Subgroups — C₆₇×#60976 #30740227

Order 17152.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1298 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×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3262	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3243	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3224	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3213	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3190	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×#3175	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3108	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	—	2	1	no	—
34	#542×C₆₇	—	2	1	no	—
35	#542×C₆₇	—	2	1	no	—
36	#542×C₆₇	—	2	1	no	—
37	#542×C₆₇	C₂²	1	2	yes	—
38	#542×C₆₇	C₂²	1	2	yes	—
39	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#542×C₆₇	C₂²	1	2	yes	complemented
41	#542×C₆₇	C₂²	1	2	yes	complemented
42	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#540×C₆₇	C₂²	1	1	yes	characteristic, 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×C₄⋊Q₈×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×#126×C₆₇	—	2	1	no	—
52	C₂×#124×C₆₇	—	2	1	no	—
53	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#525×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#123×C₆₇	—	2	1	no	—
56	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
57	C₂×C₂²⋊Q₈×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×Q₈×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	#500×C₆₇	C₂²	1	2	yes	complemented
67	#496×C₆₇	C₂²	1	2	yes	complemented
68	#495×C₆₇	C₂²	1	2	yes	complemented
69	#489×C₆₇	C₂²	1	2	yes	complemented
70	#489×C₆₇	C₂²	1	2	yes	complemented
71	#488×C₆₇	C₂²	1	2	yes	complemented
72	#486×C₆₇	C₂²	1	2	yes	complemented
73	#485×C₆₇	C₂²	1	2	yes	complemented
74	#484×C₆₇	C₂²	1	2	yes	complemented
75	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#482×C₆₇	C₂²	1	2	yes	—
78	#480×C₆₇	C₂²	1	1	yes	characteristic
79	#480×C₆₇	C₂²	1	1	yes	characteristic
80	#480×C₆₇	C₂²	1	1	yes	characteristic
81	#480×C₆₇	C₂²	1	1	yes	characteristic
82	#480×C₆₇	C₂²	1	2	yes	—
83	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#479×C₆₇	C₂²	1	2	yes	complemented
86	#478×C₆₇	C₂²	1	2	yes	complemented
87	#477×C₆₇	C₂²	1	2	yes	complemented
88	#477×C₆₇	C₂²	1	2	yes	complemented
89	#476×C₆₇	C₂²	1	2	yes	complemented
90	#474×C₆₇	C₂²	1	2	yes	complemented
91	#474×C₆₇	C₂²	1	2	yes	complemented
92	#474×C₆₇	C₂²	1	2	yes	complemented
93	#469×C₆₇	C₂²	1	2	yes	complemented
94	#468×C₆₇	C₂²	1	2	yes	complemented
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	—
100	#465×C₆₇	C₂²	1	2	yes	complemented
101	#464×C₆₇	C₂²	1	2	yes	complemented
102	#464×C₆₇	C₂²	1	2	yes	complemented
103	#463×C₆₇	C₂²	1	2	yes	complemented
104	#463×C₆₇	C₂²	1	2	yes	complemented
105	#463×C₆₇	C₂²	1	2	yes	complemented
106	#463×C₆₇	C₂²	1	2	yes	complemented
107	#460×C₆₇	C₂²	1	2	yes	complemented
108	#459×C₆₇	C₂²	1	2	yes	complemented
109	#452×C₆₇	C₂²	1	2	yes	complemented
110	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#450×C₆₇	C₂²	1	2	yes	complemented
113	#449×C₆₇	C₂²	1	2	yes	—
114	#448×C₆₇	C₂²	1	1	yes	characteristic
115	#448×C₆₇	C₂²	1	1	yes	characteristic
116	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#447×C₆₇	C₂²	1	1	yes	characteristic
118	#447×C₆₇	C₂²	1	1	yes	characteristic
119	#447×C₆₇	C₂²	1	2	yes	—
120	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#442×C₆₇	C₂²	1	2	yes	complemented
122	#440×C₆₇	C₂²	1	2	yes	complemented
123	#440×C₆₇	C₂²	1	2	yes	complemented
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	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×Q₈×C₆₇	—	2	1	no	—
143	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	—	2	1	no	—
146	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	—	2	1	no	—
149	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆×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×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×M₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	—	2	1	no	—
161	C₄⋊Q₈×C₆₇	—	2	1	no	—
162	C₄⋊Q₈×C₆₇	—	2	1	no	—
163	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	C₂³	1	1	yes	characteristic
168	#127×C₆₇	C₂³	1	1	yes	characteristic
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#126×C₆₇	—	2	1	no	—
174	#126×C₆₇	—	2	1	no	—
175	#126×C₆₇	—	2	1	no	—
176	#126×C₆₇	—	2	1	no	—
177	#125×C₆₇	—	2	1	no	—
178	#125×C₆₇	C₂³	1	1	yes	characteristic
179	#125×C₆₇	C₂³	1	1	yes	characteristic
180	#124×C₆₇	—	2	2	no	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	—	2	2	no	—
183	#124×C₆₇	—	2	2	no	—
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	—	2	1	no	—
186	#124×C₆₇	—	2	1	no	—
187	#124×C₆₇	—	2	1	no	—
188	#124×C₆₇	—	2	1	no	—
189	#124×C₆₇	—	2	1	no	—
190	#124×C₆₇	C₂³	1	2	yes	—
191	#124×C₆₇	C₂³	1	1	yes	characteristic
192	#124×C₆₇	C₂³	1	2	yes	—
193	#124×C₆₇	C₂³	1	1	yes	characteristic
194	#123×C₆₇	—	2	1	no	—
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	2	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	—	2	2	no	—
205	#123×C₆₇	—	2	1	no	—
206	#123×C₆₇	—	2	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	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	—	2	1	no	—
216	C₂²⋊Q₈×C₆₇	—	2	1	no	—
217	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	1	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	C₂³	1	1	yes	characteristic
234	#121×C₆₇	C₂³	1	1	yes	characteristic
235	#121×C₆₇	C₂³	1	1	yes	characteristic
236	#121×C₆₇	C₂³	1	2	yes	—
237	#121×C₆₇	C₂³	1	1	yes	characteristic
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	1	yes	characteristic
240	#121×C₆₇	C₂³	1	2	yes	—
241	#120×C₆₇	—	2	1	no	—
242	#120×C₆₇	—	2	1	no	—
243	#120×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	—	2	1	no	—
245	C₄×Q₈×C₆₇	—	2	1	no	—
246	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
249	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
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	1	yes	characteristic
268	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
270	#117×C₆₇	—	2	1	no	—
271	#117×C₆₇	—	2	1	no	—
272	#117×C₆₇	—	2	1	no	—
273	#117×C₆₇	D₄	1	1	yes	characteristic
274	#117×C₆₇	D₄	1	1	yes	characteristic
275	#117×C₆₇	D₄	1	1	yes	characteristic
276	#117×C₆₇	D₄	1	1	yes	characteristic
277	#117×C₆₇	C₂³	1	1	yes	characteristic
278	#117×C₆₇	C₂³	1	1	yes	characteristic
279	#117×C₆₇	C₂³	1	1	yes	characteristic
280	#117×C₆₇	C₂³	1	1	yes	characteristic
281	#117×C₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
283	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
284	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
285	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
286	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
292	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
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	D₄	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
301	C₂×C₄²×C₆₇	—	2	1	no	—
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	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	#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	#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	1	yes	characteristic
333	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	—	2	1	no	—
344	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
345	#41×C₆₇	—	4	2	no	—
346	#41×C₆₇	—	8	2	no	—
347	#41×C₆₇	—	8	2	no	—
348	C₂×Q₈×C₆₇	—	2	1	no	—
349	C₂×Q₈×C₆₇	—	2	2	no	—
350	C₂×Q₈×C₆₇	—	2	2	no	—
351	C₂×Q₈×C₆₇	—	2	1	no	—
352	C₂×Q₈×C₆₇	—	2	1	no	—
353	C₂×Q₈×C₆₇	—	4	2	no	—
354	C₂×Q₈×C₆₇	—	8	2	no	—
355	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₆₇	—	2	1	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	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	1	no	—
364	C₂×D₄×C₆₇	—	2	2	no	—
365	C₂×D₄×C₆₇	—	2	2	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	1	no	—
371	C₂×D₄×C₆₇	—	2	1	no	—
372	C₂×D₄×C₆₇	—	4	2	no	—
373	C₂×D₄×C₆₇	—	4	2	no	—
374	C₂×D₄×C₆₇	—	8	2	no	—
375	C₂×D₄×C₆₇	—	8	2	no	—
376	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
377	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	2	1	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	2	1	no	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
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	2	no	—
392	C₂²×C₄×C₆₇	—	2	2	no	—
393	C₂²×C₄×C₆₇	—	4	2	no	—
394	C₂²×C₄×C₆₇	—	8	2	no	—
395	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	Q₁₆×C₆₇	—	4	2	no	—
406	SD₁₆×C₆₇	—	4	2	no	—
407	SD₁₆×C₆₇	—	4	2	no	—
408	SD₁₆×C₆₇	—	4	2	no	—
409	SD₁₆×C₆₇	—	4	2	no	—
410	D₈×C₆₇	—	4	2	no	—
411	D₈×C₆₇	—	4	2	no	—
412	D₈×C₆₇	—	4	2	no	—
413	M₁₆×C₆₇	—	4	2	no	—
414	C₂×C₈×C₆₇	—	4	2	no	—
415	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
416	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
417	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
418	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	1	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	2	no	—
427	C₄⋊C₄×C₆₇	—	2	2	no	—
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	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	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	no	—
465	C₂²⋊C₄×C₆₇	—	2	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	2	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	2	no	—
470	C₂²⋊C₄×C₆₇	—	2	2	no	—
471	C₂²⋊C₄×C₆₇	—	2	2	no	—
472	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
479	C₂²⋊C₄×C₆₇	—	2	1	no	—
480	C₂²⋊C₄×C₆₇	—	2	1	no	—
481	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₆₇	—	2	2	no	—
490	C₄²×C₆₇	—	2	2	no	—
491	C₄²×C₆₇	—	2	1	no	—
492	C₄²×C₆₇	—	2	1	no	—
493	C₄²×C₆₇	—	2	1	no	—
494	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
499	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
500	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₂³×C₆₇	—	2	2	no	—
503	C₂³×C₆₇	—	2	2	no	—
504	C₂³×C₆₇	—	2	1	no	—
505	C₂³×C₆₇	—	2	1	no	—
506	C₂³×C₆₇	—	2	1	no	—
507	C₂³×C₆₇	—	4	1	no	—
508	C₂³×C₆₇	—	4	1	no	—
509	C₂³×C₆₇	—	4	2	no	—
510	C₂³×C₆₇	—	4	2	no	—
511	C₂³×C₆₇	—	4	2	no	—
512	C₂³×C₆₇	—	4	2	no	—
513	C₂³×C₆₇	—	8	1	no	—
514	C₂³×C₆₇	—	8	1	no	—
515	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
517	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
518	Q₈×C₆₇	—	2	2	no	—
519	Q₈×C₆₇	—	2	2	no	—
520	Q₈×C₆₇	—	2	2	no	—
521	Q₈×C₆₇	—	4	2	no	—
522	Q₈×C₆₇	—	8	2	no	—
523	Q₈×C₆₇	—	8	2	no	—
524	Q₈×C₆₇	—	8	1	no	—
525	Q₈×C₆₇	—	8	1	no	—
526	D₄×C₆₇	—	2	2	no	—
527	D₄×C₆₇	—	2	2	no	—
528	D₄×C₆₇	—	2	2	no	—
529	D₄×C₆₇	—	2	2	no	—
530	D₄×C₆₇	—	2	2	no	—
531	D₄×C₆₇	—	4	2	no	—
532	D₄×C₆₇	—	4	2	no	—
533	D₄×C₆₇	—	4	2	no	—
534	D₄×C₆₇	—	4	2	no	—
535	D₄×C₆₇	—	4	2	no	—
536	D₄×C₆₇	—	4	2	no	—
537	D₄×C₆₇	—	8	1	no	—
538	D₄×C₆₇	—	8	1	no	—
539	D₄×C₆₇	—	8	1	no	—
540	D₄×C₆₇	—	8	1	no	—
541	D₄×C₆₇	—	8	1	no	—
542	D₄×C₆₇	—	8	2	no	—
543	D₄×C₆₇	—	8	2	no	—
544	D₄×C₆₇	—	8	1	no	—
545	D₄×C₆₇	—	8	1	no	—
546	C₂×C₄×C₆₇	—	2	2	no	—
547	C₂×C₄×C₆₇	—	2	2	no	—
548	C₂×C₄×C₆₇	—	2	2	no	—
549	C₂×C₄×C₆₇	—	2	2	no	—
550	C₂×C₄×C₆₇	—	2	2	no	—
551	C₂×C₄×C₆₇	—	2	1	no	—
552	C₂×C₄×C₆₇	—	2	2	no	—
553	C₂×C₄×C₆₇	—	2	2	no	—
554	C₂×C₄×C₆₇	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	2	no	—
559	C₂×C₄×C₆₇	—	4	1	no	—
560	C₂×C₄×C₆₇	—	4	1	no	—
561	C₂×C₄×C₆₇	—	4	1	no	—
562	C₂×C₄×C₆₇	—	4	1	no	—
563	C₂×C₄×C₆₇	—	4	1	no	—
564	C₂×C₄×C₆₇	—	4	2	no	—
565	C₂×C₄×C₆₇	—	4	2	no	—
566	C₂×C₄×C₆₇	—	4	2	no	—
567	C₂×C₄×C₆₇	—	4	2	no	—
568	C₂×C₄×C₆₇	—	8	1	no	—
569	C₂×C₄×C₆₇	—	8	1	no	—
570	C₂×C₄×C₆₇	—	8	2	no	—
571	C₂×C₄×C₆₇	—	8	2	no	—
572	C₂×C₄×C₆₇	—	8	1	no	—
573	C₂×C₄×C₆₇	—	8	1	no	—
574	C₂×C₄×C₆₇	—	8	1	no	—
575	C₂×C₄×C₆₇	—	8	1	no	—
576	C₂×C₄×C₆₇	—	8	1	no	—
577	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
589	C₈×C₆₇	—	2	2	no	—
590	C₈×C₆₇	—	2	2	no	—
591	C₈×C₆₇	—	2	2	no	—
592	C₈×C₆₇	—	2	2	no	—
593	C₂²×C₆₇	—	2	1	no	—
594	C₂²×C₆₇	—	2	1	no	—
595	C₂²×C₆₇	—	2	1	no	—
596	C₂²×C₆₇	—	2	1	no	—
597	C₂²×C₆₇	—	2	1	no	—
598	C₂²×C₆₇	—	2	1	no	—
599	C₂²×C₆₇	—	2	1	no	—
600	C₂²×C₆₇	—	2	1	no	—
601	C₂²×C₆₇	—	4	1	no	—
602	C₂²×C₆₇	—	4	1	no	—
603	C₂²×C₆₇	—	4	1	no	—
604	C₂²×C₆₇	—	4	2	no	—
605	C₂²×C₆₇	—	4	1	no	—
606	C₂²×C₆₇	—	4	2	no	—
607	C₂²×C₆₇	—	4	1	no	—
608	C₂²×C₆₇	—	4	1	no	—
609	C₂²×C₆₇	—	4	1	no	—
610	C₂²×C₆₇	—	4	2	no	—
611	C₂²×C₆₇	—	4	1	no	—
612	C₂²×C₆₇	—	4	1	no	—
613	C₂²×C₆₇	—	8	2	no	—
614	C₂²×C₆₇	—	8	4	no	—
615	C₂²×C₆₇	—	16	2	no	—
616	C₂²×C₆₇	#576	1	2	yes	—
617	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₆₇	—	2	1	no	—
619	C₄×C₆₇	—	2	1	no	—
620	C₄×C₆₇	—	2	1	no	—
621	C₄×C₆₇	—	2	1	no	—
622	C₄×C₆₇	—	2	1	no	—
623	C₄×C₆₇	—	2	1	no	—
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	—	4	1	no	—
630	C₄×C₆₇	—	4	1	no	—
631	C₄×C₆₇	—	4	2	no	—
632	C₄×C₆₇	—	4	2	no	—
633	C₄×C₆₇	—	4	2	no	—
634	C₄×C₆₇	—	4	1	no	—
635	C₄×C₆₇	—	4	1	no	—
636	C₄×C₆₇	—	4	1	no	—
637	C₄×C₆₇	#585	1	2	yes	—
638	#60976	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
639	C₂×C₆₇	—	2	2	no	—
640	C₂×C₆₇	—	4	1	no	—
641	C₂×C₆₇	—	4	1	no	—
642	C₂×C₆₇	—	8	1	no	—
643	C₂×C₆₇	—	8	2	no	—
644	C₂×C₆₇	—	8	1	no	—
645	C₂×C₆₇	—	8	1	no	—
646	C₂×C₆₇	#3449	1	1	yes	characteristic
647	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
648	C₂×C₆₇	#3586	1	1	yes	characteristic
649	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
650	C₂×#542	C₂×C₆₇	1	1	yes	characteristic, complemented
651	#3262	C₂×C₆₇	1	2	yes	complemented
652	#3257	C₂×C₆₇	1	2	yes	complemented
653	#3243	C₂×C₆₇	1	2	yes	complemented
654	#3238	C₂×C₆₇	1	1	yes	characteristic, complemented
655	#3226	C₂×C₆₇	1	1	yes	characteristic, complemented
656	#3224	C₂×C₆₇	1	2	yes	complemented
657	#3213	C₂×C₆₇	1	1	yes	characteristic, complemented
658	#3211	C₂×C₆₇	1	1	yes	characteristic, complemented
659	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
660	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
661	#3190	C₂×C₆₇	1	1	yes	characteristic, complemented
662	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
663	#3179	C₂×C₆₇	1	2	yes	complemented
664	#3175	C₂×C₆₇	1	2	yes	complemented
665	#3124	C₂×C₆₇	1	2	yes	complemented
666	#3118	C₂×C₆₇	1	2	yes	complemented
667	#3114	C₂×C₆₇	1	1	yes	characteristic, complemented
668	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
669	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
670	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
671	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
672	C₆₇	#60976	1	1	yes	characteristic, direct product factor, Sylow
673	#555	—	2	1	no	—
674	#553	—	2	1	no	—
675	#553	—	2	1	no	—
676	#551	—	2	1	no	—
677	#551	—	2	1	no	—
678	#547	—	2	1	no	—
679	#546	—	2	1	no	—
680	#546	—	2	1	no	—
681	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	#542	—	2	1	no	—
683	#542	—	2	1	no	—
684	#542	—	2	1	no	—
685	#542	—	2	1	no	—
686	#542	C₂²×C₆₇	1	2	yes	—
687	#542	C₂²×C₆₇	1	2	yes	—
688	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#542	C₂²×C₆₇	1	2	yes	complemented
690	#542	C₂²×C₆₇	1	2	yes	complemented
691	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#540	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#540	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	#532	C₂²×C₆₇	1	1	yes	characteristic
696	#532	C₂²×C₆₇	1	1	yes	characteristic
697	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#529	C₂²×C₆₇	1	1	yes	characteristic
699	#529	C₂²×C₆₇	1	1	yes	characteristic
700	C₂×#126	—	2	1	no	—
701	C₂×#124	—	2	1	no	—
702	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#525	C₂²×C₆₇	1	1	yes	characteristic
704	C₂×#123	—	2	1	no	—
705	C₂×C₂²⋊Q₈	—	2	1	no	—
706	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
708	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
709	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
714	#501	C₂²×C₆₇	1	2	yes	complemented
715	#500	C₂²×C₆₇	1	2	yes	complemented
716	#496	C₂²×C₆₇	1	2	yes	complemented
717	#495	C₂²×C₆₇	1	2	yes	complemented
718	#489	C₂²×C₆₇	1	2	yes	complemented
719	#489	C₂²×C₆₇	1	2	yes	complemented
720	#488	C₂²×C₆₇	1	2	yes	complemented
721	#486	C₂²×C₆₇	1	2	yes	complemented
722	#485	C₂²×C₆₇	1	2	yes	complemented
723	#484	C₂²×C₆₇	1	2	yes	complemented
724	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	#482	C₂²×C₆₇	1	2	yes	—
727	#480	C₂²×C₆₇	1	1	yes	characteristic
728	#480	C₂²×C₆₇	1	1	yes	characteristic
729	#480	C₂²×C₆₇	1	1	yes	characteristic
730	#480	C₂²×C₆₇	1	1	yes	characteristic
731	#480	C₂²×C₆₇	1	2	yes	—
732	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
734	#479	C₂²×C₆₇	1	2	yes	complemented
735	#478	C₂²×C₆₇	1	2	yes	complemented
736	#477	C₂²×C₆₇	1	2	yes	complemented
737	#477	C₂²×C₆₇	1	2	yes	complemented
738	#476	C₂²×C₆₇	1	2	yes	complemented
739	#474	C₂²×C₆₇	1	2	yes	complemented
740	#474	C₂²×C₆₇	1	2	yes	complemented
741	#474	C₂²×C₆₇	1	2	yes	complemented
742	#469	C₂²×C₆₇	1	2	yes	complemented
743	#468	C₂²×C₆₇	1	2	yes	complemented
744	#468	C₂²×C₆₇	1	2	yes	complemented
745	#468	C₂²×C₆₇	1	2	yes	complemented
746	#467	C₂²×C₆₇	1	2	yes	complemented
747	#466	C₂²×C₆₇	1	2	yes	—
748	#466	C₂²×C₆₇	1	2	yes	—
749	#465	C₂²×C₆₇	1	2	yes	complemented
750	#464	C₂²×C₆₇	1	2	yes	complemented
751	#464	C₂²×C₆₇	1	2	yes	complemented
752	#463	C₂²×C₆₇	1	2	yes	complemented
753	#463	C₂²×C₆₇	1	2	yes	complemented
754	#463	C₂²×C₆₇	1	2	yes	complemented
755	#463	C₂²×C₆₇	1	2	yes	complemented
756	#460	C₂²×C₆₇	1	2	yes	complemented
757	#459	C₂²×C₆₇	1	2	yes	complemented
758	#452	C₂²×C₆₇	1	2	yes	complemented
759	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
761	#450	C₂²×C₆₇	1	2	yes	complemented
762	#449	C₂²×C₆₇	1	2	yes	—
763	#448	C₂²×C₆₇	1	1	yes	characteristic
764	#448	C₂²×C₆₇	1	1	yes	characteristic
765	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	#447	C₂²×C₆₇	1	1	yes	characteristic
767	#447	C₂²×C₆₇	1	1	yes	characteristic
768	#447	C₂²×C₆₇	1	2	yes	—
769	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
770	#442	C₂²×C₆₇	1	2	yes	complemented
771	#440	C₂²×C₆₇	1	2	yes	complemented
772	#440	C₂²×C₆₇	1	2	yes	complemented
773	#440	C₂²×C₆₇	1	2	yes	complemented
774	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
775	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
776	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
777	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
778	#433	C₂²×C₆₇	1	2	yes	complemented
779	#433	C₂²×C₆₇	1	2	yes	complemented
780	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
781	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#424	C₂²×C₆₇	1	2	yes	complemented
785	#407	C₂²×C₆₇	1	1	yes	characteristic
786	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
787	#405	C₂²×C₆₇	1	2	yes	complemented
788	C₂×#41	—	2	1	no	—
789	C₂×#41	—	2	1	no	—
790	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
791	C₂²×Q₈	—	2	1	no	—
792	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
793	C₂²×D₄	—	2	1	no	—
794	C₂²×D₄	—	2	1	no	—
795	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
796	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
797	C₂³×C₄	—	2	1	no	—
798	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
800	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
802	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
803	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
804	C₂×D₈	C₂³×C₆₇	1	2	yes	—
805	C₂×D₈	C₂³×C₆₇	1	2	yes	—
806	C₂×D₈	C₂³×C₆₇	1	2	yes	—
807	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
808	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
809	C₄⋊Q₈	—	2	1	no	—
810	C₄⋊Q₈	—	2	1	no	—
811	C₄⋊Q₈	—	2	1	no	—
812	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
813	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
814	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
815	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
816	#127	C₂³×C₆₇	1	1	yes	characteristic
817	#127	C₂³×C₆₇	1	1	yes	characteristic
818	#126	—	2	2	no	—
819	#126	—	2	2	no	—
820	#126	—	2	2	no	—
821	#126	—	2	2	no	—
822	#126	—	2	1	no	—
823	#126	—	2	1	no	—
824	#126	—	2	1	no	—
825	#126	—	2	1	no	—
826	#125	—	2	1	no	—
827	#125	C₂³×C₆₇	1	1	yes	characteristic
828	#125	C₂³×C₆₇	1	1	yes	characteristic
829	#124	—	2	2	no	—
830	#124	—	2	2	no	—
831	#124	—	2	2	no	—
832	#124	—	2	2	no	—
833	#124	—	2	1	no	—
834	#124	—	2	1	no	—
835	#124	—	2	1	no	—
836	#124	—	2	1	no	—
837	#124	—	2	1	no	—
838	#124	—	2	1	no	—
839	#124	C₂³×C₆₇	1	2	yes	—
840	#124	C₂³×C₆₇	1	2	yes	—
841	#124	C₂³×C₆₇	1	1	yes	characteristic
842	#124	C₂³×C₆₇	1	1	yes	characteristic
843	#123	—	2	1	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	#123	—	2	1	no	—
849	#123	—	2	1	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	#123	—	2	2	no	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	2	no	—
859	C₂²⋊Q₈	—	2	2	no	—
860	C₂²⋊Q₈	—	2	2	no	—
861	C₂²⋊Q₈	—	2	2	no	—
862	C₂²⋊Q₈	—	2	1	no	—
863	C₂²⋊Q₈	—	2	1	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
867	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
868	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
869	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
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	C₂³×C₆₇	1	1	yes	characteristic
883	#121	C₂³×C₆₇	1	1	yes	characteristic
884	#121	C₂³×C₆₇	1	1	yes	characteristic
885	#121	C₂³×C₆₇	1	1	yes	characteristic
886	#121	C₂³×C₆₇	1	2	yes	—
887	#121	C₂³×C₆₇	1	2	yes	—
888	#121	C₂³×C₆₇	1	1	yes	characteristic
889	#121	C₂³×C₆₇	1	1	yes	characteristic
890	#120	—	2	1	no	—
891	#120	—	2	1	no	—
892	#120	—	2	1	no	—
893	C₄×Q₈	—	2	1	no	—
894	C₄×Q₈	—	2	1	no	—
895	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
896	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
897	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
898	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	1	no	—
907	C₄×D₄	—	2	1	no	—
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	C₂³×C₆₇	1	2	yes	—
912	C₄×D₄	C₂³×C₆₇	1	2	yes	—
913	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
918	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
919	#117	—	2	1	no	—
920	#117	—	2	1	no	—
921	#117	—	2	1	no	—
922	#117	D₄×C₆₇	1	1	yes	characteristic
923	#117	D₄×C₆₇	1	1	yes	characteristic
924	#117	D₄×C₆₇	1	1	yes	characteristic
925	#117	D₄×C₆₇	1	1	yes	characteristic
926	#117	C₂³×C₆₇	1	1	yes	characteristic
927	#117	C₂³×C₆₇	1	1	yes	characteristic
928	#117	C₂³×C₆₇	1	1	yes	characteristic
929	#117	C₂³×C₆₇	1	1	yes	characteristic
930	#117	C₂³×C₆₇	1	1	yes	characteristic
931	C₂×C₄⋊C₄	—	2	1	no	—
932	C₂×C₄⋊C₄	—	2	1	no	—
933	C₂×C₄⋊C₄	—	2	1	no	—
934	C₂×C₄⋊C₄	—	2	1	no	—
935	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
936	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
937	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	—	2	1	no	—
941	C₂×C₂²⋊C₄	—	2	1	no	—
942	C₂×C₂²⋊C₄	—	2	1	no	—
943	C₂×C₂²⋊C₄	—	2	1	no	—
944	C₂×C₂²⋊C₄	—	2	1	no	—
945	C₂×C₂²⋊C₄	—	2	1	no	—
946	C₂×C₂²⋊C₄	—	2	1	no	—
947	C₂×C₂²⋊C₄	—	2	1	no	—
948	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
949	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
950	C₂×C₄²	—	2	1	no	—
951	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
952	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
953	#107	C₂³×C₆₇	1	2	yes	—
954	#107	C₂³×C₆₇	1	2	yes	—
955	#107	C₂³×C₆₇	1	2	yes	—
956	#107	C₂³×C₆₇	1	2	yes	—
957	#107	C₂³×C₆₇	1	2	yes	—
958	#107	C₂³×C₆₇	1	2	yes	—
959	#106	C₂³×C₆₇	1	2	yes	—
960	#106	C₂³×C₆₇	1	2	yes	—
961	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
962	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
963	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
964	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
965	#103	C₂³×C₆₇	1	2	yes	—
966	#103	C₂³×C₆₇	1	2	yes	—
967	#103	C₂³×C₆₇	1	2	yes	—
968	#103	C₂³×C₆₇	1	2	yes	—
969	#103	C₂³×C₆₇	1	2	yes	—
970	#103	C₂³×C₆₇	1	2	yes	—
971	#102	C₂³×C₆₇	1	2	yes	—
972	#102	C₂³×C₆₇	1	2	yes	—
973	#102	C₂³×C₆₇	1	2	yes	—
974	#102	C₂³×C₆₇	1	2	yes	—
975	#102	C₂³×C₆₇	1	2	yes	—
976	#102	C₂³×C₆₇	1	2	yes	—
977	#102	C₂³×C₆₇	1	2	yes	—
978	#102	C₂³×C₆₇	1	2	yes	—
979	#102	C₂³×C₆₇	1	2	yes	—
980	#102	C₂³×C₆₇	1	2	yes	—
981	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
982	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
983	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
984	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
985	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
986	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
987	#97	C₂³×C₆₇	1	2	yes	—
988	#97	C₂³×C₆₇	1	2	yes	—
989	C₄×C₈	C₂³×C₆₇	1	2	yes	—
990	C₄×C₈	C₂³×C₆₇	1	2	yes	—
991	C₂⁴	—	2	1	no	—
992	C₂⁴	—	2	1	no	—
993	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
994	#41	—	4	2	no	—
995	#41	—	8	2	no	—
996	#41	—	8	2	no	—
997	C₂×Q₈	—	2	1	no	—
998	C₂×Q₈	—	2	2	no	—
999	C₂×Q₈	—	2	2	no	—
1000	C₂×Q₈	—	2	1	no	—
1001	C₂×Q₈	—	2	1	no	—
1002	C₂×Q₈	—	4	2	no	—
1003	C₂×Q₈	—	8	2	no	—
1004	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1005	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	1	no	—
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	—	4	2	no	—
1022	C₂×D₄	—	4	2	no	—
1023	C₂×D₄	—	8	2	no	—
1024	C₂×D₄	—	8	2	no	—
1025	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1026	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1027	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1028	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	1	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	4	2	no	—
1043	C₂²×C₄	—	8	2	no	—
1044	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1047	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1048	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1050	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1054	Q₁₆	—	4	2	no	—
1055	SD₁₆	—	4	2	no	—
1056	SD₁₆	—	4	2	no	—
1057	SD₁₆	—	4	2	no	—
1058	SD₁₆	—	4	2	no	—
1059	D₈	—	4	2	no	—
1060	D₈	—	4	2	no	—
1061	D₈	—	4	2	no	—
1062	M₁₆	—	4	2	no	—
1063	C₂×C₈	—	4	2	no	—
1064	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1065	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1066	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1067	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1088	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1089	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1090	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1091	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1092	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1094	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1095	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1096	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1097	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	1	no	—
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	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1132	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1133	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1134	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1135	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1136	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1137	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1138	C₄²	—	2	2	no	—
1139	C₄²	—	2	2	no	—
1140	C₄²	—	2	1	no	—
1141	C₄²	—	2	1	no	—
1142	C₄²	—	2	1	no	—
1143	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1144	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1145	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1146	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1147	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1148	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1149	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1150	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	2	no	—
1153	C₂³	—	2	1	no	—
1154	C₂³	—	2	1	no	—
1155	C₂³	—	2	1	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	1	no	—
1158	C₂³	—	4	2	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	—	4	2	no	—
1162	C₂³	—	8	1	no	—
1163	C₂³	—	8	1	no	—
1164	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1165	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1166	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1167	Q₈	—	2	2	no	—
1168	Q₈	—	2	2	no	—
1169	Q₈	—	2	2	no	—
1170	Q₈	—	4	2	no	—
1171	Q₈	—	8	2	no	—
1172	Q₈	—	8	2	no	—
1173	Q₈	—	8	1	no	—
1174	Q₈	—	8	1	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	8	1	no	—
1187	D₄	—	8	1	no	—
1188	D₄	—	8	1	no	—
1189	D₄	—	8	1	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	1	no	—
1193	D₄	—	8	1	no	—
1194	D₄	—	8	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	4	1	no	—
1209	C₂×C₄	—	4	1	no	—
1210	C₂×C₄	—	4	1	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	1	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	8	2	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	1	no	—
1220	C₂×C₄	—	8	1	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	—	8	1	no	—
1224	C₂×C₄	—	8	1	no	—
1225	C₂×C₄	—	8	1	no	—
1226	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1228	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1232	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1233	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1234	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1235	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1236	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1237	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1238	C₈	—	2	2	no	—
1239	C₈	—	2	2	no	—
1240	C₈	—	2	2	no	—
1241	C₈	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	4	1	no	—
1261	C₂²	—	4	1	no	—
1262	C₂²	—	8	2	no	—
1263	C₂²	—	8	4	no	—
1264	C₂²	—	16	2	no	—
1265	C₂²	#576×C₆₇	1	2	yes	—
1266	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	2	1	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	2	1	no	—
1276	C₄	—	2	1	no	—
1277	C₄	—	2	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	—	4	1	no	—
1284	C₄	—	4	1	no	—
1285	C₄	—	4	2	no	—
1286	C₄	#585×C₆₇	1	2	yes	—
1287	C₂	—	2	2	no	—
1288	C₂	—	4	1	no	—
1289	C₂	—	4	1	no	—
1290	C₂	—	8	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	—	8	1	no	—
1293	C₂	—	8	1	no	—
1294	C₂	C₆₇×#3449	1	1	yes	characteristic
1295	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1296	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 ◁ 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×#542×C₆₇	C₂	semidirect
3. C₆₇×#3262	C₂	semidirect
4. C₆₇×#3257	C₂	semidirect
5. C₆₇×#3243	C₂	semidirect
6. C₆₇×#3238	C₂	semidirect
7. C₆₇×#3226	C₂	semidirect
8. C₆₇×#3224	C₂	semidirect
9. C₆₇×#3213	C₂	semidirect
10. C₆₇×#3211	C₂	semidirect
11. C₆₇×#3194	C₂	semidirect
12. C₆₇×#3193	C₂	semidirect
13. C₆₇×#3190	C₂	semidirect
14. C₆₇×#3186	C₂	semidirect
15. C₆₇×#3179	C₂	semidirect
16. C₆₇×#3175	C₂	semidirect
17. C₆₇×#3124	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#3114	C₂	semidirect
20. C₆₇×#3112	C₂	semidirect
21. C₆₇×#3108	C₂	semidirect
22. C₆₇×#3100	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
32. #544×C₆₇	C₂²	semidirect
39. #542×C₆₇	C₂²	semidirect
40. #542×C₆₇	C₂²	semidirect
41. #542×C₆₇	C₂²	semidirect
42. #542×C₆₇	C₂²	semidirect
43. #540×C₆₇	C₂²	semidirect
44. #540×C₆₇	C₂²	semidirect
45. #535×C₆₇	C₂²	semidirect
48. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
53. C₂×#124×C₆₇	C₂²	semidirect
60. #520×C₆₇	C₂²	semidirect
61. #518×C₆₇	C₂²	semidirect
62. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
63. C₂×C₄×D₄×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #500×C₆₇	C₂²	semidirect
67. #496×C₆₇	C₂²	semidirect
68. #495×C₆₇	C₂²	semidirect
69. #489×C₆₇	C₂²	semidirect
70. #489×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
72. #486×C₆₇	C₂²	semidirect
73. #485×C₆₇	C₂²	semidirect
74. #484×C₆₇	C₂²	semidirect
75. #483×C₆₇	C₂²	semidirect
76. #483×C₆₇	C₂²	semidirect
83. #480×C₆₇	C₂²	semidirect
84. #480×C₆₇	C₂²	semidirect
85. #479×C₆₇	C₂²	semidirect
86. #478×C₆₇	C₂²	semidirect
87. #477×C₆₇	C₂²	semidirect
88. #477×C₆₇	C₂²	semidirect
89. #476×C₆₇	C₂²	semidirect
90. #474×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #474×C₆₇	C₂²	semidirect
93. #469×C₆₇	C₂²	semidirect
94. #468×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #467×C₆₇	C₂²	semidirect
100. #465×C₆₇	C₂²	semidirect
101. #464×C₆₇	C₂²	semidirect
102. #464×C₆₇	C₂²	semidirect
103. #463×C₆₇	C₂²	semidirect
104. #463×C₆₇	C₂²	semidirect
105. #463×C₆₇	C₂²	semidirect
106. #463×C₆₇	C₂²	semidirect
107. #460×C₆₇	C₂²	semidirect
108. #459×C₆₇	C₂²	semidirect
109. #452×C₆₇	C₂²	semidirect
110. #451×C₆₇	C₂²	semidirect
111. #450×C₆₇	C₂²	semidirect
112. #450×C₆₇	C₂²	semidirect
116. #448×C₆₇	C₂²	semidirect
120. #447×C₆₇	C₂²	semidirect
121. #442×C₆₇	C₂²	semidirect
122. #440×C₆₇	C₂²	semidirect
123. #440×C₆₇	C₂²	semidirect
124. #440×C₆₇	C₂²	semidirect
125. C₄×Q₁₆×C₆₇	C₂²	semidirect
126. C₄×SD₁₆×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
638. #60976	C₆₇	direct (N × H)
649. #3494	C₂×C₆₇	semidirect
650. C₂×#542	C₂×C₆₇	semidirect
651. #3262	C₂×C₆₇	semidirect
652. #3257	C₂×C₆₇	semidirect
653. #3243	C₂×C₆₇	semidirect
654. #3238	C₂×C₆₇	semidirect
655. #3226	C₂×C₆₇	semidirect
656. #3224	C₂×C₆₇	semidirect
657. #3213	C₂×C₆₇	semidirect
658. #3211	C₂×C₆₇	semidirect
659. #3194	C₂×C₆₇	semidirect
660. #3193	C₂×C₆₇	semidirect
661. #3190	C₂×C₆₇	semidirect
662. #3186	C₂×C₆₇	semidirect
663. #3179	C₂×C₆₇	semidirect
664. #3175	C₂×C₆₇	semidirect
665. #3124	C₂×C₆₇	semidirect
666. #3118	C₂×C₆₇	semidirect
667. #3114	C₂×C₆₇	semidirect
668. #3112	C₂×C₆₇	semidirect
669. #3108	C₂×C₆₇	semidirect
670. #3100	C₂×C₆₇	semidirect
671. #2924	C₂×C₆₇	semidirect
672. C₆₇	#60976	direct (N × H)
681. #544	C₂²×C₆₇	semidirect
688. #542	C₂²×C₆₇	semidirect
689. #542	C₂²×C₆₇	semidirect
690. #542	C₂²×C₆₇	semidirect
691. #542	C₂²×C₆₇	semidirect
692. #540	C₂²×C₆₇	semidirect
693. #540	C₂²×C₆₇	semidirect
694. #535	C₂²×C₆₇	semidirect
697. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
702. C₂×#124	C₂²×C₆₇	semidirect
709. #520	C₂²×C₆₇	semidirect
710. #518	C₂²×C₆₇	semidirect
711. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
712. C₂×C₄×D₄	C₂²×C₆₇	semidirect
714. #501	C₂²×C₆₇	semidirect
715. #500	C₂²×C₆₇	semidirect
716. #496	C₂²×C₆₇	semidirect
717. #495	C₂²×C₆₇	semidirect
718. #489	C₂²×C₆₇	semidirect
719. #489	C₂²×C₆₇	semidirect
720. #488	C₂²×C₆₇	semidirect
721. #486	C₂²×C₆₇	semidirect
722. #485	C₂²×C₆₇	semidirect
723. #484	C₂²×C₆₇	semidirect
724. #483	C₂²×C₆₇	semidirect
725. #483	C₂²×C₆₇	semidirect
732. #480	C₂²×C₆₇	semidirect
733. #480	C₂²×C₆₇	semidirect
734. #479	C₂²×C₆₇	semidirect
735. #478	C₂²×C₆₇	semidirect
736. #477	C₂²×C₆₇	semidirect
737. #477	C₂²×C₆₇	semidirect
738. #476	C₂²×C₆₇	semidirect
739. #474	C₂²×C₆₇	semidirect
740. #474	C₂²×C₆₇	semidirect
741. #474	C₂²×C₆₇	semidirect
742. #469	C₂²×C₆₇	semidirect
743. #468	C₂²×C₆₇	semidirect
744. #468	C₂²×C₆₇	semidirect
745. #468	C₂²×C₆₇	semidirect
746. #467	C₂²×C₆₇	semidirect
749. #465	C₂²×C₆₇	semidirect
750. #464	C₂²×C₆₇	semidirect
751. #464	C₂²×C₆₇	semidirect
752. #463	C₂²×C₆₇	semidirect
753. #463	C₂²×C₆₇	semidirect
754. #463	C₂²×C₆₇	semidirect
755. #463	C₂²×C₆₇	semidirect
756. #460	C₂²×C₆₇	semidirect
757. #459	C₂²×C₆₇	semidirect
758. #452	C₂²×C₆₇	semidirect
759. #451	C₂²×C₆₇	semidirect
760. #450	C₂²×C₆₇	semidirect
761. #450	C₂²×C₆₇	semidirect
765. #448	C₂²×C₆₇	semidirect
769. #447	C₂²×C₆₇	semidirect
770. #442	C₂²×C₆₇	semidirect
771. #440	C₂²×C₆₇	semidirect
772. #440	C₂²×C₆₇	semidirect
773. #440	C₂²×C₆₇	semidirect
774. C₄×Q₁₆	C₂²×C₆₇	semidirect
775. C₄×SD₁₆	C₂²×C₆₇	semidirect
776. C₄×D₈	C₂²×C₆₇	semidirect
777. C₄×D₈	C₂²×C₆₇	semidirect
778. #433	C₂²×C₆₇	semidirect
779. #433	C₂²×C₆₇	semidirect
780. #432	C₂²×C₆₇	semidirect
781. #432	C₂²×C₆₇	semidirect
782. #431	C₂²×C₆₇	semidirect
783. #431	C₂²×C₆₇	semidirect
784. #424	C₂²×C₆₇	semidirect
787. #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×#542×C₆₇	2
C₆₇×#3262	2
C₆₇×#3257	2
C₆₇×#3243	2
C₆₇×#3238	2
C₆₇×#3226	2
C₆₇×#3224	2
C₆₇×#3213	2
C₆₇×#3211	2
C₆₇×#3194	2
C₆₇×#3193	2
C₆₇×#3190	2
C₆₇×#3186	2
C₆₇×#3179	2
C₆₇×#3175	2
C₆₇×#3124	2
C₆₇×#3118	2
C₆₇×#3114	2
C₆₇×#3112	2
C₆₇×#3108	2
C₆₇×#3100	2
C₆₇×#2924	2
#60976	67

Subgroups — C67×#60976 #30740227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60976 #30740227