Subgroups — C₆₇×#60570 #30739821

Order 17152.

2152 conjugacy classes of subgroups.

The subgroup lattice has 1212 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×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3106	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3105	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3102	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3100	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×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×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×D₈×C₆₇	C₂²	1	1	yes	characteristic
29	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#542×C₆₇	—	2	1	no	—
31	#542×C₆₇	C₂²	1	2	yes	complemented
32	#540×C₆₇	—	2	1	no	—
33	#540×C₆₇	C₂²	1	2	yes	complemented
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, complemented
38	#532×C₆₇	—	2	1	no	—
39	#532×C₆₇	C₂²	1	2	yes	complemented
40	#529×C₆₇	—	2	1	no	—
41	#529×C₆₇	C₂²	1	2	yes	complemented
42	#525×C₆₇	—	2	2	no	—
43	#520×C₆₇	—	2	1	no	—
44	#520×C₆₇	C₂²	1	1	yes	characteristic
45	#520×C₆₇	C₂²	1	1	yes	characteristic
46	#520×C₆₇	C₂²	1	2	yes	complemented
47	#518×C₆₇	—	2	2	no	—
48	#518×C₆₇	—	2	1	no	—
49	#518×C₆₇	C₂²	1	1	yes	characteristic
50	#518×C₆₇	C₂²	1	2	yes	complemented
51	C₄×#41×C₆₇	—	2	1	no	—
52	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
53	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
55	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₆₇	—	2	1	no	—
57	C₂×C₄×D₄×C₆₇	—	2	2	no	—
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
60	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#485×C₆₇	C₂²	1	2	yes	complemented
62	#484×C₆₇	C₂²	1	2	yes	complemented
63	#482×C₆₇	C₂²	1	2	yes	complemented
64	#482×C₆₇	C₂²	1	2	yes	complemented
65	#482×C₆₇	C₂²	1	2	yes	complemented
66	#481×C₆₇	C₂²	1	2	yes	complemented
67	#480×C₆₇	C₂²	1	2	yes	complemented
68	#480×C₆₇	C₂²	1	2	yes	complemented
69	#479×C₆₇	C₂²	1	2	yes	complemented
70	#478×C₆₇	C₂²	1	2	yes	complemented
71	#478×C₆₇	C₂²	1	2	yes	complemented
72	#478×C₆₇	C₂²	1	2	yes	complemented
73	#477×C₆₇	C₂²	1	2	yes	complemented
74	#476×C₆₇	C₂²	1	2	yes	complemented
75	#474×C₆₇	C₂²	1	2	yes	complemented
76	#474×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#463×C₆₇	C₂²	1	2	yes	complemented
79	#463×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#460×C₆₇	C₂²	1	2	yes	complemented
82	#459×C₆₇	C₂²	1	2	yes	complemented
83	#459×C₆₇	C₂²	1	2	yes	complemented
84	#459×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#450×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	#447×C₆₇	C₂²	1	2	yes	—
91	#447×C₆₇	C₂²	1	2	yes	—
92	#447×C₆₇	C₂²	1	2	yes	complemented
93	#442×C₆₇	C₂²	1	2	yes	complemented
94	#442×C₆₇	C₂²	1	2	yes	complemented
95	#440×C₆₇	C₂²	1	2	yes	complemented
96	#440×C₆₇	C₂²	1	2	yes	complemented
97	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
107	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
108	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
109	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
110	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
111	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
113	#433×C₆₇	C₂²	1	2	yes	complemented
114	#433×C₆₇	C₂²	1	2	yes	complemented
115	#431×C₆₇	C₂²	1	2	yes	complemented
116	#431×C₆₇	C₂²	1	2	yes	complemented
117	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#418×C₆₇	C₂²	1	1	yes	characteristic
124	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#417×C₆₇	C₂²	1	1	yes	characteristic
126	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#416×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
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, complemented
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₆₇	—	2	4	no	—
136	H(5,𝔽₂)×C₆₇	—	2	4	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	2	no	—
139	C₂×#41×C₆₇	C₂³	1	2	yes	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	—	2	2	no	—
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
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	—	2	2	no	—
150	C₂³×C₄×C₆₇	—	2	1	no	—
151	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
152	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
153	#135×C₆₇	—	2	4	no	—
154	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×D₈×C₆₇	—	2	4	no	—
160	C₂×D₈×C₆₇	C₂³	1	2	yes	—
161	C₂×D₈×C₆₇	C₂³	1	2	yes	—
162	C₂×D₈×C₆₇	C₂³	1	2	yes	—
163	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×D₈×C₆₇	C₂³	1	2	yes	—
165	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₆₇	—	2	1	no	—
170	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
171	#127×C₆₇	—	2	1	no	—
172	#127×C₆₇	C₂³	1	2	yes	—
173	#126×C₆₇	—	2	2	no	—
174	#126×C₆₇	—	2	2	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	C₂³	1	2	yes	—
177	#124×C₆₇	—	2	1	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	2	no	—
180	#124×C₆₇	C₂³	1	2	yes	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
189	#121×C₆₇	—	2	2	no	—
190	#121×C₆₇	—	2	1	no	—
191	#121×C₆₇	—	2	2	no	—
192	#121×C₆₇	—	2	1	no	—
193	#121×C₆₇	—	2	1	no	—
194	#121×C₆₇	—	2	2	no	—
195	#121×C₆₇	—	2	2	no	—
196	#121×C₆₇	C₂³	1	2	yes	—
197	#121×C₆₇	C₂³	1	2	yes	—
198	#121×C₆₇	C₂³	1	2	yes	—
199	#120×C₆₇	—	2	2	no	—
200	#120×C₆₇	—	2	2	no	—
201	C₄×Q₈×C₆₇	—	2	1	no	—
202	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
203	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
205	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
209	C₄×D₄×C₆₇	—	2	2	no	—
210	C₄×D₄×C₆₇	—	2	1	no	—
211	C₄×D₄×C₆₇	—	2	1	no	—
212	C₄×D₄×C₆₇	—	2	2	no	—
213	C₄×D₄×C₆₇	—	2	1	no	—
214	C₄×D₄×C₆₇	—	2	2	no	—
215	C₄×D₄×C₆₇	—	2	1	no	—
216	C₄×D₄×C₆₇	—	2	1	no	—
217	C₄×D₄×C₆₇	—	2	2	no	—
218	C₄×D₄×C₆₇	—	2	1	no	—
219	C₄×D₄×C₆₇	—	2	2	no	—
220	C₄×D₄×C₆₇	—	2	1	no	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	1	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	1	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	D₄	1	2	yes	—
233	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
234	C₄×D₄×C₆₇	D₄	1	2	yes	—
235	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
236	C₄×D₄×C₆₇	C₂³	1	2	yes	—
237	C₄×D₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	#117×C₆₇	—	2	1	no	—
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	—	2	1	no	—
250	#117×C₆₇	—	2	2	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	1	yes	characteristic
257	#117×C₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂×C₂²⋊C₄×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	1	yes	characteristic
275	#107×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
283	#106×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	2	yes	—
294	#102×C₆₇	C₂³	1	2	yes	—
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	C₂⁴×C₆₇	—	2	2	no	—
319	C₂⁴×C₆₇	—	2	1	no	—
320	C₂⁴×C₆₇	—	2	1	no	—
321	#41×C₆₇	—	2	8	no	—
322	#41×C₆₇	—	2	4	no	—
323	#41×C₆₇	—	2	4	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	—	2	2	no	—
329	#41×C₆₇	—	8	4	no	—
330	#41×C₆₇	#41	1	4	yes	complemented
331	C₂×Q₈×C₆₇	—	2	2	no	—
332	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₆₇	—	2	16	no	—
336	C₂×D₄×C₆₇	—	2	8	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	4	no	—
340	C₂×D₄×C₆₇	—	2	4	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
342	C₂×D₄×C₆₇	—	2	2	no	—
343	C₂×D₄×C₆₇	—	2	2	no	—
344	C₂×D₄×C₆₇	—	2	2	no	—
345	C₂×D₄×C₆₇	—	2	2	no	—
346	C₂×D₄×C₆₇	—	2	1	no	—
347	C₂×D₄×C₆₇	—	2	1	no	—
348	C₂×D₄×C₆₇	—	2	2	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	#41	1	4	yes	complemented
356	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
357	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
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	2	no	—
368	C₂²×C₄×C₆₇	—	2	1	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	2	1	no	—
371	C₂²×C₄×C₆₇	—	2	2	no	—
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	—	2	2	no	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	8	2	no	—
378	C₂²×C₄×C₆₇	—	8	2	no	—
379	C₂²×C₄×C₆₇	—	8	4	no	—
380	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
382	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
386	Q₁₆×C₆₇	—	2	2	no	—
387	SD₁₆×C₆₇	—	2	2	no	—
388	SD₁₆×C₆₇	—	2	4	no	—
389	SD₁₆×C₆₇	—	2	2	no	—
390	SD₁₆×C₆₇	—	2	4	no	—
391	D₈×C₆₇	—	2	4	no	—
392	D₈×C₆₇	—	2	4	no	—
393	D₈×C₆₇	—	2	2	no	—
394	D₈×C₆₇	—	2	4	no	—
395	D₈×C₆₇	—	2	4	no	—
396	M₁₆×C₆₇	—	2	2	no	—
397	M₁₆×C₆₇	—	2	2	no	—
398	C₂×C₈×C₆₇	—	2	2	no	—
399	C₂×C₈×C₆₇	—	2	2	no	—
400	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
403	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
404	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	1	no	—
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	1	no	—
413	C₄⋊C₄×C₆₇	—	2	1	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	C₂×D₄	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	1	yes	characteristic
425	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	1	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	1	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	1	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₂²⋊C₄×C₆₇	—	2	1	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
451	C₄²×C₆₇	—	2	1	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	—	2	1	no	—
458	C₄²×C₆₇	—	2	1	no	—
459	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₆₇	C₂×D₄	1	2	yes	—
461	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
462	C₄²×C₆₇	C₂×D₄	1	2	yes	—
463	C₄²×C₆₇	C₂⁴	1	2	yes	—
464	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
465	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
466	C₂³×C₆₇	—	2	8	no	—
467	C₂³×C₆₇	—	2	2	no	—
468	C₂³×C₆₇	—	2	1	no	—
469	C₂³×C₆₇	—	2	4	no	—
470	C₂³×C₆₇	—	2	2	no	—
471	C₂³×C₆₇	—	2	1	no	—
472	C₂³×C₆₇	—	4	2	no	—
473	C₂³×C₆₇	—	8	1	no	—
474	C₂³×C₆₇	—	8	1	no	—
475	C₂³×C₆₇	—	8	2	no	—
476	C₂³×C₆₇	—	8	1	no	—
477	C₂³×C₆₇	—	8	1	no	—
478	C₂³×C₆₇	—	8	2	no	—
479	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
480	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
481	Q₈×C₆₇	—	2	2	no	—
482	Q₈×C₆₇	—	2	1	no	—
483	Q₈×C₆₇	—	2	1	no	—
484	Q₈×C₆₇	—	2	1	no	—
485	Q₈×C₆₇	—	8	2	no	—
486	Q₈×C₆₇	C₂×#41	1	2	yes	—
487	D₄×C₆₇	—	2	8	no	—
488	D₄×C₆₇	—	2	8	no	—
489	D₄×C₆₇	—	2	4	no	—
490	D₄×C₆₇	—	2	4	no	—
491	D₄×C₆₇	—	2	2	no	—
492	D₄×C₆₇	—	2	4	no	—
493	D₄×C₆₇	—	2	2	no	—
494	D₄×C₆₇	—	2	1	no	—
495	D₄×C₆₇	—	2	2	no	—
496	D₄×C₆₇	—	2	1	no	—
497	D₄×C₆₇	—	2	2	no	—
498	D₄×C₆₇	—	2	1	no	—
499	D₄×C₆₇	—	4	2	no	—
500	D₄×C₆₇	—	4	2	no	—
501	D₄×C₆₇	—	8	2	no	—
502	D₄×C₆₇	—	8	2	no	—
503	D₄×C₆₇	—	8	2	no	—
504	D₄×C₆₇	—	8	2	no	—
505	D₄×C₆₇	—	8	2	no	—
506	D₄×C₆₇	C₂×#41	1	2	yes	—
507	D₄×C₆₇	C₂×#41	1	4	yes	—
508	C₂×C₄×C₆₇	—	2	8	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	4	no	—
511	C₂×C₄×C₆₇	—	2	2	no	—
512	C₂×C₄×C₆₇	—	2	4	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	2	2	no	—
515	C₂×C₄×C₆₇	—	2	1	no	—
516	C₂×C₄×C₆₇	—	2	1	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	2	1	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	4	1	no	—
523	C₂×C₄×C₆₇	—	4	2	no	—
524	C₂×C₄×C₆₇	—	4	2	no	—
525	C₂×C₄×C₆₇	—	4	2	no	—
526	C₂×C₄×C₆₇	—	4	4	no	—
527	C₂×C₄×C₆₇	—	4	4	no	—
528	C₂×C₄×C₆₇	—	4	2	no	—
529	C₂×C₄×C₆₇	—	8	1	no	—
530	C₂×C₄×C₆₇	—	8	1	no	—
531	C₂×C₄×C₆₇	—	8	2	no	—
532	C₂×C₄×C₆₇	—	8	2	no	—
533	C₂×C₄×C₆₇	—	8	2	no	—
534	C₂×C₄×C₆₇	—	8	2	no	—
535	C₂×C₄×C₆₇	—	8	2	no	—
536	C₂×C₄×C₆₇	—	8	1	no	—
537	C₂×C₄×C₆₇	—	8	2	no	—
538	C₂×C₄×C₆₇	—	8	1	no	—
539	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
548	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
549	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
550	C₈×C₆₇	—	2	1	no	—
551	C₈×C₆₇	—	2	1	no	—
552	C₈×C₆₇	—	2	1	no	—
553	C₈×C₆₇	—	2	1	no	—
554	C₈×C₆₇	—	2	2	no	—
555	C₈×C₆₇	—	2	2	no	—
556	C₂²×C₆₇	—	2	1	no	—
557	C₂²×C₆₇	—	2	1	no	—
558	C₂²×C₆₇	—	2	2	no	—
559	C₂²×C₆₇	—	2	2	no	—
560	C₂²×C₆₇	—	2	4	no	—
561	C₂²×C₆₇	—	2	2	no	—
562	C₂²×C₆₇	—	2	2	no	—
563	C₂²×C₆₇	—	4	2	no	—
564	C₂²×C₆₇	—	4	1	no	—
565	C₂²×C₆₇	—	4	2	no	—
566	C₂²×C₆₇	—	4	1	no	—
567	C₂²×C₆₇	—	4	1	no	—
568	C₂²×C₆₇	—	4	2	no	—
569	C₂²×C₆₇	—	4	1	no	—
570	C₂²×C₆₇	—	4	2	no	—
571	C₂²×C₆₇	—	4	2	no	—
572	C₂²×C₆₇	—	4	1	no	—
573	C₂²×C₆₇	—	8	4	no	—
574	C₂²×C₆₇	—	8	4	no	—
575	C₂²×C₆₇	—	8	8	no	—
576	C₂²×C₆₇	#525	1	2	yes	—
577	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
578	C₄×C₆₇	—	2	1	no	—
579	C₄×C₆₇	—	2	1	no	—
580	C₄×C₆₇	—	2	2	no	—
581	C₄×C₆₇	—	2	2	no	—
582	C₄×C₆₇	—	2	2	no	—
583	C₄×C₆₇	—	2	1	no	—
584	C₄×C₆₇	—	2	2	no	—
585	C₄×C₆₇	—	4	1	no	—
586	C₄×C₆₇	—	4	1	no	—
587	C₄×C₆₇	—	4	1	no	—
588	C₄×C₆₇	—	4	2	no	—
589	C₄×C₆₇	—	4	1	no	—
590	C₄×C₆₇	—	4	2	no	—
591	C₄×C₆₇	—	4	1	no	—
592	C₄×C₆₇	#525	1	2	yes	—
593	C₄×C₆₇	#576	1	2	yes	—
594	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
595	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
596	#60570	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
597	C₂×C₆₇	—	2	2	no	—
598	C₂×C₆₇	—	4	2	no	—
599	C₂×C₆₇	—	4	4	no	—
600	C₂×C₆₇	—	4	2	no	—
601	C₂×C₆₇	—	8	1	no	—
602	C₂×C₆₇	—	8	2	no	—
603	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
604	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
605	C₂×C₆₇	#3584	1	1	yes	characteristic
606	#3460	C₂×C₆₇	1	1	yes	characteristic, complemented
607	C₄×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#3124	C₂×C₆₇	1	2	yes	complemented
609	#3122	C₂×C₆₇	1	2	yes	complemented
610	#3119	C₂×C₆₇	1	2	yes	complemented
611	#3118	C₂×C₆₇	1	2	yes	complemented
612	#3106	C₂×C₆₇	1	2	yes	complemented
613	#3105	C₂×C₆₇	1	2	yes	complemented
614	#3102	C₂×C₆₇	1	2	yes	complemented
615	#3100	C₂×C₆₇	1	2	yes	complemented
616	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3096	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#3041	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
624	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
625	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
626	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
627	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#2922	C₂×C₆₇	1	1	yes	characteristic, complemented
629	C₆₇	#60570	1	1	yes	characteristic, direct product factor, Sylow
630	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
631	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
632	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
633	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
634	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
635	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	#542	—	2	1	no	—
637	#542	C₂²×C₆₇	1	2	yes	complemented
638	#540	—	2	1	no	—
639	#540	C₂²×C₆₇	1	2	yes	complemented
640	#538	—	2	2	no	—
641	#537	C₂²×C₆₇	1	1	yes	characteristic
642	#535	C₂²×C₆₇	1	1	yes	characteristic
643	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	#532	—	2	1	no	—
645	#532	C₂²×C₆₇	1	2	yes	complemented
646	#529	—	2	1	no	—
647	#529	C₂²×C₆₇	1	2	yes	complemented
648	#525	—	2	2	no	—
649	#520	—	2	1	no	—
650	#520	C₂²×C₆₇	1	1	yes	characteristic
651	#520	C₂²×C₆₇	1	1	yes	characteristic
652	#520	C₂²×C₆₇	1	2	yes	complemented
653	#518	—	2	2	no	—
654	#518	—	2	1	no	—
655	#518	C₂²×C₆₇	1	1	yes	characteristic
656	#518	C₂²×C₆₇	1	2	yes	complemented
657	C₄×#41	—	2	1	no	—
658	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
659	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
660	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
661	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	C₂×C₄×D₄	—	2	1	no	—
663	C₂×C₄×D₄	—	2	2	no	—
664	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
665	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
666	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#485	C₂²×C₆₇	1	2	yes	complemented
668	#484	C₂²×C₆₇	1	2	yes	complemented
669	#482	C₂²×C₆₇	1	2	yes	complemented
670	#482	C₂²×C₆₇	1	2	yes	complemented
671	#482	C₂²×C₆₇	1	2	yes	complemented
672	#481	C₂²×C₆₇	1	2	yes	complemented
673	#480	C₂²×C₆₇	1	2	yes	complemented
674	#480	C₂²×C₆₇	1	2	yes	complemented
675	#479	C₂²×C₆₇	1	2	yes	complemented
676	#478	C₂²×C₆₇	1	2	yes	complemented
677	#478	C₂²×C₆₇	1	2	yes	complemented
678	#478	C₂²×C₆₇	1	2	yes	complemented
679	#477	C₂²×C₆₇	1	2	yes	complemented
680	#476	C₂²×C₆₇	1	2	yes	complemented
681	#474	C₂²×C₆₇	1	2	yes	complemented
682	#474	C₂²×C₆₇	1	2	yes	complemented
683	#464	C₂²×C₆₇	1	2	yes	complemented
684	#463	C₂²×C₆₇	1	2	yes	complemented
685	#463	C₂²×C₆₇	1	2	yes	complemented
686	#463	C₂²×C₆₇	1	2	yes	complemented
687	#460	C₂²×C₆₇	1	2	yes	complemented
688	#459	C₂²×C₆₇	1	2	yes	complemented
689	#459	C₂²×C₆₇	1	2	yes	complemented
690	#459	C₂²×C₆₇	1	2	yes	complemented
691	#452	C₂²×C₆₇	1	2	yes	complemented
692	#450	C₂²×C₆₇	1	2	yes	complemented
693	#449	C₂²×C₆₇	1	2	yes	—
694	#449	C₂²×C₆₇	1	2	yes	—
695	#449	C₂²×C₆₇	1	2	yes	complemented
696	#447	C₂²×C₆₇	1	2	yes	—
697	#447	C₂²×C₆₇	1	2	yes	—
698	#447	C₂²×C₆₇	1	2	yes	complemented
699	#442	C₂²×C₆₇	1	2	yes	complemented
700	#442	C₂²×C₆₇	1	2	yes	complemented
701	#440	C₂²×C₆₇	1	2	yes	complemented
702	#440	C₂²×C₆₇	1	2	yes	complemented
703	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
705	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
707	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
713	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
714	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
715	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
716	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
717	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
719	#433	C₂²×C₆₇	1	2	yes	complemented
720	#433	C₂²×C₆₇	1	2	yes	complemented
721	#431	C₂²×C₆₇	1	2	yes	complemented
722	#431	C₂²×C₆₇	1	2	yes	complemented
723	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	#418	C₂²×C₆₇	1	1	yes	characteristic
730	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	#417	C₂²×C₆₇	1	1	yes	characteristic
732	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	#416	C₂²×C₆₇	1	1	yes	characteristic
734	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
736	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
737	#408	C₂²×C₆₇	1	1	yes	characteristic
738	#408	C₂²×C₆₇	1	1	yes	characteristic
739	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
740	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	H(5,𝔽₂)	—	2	4	no	—
742	H(5,𝔽₂)	—	2	4	no	—
743	C₂×#41	—	2	1	no	—
744	C₂×#41	—	2	2	no	—
745	C₂×#41	C₂³×C₆₇	1	2	yes	—
746	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
749	C₂²×D₄	—	2	2	no	—
750	C₂²×D₄	—	2	1	no	—
751	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
752	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
753	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
754	C₂³×C₄	—	2	1	no	—
755	C₂³×C₄	—	2	2	no	—
756	C₂³×C₄	—	2	1	no	—
757	AGL(1,ℤ/8)	—	2	4	no	—
758	AGL(1,ℤ/8)	—	2	4	no	—
759	#135	—	2	4	no	—
760	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
765	C₂×D₈	—	2	4	no	—
766	C₂×D₈	C₂³×C₆₇	1	2	yes	—
767	C₂×D₈	C₂³×C₆₇	1	2	yes	—
768	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×D₈	C₂³×C₆₇	1	2	yes	—
770	C₂×D₈	C₂³×C₆₇	1	2	yes	—
771	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
774	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
775	C₄⋊Q₈	—	2	1	no	—
776	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
777	#127	—	2	1	no	—
778	#127	C₂³×C₆₇	1	2	yes	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#125	—	2	1	no	—
782	#125	C₂³×C₆₇	1	2	yes	—
783	#124	—	2	1	no	—
784	#124	—	2	2	no	—
785	#124	—	2	2	no	—
786	#124	C₂³×C₆₇	1	2	yes	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	C₂³×C₆₇	1	2	yes	—
803	#121	C₂³×C₆₇	1	2	yes	—
804	#121	C₂³×C₆₇	1	2	yes	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
809	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
813	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	D₄×C₆₇	1	2	yes	—
839	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
840	C₄×D₄	D₄×C₆₇	1	2	yes	—
841	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₆₇	1	2	yes	—
843	C₄×D₄	C₂³×C₆₇	1	2	yes	—
844	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₆₇	1	2	yes	—
846	C₄×D₄	C₂³×C₆₇	1	2	yes	—
847	C₄×D₄	C₂³×C₆₇	1	2	yes	—
848	C₄×D₄	C₂³×C₆₇	1	2	yes	—
849	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₆₇	1	2	yes	—
851	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
853	#117	—	2	1	no	—
854	#117	—	2	2	no	—
855	#117	—	2	1	no	—
856	#117	—	2	2	no	—
857	#117	—	2	1	no	—
858	#117	—	2	2	no	—
859	#117	C₂³×C₆₇	1	1	yes	characteristic
860	#117	C₂³×C₆₇	1	2	yes	—
861	#117	C₂³×C₆₇	1	1	yes	characteristic
862	#117	C₂³×C₆₇	1	1	yes	characteristic
863	#117	C₂³×C₆₇	1	2	yes	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	—	2	2	no	—
866	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
868	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
869	C₂×C₂²⋊C₄	—	2	1	no	—
870	C₂×C₂²⋊C₄	—	2	2	no	—
871	C₂×C₂²⋊C₄	—	2	1	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₂²⋊C₄	—	2	2	no	—
875	C₂×C₄²	—	2	1	no	—
876	C₂×C₄²	—	2	2	no	—
877	C₂×C₄²	—	2	1	no	—
878	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
879	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
880	#107	C₂³×C₆₇	1	2	yes	—
881	#107	C₂³×C₆₇	1	2	yes	—
882	#107	C₂³×C₆₇	1	1	yes	characteristic
883	#107	C₂³×C₆₇	1	1	yes	characteristic
884	#107	C₂³×C₆₇	1	2	yes	—
885	#107	C₂³×C₆₇	1	2	yes	—
886	#106	C₂³×C₆₇	1	1	yes	characteristic
887	#106	C₂³×C₆₇	1	1	yes	characteristic
888	#106	C₂³×C₆₇	1	2	yes	—
889	#106	C₂³×C₆₇	1	2	yes	—
890	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
891	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
892	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
893	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
894	#103	C₂³×C₆₇	1	1	yes	characteristic
895	#103	C₂³×C₆₇	1	1	yes	characteristic
896	#103	C₂³×C₆₇	1	1	yes	characteristic
897	#103	C₂³×C₆₇	1	1	yes	characteristic
898	#103	C₂³×C₆₇	1	2	yes	—
899	#103	C₂³×C₆₇	1	2	yes	—
900	#102	C₂³×C₆₇	1	2	yes	—
901	#102	C₂³×C₆₇	1	2	yes	—
902	#102	C₂³×C₆₇	1	2	yes	—
903	#102	C₂³×C₆₇	1	2	yes	—
904	#102	C₂³×C₆₇	1	1	yes	characteristic
905	#102	C₂³×C₆₇	1	1	yes	characteristic
906	#102	C₂³×C₆₇	1	1	yes	characteristic
907	#102	C₂³×C₆₇	1	1	yes	characteristic
908	#102	C₂³×C₆₇	1	2	yes	—
909	#102	C₂³×C₆₇	1	2	yes	—
910	#102	C₂³×C₆₇	1	2	yes	—
911	#102	C₂³×C₆₇	1	2	yes	—
912	#102	C₂³×C₆₇	1	2	yes	—
913	#102	C₂³×C₆₇	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
918	#97	C₂³×C₆₇	1	2	yes	—
919	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
920	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
921	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
922	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
923	C₄×C₈	C₂³×C₆₇	1	2	yes	—
924	C₂⁴	—	2	2	no	—
925	C₂⁴	—	2	1	no	—
926	C₂⁴	—	2	1	no	—
927	#41	—	2	8	no	—
928	#41	—	2	4	no	—
929	#41	—	2	4	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	8	4	no	—
936	#41	#41×C₆₇	1	4	yes	complemented
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
939	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₂×D₄	—	2	16	no	—
942	C₂×D₄	—	2	8	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
960	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
961	C₂×D₄	#41×C₆₇	1	4	yes	complemented
962	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
963	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
965	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	8	2	no	—
984	C₂²×C₄	—	8	2	no	—
985	C₂²×C₄	—	8	4	no	—
986	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
988	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
989	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
990	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
991	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
992	Q₁₆	—	2	2	no	—
993	SD₁₆	—	2	2	no	—
994	SD₁₆	—	2	4	no	—
995	SD₁₆	—	2	2	no	—
996	SD₁₆	—	2	4	no	—
997	D₈	—	2	4	no	—
998	D₈	—	2	4	no	—
999	D₈	—	2	2	no	—
1000	D₈	—	2	4	no	—
1001	D₈	—	2	4	no	—
1002	M₁₆	—	2	2	no	—
1003	M₁₆	—	2	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1010	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1011	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1025	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1026	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1027	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1028	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1029	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1031	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1033	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1055	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1056	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1066	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1067	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1068	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1069	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1070	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1071	C₄²	C₂⁴×C₆₇	1	2	yes	—
1072	C₂³	—	2	8	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	4	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	4	2	no	—
1079	C₂³	—	8	1	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	1	no	—
1083	C₂³	—	8	1	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1086	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	8	2	no	—
1092	Q₈	C₂×#41×C₆₇	1	2	yes	—
1093	D₄	—	2	8	no	—
1094	D₄	—	2	8	no	—
1095	D₄	—	2	4	no	—
1096	D₄	—	2	4	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	2	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	2	no	—
1112	D₄	C₂×#41×C₆₇	1	2	yes	—
1113	D₄	C₂×#41×C₆₇	1	4	yes	—
1114	C₂×C₄	—	2	8	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	4	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	4	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	2	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	2	no	—
1139	C₂×C₄	—	8	1	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	8	2	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	2	no	—
1144	C₂×C₄	—	8	1	no	—
1145	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1146	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1147	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1148	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1150	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1151	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1152	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1153	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1154	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1155	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	2	2	no	—
1161	C₈	—	2	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	4	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	8	4	no	—
1180	C₂²	—	8	4	no	—
1181	C₂²	—	8	8	no	—
1182	C₂²	#525×C₆₇	1	2	yes	—
1183	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1184	C₄	—	2	1	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	1	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	4	2	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	#525×C₆₇	1	2	yes	—
1199	C₄	#576×C₆₇	1	2	yes	—
1200	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1201	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1202	C₂	—	2	2	no	—
1203	C₂	—	4	2	no	—
1204	C₂	—	4	4	no	—
1205	C₂	—	4	2	no	—
1206	C₂	—	8	2	no	—
1207	C₂	—	8	1	no	—
1208	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1209	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1210	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×H(5,𝔽₂)×C₆₇	C₂	semidirect
3. C₆₇×#3124	C₂	semidirect
4. C₆₇×#3122	C₂	semidirect
5. C₆₇×#3119	C₂	semidirect
6. C₆₇×#3118	C₂	semidirect
7. C₆₇×#3106	C₂	semidirect
8. C₆₇×#3105	C₂	semidirect
9. C₆₇×#3102	C₂	semidirect
10. C₆₇×#3100	C₂	semidirect
11. C₆₇×#3098	C₂	semidirect
12. C₆₇×#3096	C₂	semidirect
13. C₆₇×#3083	C₂	semidirect
14. C₆₇×#3081	C₂	semidirect
15. C₆₇×#3045	C₂	semidirect
16. C₆₇×#3041	C₂	semidirect
17. C₆₇×#3012	C₂	semidirect
18. C₆₇×#3008	C₂	semidirect
19. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
21. C₄×#135×C₆₇	C₂	semidirect
22. C₂×C₄×D₈×C₆₇	C₂	semidirect
23. C₆₇×#2922	C₂	semidirect
29. #544×C₆₇	C₂²	semidirect
31. #542×C₆₇	C₂²	semidirect
33. #540×C₆₇	C₂²	semidirect
37. #535×C₆₇	C₂²	semidirect
39. #532×C₆₇	C₂²	semidirect
41. #529×C₆₇	C₂²	semidirect
46. #520×C₆₇	C₂²	semidirect
50. #518×C₆₇	C₂²	semidirect
54. C₄×#41×C₆₇	C₂²	semidirect
55. C₄×#41×C₆₇	C₂²	semidirect
59. C₂×C₄×D₄×C₆₇	C₂²	semidirect
60. C₂×C₄×D₄×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #484×C₆₇	C₂²	semidirect
63. #482×C₆₇	C₂²	semidirect
64. #482×C₆₇	C₂²	semidirect
65. #482×C₆₇	C₂²	semidirect
66. #481×C₆₇	C₂²	semidirect
67. #480×C₆₇	C₂²	semidirect
68. #480×C₆₇	C₂²	semidirect
69. #479×C₆₇	C₂²	semidirect
70. #478×C₆₇	C₂²	semidirect
71. #478×C₆₇	C₂²	semidirect
72. #478×C₆₇	C₂²	semidirect
73. #477×C₆₇	C₂²	semidirect
74. #476×C₆₇	C₂²	semidirect
75. #474×C₆₇	C₂²	semidirect
76. #474×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #463×C₆₇	C₂²	semidirect
79. #463×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #460×C₆₇	C₂²	semidirect
82. #459×C₆₇	C₂²	semidirect
83. #459×C₆₇	C₂²	semidirect
84. #459×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #450×C₆₇	C₂²	semidirect
89. #449×C₆₇	C₂²	semidirect
92. #447×C₆₇	C₂²	semidirect
93. #442×C₆₇	C₂²	semidirect
94. #442×C₆₇	C₂²	semidirect
95. #440×C₆₇	C₂²	semidirect
96. #440×C₆₇	C₂²	semidirect
97. C₄×Q₁₆×C₆₇	C₂²	semidirect
98. C₄×Q₁₆×C₆₇	C₂²	semidirect
99. C₄×SD₁₆×C₆₇	C₂²	semidirect
100. C₄×SD₁₆×C₆₇	C₂²	semidirect
101. C₄×SD₁₆×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. C₄×SD₁₆×C₆₇	C₂²	semidirect
104. C₄×SD₁₆×C₆₇	C₂²	semidirect
105. C₄×D₈×C₆₇	C₂²	semidirect
106. C₄×D₈×C₆₇	C₂²	semidirect
107. C₄×D₈×C₆₇	C₂²	semidirect
108. C₄×D₈×C₆₇	C₂²	semidirect
109. C₄×D₈×C₆₇	C₂²	semidirect
110. C₄×D₈×C₆₇	C₂²	semidirect
111. C₄×D₈×C₆₇	C₂²	semidirect
112. C₄×D₈×C₆₇	C₂²	semidirect
113. #433×C₆₇	C₂²	semidirect
114. #433×C₆₇	C₂²	semidirect
115. #431×C₆₇	C₂²	semidirect
116. #431×C₆₇	C₂²	semidirect
117. #428×C₆₇	C₂²	semidirect
118. #428×C₆₇	C₂²	semidirect
119. #427×C₆₇	C₂²	semidirect
120. C₂×#107×C₆₇	C₂²	semidirect
121. #424×C₆₇	C₂²	semidirect
122. #424×C₆₇	C₂²	semidirect
124. #418×C₆₇	C₂²	semidirect
126. #417×C₆₇	C₂²	semidirect
128. #416×C₆₇	C₂²	semidirect
130. C₂×#102×C₆₇	C₂²	semidirect
133. C₄×M₁₆×C₆₇	C₂²	semidirect
134. C₂×C₄×C₈×C₆₇	C₂²	semidirect
330. #41×C₆₇	#41	semidirect
355. C₂×D₄×C₆₇	#41	semidirect
596. #60570	C₆₇	direct (N × H)
606. #3460	C₂×C₆₇	semidirect
607. C₄×H(5,𝔽₂)	C₂×C₆₇	semidirect
608. #3124	C₂×C₆₇	semidirect
609. #3122	C₂×C₆₇	semidirect
610. #3119	C₂×C₆₇	semidirect
611. #3118	C₂×C₆₇	semidirect
612. #3106	C₂×C₆₇	semidirect
613. #3105	C₂×C₆₇	semidirect
614. #3102	C₂×C₆₇	semidirect
615. #3100	C₂×C₆₇	semidirect
616. #3098	C₂×C₆₇	semidirect
617. #3096	C₂×C₆₇	semidirect
618. #3083	C₂×C₆₇	semidirect
619. #3081	C₂×C₆₇	semidirect
620. #3045	C₂×C₆₇	semidirect
621. #3041	C₂×C₆₇	semidirect
622. #3012	C₂×C₆₇	semidirect
623. #3008	C₂×C₆₇	semidirect
624. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
625. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
626. C₄×#135	C₂×C₆₇	semidirect
627. C₂×C₄×D₈	C₂×C₆₇	semidirect
628. #2922	C₂×C₆₇	semidirect
629. C₆₇	#60570	direct (N × H)
635. #544	C₂²×C₆₇	semidirect
637. #542	C₂²×C₆₇	semidirect
639. #540	C₂²×C₆₇	semidirect
643. #535	C₂²×C₆₇	semidirect
645. #532	C₂²×C₆₇	semidirect
647. #529	C₂²×C₆₇	semidirect
652. #520	C₂²×C₆₇	semidirect
656. #518	C₂²×C₆₇	semidirect
660. C₄×#41	C₂²×C₆₇	semidirect
661. C₄×#41	C₂²×C₆₇	semidirect
665. C₂×C₄×D₄	C₂²×C₆₇	semidirect
666. C₂×C₄×D₄	C₂²×C₆₇	semidirect
667. #485	C₂²×C₆₇	semidirect
668. #484	C₂²×C₆₇	semidirect
669. #482	C₂²×C₆₇	semidirect
670. #482	C₂²×C₆₇	semidirect
671. #482	C₂²×C₆₇	semidirect
672. #481	C₂²×C₆₇	semidirect
673. #480	C₂²×C₆₇	semidirect
674. #480	C₂²×C₆₇	semidirect
675. #479	C₂²×C₆₇	semidirect
676. #478	C₂²×C₆₇	semidirect
677. #478	C₂²×C₆₇	semidirect
678. #478	C₂²×C₆₇	semidirect
679. #477	C₂²×C₆₇	semidirect
680. #476	C₂²×C₆₇	semidirect
681. #474	C₂²×C₆₇	semidirect
682. #474	C₂²×C₆₇	semidirect
683. #464	C₂²×C₆₇	semidirect
684. #463	C₂²×C₆₇	semidirect
685. #463	C₂²×C₆₇	semidirect
686. #463	C₂²×C₆₇	semidirect
687. #460	C₂²×C₆₇	semidirect
688. #459	C₂²×C₆₇	semidirect
689. #459	C₂²×C₆₇	semidirect
690. #459	C₂²×C₆₇	semidirect
691. #452	C₂²×C₆₇	semidirect
692. #450	C₂²×C₆₇	semidirect
695. #449	C₂²×C₆₇	semidirect
698. #447	C₂²×C₆₇	semidirect
699. #442	C₂²×C₆₇	semidirect
700. #442	C₂²×C₆₇	semidirect
701. #440	C₂²×C₆₇	semidirect
702. #440	C₂²×C₆₇	semidirect
703. C₄×Q₁₆	C₂²×C₆₇	semidirect
704. C₄×Q₁₆	C₂²×C₆₇	semidirect
705. C₄×SD₁₆	C₂²×C₆₇	semidirect
706. C₄×SD₁₆	C₂²×C₆₇	semidirect
707. C₄×SD₁₆	C₂²×C₆₇	semidirect
708. C₄×SD₁₆	C₂²×C₆₇	semidirect
709. C₄×SD₁₆	C₂²×C₆₇	semidirect
710. C₄×SD₁₆	C₂²×C₆₇	semidirect
711. C₄×D₈	C₂²×C₆₇	semidirect
712. C₄×D₈	C₂²×C₆₇	semidirect
713. C₄×D₈	C₂²×C₆₇	semidirect
714. C₄×D₈	C₂²×C₆₇	semidirect
715. C₄×D₈	C₂²×C₆₇	semidirect
716. C₄×D₈	C₂²×C₆₇	semidirect
717. C₄×D₈	C₂²×C₆₇	semidirect
718. C₄×D₈	C₂²×C₆₇	semidirect
719. #433	C₂²×C₆₇	semidirect
720. #433	C₂²×C₆₇	semidirect
721. #431	C₂²×C₆₇	semidirect
722. #431	C₂²×C₆₇	semidirect
723. #428	C₂²×C₆₇	semidirect
724. #428	C₂²×C₆₇	semidirect
725. #427	C₂²×C₆₇	semidirect
726. C₂×#107	C₂²×C₆₇	semidirect
727. #424	C₂²×C₆₇	semidirect
728. #424	C₂²×C₆₇	semidirect
730. #418	C₂²×C₆₇	semidirect
732. #417	C₂²×C₆₇	semidirect
734. #416	C₂²×C₆₇	semidirect
736. C₂×#102	C₂²×C₆₇	semidirect
739. C₄×M₁₆	C₂²×C₆₇	semidirect
740. C₂×C₄×C₈	C₂²×C₆₇	semidirect
936. #41	#41×C₆₇	semidirect
961. C₂×D₄	#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×H(5,𝔽₂)×C₆₇	2
C₆₇×#3124	2
C₆₇×#3122	2
C₆₇×#3119	2
C₆₇×#3118	2
C₆₇×#3106	2
C₆₇×#3105	2
C₆₇×#3102	2
C₆₇×#3100	2
C₆₇×#3098	2
C₆₇×#3096	2
C₆₇×#3083	2
C₆₇×#3081	2
C₆₇×#3045	2
C₆₇×#3041	2
C₆₇×#3012	2
C₆₇×#3008	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₄×#135×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₆₇×#2922	2
#60570	67

Subgroups — C67×#60570 #30739821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60570 #30739821