Subgroups — C₆₇×#60988 #30740239

Order 17152.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3248	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3243	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3224	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3212	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3203	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3179	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3175	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	—	2	1	no	—
25	#555×C₆₇	—	2	1	no	—
26	#554×C₆₇	—	2	1	no	—
27	#553×C₆₇	—	2	1	no	—
28	#553×C₆₇	—	2	1	no	—
29	#548×C₆₇	—	2	1	no	—
30	#548×C₆₇	—	2	1	no	—
31	#547×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic
33	#542×C₆₇	—	2	1	no	—
34	#542×C₆₇	C₂²	1	1	yes	characteristic
35	#542×C₆₇	C₂²	1	1	yes	characteristic
36	#542×C₆₇	C₂²	1	2	yes	—
37	#542×C₆₇	C₂²	1	2	yes	complemented
38	#540×C₆₇	—	2	1	no	—
39	#540×C₆₇	C₂²	1	1	yes	characteristic
40	#540×C₆₇	C₂²	1	1	yes	characteristic
41	#538×C₆₇	—	2	1	no	—
42	#538×C₆₇	—	2	1	no	—
43	#537×C₆₇	C₂²	1	2	yes	—
44	#537×C₆₇	C₂²	1	1	yes	characteristic
45	#535×C₆₇	C₂²	1	1	yes	characteristic
46	#535×C₆₇	C₂²	1	1	yes	characteristic
47	#533×C₆₇	C₂²	1	1	yes	characteristic
48	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#532×C₆₇	—	2	1	no	—
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	C₂²	1	1	yes	characteristic
53	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#529×C₆₇	—	2	1	no	—
57	#529×C₆₇	C₂²	1	1	yes	characteristic
58	#529×C₆₇	C₂²	1	1	yes	characteristic
59	#525×C₆₇	—	2	1	no	—
60	#525×C₆₇	—	2	1	no	—
61	#520×C₆₇	C₂²	1	2	yes	complemented
62	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
63	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#500×C₆₇	C₂²	1	2	yes	complemented
67	#496×C₆₇	C₂²	1	2	yes	—
68	#495×C₆₇	C₂²	1	2	yes	—
69	#489×C₆₇	C₂²	1	2	yes	—
70	#489×C₆₇	C₂²	1	2	yes	complemented
71	#488×C₆₇	C₂²	1	2	yes	complemented
72	#486×C₆₇	C₂²	1	2	yes	—
73	#485×C₆₇	C₂²	1	2	yes	—
74	#484×C₆₇	C₂²	1	2	yes	—
75	#484×C₆₇	C₂²	1	2	yes	complemented
76	#482×C₆₇	C₂²	1	2	yes	—
77	#481×C₆₇	C₂²	1	2	yes	—
78	#480×C₆₇	C₂²	1	2	yes	—
79	#480×C₆₇	C₂²	1	2	yes	—
80	#480×C₆₇	C₂²	1	2	yes	complemented
81	#479×C₆₇	C₂²	1	2	yes	complemented
82	#478×C₆₇	C₂²	1	2	yes	complemented
83	#477×C₆₇	C₂²	1	2	yes	complemented
84	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#474×C₆₇	C₂²	1	1	yes	characteristic
87	#474×C₆₇	C₂²	1	1	yes	characteristic
88	#474×C₆₇	C₂²	1	1	yes	characteristic
89	#474×C₆₇	C₂²	1	1	yes	characteristic
90	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#474×C₆₇	C₂²	1	2	yes	complemented
93	#469×C₆₇	C₂²	1	2	yes	—
94	#468×C₆₇	C₂²	1	2	yes	—
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#468×C₆₇	C₂²	1	2	yes	complemented
97	#467×C₆₇	C₂²	1	2	yes	complemented
98	#466×C₆₇	C₂²	1	2	yes	—
99	#466×C₆₇	C₂²	1	2	yes	complemented
100	#465×C₆₇	C₂²	1	2	yes	—
101	#464×C₆₇	C₂²	1	2	yes	—
102	#463×C₆₇	C₂²	1	2	yes	—
103	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#461×C₆₇	C₂²	1	1	yes	characteristic
105	#461×C₆₇	C₂²	1	1	yes	characteristic
106	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#460×C₆₇	C₂²	1	2	yes	—
108	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#459×C₆₇	C₂²	1	1	yes	characteristic
110	#459×C₆₇	C₂²	1	1	yes	characteristic
111	#459×C₆₇	C₂²	1	2	yes	—
112	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#452×C₆₇	C₂²	1	2	yes	—
114	#452×C₆₇	C₂²	1	2	yes	complemented
115	#450×C₆₇	C₂²	1	2	yes	—
116	#449×C₆₇	C₂²	1	2	yes	—
117	#449×C₆₇	C₂²	1	2	yes	—
118	#449×C₆₇	C₂²	1	2	yes	—
119	#449×C₆₇	C₂²	1	2	yes	complemented
120	#447×C₆₇	C₂²	1	2	yes	—
121	#442×C₆₇	C₂²	1	2	yes	complemented
122	#440×C₆₇	C₂²	1	2	yes	—
123	#440×C₆₇	C₂²	1	2	yes	—
124	#440×C₆₇	C₂²	1	2	yes	complemented
125	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
126	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
127	C₄×D₈×C₆₇	C₂²	1	2	yes	—
128	C₄×D₈×C₆₇	C₂²	1	2	yes	—
129	#433×C₆₇	C₂²	1	2	yes	—
130	#433×C₆₇	C₂²	1	2	yes	complemented
131	#432×C₆₇	C₂²	1	1	yes	characteristic
132	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#431×C₆₇	C₂²	1	1	yes	characteristic
134	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	#408×C₆₇	C₂²	1	2	yes	—
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	—	2	1	no	—
142	C₂×#41×C₆₇	—	2	1	no	—
143	C₂×#41×C₆₇	C₂³	1	2	yes	—
144	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×Q₈×C₆₇	—	2	1	no	—
147	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	—	2	1	no	—
149	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×D₈×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	—	2	1	no	—
161	C₄⋊Q₈×C₆₇	—	2	1	no	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
168	#127×C₆₇	—	2	1	no	—
169	#127×C₆₇	C₂³	1	1	yes	characteristic
170	#127×C₆₇	C₂³	1	1	yes	characteristic
171	#127×C₆₇	C₂³	1	1	yes	characteristic
172	#126×C₆₇	—	2	1	no	—
173	#126×C₆₇	—	2	1	no	—
174	#126×C₆₇	—	2	2	no	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	1	no	—
177	#126×C₆₇	—	2	1	no	—
178	#125×C₆₇	—	2	1	no	—
179	#125×C₆₇	—	2	1	no	—
180	#125×C₆₇	—	2	1	no	—
181	#125×C₆₇	C₂³	1	1	yes	characteristic
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	2	no	—
187	#124×C₆₇	—	2	2	no	—
188	#124×C₆₇	—	2	1	no	—
189	#124×C₆₇	—	2	1	no	—
190	#124×C₆₇	—	2	1	no	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	C₂³	1	1	yes	characteristic
193	#124×C₆₇	C₂³	1	2	yes	—
194	#124×C₆₇	C₂³	1	1	yes	characteristic
195	#123×C₆₇	—	2	1	no	—
196	#123×C₆₇	—	2	1	no	—
197	#123×C₆₇	—	2	1	no	—
198	#123×C₆₇	—	2	1	no	—
199	#123×C₆₇	—	2	1	no	—
200	#123×C₆₇	—	2	1	no	—
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	1	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	—	2	1	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	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	—	2	1	no	—
211	C₂²⋊Q₈×C₆₇	—	2	2	no	—
212	C₂²⋊Q₈×C₆₇	—	2	2	no	—
213	C₂²⋊Q₈×C₆₇	—	2	1	no	—
214	C₂²⋊Q₈×C₆₇	—	2	1	no	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	1	no	—
226	#121×C₆₇	—	2	1	no	—
227	#121×C₆₇	—	2	1	no	—
228	#121×C₆₇	—	2	1	no	—
229	#121×C₆₇	—	2	1	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	—	2	1	no	—
235	#121×C₆₇	—	2	1	no	—
236	#121×C₆₇	—	2	1	no	—
237	#121×C₆₇	C₂³	1	1	yes	characteristic
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
244	#121×C₆₇	C₂³	1	1	yes	characteristic
245	#120×C₆₇	—	2	1	no	—
246	#120×C₆₇	—	2	1	no	—
247	#120×C₆₇	—	2	1	no	—
248	#120×C₆₇	—	2	1	no	—
249	C₄×Q₈×C₆₇	—	2	1	no	—
250	C₄×Q₈×C₆₇	—	2	1	no	—
251	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
252	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
253	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
254	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
255	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
256	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
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	2	no	—
262	C₄×D₄×C₆₇	—	2	2	no	—
263	C₄×D₄×C₆₇	—	2	1	no	—
264	C₄×D₄×C₆₇	—	2	1	no	—
265	C₄×D₄×C₆₇	—	2	1	no	—
266	C₄×D₄×C₆₇	—	2	1	no	—
267	C₄×D₄×C₆₇	—	2	1	no	—
268	C₄×D₄×C₆₇	—	2	1	no	—
269	C₄×D₄×C₆₇	—	2	1	no	—
270	C₄×D₄×C₆₇	—	2	1	no	—
271	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
272	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
273	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
274	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
275	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
276	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
277	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₆₇	C₂³	1	2	yes	—
280	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₆₇	C₂³	1	2	yes	—
285	#117×C₆₇	—	2	1	no	—
286	#117×C₆₇	—	2	1	no	—
287	#117×C₆₇	—	2	2	no	—
288	#117×C₆₇	—	2	1	no	—
289	#117×C₆₇	—	2	1	no	—
290	#117×C₆₇	—	2	1	no	—
291	#117×C₆₇	C₂³	1	1	yes	characteristic
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	C₂³	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	#107×C₆₇	C₂³	1	2	yes	—
309	#107×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	1	yes	characteristic
313	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
318	#103×C₆₇	C₂³	1	2	yes	—
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#103×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	#102×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	#41×C₆₇	—	4	1	no	—
344	#41×C₆₇	—	4	1	no	—
345	#41×C₆₇	—	4	1	no	—
346	#41×C₆₇	—	4	1	no	—
347	#41×C₆₇	—	4	2	no	—
348	#41×C₆₇	—	4	2	no	—
349	#41×C₆₇	—	8	2	no	—
350	#41×C₆₇	—	8	2	no	—
351	#41×C₆₇	—	8	2	no	—
352	#41×C₆₇	—	8	2	no	—
353	C₂×Q₈×C₆₇	—	2	1	no	—
354	C₂×Q₈×C₆₇	—	2	1	no	—
355	C₂×Q₈×C₆₇	—	2	2	no	—
356	C₂×Q₈×C₆₇	—	2	1	no	—
357	C₂×Q₈×C₆₇	—	2	1	no	—
358	C₂×Q₈×C₆₇	—	8	2	no	—
359	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
360	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
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	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	1	no	—
373	C₂×D₄×C₆₇	—	2	1	no	—
374	C₂×D₄×C₆₇	—	2	1	no	—
375	C₂×D₄×C₆₇	—	2	1	no	—
376	C₂×D₄×C₆₇	—	2	1	no	—
377	C₂×D₄×C₆₇	—	2	1	no	—
378	C₂×D₄×C₆₇	—	2	1	no	—
379	C₂×D₄×C₆₇	—	4	1	no	—
380	C₂×D₄×C₆₇	—	4	1	no	—
381	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
385	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	—	2	1	no	—
389	C₂²×C₄×C₆₇	—	2	2	no	—
390	C₂²×C₄×C₆₇	—	2	1	no	—
391	C₂²×C₄×C₆₇	—	2	1	no	—
392	C₂²×C₄×C₆₇	—	2	2	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	2	no	—
397	C₂²×C₄×C₆₇	—	2	2	no	—
398	C₂²×C₄×C₆₇	—	2	1	no	—
399	C₂²×C₄×C₆₇	—	2	1	no	—
400	C₂²×C₄×C₆₇	—	8	2	no	—
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	Q₁₆×C₆₇	—	4	2	no	—
411	SD₁₆×C₆₇	—	4	2	no	—
412	SD₁₆×C₆₇	—	4	2	no	—
413	SD₁₆×C₆₇	—	4	2	no	—
414	SD₁₆×C₆₇	—	4	2	no	—
415	D₈×C₆₇	—	4	2	no	—
416	D₈×C₆₇	—	4	2	no	—
417	D₈×C₆₇	—	4	2	no	—
418	M₁₆×C₆₇	—	4	2	no	—
419	C₂×C₈×C₆₇	—	4	2	no	—
420	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
421	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
422	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
423	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
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	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	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	2	no	—
444	C₄⋊C₄×C₆₇	—	2	2	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	C₂⁴	1	2	yes	—
452	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	1	no	—
465	C₂²⋊C₄×C₆₇	—	2	1	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	2	no	—
469	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
475	C₂²⋊C₄×C₆₇	—	2	1	no	—
476	C₂²⋊C₄×C₆₇	—	2	1	no	—
477	C₂²⋊C₄×C₆₇	—	2	1	no	—
478	C₂²⋊C₄×C₆₇	—	2	2	no	—
479	C₂²⋊C₄×C₆₇	—	2	2	no	—
480	C₂²⋊C₄×C₆₇	—	2	1	no	—
481	C₂²⋊C₄×C₆₇	—	2	1	no	—
482	C₂²⋊C₄×C₆₇	—	2	2	no	—
483	C₂²⋊C₄×C₆₇	—	2	2	no	—
484	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₆₇	—	2	1	no	—
491	C₄²×C₆₇	—	2	1	no	—
492	C₄²×C₆₇	—	2	1	no	—
493	C₄²×C₆₇	—	2	2	no	—
494	C₄²×C₆₇	—	2	2	no	—
495	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
510	C₂³×C₆₇	—	8	1	no	—
511	C₂³×C₆₇	—	8	1	no	—
512	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
515	Q₈×C₆₇	—	2	1	no	—
516	Q₈×C₆₇	—	2	2	no	—
517	Q₈×C₆₇	—	2	2	no	—
518	Q₈×C₆₇	—	2	1	no	—
519	Q₈×C₆₇	—	4	1	no	—
520	Q₈×C₆₇	—	4	2	no	—
521	Q₈×C₆₇	—	4	2	no	—
522	Q₈×C₆₇	—	8	2	no	—
523	Q₈×C₆₇	—	8	1	no	—
524	Q₈×C₆₇	—	8	1	no	—
525	D₄×C₆₇	—	2	1	no	—
526	D₄×C₆₇	—	2	1	no	—
527	D₄×C₆₇	—	2	2	no	—
528	D₄×C₆₇	—	2	1	no	—
529	D₄×C₆₇	—	2	2	no	—
530	D₄×C₆₇	—	2	1	no	—
531	D₄×C₆₇	—	2	1	no	—
532	D₄×C₆₇	—	2	1	no	—
533	D₄×C₆₇	—	4	1	no	—
534	D₄×C₆₇	—	4	1	no	—
535	D₄×C₆₇	—	4	1	no	—
536	D₄×C₆₇	—	4	2	no	—
537	D₄×C₆₇	—	4	2	no	—
538	D₄×C₆₇	—	4	4	no	—
539	D₄×C₆₇	—	4	2	no	—
540	D₄×C₆₇	—	4	2	no	—
541	D₄×C₆₇	—	8	1	no	—
542	D₄×C₆₇	—	8	1	no	—
543	D₄×C₆₇	—	8	1	no	—
544	D₄×C₆₇	—	8	1	no	—
545	D₄×C₆₇	—	8	1	no	—
546	D₄×C₆₇	—	8	1	no	—
547	D₄×C₆₇	—	8	1	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	C₂×C₄×C₆₇	—	2	2	no	—
554	C₂×C₄×C₆₇	—	2	2	no	—
555	C₂×C₄×C₆₇	—	2	2	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	2	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	2	2	no	—
567	C₂×C₄×C₆₇	—	2	2	no	—
568	C₂×C₄×C₆₇	—	2	1	no	—
569	C₂×C₄×C₆₇	—	2	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	4	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	—	4	2	no	—
578	C₂×C₄×C₆₇	—	8	1	no	—
579	C₂×C₄×C₆₇	—	8	1	no	—
580	C₂×C₄×C₆₇	—	8	1	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	2	no	—
585	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
597	C₈×C₆₇	—	2	2	no	—
598	C₈×C₆₇	—	2	2	no	—
599	C₈×C₆₇	—	2	2	no	—
600	C₈×C₆₇	—	2	2	no	—
601	C₂²×C₆₇	—	2	1	no	—
602	C₂²×C₆₇	—	2	1	no	—
603	C₂²×C₆₇	—	2	1	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	—	4	1	no	—
611	C₂²×C₆₇	—	4	2	no	—
612	C₂²×C₆₇	—	4	1	no	—
613	C₂²×C₆₇	—	4	1	no	—
614	C₂²×C₆₇	—	4	2	no	—
615	C₂²×C₆₇	—	4	1	no	—
616	C₂²×C₆₇	—	4	1	no	—
617	C₂²×C₆₇	—	4	1	no	—
618	C₂²×C₆₇	—	4	1	no	—
619	C₂²×C₆₇	—	4	1	no	—
620	C₂²×C₆₇	—	4	1	no	—
621	C₂²×C₆₇	—	4	2	no	—
622	C₂²×C₆₇	—	8	4	no	—
623	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
624	C₄×C₆₇	—	2	1	no	—
625	C₄×C₆₇	—	2	1	no	—
626	C₄×C₆₇	—	2	1	no	—
627	C₄×C₆₇	—	2	1	no	—
628	C₄×C₆₇	—	2	1	no	—
629	C₄×C₆₇	—	2	1	no	—
630	C₄×C₆₇	—	2	1	no	—
631	C₄×C₆₇	—	2	1	no	—
632	C₄×C₆₇	—	2	1	no	—
633	C₄×C₆₇	—	2	1	no	—
634	C₄×C₆₇	—	4	1	no	—
635	C₄×C₆₇	—	4	1	no	—
636	C₄×C₆₇	—	4	2	no	—
637	C₄×C₆₇	—	4	1	no	—
638	C₄×C₆₇	—	4	1	no	—
639	C₄×C₆₇	—	4	1	no	—
640	C₄×C₆₇	—	4	2	no	—
641	C₄×C₆₇	—	4	2	no	—
642	C₄×C₆₇	#576	1	2	yes	—
643	C₄×C₆₇	#585	1	1	yes	characteristic
644	C₄×C₆₇	#585	1	1	yes	characteristic
645	#60988	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
646	C₂×C₆₇	—	4	1	no	—
647	C₂×C₆₇	—	4	1	no	—
648	C₂×C₆₇	—	4	1	no	—
649	C₂×C₆₇	—	8	1	no	—
650	C₂×C₆₇	—	8	2	no	—
651	C₂×C₆₇	—	8	1	no	—
652	C₂×C₆₇	—	8	1	no	—
653	C₂×C₆₇	#3449	1	1	yes	characteristic
654	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
655	C₂×C₆₇	#3586	1	1	yes	characteristic
656	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
657	#3460	C₂×C₆₇	1	1	yes	characteristic, complemented
658	#3254	C₂×C₆₇	1	1	yes	characteristic, complemented
659	#3251	C₂×C₆₇	1	1	yes	characteristic, complemented
660	#3248	C₂×C₆₇	1	1	yes	characteristic, complemented
661	#3245	C₂×C₆₇	1	1	yes	characteristic, complemented
662	#3243	C₂×C₆₇	1	2	yes	complemented
663	#3239	C₂×C₆₇	1	1	yes	characteristic, complemented
664	#3226	C₂×C₆₇	1	1	yes	characteristic, complemented
665	#3224	C₂×C₆₇	1	2	yes	complemented
666	#3214	C₂×C₆₇	1	1	yes	characteristic, complemented
667	#3212	C₂×C₆₇	1	1	yes	characteristic, complemented
668	#3203	C₂×C₆₇	1	2	yes	complemented
669	#3198	C₂×C₆₇	1	2	yes	complemented
670	#3179	C₂×C₆₇	1	2	yes	complemented
671	#3175	C₂×C₆₇	1	2	yes	complemented
672	#3124	C₂×C₆₇	1	2	yes	complemented
673	#3119	C₂×C₆₇	1	2	yes	complemented
674	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
676	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
677	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
678	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
679	C₆₇	#60988	1	1	yes	characteristic, direct product factor, Sylow
680	#556	—	2	1	no	—
681	#555	—	2	1	no	—
682	#554	—	2	1	no	—
683	#553	—	2	1	no	—
684	#553	—	2	1	no	—
685	#548	—	2	1	no	—
686	#548	—	2	1	no	—
687	#547	—	2	1	no	—
688	#544	C₂²×C₆₇	1	1	yes	characteristic
689	#542	—	2	1	no	—
690	#542	C₂²×C₆₇	1	1	yes	characteristic
691	#542	C₂²×C₆₇	1	1	yes	characteristic
692	#542	C₂²×C₆₇	1	2	yes	—
693	#542	C₂²×C₆₇	1	2	yes	complemented
694	#540	—	2	1	no	—
695	#540	C₂²×C₆₇	1	1	yes	characteristic
696	#540	C₂²×C₆₇	1	1	yes	characteristic
697	#538	—	2	1	no	—
698	#538	—	2	1	no	—
699	#537	C₂²×C₆₇	1	2	yes	—
700	#537	C₂²×C₆₇	1	1	yes	characteristic
701	#535	C₂²×C₆₇	1	1	yes	characteristic
702	#535	C₂²×C₆₇	1	1	yes	characteristic
703	#533	C₂²×C₆₇	1	1	yes	characteristic
704	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
705	#532	—	2	1	no	—
706	#532	C₂²×C₆₇	1	1	yes	characteristic
707	#532	C₂²×C₆₇	1	1	yes	characteristic
708	#532	C₂²×C₆₇	1	1	yes	characteristic
709	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	#529	—	2	1	no	—
713	#529	C₂²×C₆₇	1	1	yes	characteristic
714	#529	C₂²×C₆₇	1	1	yes	characteristic
715	#525	—	2	1	no	—
716	#525	—	2	1	no	—
717	#520	C₂²×C₆₇	1	2	yes	complemented
718	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
719	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
720	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
721	#501	C₂²×C₆₇	1	2	yes	complemented
722	#500	C₂²×C₆₇	1	2	yes	complemented
723	#496	C₂²×C₆₇	1	2	yes	—
724	#495	C₂²×C₆₇	1	2	yes	—
725	#489	C₂²×C₆₇	1	2	yes	—
726	#489	C₂²×C₆₇	1	2	yes	complemented
727	#488	C₂²×C₆₇	1	2	yes	complemented
728	#486	C₂²×C₆₇	1	2	yes	—
729	#485	C₂²×C₆₇	1	2	yes	—
730	#484	C₂²×C₆₇	1	2	yes	—
731	#484	C₂²×C₆₇	1	2	yes	complemented
732	#482	C₂²×C₆₇	1	2	yes	—
733	#481	C₂²×C₆₇	1	2	yes	—
734	#480	C₂²×C₆₇	1	2	yes	—
735	#480	C₂²×C₆₇	1	2	yes	—
736	#480	C₂²×C₆₇	1	2	yes	complemented
737	#479	C₂²×C₆₇	1	2	yes	complemented
738	#478	C₂²×C₆₇	1	2	yes	complemented
739	#477	C₂²×C₆₇	1	2	yes	complemented
740	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
742	#474	C₂²×C₆₇	1	1	yes	characteristic
743	#474	C₂²×C₆₇	1	1	yes	characteristic
744	#474	C₂²×C₆₇	1	1	yes	characteristic
745	#474	C₂²×C₆₇	1	1	yes	characteristic
746	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
747	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	#474	C₂²×C₆₇	1	2	yes	complemented
749	#469	C₂²×C₆₇	1	2	yes	—
750	#468	C₂²×C₆₇	1	2	yes	—
751	#468	C₂²×C₆₇	1	2	yes	complemented
752	#468	C₂²×C₆₇	1	2	yes	complemented
753	#467	C₂²×C₆₇	1	2	yes	complemented
754	#466	C₂²×C₆₇	1	2	yes	—
755	#466	C₂²×C₆₇	1	2	yes	complemented
756	#465	C₂²×C₆₇	1	2	yes	—
757	#464	C₂²×C₆₇	1	2	yes	—
758	#463	C₂²×C₆₇	1	2	yes	—
759	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	#461	C₂²×C₆₇	1	1	yes	characteristic
761	#461	C₂²×C₆₇	1	1	yes	characteristic
762	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	#460	C₂²×C₆₇	1	2	yes	—
764	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	#459	C₂²×C₆₇	1	1	yes	characteristic
766	#459	C₂²×C₆₇	1	1	yes	characteristic
767	#459	C₂²×C₆₇	1	2	yes	—
768	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
769	#452	C₂²×C₆₇	1	2	yes	—
770	#452	C₂²×C₆₇	1	2	yes	complemented
771	#450	C₂²×C₆₇	1	2	yes	—
772	#449	C₂²×C₆₇	1	2	yes	—
773	#449	C₂²×C₆₇	1	2	yes	—
774	#449	C₂²×C₆₇	1	2	yes	—
775	#449	C₂²×C₆₇	1	2	yes	complemented
776	#447	C₂²×C₆₇	1	2	yes	—
777	#442	C₂²×C₆₇	1	2	yes	complemented
778	#440	C₂²×C₆₇	1	2	yes	—
779	#440	C₂²×C₆₇	1	2	yes	—
780	#440	C₂²×C₆₇	1	2	yes	complemented
781	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
782	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
783	C₄×D₈	C₂²×C₆₇	1	2	yes	—
784	C₄×D₈	C₂²×C₆₇	1	2	yes	—
785	#433	C₂²×C₆₇	1	2	yes	—
786	#433	C₂²×C₆₇	1	2	yes	complemented
787	#432	C₂²×C₆₇	1	1	yes	characteristic
788	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
789	#431	C₂²×C₆₇	1	1	yes	characteristic
790	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
791	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
792	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
793	#408	C₂²×C₆₇	1	2	yes	—
794	#405	C₂²×C₆₇	1	2	yes	complemented
795	C₂×#41	—	2	1	no	—
796	C₂×#41	—	2	1	no	—
797	C₂×#41	—	2	1	no	—
798	C₂×#41	—	2	1	no	—
799	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
800	C₂×#41	C₂³×C₆₇	1	2	yes	—
801	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
802	C₂²×Q₈	—	2	1	no	—
803	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
804	C₂³×C₄	—	2	1	no	—
805	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
806	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
807	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
808	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
809	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
810	C₂×D₈	C₂³×C₆₇	1	2	yes	—
811	C₂×D₈	C₂³×C₆₇	1	2	yes	—
812	C₂×D₈	C₂³×C₆₇	1	2	yes	—
813	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
814	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
815	C₄⋊Q₈	—	2	1	no	—
816	C₄⋊Q₈	—	2	1	no	—
817	C₄⋊Q₈	—	2	1	no	—
818	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
819	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
820	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
821	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
822	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
823	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
824	#127	—	2	1	no	—
825	#127	C₂³×C₆₇	1	1	yes	characteristic
826	#127	C₂³×C₆₇	1	1	yes	characteristic
827	#127	C₂³×C₆₇	1	1	yes	characteristic
828	#126	—	2	1	no	—
829	#126	—	2	1	no	—
830	#126	—	2	2	no	—
831	#126	—	2	2	no	—
832	#126	—	2	1	no	—
833	#126	—	2	1	no	—
834	#125	—	2	1	no	—
835	#125	—	2	1	no	—
836	#125	—	2	1	no	—
837	#125	C₂³×C₆₇	1	1	yes	characteristic
838	#125	C₂³×C₆₇	1	1	yes	characteristic
839	#124	—	2	1	no	—
840	#124	—	2	1	no	—
841	#124	—	2	1	no	—
842	#124	—	2	2	no	—
843	#124	—	2	2	no	—
844	#124	—	2	1	no	—
845	#124	—	2	1	no	—
846	#124	—	2	1	no	—
847	#124	—	2	1	no	—
848	#124	C₂³×C₆₇	1	1	yes	characteristic
849	#124	C₂³×C₆₇	1	1	yes	characteristic
850	#124	C₂³×C₆₇	1	2	yes	—
851	#123	—	2	1	no	—
852	#123	—	2	1	no	—
853	#123	—	2	1	no	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	#123	—	2	1	no	—
857	#123	—	2	1	no	—
858	#123	—	2	1	no	—
859	#123	—	2	2	no	—
860	#123	—	2	2	no	—
861	C₂²⋊Q₈	—	2	1	no	—
862	C₂²⋊Q₈	—	2	2	no	—
863	C₂²⋊Q₈	—	2	1	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	1	no	—
867	C₂²⋊Q₈	—	2	2	no	—
868	C₂²⋊Q₈	—	2	2	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
872	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
874	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	2	no	—
879	#121	—	2	2	no	—
880	#121	—	2	2	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	1	no	—
887	#121	—	2	1	no	—
888	#121	—	2	1	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	—	2	1	no	—
892	#121	—	2	1	no	—
893	#121	C₂³×C₆₇	1	1	yes	characteristic
894	#121	C₂³×C₆₇	1	1	yes	characteristic
895	#121	C₂³×C₆₇	1	1	yes	characteristic
896	#121	C₂³×C₆₇	1	1	yes	characteristic
897	#121	C₂³×C₆₇	1	1	yes	characteristic
898	#121	C₂³×C₆₇	1	1	yes	characteristic
899	#121	C₂³×C₆₇	1	2	yes	—
900	#121	C₂³×C₆₇	1	2	yes	—
901	#120	—	2	1	no	—
902	#120	—	2	1	no	—
903	#120	—	2	1	no	—
904	#120	—	2	1	no	—
905	C₄×Q₈	—	2	1	no	—
906	C₄×Q₈	—	2	1	no	—
907	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
908	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
909	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
910	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
911	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
912	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
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	2	no	—
918	C₄×D₄	—	2	2	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	D₄×C₆₇	1	1	yes	characteristic
928	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
929	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
930	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
931	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
932	C₄×D₄	D₄×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	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
938	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
939	C₄×D₄	C₂³×C₆₇	1	2	yes	—
940	C₄×D₄	C₂³×C₆₇	1	2	yes	—
941	#117	—	2	1	no	—
942	#117	—	2	1	no	—
943	#117	—	2	2	no	—
944	#117	—	2	1	no	—
945	#117	—	2	1	no	—
946	#117	—	2	1	no	—
947	#117	C₂³×C₆₇	1	1	yes	characteristic
948	#117	C₂³×C₆₇	1	1	yes	characteristic
949	#117	C₂³×C₆₇	1	1	yes	characteristic
950	#117	C₂³×C₆₇	1	1	yes	characteristic
951	C₂×C₄⋊C₄	—	2	1	no	—
952	C₂×C₄⋊C₄	—	2	2	no	—
953	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
955	C₂×C₂²⋊C₄	—	2	1	no	—
956	C₂×C₄²	—	2	1	no	—
957	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
958	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
959	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
960	#107	C₂³×C₆₇	1	2	yes	—
961	#107	C₂³×C₆₇	1	2	yes	—
962	#107	C₂³×C₆₇	1	2	yes	—
963	#107	C₂³×C₆₇	1	2	yes	—
964	#107	C₂³×C₆₇	1	2	yes	—
965	#107	C₂³×C₆₇	1	2	yes	—
966	#106	C₂³×C₆₇	1	2	yes	—
967	#106	C₂³×C₆₇	1	2	yes	—
968	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
969	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
970	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
971	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
972	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
973	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
974	#103	C₂³×C₆₇	1	2	yes	—
975	#103	C₂³×C₆₇	1	2	yes	—
976	#103	C₂³×C₆₇	1	2	yes	—
977	#103	C₂³×C₆₇	1	2	yes	—
978	#103	C₂³×C₆₇	1	2	yes	—
979	#103	C₂³×C₆₇	1	2	yes	—
980	#102	C₂³×C₆₇	1	2	yes	—
981	#102	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	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
991	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
992	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
993	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
994	#97	C₂³×C₆₇	1	2	yes	—
995	#97	C₂³×C₆₇	1	2	yes	—
996	C₄×C₈	C₂³×C₆₇	1	2	yes	—
997	C₄×C₈	C₂³×C₆₇	1	2	yes	—
998	C₂⁴	—	2	1	no	—
999	#41	—	4	1	no	—
1000	#41	—	4	1	no	—
1001	#41	—	4	1	no	—
1002	#41	—	4	1	no	—
1003	#41	—	4	2	no	—
1004	#41	—	4	2	no	—
1005	#41	—	8	2	no	—
1006	#41	—	8	2	no	—
1007	#41	—	8	2	no	—
1008	#41	—	8	2	no	—
1009	C₂×Q₈	—	2	1	no	—
1010	C₂×Q₈	—	2	1	no	—
1011	C₂×Q₈	—	2	2	no	—
1012	C₂×Q₈	—	2	1	no	—
1013	C₂×Q₈	—	2	1	no	—
1014	C₂×Q₈	—	8	2	no	—
1015	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1016	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1017	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	1	no	—
1023	C₂×D₄	—	2	1	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	—	2	2	no	—
1027	C₂×D₄	—	2	2	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	1	no	—
1035	C₂×D₄	—	4	1	no	—
1036	C₂×D₄	—	4	1	no	—
1037	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1038	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1039	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1040	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1041	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1042	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1043	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	2	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	1	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	2	2	no	—
1054	C₂²×C₄	—	2	1	no	—
1055	C₂²×C₄	—	2	1	no	—
1056	C₂²×C₄	—	8	2	no	—
1057	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1058	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1060	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1061	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1062	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1066	Q₁₆	—	4	2	no	—
1067	SD₁₆	—	4	2	no	—
1068	SD₁₆	—	4	2	no	—
1069	SD₁₆	—	4	2	no	—
1070	SD₁₆	—	4	2	no	—
1071	D₈	—	4	2	no	—
1072	D₈	—	4	2	no	—
1073	D₈	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	C₂×C₈	—	4	2	no	—
1076	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1077	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1079	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	2	no	—
1100	C₄⋊C₄	—	2	2	no	—
1101	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1102	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1103	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1104	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1105	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1106	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1107	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1108	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1109	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1111	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1112	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	1	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₆₇	1	1	yes	characteristic
1141	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1142	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1143	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1144	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1145	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1146	C₄²	—	2	1	no	—
1147	C₄²	—	2	1	no	—
1148	C₄²	—	2	1	no	—
1149	C₄²	—	2	2	no	—
1150	C₄²	—	2	2	no	—
1151	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1152	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1153	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1154	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1155	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1156	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1157	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1158	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1159	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1160	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1161	C₂³	—	2	2	no	—
1162	C₂³	—	2	1	no	—
1163	C₂³	—	2	1	no	—
1164	C₂³	—	2	1	no	—
1165	C₂³	—	4	2	no	—
1166	C₂³	—	8	1	no	—
1167	C₂³	—	8	1	no	—
1168	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1169	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1170	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1171	Q₈	—	2	1	no	—
1172	Q₈	—	2	2	no	—
1173	Q₈	—	2	2	no	—
1174	Q₈	—	2	1	no	—
1175	Q₈	—	4	1	no	—
1176	Q₈	—	4	2	no	—
1177	Q₈	—	4	2	no	—
1178	Q₈	—	8	2	no	—
1179	Q₈	—	8	1	no	—
1180	Q₈	—	8	1	no	—
1181	D₄	—	2	1	no	—
1182	D₄	—	2	1	no	—
1183	D₄	—	2	2	no	—
1184	D₄	—	2	1	no	—
1185	D₄	—	2	2	no	—
1186	D₄	—	2	1	no	—
1187	D₄	—	2	1	no	—
1188	D₄	—	2	1	no	—
1189	D₄	—	4	1	no	—
1190	D₄	—	4	1	no	—
1191	D₄	—	4	1	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	4	no	—
1195	D₄	—	4	2	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	8	1	no	—
1198	D₄	—	8	1	no	—
1199	D₄	—	8	1	no	—
1200	D₄	—	8	1	no	—
1201	D₄	—	8	1	no	—
1202	D₄	—	8	1	no	—
1203	D₄	—	8	1	no	—
1204	D₄	—	8	1	no	—
1205	D₄	—	8	2	no	—
1206	D₄	—	8	2	no	—
1207	D₄	—	8	1	no	—
1208	D₄	—	8	1	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	4	1	no	—
1227	C₂×C₄	—	4	1	no	—
1228	C₂×C₄	—	4	1	no	—
1229	C₂×C₄	—	4	4	no	—
1230	C₂×C₄	—	4	2	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	8	1	no	—
1235	C₂×C₄	—	8	1	no	—
1236	C₂×C₄	—	8	2	no	—
1237	C₂×C₄	—	8	2	no	—
1238	C₂×C₄	—	8	1	no	—
1239	C₂×C₄	—	8	1	no	—
1240	C₂×C₄	—	8	2	no	—
1241	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1242	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1243	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1244	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1245	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1251	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1252	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1253	C₈	—	2	2	no	—
1254	C₈	—	2	2	no	—
1255	C₈	—	2	2	no	—
1256	C₈	—	2	2	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	4	1	no	—
1267	C₂²	—	4	1	no	—
1268	C₂²	—	4	1	no	—
1269	C₂²	—	4	2	no	—
1270	C₂²	—	4	1	no	—
1271	C₂²	—	4	2	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	1	no	—
1274	C₂²	—	4	2	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	1	no	—
1277	C₂²	—	4	1	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1280	C₄	—	2	1	no	—
1281	C₄	—	2	1	no	—
1282	C₄	—	2	1	no	—
1283	C₄	—	2	1	no	—
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	4	1	no	—
1291	C₄	—	4	1	no	—
1292	C₄	—	4	1	no	—
1293	C₄	—	4	2	no	—
1294	C₄	—	4	2	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	2	no	—
1298	C₄	#576×C₆₇	1	2	yes	—
1299	C₄	#585×C₆₇	1	1	yes	characteristic
1300	C₄	#585×C₆₇	1	1	yes	characteristic
1301	C₂	—	4	1	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	8	1	no	—
1305	C₂	—	8	1	no	—
1306	C₂	—	8	1	no	—
1307	C₂	—	8	2	no	—
1308	C₂	C₆₇×#3449	1	1	yes	characteristic
1309	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1310	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 ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3511	C₂	semidirect
2. C₆₇×#3460	C₂	semidirect
3. C₆₇×#3254	C₂	semidirect
4. C₆₇×#3251	C₂	semidirect
5. C₆₇×#3248	C₂	semidirect
6. C₆₇×#3245	C₂	semidirect
7. C₆₇×#3243	C₂	semidirect
8. C₆₇×#3239	C₂	semidirect
9. C₆₇×#3226	C₂	semidirect
10. C₆₇×#3224	C₂	semidirect
11. C₆₇×#3214	C₂	semidirect
12. C₆₇×#3212	C₂	semidirect
13. C₆₇×#3203	C₂	semidirect
14. C₆₇×#3198	C₂	semidirect
15. C₆₇×#3179	C₂	semidirect
16. C₆₇×#3175	C₂	semidirect
17. C₆₇×#3124	C₂	semidirect
18. C₆₇×#3119	C₂	semidirect
19. C₆₇×#3115	C₂	semidirect
20. C₆₇×#3110	C₂	semidirect
21. C₆₇×#3107	C₂	semidirect
22. C₆₇×#3100	C₂	semidirect
23. C₆₇×#2925	C₂	semidirect
37. #542×C₆₇	C₂²	semidirect
48. #533×C₆₇	C₂²	semidirect
53. #532×C₆₇	C₂²	semidirect
54. #532×C₆₇	C₂²	semidirect
55. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
61. #520×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #500×C₆₇	C₂²	semidirect
70. #489×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
75. #484×C₆₇	C₂²	semidirect
80. #480×C₆₇	C₂²	semidirect
81. #479×C₆₇	C₂²	semidirect
82. #478×C₆₇	C₂²	semidirect
83. #477×C₆₇	C₂²	semidirect
84. #475×C₆₇	C₂²	semidirect
85. #475×C₆₇	C₂²	semidirect
90. #474×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #474×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #467×C₆₇	C₂²	semidirect
99. #466×C₆₇	C₂²	semidirect
103. #462×C₆₇	C₂²	semidirect
106. #461×C₆₇	C₂²	semidirect
108. #460×C₆₇	C₂²	semidirect
112. #459×C₆₇	C₂²	semidirect
114. #452×C₆₇	C₂²	semidirect
119. #449×C₆₇	C₂²	semidirect
121. #442×C₆₇	C₂²	semidirect
124. #440×C₆₇	C₂²	semidirect
125. C₄×Q₁₆×C₆₇	C₂²	semidirect
126. C₄×SD₁₆×C₆₇	C₂²	semidirect
130. #433×C₆₇	C₂²	semidirect
132. #432×C₆₇	C₂²	semidirect
134. #431×C₆₇	C₂²	semidirect
135. #423×C₆₇	C₂²	semidirect
136. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
138. #405×C₆₇	C₂²	semidirect
645. #60988	C₆₇	direct (N × H)
656. #3511	C₂×C₆₇	semidirect
657. #3460	C₂×C₆₇	semidirect
658. #3254	C₂×C₆₇	semidirect
659. #3251	C₂×C₆₇	semidirect
660. #3248	C₂×C₆₇	semidirect
661. #3245	C₂×C₆₇	semidirect
662. #3243	C₂×C₆₇	semidirect
663. #3239	C₂×C₆₇	semidirect
664. #3226	C₂×C₆₇	semidirect
665. #3224	C₂×C₆₇	semidirect
666. #3214	C₂×C₆₇	semidirect
667. #3212	C₂×C₆₇	semidirect
668. #3203	C₂×C₆₇	semidirect
669. #3198	C₂×C₆₇	semidirect
670. #3179	C₂×C₆₇	semidirect
671. #3175	C₂×C₆₇	semidirect
672. #3124	C₂×C₆₇	semidirect
673. #3119	C₂×C₆₇	semidirect
674. #3115	C₂×C₆₇	semidirect
675. #3110	C₂×C₆₇	semidirect
676. #3107	C₂×C₆₇	semidirect
677. #3100	C₂×C₆₇	semidirect
678. #2925	C₂×C₆₇	semidirect
679. C₆₇	#60988	direct (N × H)
693. #542	C₂²×C₆₇	semidirect
704. #533	C₂²×C₆₇	semidirect
709. #532	C₂²×C₆₇	semidirect
710. #532	C₂²×C₆₇	semidirect
711. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
717. #520	C₂²×C₆₇	semidirect
721. #501	C₂²×C₆₇	semidirect
722. #500	C₂²×C₆₇	semidirect
726. #489	C₂²×C₆₇	semidirect
727. #488	C₂²×C₆₇	semidirect
731. #484	C₂²×C₆₇	semidirect
736. #480	C₂²×C₆₇	semidirect
737. #479	C₂²×C₆₇	semidirect
738. #478	C₂²×C₆₇	semidirect
739. #477	C₂²×C₆₇	semidirect
740. #475	C₂²×C₆₇	semidirect
741. #475	C₂²×C₆₇	semidirect
746. #474	C₂²×C₆₇	semidirect
747. #474	C₂²×C₆₇	semidirect
748. #474	C₂²×C₆₇	semidirect
751. #468	C₂²×C₆₇	semidirect
752. #468	C₂²×C₆₇	semidirect
753. #467	C₂²×C₆₇	semidirect
755. #466	C₂²×C₆₇	semidirect
759. #462	C₂²×C₆₇	semidirect
762. #461	C₂²×C₆₇	semidirect
764. #460	C₂²×C₆₇	semidirect
768. #459	C₂²×C₆₇	semidirect
770. #452	C₂²×C₆₇	semidirect
775. #449	C₂²×C₆₇	semidirect
777. #442	C₂²×C₆₇	semidirect
780. #440	C₂²×C₆₇	semidirect
781. C₄×Q₁₆	C₂²×C₆₇	semidirect
782. C₄×SD₁₆	C₂²×C₆₇	semidirect
786. #433	C₂²×C₆₇	semidirect
788. #432	C₂²×C₆₇	semidirect
790. #431	C₂²×C₆₇	semidirect
791. #423	C₂²×C₆₇	semidirect
792. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
794. #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×#3511	2
C₆₇×#3460	2
C₆₇×#3254	2
C₆₇×#3251	2
C₆₇×#3248	2
C₆₇×#3245	2
C₆₇×#3243	2
C₆₇×#3239	2
C₆₇×#3226	2
C₆₇×#3224	2
C₆₇×#3214	2
C₆₇×#3212	2
C₆₇×#3203	2
C₆₇×#3198	2
C₆₇×#3179	2
C₆₇×#3175	2
C₆₇×#3124	2
C₆₇×#3119	2
C₆₇×#3115	2
C₆₇×#3110	2
C₆₇×#3107	2
C₆₇×#3100	2
C₆₇×#2925	2
#60988	67

Subgroups — C67×#60988 #30740239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60988 #30740239