Subgroups — C₆₇×#60981 #30740232

Order 17152.

1732 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3262	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3258	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3243	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3225	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3215	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3196	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3188	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#3178	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×#3121	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	—	2	1	no	—
25	#554×C₆₇	—	2	1	no	—
26	#552×C₆₇	—	2	1	no	—
27	#552×C₆₇	—	2	1	no	—
28	#552×C₆₇	—	2	1	no	—
29	#552×C₆₇	—	2	1	no	—
30	#551×C₆₇	—	2	1	no	—
31	#551×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	2	yes	—
40	#542×C₆₇	C₂²	1	2	yes	—
41	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#541×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#541×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#533×C₆₇	C₂²	1	1	yes	characteristic
47	#533×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
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
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×C₂²⋊Q₈×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	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
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	#497×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	#487×C₆₇	C₂²	1	2	yes	complemented
73	#485×C₆₇	C₂²	1	2	yes	complemented
74	#484×C₆₇	C₂²	1	1	yes	characteristic
75	#484×C₆₇	C₂²	1	1	yes	characteristic
76	#484×C₆₇	C₂²	1	1	yes	characteristic
77	#484×C₆₇	C₂²	1	1	yes	characteristic
78	#484×C₆₇	C₂²	1	1	yes	characteristic
79	#484×C₆₇	C₂²	1	1	yes	characteristic
80	#484×C₆₇	C₂²	1	2	yes	complemented
81	#482×C₆₇	C₂²	1	2	yes	—
82	#481×C₆₇	C₂²	1	1	yes	characteristic
83	#481×C₆₇	C₂²	1	1	yes	characteristic
84	#480×C₆₇	C₂²	1	2	yes	—
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	#477×C₆₇	C₂²	1	2	yes	complemented
90	#475×C₆₇	C₂²	1	2	yes	complemented
91	#474×C₆₇	C₂²	1	2	yes	complemented
92	#474×C₆₇	C₂²	1	2	yes	complemented
93	#470×C₆₇	C₂²	1	2	yes	complemented
94	#468×C₆₇	C₂²	1	2	yes	—
95	#468×C₆₇	C₂²	1	2	yes	—
96	#468×C₆₇	C₂²	1	2	yes	complemented
97	#467×C₆₇	C₂²	1	2	yes	complemented
98	#467×C₆₇	C₂²	1	2	yes	complemented
99	#466×C₆₇	C₂²	1	2	yes	—
100	#465×C₆₇	C₂²	1	2	yes	—
101	#464×C₆₇	C₂²	1	2	yes	complemented
102	#464×C₆₇	C₂²	1	2	yes	complemented
103	#464×C₆₇	C₂²	1	2	yes	complemented
104	#464×C₆₇	C₂²	1	2	yes	complemented
105	#463×C₆₇	C₂²	1	2	yes	complemented
106	#463×C₆₇	C₂²	1	2	yes	complemented
107	#462×C₆₇	C₂²	1	2	yes	complemented
108	#461×C₆₇	C₂²	1	2	yes	complemented
109	#452×C₆₇	C₂²	1	2	yes	complemented
110	#451×C₆₇	C₂²	1	1	yes	characteristic
111	#451×C₆₇	C₂²	1	1	yes	characteristic
112	#451×C₆₇	C₂²	1	1	yes	characteristic
113	#451×C₆₇	C₂²	1	2	yes	complemented
114	#450×C₆₇	C₂²	1	1	yes	characteristic
115	#450×C₆₇	C₂²	1	1	yes	characteristic
116	#450×C₆₇	C₂²	1	1	yes	characteristic
117	#449×C₆₇	C₂²	1	2	yes	—
118	#448×C₆₇	C₂²	1	1	yes	characteristic
119	#448×C₆₇	C₂²	1	2	yes	—
120	#447×C₆₇	C₂²	1	1	yes	characteristic
121	#441×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×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×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
132	#432×C₆₇	C₂²	1	1	yes	characteristic
133	#431×C₆₇	C₂²	1	1	yes	characteristic
134	#431×C₆₇	C₂²	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₆₇	—	2	1	no	—
141	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	—	2	1	no	—
144	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₇	—	2	1	no	—
146	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
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×M₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	1	no	—
171	#126×C₆₇	—	2	1	no	—
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	#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	—	2	1	no	—
182	#125×C₆₇	—	2	1	no	—
183	#125×C₆₇	—	2	1	no	—
184	#125×C₆₇	—	2	1	no	—
185	#125×C₆₇	C₂³	1	1	yes	characteristic
186	#125×C₆₇	C₂³	1	1	yes	characteristic
187	#124×C₆₇	—	2	2	no	—
188	#124×C₆₇	—	2	2	no	—
189	#124×C₆₇	—	2	2	no	—
190	#124×C₆₇	—	2	2	no	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	—	2	1	no	—
193	#124×C₆₇	—	2	1	no	—
194	#124×C₆₇	—	2	1	no	—
195	#124×C₆₇	C₂³	1	1	yes	characteristic
196	#124×C₆₇	C₂³	1	2	yes	—
197	#124×C₆₇	C₂³	1	2	yes	—
198	#124×C₆₇	C₂³	1	1	yes	characteristic
199	#123×C₆₇	—	2	1	no	—
200	#123×C₆₇	—	2	1	no	—
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	—	2	2	no	—
205	#123×C₆₇	—	2	2	no	—
206	#123×C₆₇	—	2	1	no	—
207	#123×C₆₇	—	2	1	no	—
208	#123×C₆₇	—	2	1	no	—
209	#123×C₆₇	—	2	1	no	—
210	C₂²⋊Q₈×C₆₇	—	2	1	no	—
211	C₂²⋊Q₈×C₆₇	—	2	1	no	—
212	C₂²⋊Q₈×C₆₇	—	2	1	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	2	no	—
217	C₂²⋊Q₈×C₆₇	—	2	2	no	—
218	C₂²⋊Q₈×C₆₇	—	2	2	no	—
219	C₂²⋊Q₈×C₆₇	—	2	2	no	—
220	C₂²⋊Q₈×C₆₇	—	2	1	no	—
221	C₂²⋊Q₈×C₆₇	—	2	1	no	—
222	C₂²⋊Q₈×C₆₇	—	2	1	no	—
223	C₂²⋊Q₈×C₆₇	—	2	1	no	—
224	C₂²⋊Q₈×C₆₇	—	2	1	no	—
225	C₂²⋊Q₈×C₆₇	—	2	1	no	—
226	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
230	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
234	#121×C₆₇	—	2	1	no	—
235	#121×C₆₇	—	2	1	no	—
236	#121×C₆₇	C₂³	1	2	yes	—
237	#121×C₆₇	C₂³	1	1	yes	characteristic
238	#121×C₆₇	C₂³	1	2	yes	—
239	#121×C₆₇	C₂³	1	1	yes	characteristic
240	#120×C₆₇	—	2	1	no	—
241	C₄×Q₈×C₆₇	—	2	1	no	—
242	C₄×Q₈×C₆₇	—	2	1	no	—
243	C₄×Q₈×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	—	2	1	no	—
245	C₄×Q₈×C₆₇	—	2	1	no	—
246	C₄×Q₈×C₆₇	—	2	1	no	—
247	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
248	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
252	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
264	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₆₇	C₂³	1	2	yes	—
266	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	—	2	1	no	—
268	#117×C₆₇	—	2	1	no	—
269	#117×C₆₇	—	2	1	no	—
270	#117×C₆₇	—	2	1	no	—
271	#117×C₆₇	—	2	1	no	—
272	#117×C₆₇	—	2	1	no	—
273	#117×C₆₇	—	2	1	no	—
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	D₄	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	#117×C₆₇	C₂³	1	1	yes	characteristic
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	—	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	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	#103×C₆₇	C₂³	1	2	yes	—
323	#103×C₆₇	C₂³	1	2	yes	—
324	#103×C₆₇	C₂³	1	2	yes	—
325	#103×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	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
344	#41×C₆₇	—	4	2	no	—
345	C₂×Q₈×C₆₇	—	2	1	no	—
346	C₂×Q₈×C₆₇	—	2	1	no	—
347	C₂×Q₈×C₆₇	—	2	1	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	—	4	2	no	—
352	C₂×Q₈×C₆₇	—	4	2	no	—
353	C₂×Q₈×C₆₇	—	8	2	no	—
354	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	2	no	—
362	C₂×D₄×C₆₇	—	2	2	no	—
363	C₂×D₄×C₆₇	—	2	1	no	—
364	C₂×D₄×C₆₇	—	4	2	no	—
365	C₂×D₄×C₆₇	—	8	2	no	—
366	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₆₇	—	2	1	no	—
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	1	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	1	no	—
374	C₂²×C₄×C₆₇	—	2	1	no	—
375	C₂²×C₄×C₆₇	—	2	1	no	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	4	2	no	—
379	C₂²×C₄×C₆₇	—	8	2	no	—
380	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
390	Q₁₆×C₆₇	—	4	2	no	—
391	Q₁₆×C₆₇	—	4	2	no	—
392	Q₁₆×C₆₇	—	4	2	no	—
393	SD₁₆×C₆₇	—	4	2	no	—
394	SD₁₆×C₆₇	—	4	2	no	—
395	SD₁₆×C₆₇	—	4	2	no	—
396	SD₁₆×C₆₇	—	4	2	no	—
397	D₈×C₆₇	—	4	2	no	—
398	M₁₆×C₆₇	—	4	2	no	—
399	C₂×C₈×C₆₇	—	4	2	no	—
400	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
401	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
402	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
403	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	1	no	—
408	C₄⋊C₄×C₆₇	—	2	1	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	1	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
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	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
449	C₂²⋊C₄×C₆₇	—	2	1	no	—
450	C₂²⋊C₄×C₆₇	—	2	1	no	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	2	no	—
461	C₂²⋊C₄×C₆₇	—	2	2	no	—
462	C₂²⋊C₄×C₆₇	—	2	2	no	—
463	C₂²⋊C₄×C₆₇	—	2	2	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	no	—
465	C₂²⋊C₄×C₆₇	—	2	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₆₇	—	2	2	no	—
483	C₄²×C₆₇	—	2	2	no	—
484	C₄²×C₆₇	—	2	1	no	—
485	C₄²×C₆₇	—	2	1	no	—
486	C₄²×C₆₇	—	2	1	no	—
487	C₄²×C₆₇	—	2	1	no	—
488	C₄²×C₆₇	—	2	1	no	—
489	C₄²×C₆₇	—	2	1	no	—
490	C₄²×C₆₇	—	2	1	no	—
491	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂³×C₆₇	—	2	2	no	—
500	C₂³×C₆₇	—	2	1	no	—
501	C₂³×C₆₇	—	2	2	no	—
502	C₂³×C₆₇	—	4	1	no	—
503	C₂³×C₆₇	—	4	1	no	—
504	C₂³×C₆₇	—	4	2	no	—
505	C₂³×C₆₇	—	4	2	no	—
506	C₂³×C₆₇	—	4	2	no	—
507	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
508	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
510	Q₈×C₆₇	—	2	2	no	—
511	Q₈×C₆₇	—	2	2	no	—
512	Q₈×C₆₇	—	2	2	no	—
513	Q₈×C₆₇	—	2	2	no	—
514	Q₈×C₆₇	—	2	2	no	—
515	Q₈×C₆₇	—	4	2	no	—
516	Q₈×C₆₇	—	4	2	no	—
517	Q₈×C₆₇	—	8	1	no	—
518	Q₈×C₆₇	—	8	1	no	—
519	Q₈×C₆₇	—	8	2	no	—
520	Q₈×C₆₇	—	8	2	no	—
521	D₄×C₆₇	—	2	2	no	—
522	D₄×C₆₇	—	2	2	no	—
523	D₄×C₆₇	—	2	2	no	—
524	D₄×C₆₇	—	4	2	no	—
525	D₄×C₆₇	—	4	2	no	—
526	D₄×C₆₇	—	4	2	no	—
527	D₄×C₆₇	—	8	1	no	—
528	D₄×C₆₇	—	8	2	no	—
529	D₄×C₆₇	—	8	2	no	—
530	C₂×C₄×C₆₇	—	2	2	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	2	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	4	1	no	—
546	C₂×C₄×C₆₇	—	4	1	no	—
547	C₂×C₄×C₆₇	—	4	1	no	—
548	C₂×C₄×C₆₇	—	4	1	no	—
549	C₂×C₄×C₆₇	—	4	1	no	—
550	C₂×C₄×C₆₇	—	4	2	no	—
551	C₂×C₄×C₆₇	—	4	2	no	—
552	C₂×C₄×C₆₇	—	4	2	no	—
553	C₂×C₄×C₆₇	—	4	2	no	—
554	C₂×C₄×C₆₇	—	4	2	no	—
555	C₂×C₄×C₆₇	—	8	1	no	—
556	C₂×C₄×C₆₇	—	8	1	no	—
557	C₂×C₄×C₆₇	—	8	2	no	—
558	C₂×C₄×C₆₇	—	8	2	no	—
559	C₂×C₄×C₆₇	—	8	1	no	—
560	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
572	C₈×C₆₇	—	2	2	no	—
573	C₈×C₆₇	—	2	2	no	—
574	C₈×C₆₇	—	2	2	no	—
575	C₈×C₆₇	—	2	2	no	—
576	C₂²×C₆₇	—	2	1	no	—
577	C₂²×C₆₇	—	2	1	no	—
578	C₂²×C₆₇	—	2	1	no	—
579	C₂²×C₆₇	—	2	1	no	—
580	C₂²×C₆₇	—	2	1	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	2	1	no	—
583	C₂²×C₆₇	—	2	1	no	—
584	C₂²×C₆₇	—	4	2	no	—
585	C₂²×C₆₇	—	4	1	no	—
586	C₂²×C₆₇	—	4	1	no	—
587	C₂²×C₆₇	—	4	2	no	—
588	C₂²×C₆₇	—	4	1	no	—
589	C₂²×C₆₇	—	4	2	no	—
590	C₂²×C₆₇	—	8	2	no	—
591	C₂²×C₆₇	—	8	4	no	—
592	C₂²×C₆₇	#578	1	2	yes	—
593	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
594	C₄×C₆₇	—	2	1	no	—
595	C₄×C₆₇	—	2	1	no	—
596	C₄×C₆₇	—	2	1	no	—
597	C₄×C₆₇	—	2	1	no	—
598	C₄×C₆₇	—	2	1	no	—
599	C₄×C₆₇	—	2	1	no	—
600	C₄×C₆₇	—	2	1	no	—
601	C₄×C₆₇	—	2	1	no	—
602	C₄×C₆₇	—	2	1	no	—
603	C₄×C₆₇	—	2	1	no	—
604	C₄×C₆₇	—	2	1	no	—
605	C₄×C₆₇	—	4	2	no	—
606	C₄×C₆₇	—	4	2	no	—
607	C₄×C₆₇	—	4	1	no	—
608	C₄×C₆₇	—	4	1	no	—
609	C₄×C₆₇	—	4	1	no	—
610	C₄×C₆₇	—	4	1	no	—
611	C₄×C₆₇	—	4	2	no	—
612	C₄×C₆₇	—	4	1	no	—
613	C₄×C₆₇	—	4	1	no	—
614	C₄×C₆₇	—	4	1	no	—
615	C₄×C₆₇	#585	1	2	yes	—
616	#60981	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
617	C₂×C₆₇	—	2	2	no	—
618	C₂×C₆₇	—	4	1	no	—
619	C₂×C₆₇	—	4	1	no	—
620	C₂×C₆₇	—	8	1	no	—
621	C₂×C₆₇	—	8	2	no	—
622	C₂×C₆₇	#3449	1	1	yes	characteristic
623	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
624	C₂×C₆₇	#3585	1	1	yes	characteristic
625	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
626	C₂×#542	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3262	C₂×C₆₇	1	2	yes	complemented
628	#3258	C₂×C₆₇	1	2	yes	complemented
629	#3243	C₂×C₆₇	1	2	yes	complemented
630	#3239	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3230	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#3225	C₂×C₆₇	1	2	yes	complemented
633	#3215	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#3211	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#3196	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
637	#3189	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#3188	C₂×C₆₇	1	1	yes	characteristic
639	#3178	C₂×C₆₇	1	2	yes	complemented
640	#3175	C₂×C₆₇	1	2	yes	complemented
641	#3124	C₂×C₆₇	1	2	yes	complemented
642	#3121	C₂×C₆₇	1	2	yes	complemented
643	#3117	C₂×C₆₇	1	1	yes	characteristic, complemented
644	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#3105	C₂×C₆₇	1	1	yes	characteristic, complemented
646	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
647	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
648	C₆₇	#60981	1	1	yes	characteristic, direct product factor, Sylow
649	#556	—	2	1	no	—
650	#554	—	2	1	no	—
651	#552	—	2	1	no	—
652	#552	—	2	1	no	—
653	#552	—	2	1	no	—
654	#552	—	2	1	no	—
655	#551	—	2	1	no	—
656	#551	—	2	1	no	—
657	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#542	—	2	1	no	—
659	#542	—	2	1	no	—
660	#542	—	2	1	no	—
661	#542	—	2	1	no	—
662	#542	C₂²×C₆₇	1	2	yes	—
663	#542	C₂²×C₆₇	1	2	yes	—
664	#542	C₂²×C₆₇	1	2	yes	—
665	#542	C₂²×C₆₇	1	2	yes	—
666	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
668	#541	C₂²×C₆₇	1	1	yes	characteristic, complemented
669	#541	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
671	#533	C₂²×C₆₇	1	1	yes	characteristic
672	#533	C₂²×C₆₇	1	1	yes	characteristic
673	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
674	#529	C₂²×C₆₇	1	1	yes	characteristic
675	#529	C₂²×C₆₇	1	1	yes	characteristic
676	C₂×#126	—	2	1	no	—
677	C₂×#124	—	2	1	no	—
678	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
679	#525	C₂²×C₆₇	1	1	yes	characteristic
680	C₂×#123	—	2	1	no	—
681	C₂×C₂²⋊Q₈	—	2	1	no	—
682	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
683	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
684	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
685	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
688	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
689	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
690	#501	C₂²×C₆₇	1	2	yes	complemented
691	#500	C₂²×C₆₇	1	2	yes	complemented
692	#497	C₂²×C₆₇	1	2	yes	complemented
693	#495	C₂²×C₆₇	1	2	yes	complemented
694	#489	C₂²×C₆₇	1	2	yes	complemented
695	#489	C₂²×C₆₇	1	2	yes	complemented
696	#488	C₂²×C₆₇	1	2	yes	complemented
697	#487	C₂²×C₆₇	1	2	yes	complemented
698	#485	C₂²×C₆₇	1	2	yes	complemented
699	#484	C₂²×C₆₇	1	1	yes	characteristic
700	#484	C₂²×C₆₇	1	1	yes	characteristic
701	#484	C₂²×C₆₇	1	1	yes	characteristic
702	#484	C₂²×C₆₇	1	1	yes	characteristic
703	#484	C₂²×C₆₇	1	1	yes	characteristic
704	#484	C₂²×C₆₇	1	1	yes	characteristic
705	#484	C₂²×C₆₇	1	2	yes	complemented
706	#482	C₂²×C₆₇	1	2	yes	—
707	#481	C₂²×C₆₇	1	1	yes	characteristic
708	#481	C₂²×C₆₇	1	1	yes	characteristic
709	#480	C₂²×C₆₇	1	2	yes	—
710	#479	C₂²×C₆₇	1	2	yes	complemented
711	#478	C₂²×C₆₇	1	2	yes	complemented
712	#477	C₂²×C₆₇	1	2	yes	complemented
713	#477	C₂²×C₆₇	1	2	yes	complemented
714	#477	C₂²×C₆₇	1	2	yes	complemented
715	#475	C₂²×C₆₇	1	2	yes	complemented
716	#474	C₂²×C₆₇	1	2	yes	complemented
717	#474	C₂²×C₆₇	1	2	yes	complemented
718	#470	C₂²×C₆₇	1	2	yes	complemented
719	#468	C₂²×C₆₇	1	2	yes	—
720	#468	C₂²×C₆₇	1	2	yes	—
721	#468	C₂²×C₆₇	1	2	yes	complemented
722	#467	C₂²×C₆₇	1	2	yes	complemented
723	#467	C₂²×C₆₇	1	2	yes	complemented
724	#466	C₂²×C₆₇	1	2	yes	—
725	#465	C₂²×C₆₇	1	2	yes	—
726	#464	C₂²×C₆₇	1	2	yes	complemented
727	#464	C₂²×C₆₇	1	2	yes	complemented
728	#464	C₂²×C₆₇	1	2	yes	complemented
729	#464	C₂²×C₆₇	1	2	yes	complemented
730	#463	C₂²×C₆₇	1	2	yes	complemented
731	#463	C₂²×C₆₇	1	2	yes	complemented
732	#462	C₂²×C₆₇	1	2	yes	complemented
733	#461	C₂²×C₆₇	1	2	yes	complemented
734	#452	C₂²×C₆₇	1	2	yes	complemented
735	#451	C₂²×C₆₇	1	1	yes	characteristic
736	#451	C₂²×C₆₇	1	1	yes	characteristic
737	#451	C₂²×C₆₇	1	1	yes	characteristic
738	#451	C₂²×C₆₇	1	2	yes	complemented
739	#450	C₂²×C₆₇	1	1	yes	characteristic
740	#450	C₂²×C₆₇	1	1	yes	characteristic
741	#450	C₂²×C₆₇	1	1	yes	characteristic
742	#449	C₂²×C₆₇	1	2	yes	—
743	#448	C₂²×C₆₇	1	1	yes	characteristic
744	#448	C₂²×C₆₇	1	2	yes	—
745	#447	C₂²×C₆₇	1	1	yes	characteristic
746	#441	C₂²×C₆₇	1	2	yes	complemented
747	#440	C₂²×C₆₇	1	2	yes	complemented
748	#440	C₂²×C₆₇	1	2	yes	complemented
749	#440	C₂²×C₆₇	1	2	yes	complemented
750	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
751	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
752	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
753	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
754	#433	C₂²×C₆₇	1	2	yes	complemented
755	#433	C₂²×C₆₇	1	2	yes	complemented
756	#432	C₂²×C₆₇	1	1	yes	characteristic
757	#432	C₂²×C₆₇	1	1	yes	characteristic
758	#431	C₂²×C₆₇	1	1	yes	characteristic
759	#431	C₂²×C₆₇	1	1	yes	characteristic
760	#424	C₂²×C₆₇	1	2	yes	complemented
761	#407	C₂²×C₆₇	1	1	yes	characteristic
762	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
763	#405	C₂²×C₆₇	1	2	yes	complemented
764	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
765	C₂²×Q₈	—	2	1	no	—
766	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
767	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
768	C₂²×D₄	—	2	1	no	—
769	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
770	C₂³×C₄	—	2	1	no	—
771	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
773	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
774	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×D₈	C₂³×C₆₇	1	2	yes	—
780	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
781	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
782	C₄⋊Q₈	—	2	1	no	—
783	C₄⋊Q₈	—	2	1	no	—
784	C₄⋊Q₈	—	2	1	no	—
785	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
786	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
787	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
788	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
789	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
791	#126	—	2	2	no	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	1	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	—	2	1	no	—
810	#125	C₂³×C₆₇	1	1	yes	characteristic
811	#125	C₂³×C₆₇	1	1	yes	characteristic
812	#124	—	2	2	no	—
813	#124	—	2	2	no	—
814	#124	—	2	2	no	—
815	#124	—	2	2	no	—
816	#124	—	2	1	no	—
817	#124	—	2	1	no	—
818	#124	—	2	1	no	—
819	#124	—	2	1	no	—
820	#124	C₂³×C₆₇	1	2	yes	—
821	#124	C₂³×C₆₇	1	2	yes	—
822	#124	C₂³×C₆₇	1	1	yes	characteristic
823	#124	C₂³×C₆₇	1	1	yes	characteristic
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	—	2	2	no	—
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	—	2	2	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	—	2	2	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
852	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
857	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	C₂³×C₆₇	1	2	yes	—
862	#121	C₂³×C₆₇	1	2	yes	—
863	#121	C₂³×C₆₇	1	1	yes	characteristic
864	#121	C₂³×C₆₇	1	1	yes	characteristic
865	#120	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
873	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
874	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	C₂³×C₆₇	1	2	yes	—
889	C₄×D₄	C₂³×C₆₇	1	2	yes	—
890	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
892	#117	—	2	1	no	—
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	—	2	1	no	—
899	#117	D₄×C₆₇	1	1	yes	characteristic
900	#117	D₄×C₆₇	1	1	yes	characteristic
901	#117	D₄×C₆₇	1	1	yes	characteristic
902	#117	D₄×C₆₇	1	1	yes	characteristic
903	#117	C₂³×C₆₇	1	1	yes	characteristic
904	#117	C₂³×C₆₇	1	1	yes	characteristic
905	#117	C₂³×C₆₇	1	1	yes	characteristic
906	#117	C₂³×C₆₇	1	1	yes	characteristic
907	#117	C₂³×C₆₇	1	1	yes	characteristic
908	C₂×C₄⋊C₄	—	2	1	no	—
909	C₂×C₄⋊C₄	—	2	1	no	—
910	C₂×C₄⋊C₄	—	2	1	no	—
911	C₂×C₄⋊C₄	—	2	1	no	—
912	C₂×C₄⋊C₄	—	2	1	no	—
913	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
914	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
918	C₂×C₂²⋊C₄	—	2	1	no	—
919	C₂×C₂²⋊C₄	—	2	1	no	—
920	C₂×C₂²⋊C₄	—	2	1	no	—
921	C₂×C₂²⋊C₄	—	2	1	no	—
922	C₂×C₂²⋊C₄	—	2	1	no	—
923	C₂×C₂²⋊C₄	—	2	1	no	—
924	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
926	C₂×C₄²	—	2	1	no	—
927	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
928	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
929	#107	C₂³×C₆₇	1	2	yes	—
930	#107	C₂³×C₆₇	1	2	yes	—
931	#107	C₂³×C₆₇	1	2	yes	—
932	#107	C₂³×C₆₇	1	2	yes	—
933	#107	C₂³×C₆₇	1	2	yes	—
934	#107	C₂³×C₆₇	1	2	yes	—
935	#106	C₂³×C₆₇	1	2	yes	—
936	#106	C₂³×C₆₇	1	2	yes	—
937	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
938	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
939	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
940	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
941	#103	C₂³×C₆₇	1	2	yes	—
942	#103	C₂³×C₆₇	1	2	yes	—
943	#103	C₂³×C₆₇	1	2	yes	—
944	#103	C₂³×C₆₇	1	2	yes	—
945	#103	C₂³×C₆₇	1	2	yes	—
946	#103	C₂³×C₆₇	1	2	yes	—
947	#103	C₂³×C₆₇	1	2	yes	—
948	#103	C₂³×C₆₇	1	2	yes	—
949	#103	C₂³×C₆₇	1	2	yes	—
950	#103	C₂³×C₆₇	1	2	yes	—
951	#102	C₂³×C₆₇	1	2	yes	—
952	#102	C₂³×C₆₇	1	2	yes	—
953	#102	C₂³×C₆₇	1	2	yes	—
954	#102	C₂³×C₆₇	1	2	yes	—
955	#102	C₂³×C₆₇	1	2	yes	—
956	#102	C₂³×C₆₇	1	2	yes	—
957	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
958	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
959	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
960	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
963	#97	C₂³×C₆₇	1	2	yes	—
964	#97	C₂³×C₆₇	1	2	yes	—
965	C₄×C₈	C₂³×C₆₇	1	2	yes	—
966	C₄×C₈	C₂³×C₆₇	1	2	yes	—
967	C₂⁴	—	2	1	no	—
968	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
969	#41	—	4	2	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	1	no	—
974	C₂×Q₈	—	2	2	no	—
975	C₂×Q₈	—	2	2	no	—
976	C₂×Q₈	—	4	2	no	—
977	C₂×Q₈	—	4	2	no	—
978	C₂×Q₈	—	8	2	no	—
979	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
980	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	8	2	no	—
991	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	8	2	no	—
1005	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1006	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1010	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1011	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1015	Q₁₆	—	4	2	no	—
1016	Q₁₆	—	4	2	no	—
1017	Q₁₆	—	4	2	no	—
1018	SD₁₆	—	4	2	no	—
1019	SD₁₆	—	4	2	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	D₈	—	4	2	no	—
1023	M₁₆	—	4	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1026	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1027	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1069	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1073	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1102	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1103	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1104	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1105	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1106	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1107	C₄²	—	2	2	no	—
1108	C₄²	—	2	2	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1117	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1118	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1119	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1120	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1121	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1122	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1123	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1124	C₂³	—	2	2	no	—
1125	C₂³	—	2	1	no	—
1126	C₂³	—	2	2	no	—
1127	C₂³	—	4	1	no	—
1128	C₂³	—	4	1	no	—
1129	C₂³	—	4	2	no	—
1130	C₂³	—	4	2	no	—
1131	C₂³	—	4	2	no	—
1132	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1133	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1134	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	8	2	no	—
1143	Q₈	—	8	2	no	—
1144	Q₈	—	8	1	no	—
1145	Q₈	—	8	1	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	2	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	4	2	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	8	2	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1191	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1192	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1196	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1197	C₈	—	2	2	no	—
1198	C₈	—	2	2	no	—
1199	C₈	—	2	2	no	—
1200	C₈	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	8	2	no	—
1216	C₂²	—	8	4	no	—
1217	C₂²	#578×C₆₇	1	2	yes	—
1218	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1219	C₄	—	2	1	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	2	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	2	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	#585×C₆₇	1	2	yes	—
1241	C₂	—	2	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	1	no	—
1244	C₂	—	8	2	no	—
1245	C₂	—	8	1	no	—
1246	C₂	C₆₇×#3449	1	1	yes	characteristic
1247	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1248	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3188	C₂
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×#3495	C₂	semidirect
2. C₂×#542×C₆₇	C₂	semidirect
3. C₆₇×#3262	C₂	semidirect
4. C₆₇×#3258	C₂	semidirect
5. C₆₇×#3243	C₂	semidirect
6. C₆₇×#3239	C₂	semidirect
7. C₆₇×#3230	C₂	semidirect
8. C₆₇×#3225	C₂	semidirect
9. C₆₇×#3215	C₂	semidirect
10. C₆₇×#3211	C₂	semidirect
11. C₆₇×#3196	C₂	semidirect
12. C₆₇×#3193	C₂	semidirect
13. C₆₇×#3189	C₂	semidirect
15. C₆₇×#3178	C₂	semidirect
16. C₆₇×#3175	C₂	semidirect
17. C₆₇×#3124	C₂	semidirect
18. C₆₇×#3121	C₂	semidirect
19. C₆₇×#3117	C₂	semidirect
20. C₆₇×#3110	C₂	semidirect
21. C₆₇×#3105	C₂	semidirect
22. C₆₇×#3104	C₂	semidirect
23. C₆₇×#2924	C₂	semidirect
32. #544×C₆₇	C₂²	semidirect
41. #542×C₆₇	C₂²	semidirect
42. #542×C₆₇	C₂²	semidirect
43. #541×C₆₇	C₂²	semidirect
44. #541×C₆₇	C₂²	semidirect
45. #536×C₆₇	C₂²	semidirect
60. #520×C₆₇	C₂²	semidirect
61. #519×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #500×C₆₇	C₂²	semidirect
67. #497×C₆₇	C₂²	semidirect
68. #495×C₆₇	C₂²	semidirect
69. #489×C₆₇	C₂²	semidirect
70. #489×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
72. #487×C₆₇	C₂²	semidirect
73. #485×C₆₇	C₂²	semidirect
80. #484×C₆₇	C₂²	semidirect
85. #479×C₆₇	C₂²	semidirect
86. #478×C₆₇	C₂²	semidirect
87. #477×C₆₇	C₂²	semidirect
88. #477×C₆₇	C₂²	semidirect
89. #477×C₆₇	C₂²	semidirect
90. #475×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #474×C₆₇	C₂²	semidirect
93. #470×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #467×C₆₇	C₂²	semidirect
98. #467×C₆₇	C₂²	semidirect
101. #464×C₆₇	C₂²	semidirect
102. #464×C₆₇	C₂²	semidirect
103. #464×C₆₇	C₂²	semidirect
104. #464×C₆₇	C₂²	semidirect
105. #463×C₆₇	C₂²	semidirect
106. #463×C₆₇	C₂²	semidirect
107. #462×C₆₇	C₂²	semidirect
108. #461×C₆₇	C₂²	semidirect
109. #452×C₆₇	C₂²	semidirect
113. #451×C₆₇	C₂²	semidirect
121. #441×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×Q₁₆×C₆₇	C₂²	semidirect
127. C₄×SD₁₆×C₆₇	C₂²	semidirect
128. C₄×D₈×C₆₇	C₂²	semidirect
129. #433×C₆₇	C₂²	semidirect
130. #433×C₆₇	C₂²	semidirect
135. #424×C₆₇	C₂²	semidirect
138. #405×C₆₇	C₂²	semidirect
616. #60981	C₆₇	direct (N × H)
625. #3495	C₂×C₆₇	semidirect
626. C₂×#542	C₂×C₆₇	semidirect
627. #3262	C₂×C₆₇	semidirect
628. #3258	C₂×C₆₇	semidirect
629. #3243	C₂×C₆₇	semidirect
630. #3239	C₂×C₆₇	semidirect
631. #3230	C₂×C₆₇	semidirect
632. #3225	C₂×C₆₇	semidirect
633. #3215	C₂×C₆₇	semidirect
634. #3211	C₂×C₆₇	semidirect
635. #3196	C₂×C₆₇	semidirect
636. #3193	C₂×C₆₇	semidirect
637. #3189	C₂×C₆₇	semidirect
639. #3178	C₂×C₆₇	semidirect
640. #3175	C₂×C₆₇	semidirect
641. #3124	C₂×C₆₇	semidirect
642. #3121	C₂×C₆₇	semidirect
643. #3117	C₂×C₆₇	semidirect
644. #3110	C₂×C₆₇	semidirect
645. #3105	C₂×C₆₇	semidirect
646. #3104	C₂×C₆₇	semidirect
647. #2924	C₂×C₆₇	semidirect
648. C₆₇	#60981	direct (N × H)
657. #544	C₂²×C₆₇	semidirect
666. #542	C₂²×C₆₇	semidirect
667. #542	C₂²×C₆₇	semidirect
668. #541	C₂²×C₆₇	semidirect
669. #541	C₂²×C₆₇	semidirect
670. #536	C₂²×C₆₇	semidirect
685. #520	C₂²×C₆₇	semidirect
686. #519	C₂²×C₆₇	semidirect
690. #501	C₂²×C₆₇	semidirect
691. #500	C₂²×C₆₇	semidirect
692. #497	C₂²×C₆₇	semidirect
693. #495	C₂²×C₆₇	semidirect
694. #489	C₂²×C₆₇	semidirect
695. #489	C₂²×C₆₇	semidirect
696. #488	C₂²×C₆₇	semidirect
697. #487	C₂²×C₆₇	semidirect
698. #485	C₂²×C₆₇	semidirect
705. #484	C₂²×C₆₇	semidirect
710. #479	C₂²×C₆₇	semidirect
711. #478	C₂²×C₆₇	semidirect
712. #477	C₂²×C₆₇	semidirect
713. #477	C₂²×C₆₇	semidirect
714. #477	C₂²×C₆₇	semidirect
715. #475	C₂²×C₆₇	semidirect
716. #474	C₂²×C₆₇	semidirect
717. #474	C₂²×C₆₇	semidirect
718. #470	C₂²×C₆₇	semidirect
721. #468	C₂²×C₆₇	semidirect
722. #467	C₂²×C₆₇	semidirect
723. #467	C₂²×C₆₇	semidirect
726. #464	C₂²×C₆₇	semidirect
727. #464	C₂²×C₆₇	semidirect
728. #464	C₂²×C₆₇	semidirect
729. #464	C₂²×C₆₇	semidirect
730. #463	C₂²×C₆₇	semidirect
731. #463	C₂²×C₆₇	semidirect
732. #462	C₂²×C₆₇	semidirect
733. #461	C₂²×C₆₇	semidirect
734. #452	C₂²×C₆₇	semidirect
738. #451	C₂²×C₆₇	semidirect
746. #441	C₂²×C₆₇	semidirect
747. #440	C₂²×C₆₇	semidirect
748. #440	C₂²×C₆₇	semidirect
749. #440	C₂²×C₆₇	semidirect
750. C₄×Q₁₆	C₂²×C₆₇	semidirect
751. C₄×Q₁₆	C₂²×C₆₇	semidirect
752. C₄×SD₁₆	C₂²×C₆₇	semidirect
753. C₄×D₈	C₂²×C₆₇	semidirect
754. #433	C₂²×C₆₇	semidirect
755. #433	C₂²×C₆₇	semidirect
760. #424	C₂²×C₆₇	semidirect
763. #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×#3495	2
C₂×#542×C₆₇	2
C₆₇×#3262	2
C₆₇×#3258	2
C₆₇×#3243	2
C₆₇×#3239	2
C₆₇×#3230	2
C₆₇×#3225	2
C₆₇×#3215	2
C₆₇×#3211	2
C₆₇×#3196	2
C₆₇×#3193	2
C₆₇×#3189	2
C₆₇×#3188	2
C₆₇×#3178	2
C₆₇×#3175	2
C₆₇×#3124	2
C₆₇×#3121	2
C₆₇×#3117	2
C₆₇×#3110	2
C₆₇×#3105	2
C₆₇×#3104	2
C₆₇×#2924	2
#60981	67

Subgroups — C67×#60981 #30740232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60981 #30740232