Subgroups — C₆₇×#60978 #30740229

Order 17152.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1328 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	C₂×#540×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3259	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3220	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3188	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3179	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3176	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#555×C₆₇	—	2	1	no	—
25	#553×C₆₇	—	2	1	no	—
26	#553×C₆₇	—	2	1	no	—
27	#551×C₆₇	—	2	1	no	—
28	#551×C₆₇	—	2	1	no	—
29	#547×C₆₇	—	2	1	no	—
30	#546×C₆₇	—	2	1	no	—
31	#546×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#540×C₆₇	—	2	1	no	—
36	#540×C₆₇	—	2	1	no	—
37	#540×C₆₇	—	2	1	no	—
38	#540×C₆₇	—	2	1	no	—
39	#540×C₆₇	C₂²	1	2	yes	—
40	#540×C₆₇	C₂²	1	2	yes	—
41	#540×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#540×C₆₇	C₂²	1	2	yes	complemented
43	#540×C₆₇	C₂²	1	2	yes	complemented
44	#540×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#532×C₆₇	C₂²	1	1	yes	characteristic
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#529×C₆₇	C₂²	1	1	yes	characteristic
50	#529×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#525×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#123×C₆₇	—	2	1	no	—
54	C₂×#123×C₆₇	—	2	1	no	—
55	C₂×#121×C₆₇	—	2	1	no	—
56	C₂×#121×C₆₇	—	2	1	no	—
57	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
60	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#496×C₆₇	C₂²	1	2	yes	complemented
68	#493×C₆₇	C₂²	1	2	yes	complemented
69	#490×C₆₇	C₂²	1	2	yes	complemented
70	#490×C₆₇	C₂²	1	2	yes	complemented
71	#488×C₆₇	C₂²	1	2	yes	complemented
72	#486×C₆₇	C₂²	1	2	yes	complemented
73	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#482×C₆₇	C₂²	1	2	yes	complemented
76	#482×C₆₇	C₂²	1	2	yes	complemented
77	#481×C₆₇	C₂²	1	1	yes	characteristic
78	#481×C₆₇	C₂²	1	1	yes	characteristic
79	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#481×C₆₇	C₂²	1	2	yes	complemented
81	#480×C₆₇	C₂²	1	1	yes	characteristic
82	#480×C₆₇	C₂²	1	1	yes	characteristic
83	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#480×C₆₇	C₂²	1	2	yes	complemented
85	#479×C₆₇	C₂²	1	2	yes	complemented
86	#478×C₆₇	C₂²	1	2	yes	complemented
87	#478×C₆₇	C₂²	1	2	yes	complemented
88	#478×C₆₇	C₂²	1	2	yes	complemented
89	#478×C₆₇	C₂²	1	2	yes	complemented
90	#478×C₆₇	C₂²	1	2	yes	complemented
91	#476×C₆₇	C₂²	1	2	yes	complemented
92	#474×C₆₇	C₂²	1	2	yes	complemented
93	#469×C₆₇	C₂²	1	2	yes	complemented
94	#469×C₆₇	C₂²	1	2	yes	complemented
95	#469×C₆₇	C₂²	1	2	yes	complemented
96	#468×C₆₇	C₂²	1	2	yes	complemented
97	#466×C₆₇	C₂²	1	2	yes	complemented
98	#466×C₆₇	C₂²	1	2	yes	complemented
99	#466×C₆₇	C₂²	1	2	yes	complemented
100	#465×C₆₇	C₂²	1	2	yes	complemented
101	#463×C₆₇	C₂²	1	2	yes	complemented
102	#463×C₆₇	C₂²	1	2	yes	complemented
103	#460×C₆₇	C₂²	1	2	yes	complemented
104	#459×C₆₇	C₂²	1	2	yes	complemented
105	#459×C₆₇	C₂²	1	2	yes	complemented
106	#459×C₆₇	C₂²	1	2	yes	complemented
107	#459×C₆₇	C₂²	1	2	yes	complemented
108	#459×C₆₇	C₂²	1	2	yes	complemented
109	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#449×C₆₇	C₂²	1	2	yes	complemented
112	#449×C₆₇	C₂²	1	2	yes	complemented
113	#447×C₆₇	C₂²	1	1	yes	characteristic
114	#447×C₆₇	C₂²	1	1	yes	characteristic
115	#447×C₆₇	C₂²	1	1	yes	characteristic
116	#447×C₆₇	C₂²	1	1	yes	characteristic
117	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#447×C₆₇	C₂²	1	2	yes	complemented
120	#447×C₆₇	C₂²	1	2	yes	complemented
121	#442×C₆₇	C₂²	1	2	yes	complemented
122	#442×C₆₇	C₂²	1	2	yes	complemented
123	#442×C₆₇	C₂²	1	2	yes	complemented
124	#440×C₆₇	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
126	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
127	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
128	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
129	#433×C₆₇	C₂²	1	2	yes	complemented
130	#433×C₆₇	C₂²	1	2	yes	complemented
131	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#424×C₆₇	C₂²	1	2	yes	complemented
136	#407×C₆₇	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
138	#405×C₆₇	C₂²	1	2	yes	complemented
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₇	—	2	1	no	—
143	C₂²×D₄×C₆₇	—	2	1	no	—
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	—	2	1	no	—
146	C₂²×D₄×C₆₇	—	2	1	no	—
147	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₆₇	—	2	1	no	—
151	C₂³×C₄×C₆₇	—	2	1	no	—
152	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×D₈×C₆₇	C₂³	1	2	yes	—
159	C₂×D₈×C₆₇	C₂³	1	2	yes	—
160	C₂×D₈×C₆₇	C₂³	1	2	yes	—
161	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₇	—	2	1	no	—
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	#127×C₆₇	—	2	1	no	—
167	#127×C₆₇	—	2	1	no	—
168	#127×C₆₇	C₂³	1	1	yes	characteristic
169	#127×C₆₇	C₂³	1	2	yes	—
170	#127×C₆₇	C₂³	1	2	yes	—
171	#127×C₆₇	C₂³	1	1	yes	characteristic
172	#126×C₆₇	—	2	1	no	—
173	#126×C₆₇	—	2	1	no	—
174	#126×C₆₇	—	2	1	no	—
175	#126×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	—	2	1	no	—
178	#125×C₆₇	—	2	1	no	—
179	#125×C₆₇	C₂³	1	1	yes	characteristic
180	#125×C₆₇	C₂³	1	2	yes	—
181	#125×C₆₇	C₂³	1	2	yes	—
182	#125×C₆₇	C₂³	1	1	yes	characteristic
183	#124×C₆₇	—	2	1	no	—
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	—	2	1	no	—
186	#124×C₆₇	—	2	1	no	—
187	#124×C₆₇	C₂³	1	1	yes	characteristic
188	#124×C₆₇	C₂³	1	1	yes	characteristic
189	#123×C₆₇	—	2	1	no	—
190	#123×C₆₇	—	2	1	no	—
191	#123×C₆₇	—	2	1	no	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	2	no	—
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	—	2	1	no	—
202	#123×C₆₇	—	2	1	no	—
203	#123×C₆₇	—	2	1	no	—
204	#123×C₆₇	—	2	1	no	—
205	#123×C₆₇	—	2	1	no	—
206	C₂²⋊Q₈×C₆₇	—	2	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	1	no	—
210	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	1	no	—
214	#121×C₆₇	—	2	1	no	—
215	#121×C₆₇	—	2	1	no	—
216	#121×C₆₇	—	2	1	no	—
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	1	no	—
219	#121×C₆₇	—	2	1	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	2	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	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	—	2	2	no	—
230	#121×C₆₇	—	2	1	no	—
231	#121×C₆₇	—	2	1	no	—
232	#121×C₆₇	—	2	1	no	—
233	#121×C₆₇	—	2	1	no	—
234	#121×C₆₇	C₂³	1	2	yes	—
235	#121×C₆₇	C₂³	1	2	yes	—
236	#121×C₆₇	C₂³	1	2	yes	—
237	#121×C₆₇	C₂³	1	2	yes	—
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	1	yes	characteristic
240	#121×C₆₇	C₂³	1	1	yes	characteristic
241	#121×C₆₇	C₂³	1	1	yes	characteristic
242	#121×C₆₇	C₂³	1	1	yes	characteristic
243	#121×C₆₇	C₂³	1	1	yes	characteristic
244	#120×C₆₇	—	2	1	no	—
245	#120×C₆₇	—	2	1	no	—
246	#120×C₆₇	—	2	1	no	—
247	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₇	—	2	1	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	1	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	1	no	—
257	C₄×D₄×C₆₇	—	2	1	no	—
258	C₄×D₄×C₆₇	—	2	1	no	—
259	C₄×D₄×C₆₇	—	2	1	no	—
260	C₄×D₄×C₆₇	—	2	1	no	—
261	C₄×D₄×C₆₇	—	2	1	no	—
262	C₄×D₄×C₆₇	—	2	1	no	—
263	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₆₇	C₂³	1	2	yes	—
267	C₄×D₄×C₆₇	C₂³	1	2	yes	—
268	C₄×D₄×C₆₇	C₂³	1	2	yes	—
269	C₄×D₄×C₆₇	C₂³	1	2	yes	—
270	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
273	#117×C₆₇	—	2	1	no	—
274	#117×C₆₇	—	2	1	no	—
275	#117×C₆₇	—	2	1	no	—
276	#117×C₆₇	D₄	1	1	yes	characteristic
277	#117×C₆₇	D₄	1	1	yes	characteristic
278	#117×C₆₇	D₄	1	1	yes	characteristic
279	#117×C₆₇	D₄	1	1	yes	characteristic
280	#117×C₆₇	C₂³	1	1	yes	characteristic
281	#117×C₆₇	C₂³	1	1	yes	characteristic
282	#117×C₆₇	C₂³	1	1	yes	characteristic
283	#117×C₆₇	C₂³	1	1	yes	characteristic
284	#117×C₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
286	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
287	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
288	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
300	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
302	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#107×C₆₇	C₂³	1	2	yes	—
308	#106×C₆₇	C₂³	1	2	yes	—
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	2	yes	—
312	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
313	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	#103×C₆₇	C₂³	1	2	yes	—
317	#103×C₆₇	C₂³	1	2	yes	—
318	#102×C₆₇	C₂³	1	2	yes	—
319	#102×C₆₇	C₂³	1	2	yes	—
320	#102×C₆₇	C₂³	1	2	yes	—
321	#102×C₆₇	C₂³	1	2	yes	—
322	#102×C₆₇	C₂³	1	2	yes	—
323	#102×C₆₇	C₂³	1	2	yes	—
324	#102×C₆₇	C₂³	1	2	yes	—
325	#102×C₆₇	C₂³	1	2	yes	—
326	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
333	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
338	#97×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	C₂⁴×C₆₇	—	2	1	no	—
343	C₂⁴×C₆₇	—	2	1	no	—
344	C₂⁴×C₆₇	—	2	1	no	—
345	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
346	#41×C₆₇	—	4	2	no	—
347	#41×C₆₇	—	8	2	no	—
348	#41×C₆₇	—	8	2	no	—
349	C₂×Q₈×C₆₇	—	2	1	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	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	1	no	—
364	C₂×D₄×C₆₇	—	2	1	no	—
365	C₂×D₄×C₆₇	—	2	1	no	—
366	C₂×D₄×C₆₇	—	2	1	no	—
367	C₂×D₄×C₆₇	—	2	1	no	—
368	C₂×D₄×C₆₇	—	2	1	no	—
369	C₂×D₄×C₆₇	—	2	1	no	—
370	C₂×D₄×C₆₇	—	2	2	no	—
371	C₂×D₄×C₆₇	—	2	2	no	—
372	C₂×D₄×C₆₇	—	2	2	no	—
373	C₂×D₄×C₆₇	—	2	2	no	—
374	C₂×D₄×C₆₇	—	4	2	no	—
375	C₂×D₄×C₆₇	—	4	2	no	—
376	C₂×D₄×C₆₇	—	4	2	no	—
377	C₂×D₄×C₆₇	—	8	2	no	—
378	C₂×D₄×C₆₇	—	8	2	no	—
379	C₂×D₄×C₆₇	—	8	2	no	—
380	C₂×D₄×C₆₇	—	8	2	no	—
381	C₂×D₄×C₆₇	—	8	2	no	—
382	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
386	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₆₇	—	2	1	no	—
388	C₂²×C₄×C₆₇	—	2	1	no	—
389	C₂²×C₄×C₆₇	—	2	1	no	—
390	C₂²×C₄×C₆₇	—	2	1	no	—
391	C₂²×C₄×C₆₇	—	2	1	no	—
392	C₂²×C₄×C₆₇	—	2	1	no	—
393	C₂²×C₄×C₆₇	—	2	1	no	—
394	C₂²×C₄×C₆₇	—	2	1	no	—
395	C₂²×C₄×C₆₇	—	2	1	no	—
396	C₂²×C₄×C₆₇	—	2	1	no	—
397	C₂²×C₄×C₆₇	—	2	2	no	—
398	C₂²×C₄×C₆₇	—	2	2	no	—
399	C₂²×C₄×C₆₇	—	2	2	no	—
400	C₂²×C₄×C₆₇	—	2	2	no	—
401	C₂²×C₄×C₆₇	—	4	2	no	—
402	C₂²×C₄×C₆₇	—	8	2	no	—
403	C₂²×C₄×C₆₇	—	8	2	no	—
404	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
414	SD₁₆×C₆₇	—	4	2	no	—
415	SD₁₆×C₆₇	—	4	2	no	—
416	D₈×C₆₇	—	4	2	no	—
417	D₈×C₆₇	—	4	2	no	—
418	D₈×C₆₇	—	4	2	no	—
419	D₈×C₆₇	—	4	2	no	—
420	D₈×C₆₇	—	4	2	no	—
421	D₈×C₆₇	—	4	2	no	—
422	M₁₆×C₆₇	—	4	2	no	—
423	C₂×C₈×C₆₇	—	4	2	no	—
424	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
425	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
426	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
427	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	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	1	no	—
439	C₄⋊C₄×C₆₇	—	2	1	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	—	2	1	no	—
442	C₄⋊C₄×C₆₇	—	2	1	no	—
443	C₄⋊C₄×C₆₇	—	2	1	no	—
444	C₄⋊C₄×C₆₇	—	2	1	no	—
445	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
458	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
459	C₂²⋊C₄×C₆₇	—	2	1	no	—
460	C₂²⋊C₄×C₆₇	—	2	1	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	2	no	—
475	C₂²⋊C₄×C₆₇	—	2	2	no	—
476	C₂²⋊C₄×C₆₇	—	2	2	no	—
477	C₂²⋊C₄×C₆₇	—	2	2	no	—
478	C₂²⋊C₄×C₆₇	—	2	1	no	—
479	C₂²⋊C₄×C₆₇	—	2	1	no	—
480	C₂²⋊C₄×C₆₇	—	2	1	no	—
481	C₂²⋊C₄×C₆₇	—	2	1	no	—
482	C₂²⋊C₄×C₆₇	—	2	1	no	—
483	C₂²⋊C₄×C₆₇	—	2	1	no	—
484	C₂²⋊C₄×C₆₇	—	2	1	no	—
485	C₂²⋊C₄×C₆₇	—	2	1	no	—
486	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₇	—	2	1	no	—
495	C₄²×C₆₇	—	2	1	no	—
496	C₄²×C₆₇	—	2	1	no	—
497	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
501	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
504	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂³×C₆₇	—	2	2	no	—
506	C₂³×C₆₇	—	2	1	no	—
507	C₂³×C₆₇	—	2	1	no	—
508	C₂³×C₆₇	—	2	1	no	—
509	C₂³×C₆₇	—	2	2	no	—
510	C₂³×C₆₇	—	2	2	no	—
511	C₂³×C₆₇	—	4	1	no	—
512	C₂³×C₆₇	—	4	1	no	—
513	C₂³×C₆₇	—	4	2	no	—
514	C₂³×C₆₇	—	4	2	no	—
515	C₂³×C₆₇	—	4	2	no	—
516	C₂³×C₆₇	—	4	2	no	—
517	C₂³×C₆₇	—	4	2	no	—
518	C₂³×C₆₇	—	4	2	no	—
519	C₂³×C₆₇	—	4	2	no	—
520	C₂³×C₆₇	—	8	1	no	—
521	C₂³×C₆₇	—	8	1	no	—
522	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
523	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
524	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
525	Q₈×C₆₇	—	2	2	no	—
526	Q₈×C₆₇	—	8	1	no	—
527	Q₈×C₆₇	—	8	1	no	—
528	D₄×C₆₇	—	2	2	no	—
529	D₄×C₆₇	—	2	2	no	—
530	D₄×C₆₇	—	2	2	no	—
531	D₄×C₆₇	—	2	2	no	—
532	D₄×C₆₇	—	2	2	no	—
533	D₄×C₆₇	—	2	2	no	—
534	D₄×C₆₇	—	2	2	no	—
535	D₄×C₆₇	—	4	2	no	—
536	D₄×C₆₇	—	4	2	no	—
537	D₄×C₆₇	—	4	2	no	—
538	D₄×C₆₇	—	4	2	no	—
539	D₄×C₆₇	—	4	2	no	—
540	D₄×C₆₇	—	4	2	no	—
541	D₄×C₆₇	—	4	2	no	—
542	D₄×C₆₇	—	8	1	no	—
543	D₄×C₆₇	—	8	1	no	—
544	D₄×C₆₇	—	8	2	no	—
545	D₄×C₆₇	—	8	2	no	—
546	D₄×C₆₇	—	8	2	no	—
547	D₄×C₆₇	—	8	2	no	—
548	D₄×C₆₇	—	8	1	no	—
549	D₄×C₆₇	—	8	1	no	—
550	D₄×C₆₇	—	8	1	no	—
551	D₄×C₆₇	—	8	2	no	—
552	D₄×C₆₇	—	8	2	no	—
553	D₄×C₆₇	—	8	2	no	—
554	D₄×C₆₇	—	8	2	no	—
555	D₄×C₆₇	—	8	1	no	—
556	D₄×C₆₇	—	8	1	no	—
557	C₂×C₄×C₆₇	—	2	2	no	—
558	C₂×C₄×C₆₇	—	2	2	no	—
559	C₂×C₄×C₆₇	—	2	2	no	—
560	C₂×C₄×C₆₇	—	2	2	no	—
561	C₂×C₄×C₆₇	—	2	2	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	2	1	no	—
567	C₂×C₄×C₆₇	—	2	2	no	—
568	C₂×C₄×C₆₇	—	2	2	no	—
569	C₂×C₄×C₆₇	—	4	1	no	—
570	C₂×C₄×C₆₇	—	4	1	no	—
571	C₂×C₄×C₆₇	—	4	1	no	—
572	C₂×C₄×C₆₇	—	4	1	no	—
573	C₂×C₄×C₆₇	—	4	1	no	—
574	C₂×C₄×C₆₇	—	4	2	no	—
575	C₂×C₄×C₆₇	—	4	2	no	—
576	C₂×C₄×C₆₇	—	4	2	no	—
577	C₂×C₄×C₆₇	—	8	1	no	—
578	C₂×C₄×C₆₇	—	8	1	no	—
579	C₂×C₄×C₆₇	—	8	2	no	—
580	C₂×C₄×C₆₇	—	8	2	no	—
581	C₂×C₄×C₆₇	—	8	2	no	—
582	C₂×C₄×C₆₇	—	8	2	no	—
583	C₂×C₄×C₆₇	—	8	1	no	—
584	C₂×C₄×C₆₇	—	8	1	no	—
585	C₂×C₄×C₆₇	—	8	1	no	—
586	C₂×C₄×C₆₇	—	8	1	no	—
587	C₂×C₄×C₆₇	—	8	1	no	—
588	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
600	C₈×C₆₇	—	2	2	no	—
601	C₈×C₆₇	—	2	2	no	—
602	C₈×C₆₇	—	2	2	no	—
603	C₈×C₆₇	—	2	2	no	—
604	C₂²×C₆₇	—	2	1	no	—
605	C₂²×C₆₇	—	2	1	no	—
606	C₂²×C₆₇	—	2	1	no	—
607	C₂²×C₆₇	—	2	1	no	—
608	C₂²×C₆₇	—	2	1	no	—
609	C₂²×C₆₇	—	2	1	no	—
610	C₂²×C₆₇	—	2	1	no	—
611	C₂²×C₆₇	—	2	1	no	—
612	C₂²×C₆₇	—	4	2	no	—
613	C₂²×C₆₇	—	4	1	no	—
614	C₂²×C₆₇	—	4	1	no	—
615	C₂²×C₆₇	—	4	2	no	—
616	C₂²×C₆₇	—	4	1	no	—
617	C₂²×C₆₇	—	4	1	no	—
618	C₂²×C₆₇	—	4	2	no	—
619	C₂²×C₆₇	—	4	2	no	—
620	C₂²×C₆₇	—	4	1	no	—
621	C₂²×C₆₇	—	4	1	no	—
622	C₂²×C₆₇	—	4	1	no	—
623	C₂²×C₆₇	—	4	2	no	—
624	C₂²×C₆₇	—	4	1	no	—
625	C₂²×C₆₇	—	4	1	no	—
626	C₂²×C₆₇	—	4	2	no	—
627	C₂²×C₆₇	—	8	2	no	—
628	C₂²×C₆₇	—	8	4	no	—
629	C₂²×C₆₇	—	8	4	no	—
630	C₂²×C₆₇	—	16	2	no	—
631	C₂²×C₆₇	#576	1	2	yes	—
632	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
633	C₄×C₆₇	—	2	1	no	—
634	C₄×C₆₇	—	2	1	no	—
635	C₄×C₆₇	—	2	1	no	—
636	C₄×C₆₇	—	2	1	no	—
637	C₄×C₆₇	—	2	1	no	—
638	C₄×C₆₇	—	2	1	no	—
639	C₄×C₆₇	—	2	1	no	—
640	C₄×C₆₇	—	2	1	no	—
641	C₄×C₆₇	—	2	1	no	—
642	C₄×C₆₇	—	2	1	no	—
643	C₄×C₆₇	—	2	1	no	—
644	C₄×C₆₇	—	4	2	no	—
645	C₄×C₆₇	—	4	1	no	—
646	C₄×C₆₇	—	4	1	no	—
647	C₄×C₆₇	—	4	2	no	—
648	C₄×C₆₇	—	4	1	no	—
649	C₄×C₆₇	—	4	1	no	—
650	C₄×C₆₇	—	4	1	no	—
651	C₄×C₆₇	#585	1	2	yes	—
652	#60978	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
653	C₂×C₆₇	—	2	2	no	—
654	C₂×C₆₇	—	4	1	no	—
655	C₂×C₆₇	—	4	1	no	—
656	C₂×C₆₇	—	8	1	no	—
657	C₂×C₆₇	—	8	2	no	—
658	C₂×C₆₇	—	8	2	no	—
659	C₂×C₆₇	—	8	1	no	—
660	C₂×C₆₇	—	8	1	no	—
661	C₂×C₆₇	#3449	1	1	yes	characteristic
662	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
663	C₂×C₆₇	#3585	1	1	yes	characteristic
664	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
665	C₂×#540	C₂×C₆₇	1	1	yes	characteristic, complemented
666	#3259	C₂×C₆₇	1	2	yes	complemented
667	#3257	C₂×C₆₇	1	2	yes	complemented
668	#3241	C₂×C₆₇	1	2	yes	complemented
669	#3234	C₂×C₆₇	1	1	yes	characteristic, complemented
670	#3232	C₂×C₆₇	1	1	yes	characteristic, complemented
671	#3220	C₂×C₆₇	1	2	yes	complemented
672	#3217	C₂×C₆₇	1	1	yes	characteristic, complemented
673	#3205	C₂×C₆₇	1	1	yes	characteristic, complemented
674	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#3192	C₂×C₆₇	1	1	yes	characteristic, complemented
676	#3188	C₂×C₆₇	1	1	yes	characteristic, complemented
677	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
678	#3179	C₂×C₆₇	1	2	yes	complemented
679	#3176	C₂×C₆₇	1	2	yes	complemented
680	#3122	C₂×C₆₇	1	2	yes	complemented
681	#3119	C₂×C₆₇	1	2	yes	complemented
682	#3114	C₂×C₆₇	1	1	yes	characteristic, complemented
683	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
684	#3105	C₂×C₆₇	1	1	yes	characteristic, complemented
685	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
686	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
687	C₆₇	#60978	1	1	yes	characteristic, direct product factor, Sylow
688	#555	—	2	1	no	—
689	#553	—	2	1	no	—
690	#553	—	2	1	no	—
691	#551	—	2	1	no	—
692	#551	—	2	1	no	—
693	#547	—	2	1	no	—
694	#546	—	2	1	no	—
695	#546	—	2	1	no	—
696	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#540	—	2	1	no	—
700	#540	—	2	1	no	—
701	#540	—	2	1	no	—
702	#540	—	2	1	no	—
703	#540	C₂²×C₆₇	1	2	yes	—
704	#540	C₂²×C₆₇	1	2	yes	—
705	#540	C₂²×C₆₇	1	1	yes	characteristic, complemented
706	#540	C₂²×C₆₇	1	2	yes	complemented
707	#540	C₂²×C₆₇	1	2	yes	complemented
708	#540	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#532	C₂²×C₆₇	1	1	yes	characteristic
711	#532	C₂²×C₆₇	1	1	yes	characteristic
712	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#529	C₂²×C₆₇	1	1	yes	characteristic
714	#529	C₂²×C₆₇	1	1	yes	characteristic
715	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
716	#525	C₂²×C₆₇	1	1	yes	characteristic
717	C₂×#123	—	2	1	no	—
718	C₂×#123	—	2	1	no	—
719	C₂×#121	—	2	1	no	—
720	C₂×#121	—	2	1	no	—
721	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
722	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
723	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
724	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
729	#501	C₂²×C₆₇	1	2	yes	complemented
730	#499	C₂²×C₆₇	1	2	yes	complemented
731	#496	C₂²×C₆₇	1	2	yes	complemented
732	#493	C₂²×C₆₇	1	2	yes	complemented
733	#490	C₂²×C₆₇	1	2	yes	complemented
734	#490	C₂²×C₆₇	1	2	yes	complemented
735	#488	C₂²×C₆₇	1	2	yes	complemented
736	#486	C₂²×C₆₇	1	2	yes	complemented
737	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	#482	C₂²×C₆₇	1	2	yes	complemented
740	#482	C₂²×C₆₇	1	2	yes	complemented
741	#481	C₂²×C₆₇	1	1	yes	characteristic
742	#481	C₂²×C₆₇	1	1	yes	characteristic
743	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
744	#481	C₂²×C₆₇	1	2	yes	complemented
745	#480	C₂²×C₆₇	1	1	yes	characteristic
746	#480	C₂²×C₆₇	1	1	yes	characteristic
747	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	#480	C₂²×C₆₇	1	2	yes	complemented
749	#479	C₂²×C₆₇	1	2	yes	complemented
750	#478	C₂²×C₆₇	1	2	yes	complemented
751	#478	C₂²×C₆₇	1	2	yes	complemented
752	#478	C₂²×C₆₇	1	2	yes	complemented
753	#478	C₂²×C₆₇	1	2	yes	complemented
754	#478	C₂²×C₆₇	1	2	yes	complemented
755	#476	C₂²×C₆₇	1	2	yes	complemented
756	#474	C₂²×C₆₇	1	2	yes	complemented
757	#469	C₂²×C₆₇	1	2	yes	complemented
758	#469	C₂²×C₆₇	1	2	yes	complemented
759	#469	C₂²×C₆₇	1	2	yes	complemented
760	#468	C₂²×C₆₇	1	2	yes	complemented
761	#466	C₂²×C₆₇	1	2	yes	complemented
762	#466	C₂²×C₆₇	1	2	yes	complemented
763	#466	C₂²×C₆₇	1	2	yes	complemented
764	#465	C₂²×C₆₇	1	2	yes	complemented
765	#463	C₂²×C₆₇	1	2	yes	complemented
766	#463	C₂²×C₆₇	1	2	yes	complemented
767	#460	C₂²×C₆₇	1	2	yes	complemented
768	#459	C₂²×C₆₇	1	2	yes	complemented
769	#459	C₂²×C₆₇	1	2	yes	complemented
770	#459	C₂²×C₆₇	1	2	yes	complemented
771	#459	C₂²×C₆₇	1	2	yes	complemented
772	#459	C₂²×C₆₇	1	2	yes	complemented
773	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
774	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	#449	C₂²×C₆₇	1	2	yes	complemented
776	#449	C₂²×C₆₇	1	2	yes	complemented
777	#447	C₂²×C₆₇	1	1	yes	characteristic
778	#447	C₂²×C₆₇	1	1	yes	characteristic
779	#447	C₂²×C₆₇	1	1	yes	characteristic
780	#447	C₂²×C₆₇	1	1	yes	characteristic
781	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	#447	C₂²×C₆₇	1	2	yes	complemented
784	#447	C₂²×C₆₇	1	2	yes	complemented
785	#442	C₂²×C₆₇	1	2	yes	complemented
786	#442	C₂²×C₆₇	1	2	yes	complemented
787	#442	C₂²×C₆₇	1	2	yes	complemented
788	#440	C₂²×C₆₇	1	2	yes	complemented
789	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
790	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
791	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
792	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
793	#433	C₂²×C₆₇	1	2	yes	complemented
794	#433	C₂²×C₆₇	1	2	yes	complemented
795	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
796	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
797	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
798	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
799	#424	C₂²×C₆₇	1	2	yes	complemented
800	#407	C₂²×C₆₇	1	1	yes	characteristic
801	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
802	#405	C₂²×C₆₇	1	2	yes	complemented
803	C₂×#41	—	2	1	no	—
804	C₂×#41	—	2	1	no	—
805	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
806	C₂²×D₄	—	2	1	no	—
807	C₂²×D₄	—	2	1	no	—
808	C₂²×D₄	—	2	1	no	—
809	C₂²×D₄	—	2	1	no	—
810	C₂²×D₄	—	2	1	no	—
811	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
812	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
813	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
814	C₂³×C₄	—	2	1	no	—
815	C₂³×C₄	—	2	1	no	—
816	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
818	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
819	C₂×D₈	C₂³×C₆₇	1	2	yes	—
820	C₂×D₈	C₂³×C₆₇	1	2	yes	—
821	C₂×D₈	C₂³×C₆₇	1	2	yes	—
822	C₂×D₈	C₂³×C₆₇	1	2	yes	—
823	C₂×D₈	C₂³×C₆₇	1	2	yes	—
824	C₂×D₈	C₂³×C₆₇	1	2	yes	—
825	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
826	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
827	C₄⋊Q₈	—	2	1	no	—
828	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
829	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
830	#127	—	2	1	no	—
831	#127	—	2	1	no	—
832	#127	C₂³×C₆₇	1	2	yes	—
833	#127	C₂³×C₆₇	1	2	yes	—
834	#127	C₂³×C₆₇	1	1	yes	characteristic
835	#127	C₂³×C₆₇	1	1	yes	characteristic
836	#126	—	2	1	no	—
837	#126	—	2	1	no	—
838	#126	—	2	1	no	—
839	#126	—	2	1	no	—
840	#125	—	2	1	no	—
841	#125	—	2	1	no	—
842	#125	—	2	1	no	—
843	#125	C₂³×C₆₇	1	2	yes	—
844	#125	C₂³×C₆₇	1	2	yes	—
845	#125	C₂³×C₆₇	1	1	yes	characteristic
846	#125	C₂³×C₆₇	1	1	yes	characteristic
847	#124	—	2	1	no	—
848	#124	—	2	1	no	—
849	#124	—	2	1	no	—
850	#124	—	2	1	no	—
851	#124	C₂³×C₆₇	1	1	yes	characteristic
852	#124	C₂³×C₆₇	1	1	yes	characteristic
853	#123	—	2	1	no	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	#123	—	2	2	no	—
857	#123	—	2	2	no	—
858	#123	—	2	2	no	—
859	#123	—	2	2	no	—
860	#123	—	2	2	no	—
861	#123	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	1	no	—
865	#123	—	2	1	no	—
866	#123	—	2	1	no	—
867	#123	—	2	1	no	—
868	#123	—	2	1	no	—
869	#123	—	2	1	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	1	no	—
873	C₂²⋊Q₈	—	2	1	no	—
874	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	—	2	1	no	—
880	#121	—	2	1	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	1	no	—
884	#121	—	2	1	no	—
885	#121	—	2	1	no	—
886	#121	—	2	2	no	—
887	#121	—	2	2	no	—
888	#121	—	2	2	no	—
889	#121	—	2	2	no	—
890	#121	—	2	2	no	—
891	#121	—	2	2	no	—
892	#121	—	2	2	no	—
893	#121	—	2	2	no	—
894	#121	—	2	1	no	—
895	#121	—	2	1	no	—
896	#121	—	2	1	no	—
897	#121	—	2	1	no	—
898	#121	C₂³×C₆₇	1	1	yes	characteristic
899	#121	C₂³×C₆₇	1	1	yes	characteristic
900	#121	C₂³×C₆₇	1	2	yes	—
901	#121	C₂³×C₆₇	1	2	yes	—
902	#121	C₂³×C₆₇	1	2	yes	—
903	#121	C₂³×C₆₇	1	2	yes	—
904	#121	C₂³×C₆₇	1	1	yes	characteristic
905	#121	C₂³×C₆₇	1	1	yes	characteristic
906	#121	C₂³×C₆₇	1	1	yes	characteristic
907	#121	C₂³×C₆₇	1	1	yes	characteristic
908	#120	—	2	1	no	—
909	#120	—	2	1	no	—
910	#120	—	2	1	no	—
911	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
912	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	1	no	—
915	C₄×D₄	—	2	1	no	—
916	C₄×D₄	—	2	1	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	1	no	—
921	C₄×D₄	—	2	1	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	—	2	1	no	—
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	C₂³×C₆₇	1	2	yes	—
928	C₄×D₄	C₂³×C₆₇	1	2	yes	—
929	C₄×D₄	C₂³×C₆₇	1	2	yes	—
930	C₄×D₄	C₂³×C₆₇	1	2	yes	—
931	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
932	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
933	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
934	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
935	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
936	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
937	#117	—	2	1	no	—
938	#117	—	2	1	no	—
939	#117	—	2	1	no	—
940	#117	D₄×C₆₇	1	1	yes	characteristic
941	#117	D₄×C₆₇	1	1	yes	characteristic
942	#117	D₄×C₆₇	1	1	yes	characteristic
943	#117	D₄×C₆₇	1	1	yes	characteristic
944	#117	C₂³×C₆₇	1	1	yes	characteristic
945	#117	C₂³×C₆₇	1	1	yes	characteristic
946	#117	C₂³×C₆₇	1	1	yes	characteristic
947	#117	C₂³×C₆₇	1	1	yes	characteristic
948	#117	C₂³×C₆₇	1	1	yes	characteristic
949	C₂×C₄⋊C₄	—	2	1	no	—
950	C₂×C₄⋊C₄	—	2	1	no	—
951	C₂×C₄⋊C₄	—	2	1	no	—
952	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
953	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
957	C₂×C₂²⋊C₄	—	2	1	no	—
958	C₂×C₂²⋊C₄	—	2	1	no	—
959	C₂×C₂²⋊C₄	—	2	1	no	—
960	C₂×C₂²⋊C₄	—	2	1	no	—
961	C₂×C₂²⋊C₄	—	2	1	no	—
962	C₂×C₂²⋊C₄	—	2	1	no	—
963	C₂×C₂²⋊C₄	—	2	1	no	—
964	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
966	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
967	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
968	#107	C₂³×C₆₇	1	2	yes	—
969	#107	C₂³×C₆₇	1	2	yes	—
970	#107	C₂³×C₆₇	1	2	yes	—
971	#107	C₂³×C₆₇	1	2	yes	—
972	#106	C₂³×C₆₇	1	2	yes	—
973	#106	C₂³×C₆₇	1	2	yes	—
974	#106	C₂³×C₆₇	1	2	yes	—
975	#106	C₂³×C₆₇	1	2	yes	—
976	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
977	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
978	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
979	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
980	#103	C₂³×C₆₇	1	2	yes	—
981	#103	C₂³×C₆₇	1	2	yes	—
982	#102	C₂³×C₆₇	1	2	yes	—
983	#102	C₂³×C₆₇	1	2	yes	—
984	#102	C₂³×C₆₇	1	2	yes	—
985	#102	C₂³×C₆₇	1	2	yes	—
986	#102	C₂³×C₆₇	1	2	yes	—
987	#102	C₂³×C₆₇	1	2	yes	—
988	#102	C₂³×C₆₇	1	2	yes	—
989	#102	C₂³×C₆₇	1	2	yes	—
990	#102	C₂³×C₆₇	1	2	yes	—
991	#102	C₂³×C₆₇	1	2	yes	—
992	#102	C₂³×C₆₇	1	2	yes	—
993	#102	C₂³×C₆₇	1	2	yes	—
994	#102	C₂³×C₆₇	1	2	yes	—
995	#102	C₂³×C₆₇	1	2	yes	—
996	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
997	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
998	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
999	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1000	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1001	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1002	#97	C₂³×C₆₇	1	2	yes	—
1003	#97	C₂³×C₆₇	1	2	yes	—
1004	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1005	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1006	C₂⁴	—	2	1	no	—
1007	C₂⁴	—	2	1	no	—
1008	C₂⁴	—	2	1	no	—
1009	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1010	#41	—	4	2	no	—
1011	#41	—	8	2	no	—
1012	#41	—	8	2	no	—
1013	C₂×Q₈	—	2	1	no	—
1014	C₂×Q₈	—	2	1	no	—
1015	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1016	C₂×D₄	—	2	1	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	2	2	no	—
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	1	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	1	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	2	no	—
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	4	2	no	—
1039	C₂×D₄	—	4	2	no	—
1040	C₂×D₄	—	4	2	no	—
1041	C₂×D₄	—	8	2	no	—
1042	C₂×D₄	—	8	2	no	—
1043	C₂×D₄	—	8	2	no	—
1044	C₂×D₄	—	8	2	no	—
1045	C₂×D₄	—	8	2	no	—
1046	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1047	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1048	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1050	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1051	C₂²×C₄	—	2	1	no	—
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	1	no	—
1057	C₂²×C₄	—	2	1	no	—
1058	C₂²×C₄	—	2	1	no	—
1059	C₂²×C₄	—	2	1	no	—
1060	C₂²×C₄	—	2	1	no	—
1061	C₂²×C₄	—	2	2	no	—
1062	C₂²×C₄	—	2	2	no	—
1063	C₂²×C₄	—	2	2	no	—
1064	C₂²×C₄	—	2	2	no	—
1065	C₂²×C₄	—	4	2	no	—
1066	C₂²×C₄	—	8	2	no	—
1067	C₂²×C₄	—	8	2	no	—
1068	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1069	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1070	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1071	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1072	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1073	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1074	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1075	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1076	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1077	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1078	SD₁₆	—	4	2	no	—
1079	SD₁₆	—	4	2	no	—
1080	D₈	—	4	2	no	—
1081	D₈	—	4	2	no	—
1082	D₈	—	4	2	no	—
1083	D₈	—	4	2	no	—
1084	D₈	—	4	2	no	—
1085	D₈	—	4	2	no	—
1086	M₁₆	—	4	2	no	—
1087	C₂×C₈	—	4	2	no	—
1088	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1089	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1090	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1091	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	1	no	—
1108	C₄⋊C₄	—	2	1	no	—
1109	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1110	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1111	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1112	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1113	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1114	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1115	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1116	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1117	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1118	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1119	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1120	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1121	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1122	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	2	no	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	1	no	—
1135	C₂²⋊C₄	—	2	1	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	1	no	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	2	no	—
1140	C₂²⋊C₄	—	2	2	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	1	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	1	no	—
1148	C₂²⋊C₄	—	2	1	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1151	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1152	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1153	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1154	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1155	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1156	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1157	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1158	C₄²	—	2	1	no	—
1159	C₄²	—	2	1	no	—
1160	C₄²	—	2	1	no	—
1161	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1162	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1163	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1164	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1165	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1166	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1167	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1168	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1169	C₂³	—	2	2	no	—
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	1	no	—
1172	C₂³	—	2	1	no	—
1173	C₂³	—	2	2	no	—
1174	C₂³	—	2	2	no	—
1175	C₂³	—	4	1	no	—
1176	C₂³	—	4	1	no	—
1177	C₂³	—	4	2	no	—
1178	C₂³	—	4	2	no	—
1179	C₂³	—	4	2	no	—
1180	C₂³	—	4	2	no	—
1181	C₂³	—	4	2	no	—
1182	C₂³	—	4	2	no	—
1183	C₂³	—	4	2	no	—
1184	C₂³	—	8	1	no	—
1185	C₂³	—	8	1	no	—
1186	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1187	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1188	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1189	Q₈	—	2	2	no	—
1190	Q₈	—	8	1	no	—
1191	Q₈	—	8	1	no	—
1192	D₄	—	2	2	no	—
1193	D₄	—	2	2	no	—
1194	D₄	—	2	2	no	—
1195	D₄	—	2	2	no	—
1196	D₄	—	2	2	no	—
1197	D₄	—	2	2	no	—
1198	D₄	—	2	2	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	2	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	4	2	no	—
1205	D₄	—	4	2	no	—
1206	D₄	—	8	2	no	—
1207	D₄	—	8	2	no	—
1208	D₄	—	8	2	no	—
1209	D₄	—	8	2	no	—
1210	D₄	—	8	1	no	—
1211	D₄	—	8	1	no	—
1212	D₄	—	8	1	no	—
1213	D₄	—	8	1	no	—
1214	D₄	—	8	2	no	—
1215	D₄	—	8	2	no	—
1216	D₄	—	8	1	no	—
1217	D₄	—	8	1	no	—
1218	D₄	—	8	2	no	—
1219	D₄	—	8	2	no	—
1220	D₄	—	8	1	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	2	no	—
1233	C₂×C₄	—	4	1	no	—
1234	C₂×C₄	—	4	1	no	—
1235	C₂×C₄	—	4	1	no	—
1236	C₂×C₄	—	4	1	no	—
1237	C₂×C₄	—	4	1	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	4	2	no	—
1241	C₂×C₄	—	8	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	2	no	—
1244	C₂×C₄	—	8	2	no	—
1245	C₂×C₄	—	8	1	no	—
1246	C₂×C₄	—	8	1	no	—
1247	C₂×C₄	—	8	1	no	—
1248	C₂×C₄	—	8	1	no	—
1249	C₂×C₄	—	8	1	no	—
1250	C₂×C₄	—	8	1	no	—
1251	C₂×C₄	—	8	1	no	—
1252	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1254	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1255	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1256	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1257	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1258	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1259	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1260	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1261	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1262	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1263	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1264	C₈	—	2	2	no	—
1265	C₈	—	2	2	no	—
1266	C₈	—	2	2	no	—
1267	C₈	—	2	2	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	4	1	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	2	no	—
1281	C₂²	—	4	2	no	—
1282	C₂²	—	4	1	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	2	no	—
1285	C₂²	—	4	1	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	2	no	—
1288	C₂²	—	4	2	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	8	2	no	—
1292	C₂²	—	8	4	no	—
1293	C₂²	—	8	4	no	—
1294	C₂²	—	16	2	no	—
1295	C₂²	#576×C₆₇	1	2	yes	—
1296	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1297	C₄	—	2	1	no	—
1298	C₄	—	2	1	no	—
1299	C₄	—	2	1	no	—
1300	C₄	—	2	1	no	—
1301	C₄	—	2	1	no	—
1302	C₄	—	2	1	no	—
1303	C₄	—	2	1	no	—
1304	C₄	—	2	1	no	—
1305	C₄	—	2	1	no	—
1306	C₄	—	2	1	no	—
1307	C₄	—	2	1	no	—
1308	C₄	—	4	2	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	1	no	—
1311	C₄	—	4	1	no	—
1312	C₄	—	4	2	no	—
1313	C₄	—	4	1	no	—
1314	C₄	—	4	1	no	—
1315	C₄	#585×C₆₇	1	2	yes	—
1316	C₂	—	2	2	no	—
1317	C₂	—	4	1	no	—
1318	C₂	—	4	1	no	—
1319	C₂	—	8	2	no	—
1320	C₂	—	8	2	no	—
1321	C₂	—	8	1	no	—
1322	C₂	—	8	1	no	—
1323	C₂	—	8	1	no	—
1324	C₂	C₆₇×#3449	1	1	yes	characteristic
1325	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1326	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. C₂×#540×C₆₇	C₂	semidirect
3. C₆₇×#3259	C₂	semidirect
4. C₆₇×#3257	C₂	semidirect
5. C₆₇×#3241	C₂	semidirect
6. C₆₇×#3234	C₂	semidirect
7. C₆₇×#3232	C₂	semidirect
8. C₆₇×#3220	C₂	semidirect
9. C₆₇×#3217	C₂	semidirect
10. C₆₇×#3205	C₂	semidirect
11. C₆₇×#3194	C₂	semidirect
12. C₆₇×#3192	C₂	semidirect
13. C₆₇×#3188	C₂	semidirect
14. C₆₇×#3186	C₂	semidirect
15. C₆₇×#3179	C₂	semidirect
16. C₆₇×#3176	C₂	semidirect
17. C₆₇×#3122	C₂	semidirect
18. C₆₇×#3119	C₂	semidirect
19. C₆₇×#3114	C₂	semidirect
20. C₆₇×#3109	C₂	semidirect
21. C₆₇×#3105	C₂	semidirect
22. C₆₇×#3100	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
32. #544×C₆₇	C₂²	semidirect
33. #542×C₆₇	C₂²	semidirect
34. #542×C₆₇	C₂²	semidirect
41. #540×C₆₇	C₂²	semidirect
42. #540×C₆₇	C₂²	semidirect
43. #540×C₆₇	C₂²	semidirect
44. #540×C₆₇	C₂²	semidirect
45. #535×C₆₇	C₂²	semidirect
48. C₂×#127×C₆₇	C₂²	semidirect
51. C₂×#125×C₆₇	C₂²	semidirect
60. #520×C₆₇	C₂²	semidirect
61. #518×C₆₇	C₂²	semidirect
62. C₂×C₄×D₄×C₆₇	C₂²	semidirect
63. C₂×C₄×D₄×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
67. #496×C₆₇	C₂²	semidirect
68. #493×C₆₇	C₂²	semidirect
69. #490×C₆₇	C₂²	semidirect
70. #490×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
72. #486×C₆₇	C₂²	semidirect
73. #484×C₆₇	C₂²	semidirect
74. #483×C₆₇	C₂²	semidirect
75. #482×C₆₇	C₂²	semidirect
76. #482×C₆₇	C₂²	semidirect
79. #481×C₆₇	C₂²	semidirect
80. #481×C₆₇	C₂²	semidirect
83. #480×C₆₇	C₂²	semidirect
84. #480×C₆₇	C₂²	semidirect
85. #479×C₆₇	C₂²	semidirect
86. #478×C₆₇	C₂²	semidirect
87. #478×C₆₇	C₂²	semidirect
88. #478×C₆₇	C₂²	semidirect
89. #478×C₆₇	C₂²	semidirect
90. #478×C₆₇	C₂²	semidirect
91. #476×C₆₇	C₂²	semidirect
92. #474×C₆₇	C₂²	semidirect
93. #469×C₆₇	C₂²	semidirect
94. #469×C₆₇	C₂²	semidirect
95. #469×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #466×C₆₇	C₂²	semidirect
98. #466×C₆₇	C₂²	semidirect
99. #466×C₆₇	C₂²	semidirect
100. #465×C₆₇	C₂²	semidirect
101. #463×C₆₇	C₂²	semidirect
102. #463×C₆₇	C₂²	semidirect
103. #460×C₆₇	C₂²	semidirect
104. #459×C₆₇	C₂²	semidirect
105. #459×C₆₇	C₂²	semidirect
106. #459×C₆₇	C₂²	semidirect
107. #459×C₆₇	C₂²	semidirect
108. #459×C₆₇	C₂²	semidirect
109. #450×C₆₇	C₂²	semidirect
110. #450×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
117. #447×C₆₇	C₂²	semidirect
118. #447×C₆₇	C₂²	semidirect
119. #447×C₆₇	C₂²	semidirect
120. #447×C₆₇	C₂²	semidirect
121. #442×C₆₇	C₂²	semidirect
122. #442×C₆₇	C₂²	semidirect
123. #442×C₆₇	C₂²	semidirect
124. #440×C₆₇	C₂²	semidirect
125. C₄×SD₁₆×C₆₇	C₂²	semidirect
126. C₄×D₈×C₆₇	C₂²	semidirect
127. C₄×D₈×C₆₇	C₂²	semidirect
128. C₄×D₈×C₆₇	C₂²	semidirect
129. #433×C₆₇	C₂²	semidirect
130. #433×C₆₇	C₂²	semidirect
131. #432×C₆₇	C₂²	semidirect
132. #432×C₆₇	C₂²	semidirect
133. #431×C₆₇	C₂²	semidirect
134. #431×C₆₇	C₂²	semidirect
135. #424×C₆₇	C₂²	semidirect
138. #405×C₆₇	C₂²	semidirect
652. #60978	C₆₇	direct (N × H)
664. #3494	C₂×C₆₇	semidirect
665. C₂×#540	C₂×C₆₇	semidirect
666. #3259	C₂×C₆₇	semidirect
667. #3257	C₂×C₆₇	semidirect
668. #3241	C₂×C₆₇	semidirect
669. #3234	C₂×C₆₇	semidirect
670. #3232	C₂×C₆₇	semidirect
671. #3220	C₂×C₆₇	semidirect
672. #3217	C₂×C₆₇	semidirect
673. #3205	C₂×C₆₇	semidirect
674. #3194	C₂×C₆₇	semidirect
675. #3192	C₂×C₆₇	semidirect
676. #3188	C₂×C₆₇	semidirect
677. #3186	C₂×C₆₇	semidirect
678. #3179	C₂×C₆₇	semidirect
679. #3176	C₂×C₆₇	semidirect
680. #3122	C₂×C₆₇	semidirect
681. #3119	C₂×C₆₇	semidirect
682. #3114	C₂×C₆₇	semidirect
683. #3109	C₂×C₆₇	semidirect
684. #3105	C₂×C₆₇	semidirect
685. #3100	C₂×C₆₇	semidirect
686. #2924	C₂×C₆₇	semidirect
687. C₆₇	#60978	direct (N × H)
696. #544	C₂²×C₆₇	semidirect
697. #542	C₂²×C₆₇	semidirect
698. #542	C₂²×C₆₇	semidirect
705. #540	C₂²×C₆₇	semidirect
706. #540	C₂²×C₆₇	semidirect
707. #540	C₂²×C₆₇	semidirect
708. #540	C₂²×C₆₇	semidirect
709. #535	C₂²×C₆₇	semidirect
712. C₂×#127	C₂²×C₆₇	semidirect
715. C₂×#125	C₂²×C₆₇	semidirect
724. #520	C₂²×C₆₇	semidirect
725. #518	C₂²×C₆₇	semidirect
726. C₂×C₄×D₄	C₂²×C₆₇	semidirect
727. C₂×C₄×D₄	C₂²×C₆₇	semidirect
729. #501	C₂²×C₆₇	semidirect
730. #499	C₂²×C₆₇	semidirect
731. #496	C₂²×C₆₇	semidirect
732. #493	C₂²×C₆₇	semidirect
733. #490	C₂²×C₆₇	semidirect
734. #490	C₂²×C₆₇	semidirect
735. #488	C₂²×C₆₇	semidirect
736. #486	C₂²×C₆₇	semidirect
737. #484	C₂²×C₆₇	semidirect
738. #483	C₂²×C₆₇	semidirect
739. #482	C₂²×C₆₇	semidirect
740. #482	C₂²×C₆₇	semidirect
743. #481	C₂²×C₆₇	semidirect
744. #481	C₂²×C₆₇	semidirect
747. #480	C₂²×C₆₇	semidirect
748. #480	C₂²×C₆₇	semidirect
749. #479	C₂²×C₆₇	semidirect
750. #478	C₂²×C₆₇	semidirect
751. #478	C₂²×C₆₇	semidirect
752. #478	C₂²×C₆₇	semidirect
753. #478	C₂²×C₆₇	semidirect
754. #478	C₂²×C₆₇	semidirect
755. #476	C₂²×C₆₇	semidirect
756. #474	C₂²×C₆₇	semidirect
757. #469	C₂²×C₆₇	semidirect
758. #469	C₂²×C₆₇	semidirect
759. #469	C₂²×C₆₇	semidirect
760. #468	C₂²×C₆₇	semidirect
761. #466	C₂²×C₆₇	semidirect
762. #466	C₂²×C₆₇	semidirect
763. #466	C₂²×C₆₇	semidirect
764. #465	C₂²×C₆₇	semidirect
765. #463	C₂²×C₆₇	semidirect
766. #463	C₂²×C₆₇	semidirect
767. #460	C₂²×C₆₇	semidirect
768. #459	C₂²×C₆₇	semidirect
769. #459	C₂²×C₆₇	semidirect
770. #459	C₂²×C₆₇	semidirect
771. #459	C₂²×C₆₇	semidirect
772. #459	C₂²×C₆₇	semidirect
773. #450	C₂²×C₆₇	semidirect
774. #450	C₂²×C₆₇	semidirect
775. #449	C₂²×C₆₇	semidirect
776. #449	C₂²×C₆₇	semidirect
781. #447	C₂²×C₆₇	semidirect
782. #447	C₂²×C₆₇	semidirect
783. #447	C₂²×C₆₇	semidirect
784. #447	C₂²×C₆₇	semidirect
785. #442	C₂²×C₆₇	semidirect
786. #442	C₂²×C₆₇	semidirect
787. #442	C₂²×C₆₇	semidirect
788. #440	C₂²×C₆₇	semidirect
789. C₄×SD₁₆	C₂²×C₆₇	semidirect
790. C₄×D₈	C₂²×C₆₇	semidirect
791. C₄×D₈	C₂²×C₆₇	semidirect
792. C₄×D₈	C₂²×C₆₇	semidirect
793. #433	C₂²×C₆₇	semidirect
794. #433	C₂²×C₆₇	semidirect
795. #432	C₂²×C₆₇	semidirect
796. #432	C₂²×C₆₇	semidirect
797. #431	C₂²×C₆₇	semidirect
798. #431	C₂²×C₆₇	semidirect
799. #424	C₂²×C₆₇	semidirect
802. #405	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3494	2
C₂×#540×C₆₇	2
C₆₇×#3259	2
C₆₇×#3257	2
C₆₇×#3241	2
C₆₇×#3234	2
C₆₇×#3232	2
C₆₇×#3220	2
C₆₇×#3217	2
C₆₇×#3205	2
C₆₇×#3194	2
C₆₇×#3192	2
C₆₇×#3188	2
C₆₇×#3186	2
C₆₇×#3179	2
C₆₇×#3176	2
C₆₇×#3122	2
C₆₇×#3119	2
C₆₇×#3114	2
C₆₇×#3109	2
C₆₇×#3105	2
C₆₇×#3100	2
C₆₇×#2924	2
#60978	67

Subgroups — C67×#60978 #30740229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60978 #30740229