Subgroups — C₆₇×#60576 #30739827

Order 17152.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3126	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3115	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3112	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	#544×C₆₇	C₂²	1	1	yes	characteristic
30	#542×C₆₇	—	2	1	no	—
31	#542×C₆₇	C₂²	1	2	yes	—
32	#540×C₆₇	—	2	1	no	—
33	#540×C₆₇	C₂²	1	2	yes	—
34	#538×C₆₇	—	2	2	no	—
35	#537×C₆₇	C₂²	1	1	yes	characteristic
36	#535×C₆₇	C₂²	1	1	yes	characteristic
37	#535×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	—	2	1	no	—
39	#532×C₆₇	C₂²	1	2	yes	—
40	#529×C₆₇	—	2	1	no	—
41	#529×C₆₇	C₂²	1	2	yes	—
42	#525×C₆₇	—	2	2	no	—
43	#520×C₆₇	—	2	2	no	—
44	#520×C₆₇	—	2	1	no	—
45	#520×C₆₇	C₂²	1	1	yes	characteristic
46	#520×C₆₇	C₂²	1	1	yes	characteristic
47	#520×C₆₇	C₂²	1	2	yes	complemented
48	#519×C₆₇	—	2	1	no	—
49	#519×C₆₇	C₂²	1	1	yes	characteristic
50	#519×C₆₇	C₂²	1	2	yes	complemented
51	C₄×#41×C₆₇	—	2	2	no	—
52	C₄×#41×C₆₇	—	2	1	no	—
53	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
56	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
57	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
58	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
60	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
61	#485×C₆₇	C₂²	1	2	yes	complemented
62	#484×C₆₇	C₂²	1	2	yes	complemented
63	#482×C₆₇	C₂²	1	2	yes	—
64	#482×C₆₇	C₂²	1	2	yes	—
65	#482×C₆₇	C₂²	1	2	yes	complemented
66	#481×C₆₇	C₂²	1	2	yes	—
67	#480×C₆₇	C₂²	1	2	yes	—
68	#480×C₆₇	C₂²	1	2	yes	complemented
69	#479×C₆₇	C₂²	1	2	yes	complemented
70	#479×C₆₇	C₂²	1	2	yes	complemented
71	#479×C₆₇	C₂²	1	2	yes	complemented
72	#478×C₆₇	C₂²	1	2	yes	complemented
73	#477×C₆₇	C₂²	1	2	yes	complemented
74	#477×C₆₇	C₂²	1	2	yes	complemented
75	#475×C₆₇	C₂²	1	2	yes	complemented
76	#474×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	—
78	#464×C₆₇	C₂²	1	2	yes	—
79	#464×C₆₇	C₂²	1	2	yes	—
80	#463×C₆₇	C₂²	1	2	yes	—
81	#460×C₆₇	C₂²	1	2	yes	—
82	#460×C₆₇	C₂²	1	2	yes	—
83	#460×C₆₇	C₂²	1	2	yes	—
84	#459×C₆₇	C₂²	1	2	yes	—
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#451×C₆₇	C₂²	1	2	yes	complemented
87	#449×C₆₇	C₂²	1	2	yes	—
88	#449×C₆₇	C₂²	1	2	yes	—
89	#449×C₆₇	C₂²	1	2	yes	complemented
90	#448×C₆₇	C₂²	1	2	yes	—
91	#448×C₆₇	C₂²	1	2	yes	—
92	#448×C₆₇	C₂²	1	2	yes	complemented
93	#442×C₆₇	C₂²	1	2	yes	—
94	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#441×C₆₇	C₂²	1	2	yes	complemented
97	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#440×C₆₇	C₂²	1	2	yes	—
100	#440×C₆₇	C₂²	1	2	yes	—
101	#440×C₆₇	C₂²	1	2	yes	—
102	#440×C₆₇	C₂²	1	2	yes	—
103	#440×C₆₇	C₂²	1	2	yes	—
104	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#440×C₆₇	C₂²	1	2	yes	complemented
107	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×D₈×C₆₇	C₂²	1	2	yes	—
113	#433×C₆₇	C₂²	1	2	yes	complemented
114	#433×C₆₇	C₂²	1	2	yes	complemented
115	#432×C₆₇	C₂²	1	2	yes	complemented
116	#432×C₆₇	C₂²	1	2	yes	complemented
117	#428×C₆₇	C₂²	1	1	yes	characteristic
118	#428×C₆₇	C₂²	1	1	yes	characteristic
119	#427×C₆₇	C₂²	1	1	yes	characteristic
120	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
121	#424×C₆₇	C₂²	1	1	yes	characteristic
122	#424×C₆₇	C₂²	1	1	yes	characteristic
123	#419×C₆₇	C₂²	1	1	yes	characteristic
124	#418×C₆₇	C₂²	1	1	yes	characteristic
125	#417×C₆₇	C₂²	1	1	yes	characteristic
126	#417×C₆₇	C₂²	1	1	yes	characteristic
127	#416×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
131	#408×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
134	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	2	4	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	—	2	2	no	—
140	C₂×#41×C₆₇	C₂³	1	2	yes	—
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₇	—	2	1	no	—
145	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	—	2	1	no	—
149	#137×C₆₇	—	2	4	no	—
150	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
151	#135×C₆₇	—	2	4	no	—
152	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	—	2	4	no	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₆₇	C₂³	1	2	yes	—
162	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₇	—	2	1	no	—
168	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
169	#127×C₆₇	—	2	1	no	—
170	#127×C₆₇	C₂³	1	2	yes	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	1	no	—
174	#125×C₆₇	C₂³	1	2	yes	—
175	#124×C₆₇	—	2	1	no	—
176	#124×C₆₇	—	2	2	no	—
177	#124×C₆₇	—	2	2	no	—
178	#124×C₆₇	C₂³	1	2	yes	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	C₂²⋊Q₈×C₆₇	—	2	1	no	—
184	C₂²⋊Q₈×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	2	no	—
186	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
187	#121×C₆₇	—	2	2	no	—
188	#121×C₆₇	—	2	1	no	—
189	#121×C₆₇	—	2	2	no	—
190	#121×C₆₇	—	2	1	no	—
191	#121×C₆₇	—	2	1	no	—
192	#121×C₆₇	—	2	2	no	—
193	#121×C₆₇	—	2	2	no	—
194	#121×C₆₇	C₂³	1	2	yes	—
195	#121×C₆₇	C₂³	1	2	yes	—
196	#121×C₆₇	C₂³	1	2	yes	—
197	#120×C₆₇	—	2	2	no	—
198	#120×C₆₇	—	2	2	no	—
199	C₄×Q₈×C₆₇	—	2	1	no	—
200	C₄×Q₈×C₆₇	—	2	1	no	—
201	C₄×Q₈×C₆₇	—	2	2	no	—
202	C₄×Q₈×C₆₇	—	2	1	no	—
203	C₄×Q₈×C₆₇	—	2	2	no	—
204	C₄×Q₈×C₆₇	—	2	1	no	—
205	C₄×Q₈×C₆₇	—	2	2	no	—
206	C₄×Q₈×C₆₇	—	2	1	no	—
207	C₄×Q₈×C₆₇	—	2	2	no	—
208	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
209	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
210	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
211	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
212	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
213	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
214	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
215	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₆₇	—	2	2	no	—
220	C₄×D₄×C₆₇	—	2	1	no	—
221	C₄×D₄×C₆₇	—	2	1	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	1	no	—
224	C₄×D₄×C₆₇	—	2	1	no	—
225	C₄×D₄×C₆₇	—	2	1	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	D₄	1	2	yes	—
235	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
236	C₄×D₄×C₆₇	D₄	1	2	yes	—
237	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	2	yes	—
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	#117×C₆₇	—	2	1	no	—
246	#117×C₆₇	—	2	2	no	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	—	2	2	no	—
250	#117×C₆₇	—	2	1	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	—	2	2	no	—
254	#117×C₆₇	C₂³	1	2	yes	—
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	1	yes	characteristic
257	#117×C₆₇	C₂³	1	1	yes	characteristic
258	#117×C₆₇	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
263	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
267	C₂×C₄²×C₆₇	—	2	1	no	—
268	C₂×C₄²×C₆₇	—	2	2	no	—
269	C₂×C₄²×C₆₇	—	2	1	no	—
270	C₂×C₄²×C₆₇	—	2	2	no	—
271	C₂×C₄²×C₆₇	—	2	1	no	—
272	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
274	#107×C₆₇	C₂³	1	2	yes	—
275	#107×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	1	yes	characteristic
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#106×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	1	yes	characteristic
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#102×C₆₇	C₂³	1	1	yes	characteristic
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	#97×C₆₇	C₂³	1	1	yes	characteristic
313	#97×C₆₇	C₂³	1	1	yes	characteristic
314	#97×C₆₇	C₂³	1	1	yes	characteristic
315	#97×C₆₇	C₂³	1	1	yes	characteristic
316	#97×C₆₇	C₂³	1	2	yes	—
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	C₂⁴×C₆₇	—	2	1	no	—
319	#41×C₆₇	—	2	16	no	—
320	#41×C₆₇	—	2	8	no	—
321	#41×C₆₇	—	2	4	no	—
322	#41×C₆₇	—	2	4	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	8	4	no	—
329	#41×C₆₇	#41	1	4	yes	complemented
330	C₂×Q₈×C₆₇	—	2	8	no	—
331	C₂×Q₈×C₆₇	—	2	4	no	—
332	C₂×Q₈×C₆₇	—	2	4	no	—
333	C₂×Q₈×C₆₇	—	2	2	no	—
334	C₂×Q₈×C₆₇	—	2	1	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	—	2	2	no	—
337	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
338	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
339	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
342	C₂×D₄×C₆₇	—	2	2	no	—
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	2	1	no	—
345	C₂×D₄×C₆₇	—	2	2	no	—
346	C₂×D₄×C₆₇	—	2	2	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	—	2	1	no	—
349	C₂×D₄×C₆₇	—	2	2	no	—
350	C₂×D₄×C₆₇	—	2	2	no	—
351	C₂×D₄×C₆₇	—	2	2	no	—
352	C₂×D₄×C₆₇	—	2	2	no	—
353	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
356	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	2	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	1	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	2	2	no	—
373	C₂²×C₄×C₆₇	—	8	2	no	—
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
378	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	Q₁₆×C₆₇	—	2	2	no	—
381	Q₁₆×C₆₇	—	2	4	no	—
382	SD₁₆×C₆₇	—	2	4	no	—
383	SD₁₆×C₆₇	—	2	4	no	—
384	SD₁₆×C₆₇	—	2	2	no	—
385	SD₁₆×C₆₇	—	2	4	no	—
386	SD₁₆×C₆₇	—	2	4	no	—
387	SD₁₆×C₆₇	—	2	2	no	—
388	D₈×C₆₇	—	2	2	no	—
389	D₈×C₆₇	—	2	4	no	—
390	M₁₆×C₆₇	—	2	2	no	—
391	M₁₆×C₆₇	—	2	2	no	—
392	C₂×C₈×C₆₇	—	2	2	no	—
393	C₂×C₈×C₆₇	—	2	2	no	—
394	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	2	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	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	1	no	—
433	C₂²⋊C₄×C₆₇	—	2	1	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	1	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	1	no	—
447	C₄²×C₆₇	—	2	1	no	—
448	C₄²×C₆₇	—	2	1	no	—
449	C₄²×C₆₇	—	2	2	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	2	no	—
452	C₄²×C₆₇	—	2	2	no	—
453	C₄²×C₆₇	—	2	2	no	—
454	C₄²×C₆₇	—	2	1	no	—
455	C₄²×C₆₇	—	2	1	no	—
456	C₄²×C₆₇	—	2	1	no	—
457	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₆₇	C₂×D₄	1	2	yes	—
460	C₄²×C₆₇	C₂×D₄	1	2	yes	—
461	C₄²×C₆₇	C₂⁴	1	2	yes	—
462	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
464	C₂³×C₆₇	—	2	1	no	—
465	C₂³×C₆₇	—	2	2	no	—
466	C₂³×C₆₇	—	2	1	no	—
467	C₂³×C₆₇	—	4	2	no	—
468	C₂³×C₆₇	—	8	1	no	—
469	C₂³×C₆₇	—	8	1	no	—
470	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
471	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₆₇	—	2	8	no	—
473	Q₈×C₆₇	—	2	2	no	—
474	Q₈×C₆₇	—	2	4	no	—
475	Q₈×C₆₇	—	2	1	no	—
476	Q₈×C₆₇	—	2	2	no	—
477	Q₈×C₆₇	—	2	1	no	—
478	Q₈×C₆₇	—	2	1	no	—
479	Q₈×C₆₇	—	8	2	no	—
480	Q₈×C₆₇	C₂×#41	1	2	yes	—
481	Q₈×C₆₇	C₂×#41	1	4	yes	—
482	D₄×C₆₇	—	2	8	no	—
483	D₄×C₆₇	—	2	4	no	—
484	D₄×C₆₇	—	2	4	no	—
485	D₄×C₆₇	—	2	2	no	—
486	D₄×C₆₇	—	2	1	no	—
487	D₄×C₆₇	—	2	2	no	—
488	D₄×C₆₇	—	2	1	no	—
489	D₄×C₆₇	—	2	2	no	—
490	D₄×C₆₇	—	2	1	no	—
491	D₄×C₆₇	—	4	2	no	—
492	D₄×C₆₇	—	4	2	no	—
493	D₄×C₆₇	—	8	2	no	—
494	D₄×C₆₇	—	8	2	no	—
495	D₄×C₆₇	—	8	2	no	—
496	D₄×C₆₇	—	8	2	no	—
497	D₄×C₆₇	—	8	2	no	—
498	D₄×C₆₇	C₂×#41	1	2	yes	—
499	C₂×C₄×C₆₇	—	2	8	no	—
500	C₂×C₄×C₆₇	—	2	8	no	—
501	C₂×C₄×C₆₇	—	2	4	no	—
502	C₂×C₄×C₆₇	—	2	2	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	4	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	2	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	4	1	no	—
515	C₂×C₄×C₆₇	—	4	1	no	—
516	C₂×C₄×C₆₇	—	4	2	no	—
517	C₂×C₄×C₆₇	—	4	2	no	—
518	C₂×C₄×C₆₇	—	4	2	no	—
519	C₂×C₄×C₆₇	—	4	4	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	4	2	no	—
522	C₂×C₄×C₆₇	—	8	1	no	—
523	C₂×C₄×C₆₇	—	8	2	no	—
524	C₂×C₄×C₆₇	—	8	1	no	—
525	C₂×C₄×C₆₇	—	8	2	no	—
526	C₂×C₄×C₆₇	—	8	1	no	—
527	C₂×C₄×C₆₇	—	8	2	no	—
528	C₂×C₄×C₆₇	—	8	1	no	—
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
538	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
539	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
540	C₈×C₆₇	—	2	1	no	—
541	C₈×C₆₇	—	2	1	no	—
542	C₈×C₆₇	—	2	1	no	—
543	C₈×C₆₇	—	2	1	no	—
544	C₈×C₆₇	—	2	2	no	—
545	C₈×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	2	1	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	2	no	—
550	C₂²×C₆₇	—	2	2	no	—
551	C₂²×C₆₇	—	2	2	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	4	1	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	2	no	—
558	C₂²×C₆₇	—	4	1	no	—
559	C₂²×C₆₇	—	4	2	no	—
560	C₂²×C₆₇	—	8	4	no	—
561	C₂²×C₆₇	#525	1	2	yes	—
562	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
563	C₄×C₆₇	—	2	1	no	—
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	2	1	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	2	no	—
569	C₄×C₆₇	—	2	4	no	—
570	C₄×C₆₇	—	2	2	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	4	2	no	—
573	C₄×C₆₇	—	4	1	no	—
574	C₄×C₆₇	—	4	1	no	—
575	C₄×C₆₇	—	4	2	no	—
576	C₄×C₆₇	—	4	1	no	—
577	C₄×C₆₇	—	4	1	no	—
578	C₄×C₆₇	—	4	1	no	—
579	C₄×C₆₇	#525	1	2	yes	—
580	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
581	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
582	#60576	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
583	C₂×C₆₇	—	2	2	no	—
584	C₂×C₆₇	—	4	2	no	—
585	C₂×C₆₇	—	4	2	no	—
586	C₂×C₆₇	—	8	1	no	—
587	C₂×C₆₇	—	8	2	no	—
588	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
589	C₂×C₆₇	#3585	1	1	yes	characteristic
590	C₂×C₆₇	#3586	1	1	yes	characteristic
591	#3460	C₂×C₆₇	1	1	yes	characteristic, complemented
592	C₄×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#3126	C₂×C₆₇	1	2	yes	complemented
594	#3124	C₂×C₆₇	1	2	yes	complemented
595	#3121	C₂×C₆₇	1	2	yes	complemented
596	#3119	C₂×C₆₇	1	2	yes	complemented
597	#3117	C₂×C₆₇	1	2	yes	complemented
598	#3115	C₂×C₆₇	1	2	yes	complemented
599	#3112	C₂×C₆₇	1	2	yes	complemented
600	#3111	C₂×C₆₇	1	2	yes	complemented
601	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3096	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#3043	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
609	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
610	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#2943	C₂×C₆₇	1	1	yes	characteristic, complemented
612	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
614	C₆₇	#60576	1	1	yes	characteristic, direct product factor, Sylow
615	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
616	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
617	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
618	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
619	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
620	#544	C₂²×C₆₇	1	1	yes	characteristic
621	#542	—	2	1	no	—
622	#542	C₂²×C₆₇	1	2	yes	—
623	#540	—	2	1	no	—
624	#540	C₂²×C₆₇	1	2	yes	—
625	#538	—	2	2	no	—
626	#537	C₂²×C₆₇	1	1	yes	characteristic
627	#535	C₂²×C₆₇	1	1	yes	characteristic
628	#535	C₂²×C₆₇	1	1	yes	characteristic
629	#532	—	2	1	no	—
630	#532	C₂²×C₆₇	1	2	yes	—
631	#529	—	2	1	no	—
632	#529	C₂²×C₆₇	1	2	yes	—
633	#525	—	2	2	no	—
634	#520	—	2	2	no	—
635	#520	—	2	1	no	—
636	#520	C₂²×C₆₇	1	1	yes	characteristic
637	#520	C₂²×C₆₇	1	1	yes	characteristic
638	#520	C₂²×C₆₇	1	2	yes	complemented
639	#519	—	2	1	no	—
640	#519	C₂²×C₆₇	1	1	yes	characteristic
641	#519	C₂²×C₆₇	1	2	yes	complemented
642	C₄×#41	—	2	2	no	—
643	C₄×#41	—	2	1	no	—
644	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
645	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
646	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
647	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
648	C₂×C₄×Q₈	—	2	1	no	—
649	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
650	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
651	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
652	#485	C₂²×C₆₇	1	2	yes	complemented
653	#484	C₂²×C₆₇	1	2	yes	complemented
654	#482	C₂²×C₆₇	1	2	yes	—
655	#482	C₂²×C₆₇	1	2	yes	—
656	#482	C₂²×C₆₇	1	2	yes	complemented
657	#481	C₂²×C₆₇	1	2	yes	—
658	#480	C₂²×C₆₇	1	2	yes	—
659	#480	C₂²×C₆₇	1	2	yes	complemented
660	#479	C₂²×C₆₇	1	2	yes	complemented
661	#479	C₂²×C₆₇	1	2	yes	complemented
662	#479	C₂²×C₆₇	1	2	yes	complemented
663	#478	C₂²×C₆₇	1	2	yes	complemented
664	#477	C₂²×C₆₇	1	2	yes	complemented
665	#477	C₂²×C₆₇	1	2	yes	complemented
666	#475	C₂²×C₆₇	1	2	yes	complemented
667	#474	C₂²×C₆₇	1	2	yes	complemented
668	#464	C₂²×C₆₇	1	2	yes	—
669	#464	C₂²×C₆₇	1	2	yes	—
670	#464	C₂²×C₆₇	1	2	yes	—
671	#463	C₂²×C₆₇	1	2	yes	—
672	#460	C₂²×C₆₇	1	2	yes	—
673	#460	C₂²×C₆₇	1	2	yes	—
674	#460	C₂²×C₆₇	1	2	yes	—
675	#459	C₂²×C₆₇	1	2	yes	—
676	#452	C₂²×C₆₇	1	2	yes	complemented
677	#451	C₂²×C₆₇	1	2	yes	complemented
678	#449	C₂²×C₆₇	1	2	yes	—
679	#449	C₂²×C₆₇	1	2	yes	—
680	#449	C₂²×C₆₇	1	2	yes	complemented
681	#448	C₂²×C₆₇	1	2	yes	—
682	#448	C₂²×C₆₇	1	2	yes	—
683	#448	C₂²×C₆₇	1	2	yes	complemented
684	#442	C₂²×C₆₇	1	2	yes	—
685	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#441	C₂²×C₆₇	1	2	yes	complemented
688	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#440	C₂²×C₆₇	1	2	yes	—
691	#440	C₂²×C₆₇	1	2	yes	—
692	#440	C₂²×C₆₇	1	2	yes	—
693	#440	C₂²×C₆₇	1	2	yes	—
694	#440	C₂²×C₆₇	1	2	yes	—
695	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#440	C₂²×C₆₇	1	2	yes	complemented
698	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
700	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
702	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
703	C₄×D₈	C₂²×C₆₇	1	2	yes	—
704	#433	C₂²×C₆₇	1	2	yes	complemented
705	#433	C₂²×C₆₇	1	2	yes	complemented
706	#432	C₂²×C₆₇	1	2	yes	complemented
707	#432	C₂²×C₆₇	1	2	yes	complemented
708	#428	C₂²×C₆₇	1	1	yes	characteristic
709	#428	C₂²×C₆₇	1	1	yes	characteristic
710	#427	C₂²×C₆₇	1	1	yes	characteristic
711	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
712	#424	C₂²×C₆₇	1	1	yes	characteristic
713	#424	C₂²×C₆₇	1	1	yes	characteristic
714	#419	C₂²×C₆₇	1	1	yes	characteristic
715	#418	C₂²×C₆₇	1	1	yes	characteristic
716	#417	C₂²×C₆₇	1	1	yes	characteristic
717	#417	C₂²×C₆₇	1	1	yes	characteristic
718	#416	C₂²×C₆₇	1	1	yes	characteristic
719	#416	C₂²×C₆₇	1	1	yes	characteristic
720	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
721	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
722	#408	C₂²×C₆₇	1	1	yes	characteristic
723	#408	C₂²×C₆₇	1	1	yes	characteristic
724	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
725	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
726	2₋¹⁺⁴	—	2	4	no	—
727	2₋¹⁺⁴	—	2	4	no	—
728	C₂×#41	—	2	2	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	—	2	2	no	—
731	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×#41	C₂³×C₆₇	1	2	yes	—
733	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
735	C₂²×Q₈	—	2	1	no	—
736	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
737	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
738	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂³×C₄	—	2	1	no	—
740	#137	—	2	4	no	—
741	AGL(1,ℤ/8)	—	2	4	no	—
742	#135	—	2	4	no	—
743	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
745	C₂×SD₁₆	—	2	4	no	—
746	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
752	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×D₈	C₂³×C₆₇	1	2	yes	—
754	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
757	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
758	C₄⋊Q₈	—	2	1	no	—
759	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
760	#127	—	2	1	no	—
761	#127	C₂³×C₆₇	1	2	yes	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	C₂³×C₆₇	1	2	yes	—
766	#124	—	2	1	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	C₂³×C₆₇	1	2	yes	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	C₂³×C₆₇	1	2	yes	—
786	#121	C₂³×C₆₇	1	2	yes	—
787	#121	C₂³×C₆₇	1	2	yes	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	2	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	2	no	—
799	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
800	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
805	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
806	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	D₄×C₆₇	1	2	yes	—
826	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
827	C₄×D₄	D₄×C₆₇	1	2	yes	—
828	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₆₇	1	2	yes	—
830	C₄×D₄	C₂³×C₆₇	1	2	yes	—
831	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₆₇	1	2	yes	—
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	2	no	—
839	#117	—	2	2	no	—
840	#117	—	2	2	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	C₂³×C₆₇	1	1	yes	characteristic
846	#117	C₂³×C₆₇	1	1	yes	characteristic
847	#117	C₂³×C₆₇	1	2	yes	—
848	#117	C₂³×C₆₇	1	1	yes	characteristic
849	#117	C₂³×C₆₇	1	2	yes	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	2	no	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	2	no	—
854	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
857	C₂×C₂²⋊C₄	—	2	1	no	—
858	C₂×C₄²	—	2	1	no	—
859	C₂×C₄²	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	2	2	no	—
862	C₂×C₄²	—	2	1	no	—
863	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
864	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
865	#107	C₂³×C₆₇	1	2	yes	—
866	#107	C₂³×C₆₇	1	2	yes	—
867	#107	C₂³×C₆₇	1	1	yes	characteristic
868	#107	C₂³×C₆₇	1	1	yes	characteristic
869	#107	C₂³×C₆₇	1	2	yes	—
870	#107	C₂³×C₆₇	1	2	yes	—
871	#106	C₂³×C₆₇	1	1	yes	characteristic
872	#106	C₂³×C₆₇	1	1	yes	characteristic
873	#106	C₂³×C₆₇	1	2	yes	—
874	#106	C₂³×C₆₇	1	2	yes	—
875	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
876	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
877	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
878	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
879	#103	C₂³×C₆₇	1	2	yes	—
880	#103	C₂³×C₆₇	1	2	yes	—
881	#103	C₂³×C₆₇	1	1	yes	characteristic
882	#103	C₂³×C₆₇	1	1	yes	characteristic
883	#103	C₂³×C₆₇	1	1	yes	characteristic
884	#103	C₂³×C₆₇	1	1	yes	characteristic
885	#103	C₂³×C₆₇	1	2	yes	—
886	#103	C₂³×C₆₇	1	2	yes	—
887	#103	C₂³×C₆₇	1	2	yes	—
888	#103	C₂³×C₆₇	1	2	yes	—
889	#102	C₂³×C₆₇	1	2	yes	—
890	#102	C₂³×C₆₇	1	2	yes	—
891	#102	C₂³×C₆₇	1	1	yes	characteristic
892	#102	C₂³×C₆₇	1	1	yes	characteristic
893	#102	C₂³×C₆₇	1	1	yes	characteristic
894	#102	C₂³×C₆₇	1	1	yes	characteristic
895	#102	C₂³×C₆₇	1	2	yes	—
896	#102	C₂³×C₆₇	1	2	yes	—
897	#102	C₂³×C₆₇	1	2	yes	—
898	#102	C₂³×C₆₇	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
903	#97	C₂³×C₆₇	1	1	yes	characteristic
904	#97	C₂³×C₆₇	1	1	yes	characteristic
905	#97	C₂³×C₆₇	1	1	yes	characteristic
906	#97	C₂³×C₆₇	1	1	yes	characteristic
907	#97	C₂³×C₆₇	1	2	yes	—
908	C₄×C₈	C₂³×C₆₇	1	2	yes	—
909	C₂⁴	—	2	1	no	—
910	#41	—	2	16	no	—
911	#41	—	2	8	no	—
912	#41	—	2	4	no	—
913	#41	—	2	4	no	—
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	8	4	no	—
920	#41	#41×C₆₇	1	4	yes	complemented
921	C₂×Q₈	—	2	8	no	—
922	C₂×Q₈	—	2	4	no	—
923	C₂×Q₈	—	2	4	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	2	no	—
927	C₂×Q₈	—	2	2	no	—
928	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
929	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
930	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
931	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
945	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
947	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
948	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	8	2	no	—
965	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
966	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
967	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
968	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
970	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
971	Q₁₆	—	2	2	no	—
972	Q₁₆	—	2	4	no	—
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	SD₁₆	—	2	2	no	—
976	SD₁₆	—	2	4	no	—
977	SD₁₆	—	2	4	no	—
978	SD₁₆	—	2	2	no	—
979	D₈	—	2	2	no	—
980	D₈	—	2	4	no	—
981	M₁₆	—	2	2	no	—
982	M₁₆	—	2	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	—	2	2	no	—
985	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
986	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
987	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1009	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1013	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1014	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1034	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1035	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	2	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1051	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1052	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₆₇	1	2	yes	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	4	2	no	—
1059	C₂³	—	8	1	no	—
1060	C₂³	—	8	1	no	—
1061	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1062	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1063	Q₈	—	2	8	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	4	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	8	2	no	—
1071	Q₈	C₂×#41×C₆₇	1	2	yes	—
1072	Q₈	C₂×#41×C₆₇	1	4	yes	—
1073	D₄	—	2	8	no	—
1074	D₄	—	2	4	no	—
1075	D₄	—	2	4	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	4	2	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	C₂×#41×C₆₇	1	2	yes	—
1090	C₂×C₄	—	2	8	no	—
1091	C₂×C₄	—	2	8	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	4	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	1	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	—	8	1	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1128	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1129	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1130	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	8	4	no	—
1152	C₂²	#525×C₆₇	1	2	yes	—
1153	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	4	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	#525×C₆₇	1	2	yes	—
1171	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1172	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1173	C₂	—	2	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	2	no	—
1176	C₂	—	8	2	no	—
1177	C₂	—	8	1	no	—
1178	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1179	C₂	C₆₇×#3585	1	1	yes	characteristic
1180	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×#3460	C₂	semidirect
2. C₄×2₋¹⁺⁴×C₆₇	C₂	semidirect
3. C₆₇×#3126	C₂	semidirect
4. C₆₇×#3124	C₂	semidirect
5. C₆₇×#3121	C₂	semidirect
6. C₆₇×#3119	C₂	semidirect
7. C₆₇×#3117	C₂	semidirect
8. C₆₇×#3115	C₂	semidirect
9. C₆₇×#3112	C₂	semidirect
10. C₆₇×#3111	C₂	semidirect
11. C₆₇×#3098	C₂	semidirect
12. C₆₇×#3096	C₂	semidirect
13. C₆₇×#3083	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3045	C₂	semidirect
16. C₆₇×#3043	C₂	semidirect
17. C₆₇×#3013	C₂	semidirect
18. C₆₇×#3010	C₂	semidirect
19. C₄×#137×C₆₇	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
21. C₆₇×#2943	C₂	semidirect
22. C₂×#440×C₆₇	C₂	semidirect
23. C₆₇×#2923	C₂	semidirect
47. #520×C₆₇	C₂²	semidirect
50. #519×C₆₇	C₂²	semidirect
56. C₄×#41×C₆₇	C₂²	semidirect
59. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #484×C₆₇	C₂²	semidirect
65. #482×C₆₇	C₂²	semidirect
68. #480×C₆₇	C₂²	semidirect
69. #479×C₆₇	C₂²	semidirect
70. #479×C₆₇	C₂²	semidirect
71. #479×C₆₇	C₂²	semidirect
72. #478×C₆₇	C₂²	semidirect
73. #477×C₆₇	C₂²	semidirect
74. #477×C₆₇	C₂²	semidirect
75. #475×C₆₇	C₂²	semidirect
76. #474×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #451×C₆₇	C₂²	semidirect
89. #449×C₆₇	C₂²	semidirect
92. #448×C₆₇	C₂²	semidirect
94. #442×C₆₇	C₂²	semidirect
95. #442×C₆₇	C₂²	semidirect
96. #441×C₆₇	C₂²	semidirect
97. #441×C₆₇	C₂²	semidirect
98. #441×C₆₇	C₂²	semidirect
104. #440×C₆₇	C₂²	semidirect
105. #440×C₆₇	C₂²	semidirect
106. #440×C₆₇	C₂²	semidirect
107. #440×C₆₇	C₂²	semidirect
108. #440×C₆₇	C₂²	semidirect
109. C₄×Q₁₆×C₆₇	C₂²	semidirect
111. C₄×SD₁₆×C₆₇	C₂²	semidirect
113. #433×C₆₇	C₂²	semidirect
114. #433×C₆₇	C₂²	semidirect
115. #432×C₆₇	C₂²	semidirect
116. #432×C₆₇	C₂²	semidirect
329. #41×C₆₇	#41	semidirect
338. C₂×Q₈×C₆₇	#41	semidirect
582. #60576	C₆₇	direct (N × H)
591. #3460	C₂×C₆₇	semidirect
592. C₄×2₋¹⁺⁴	C₂×C₆₇	semidirect
593. #3126	C₂×C₆₇	semidirect
594. #3124	C₂×C₆₇	semidirect
595. #3121	C₂×C₆₇	semidirect
596. #3119	C₂×C₆₇	semidirect
597. #3117	C₂×C₆₇	semidirect
598. #3115	C₂×C₆₇	semidirect
599. #3112	C₂×C₆₇	semidirect
600. #3111	C₂×C₆₇	semidirect
601. #3098	C₂×C₆₇	semidirect
602. #3096	C₂×C₆₇	semidirect
603. #3083	C₂×C₆₇	semidirect
604. #3082	C₂×C₆₇	semidirect
605. #3045	C₂×C₆₇	semidirect
606. #3043	C₂×C₆₇	semidirect
607. #3013	C₂×C₆₇	semidirect
608. #3010	C₂×C₆₇	semidirect
609. C₄×#137	C₂×C₆₇	semidirect
610. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
611. #2943	C₂×C₆₇	semidirect
612. C₂×#440	C₂×C₆₇	semidirect
613. #2923	C₂×C₆₇	semidirect
614. C₆₇	#60576	direct (N × H)
638. #520	C₂²×C₆₇	semidirect
641. #519	C₂²×C₆₇	semidirect
647. C₄×#41	C₂²×C₆₇	semidirect
650. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
652. #485	C₂²×C₆₇	semidirect
653. #484	C₂²×C₆₇	semidirect
656. #482	C₂²×C₆₇	semidirect
659. #480	C₂²×C₆₇	semidirect
660. #479	C₂²×C₆₇	semidirect
661. #479	C₂²×C₆₇	semidirect
662. #479	C₂²×C₆₇	semidirect
663. #478	C₂²×C₆₇	semidirect
664. #477	C₂²×C₆₇	semidirect
665. #477	C₂²×C₆₇	semidirect
666. #475	C₂²×C₆₇	semidirect
667. #474	C₂²×C₆₇	semidirect
676. #452	C₂²×C₆₇	semidirect
677. #451	C₂²×C₆₇	semidirect
680. #449	C₂²×C₆₇	semidirect
683. #448	C₂²×C₆₇	semidirect
685. #442	C₂²×C₆₇	semidirect
686. #442	C₂²×C₆₇	semidirect
687. #441	C₂²×C₆₇	semidirect
688. #441	C₂²×C₆₇	semidirect
689. #441	C₂²×C₆₇	semidirect
695. #440	C₂²×C₆₇	semidirect
696. #440	C₂²×C₆₇	semidirect
697. #440	C₂²×C₆₇	semidirect
698. #440	C₂²×C₆₇	semidirect
699. #440	C₂²×C₆₇	semidirect
700. C₄×Q₁₆	C₂²×C₆₇	semidirect
702. C₄×SD₁₆	C₂²×C₆₇	semidirect
704. #433	C₂²×C₆₇	semidirect
705. #433	C₂²×C₆₇	semidirect
706. #432	C₂²×C₆₇	semidirect
707. #432	C₂²×C₆₇	semidirect
920. #41	#41×C₆₇	semidirect
929. C₂×Q₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3460	2
C₄×2₋¹⁺⁴×C₆₇	2
C₆₇×#3126	2
C₆₇×#3124	2
C₆₇×#3121	2
C₆₇×#3119	2
C₆₇×#3117	2
C₆₇×#3115	2
C₆₇×#3112	2
C₆₇×#3111	2
C₆₇×#3098	2
C₆₇×#3096	2
C₆₇×#3083	2
C₆₇×#3082	2
C₆₇×#3045	2
C₆₇×#3043	2
C₆₇×#3013	2
C₆₇×#3010	2
C₄×#137×C₆₇	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2943	2
C₂×#440×C₆₇	2
C₆₇×#2923	2
#60576	67

Subgroups — C67×#60576 #30739827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60576 #30739827