect
615. #3317	C₂×C₆₇	semidirect
616. #3317	C₂×C₆₇	semidirect
617. #3316	C₂×C₆₇	semidirect
618. #3313	C₂×C₆₇	semidirect
619. #3304	C₂×C₆₇	semidirect
620. #3300	C₂×C₆₇	semidirect
621. #3136	C₂×C₆₇	semidirect
622. #3096	C₂×C₆₇	semidirect
623. #3091	C₂×C₆₇	semidirect
624. #3082	C₂×C₆₇	semidirect
625. #3057	C₂×C₆₇	semidirect
626. #3056	C₂×C₆₇	semidirect
627. #3043	C₂×C₆₇	semidirect
628. #3011	C₂×C₆₇	semidirect
629. C₂×#452	C₂×C₆₇	semidirect
630. #2950	C₂×C₆₇	semidirect
631. #2933	C₂×C₆₇	semidirect
632. #2898	C₂×C₆₇	semidirect
633. #2896	C₂×C₆₇	semidirect
634. C₆₇	#61190	direct (N × H)
642. #556	C₂²×C₆₇	semidirect
643. #554	C₂²×C₆₇	semidirect
645. #552	C₂²×C₆₇	semidirect
646. #552	C₂²×C₆₇	semidirect
673. #490	C₂²×C₆₇	semidirect
674. #489	C₂²×C₆₇	semidirect
675. #488	C₂²×C₆₇	semidirect
676. #486	C₂²×C₆₇	semidirect
677. #485	C₂²×C₆₇	semidirect
678. #485	C₂²×C₆₇	semidirect
679. #484	C₂²×C₆₇	semidirect
680. #483	C₂²×C₆₇	semidirect
681. #482	C₂²×C₆₇	semidirect
682. #482	C₂²×C₆₇	semidirect
683. #482	C₂²×C₆₇	semidirect
684. #482	C₂²×C₆₇	semidirect
685. #481	C₂²×C₆₇	semidirect
686. #481	C₂²×C₆₇	semidirect
687. #480	C₂²×C₆₇	semidirect
688. #480	C₂²×C₆₇	semidirect
689. #479	C₂²×C₆₇	semidirect
690. #479	C₂²×C₆₇	semidirect
691. #477	C₂²×C₆₇	semidirect
692. #475	C₂²×C₆₇	semidirect
693. #470	C₂²×C₆₇	semidirect
694. #468	C₂²×C₆₇	semidirect
695. #468	C₂²×C₆₇	semidirect
696. #468	C₂²×C₆₇	semidirect
697. #467	C₂²×C₆₇	semidirect
698. #465	C₂²×C₆₇	semidirect
699. #465	C₂²×C₆₇	semidirect
700. #465	C₂²×C₆₇	semidirect
701. #464	C₂²×C₆₇	semidirect
702. #464	C₂²×C₆₇	semidirect
703. #460	C₂²×C₆₇	semidirect
704. #460	C₂²×C₆₇	semidirect
709. #452	C₂²×C₆₇	semidirect
710. #452	C₂²×C₆₇	semidirect
711. #451	C₂²×C₆₇	semidirect
712. #451	C₂²×C₆₇	semidirect
713. #441	C₂²×C₆₇	semidirect
714. #441	C₂²×C₆₇	semidirect
715. C₄×Q₁₆	C₂²×C₆₇	semidirect
716. C₄×Q₁₆	C₂²×C₆₇	semidirect
717. #436	C₂²×C₆₇	semidirect
718. #435	C₂²×C₆₇	semidirect
719. #435	C₂²×C₆₇	semidirect
720. C₈×D₄	C₂²×C₆₇	semidirect
728. #419	C₂²×C₆₇	semidirect
734. #417	C₂²×C₆₇	semidirect
739. #416	C₂²×C₆₇	semidirect
741. C₂×#103	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×#3487	2
C₆₇×#3333	2
C₆₇×#3327	2
C₆₇×#3317	2
C₆₇×#3316	2
C₆₇×#3313	2
C₆₇×#3304	2
C₆₇×#3300	2
C₆₇×#3136	2
C₆₇×#3096	2
C₆₇×#3091	2
C₆₇×#3082	2
C₆₇×#3057	2
C₆₇×#3056	2
C₆₇×#3043	2
C₆₇×#3011	2
C₂×#452×C₆₇	2
C₆₇×#2950	2
C₆₇×#2933	2
C₆₇×#2898	2
C₆₇×#2896	2
#61190	67

Subgroups — C67×#61190 #30740441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61190 #30740441