Subgroups — C₆₇×#61543 #30740794

Order 17152.

1884 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3324	C₂	1	2	yes	maximal, complemented
13	D₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3265	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3179	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3126	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2949	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
26	Q₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	#556×C₆₇	—	2	2	no	—
28	#556×C₆₇	—	2	1	no	—
29	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#556×C₆₇	C₂²	1	2	yes	complemented
31	#555×C₆₇	—	2	1	no	—
32	#555×C₆₇	C₂²	1	1	yes	characteristic
33	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#554×C₆₇	C₂²	1	1	yes	characteristic
35	#553×C₆₇	—	2	1	no	—
36	#553×C₆₇	C₂²	1	2	yes	—
37	#550×C₆₇	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#548×C₆₇	C₂²	1	2	yes	complemented
40	#546×C₆₇	—	2	1	no	—
41	#546×C₆₇	—	2	2	no	—
42	D₄²×C₆₇	C₂²	1	2	yes	—
43	D₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#542×C₆₇	—	2	2	no	—
45	#542×C₆₇	C₂²	1	2	yes	complemented
46	#540×C₆₇	C₂²	1	2	yes	—
47	#538×C₆₇	—	2	2	no	—
48	#533×C₆₇	—	2	1	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#529×C₆₇	—	2	1	no	—
52	#529×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	—	2	1	no	—
54	C₂×#121×C₆₇	—	2	1	no	—
55	#519×C₆₇	C₂²	1	2	yes	complemented
56	#518×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
59	#501×C₆₇	C₂²	1	2	yes	complemented
60	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#496×C₆₇	C₂²	1	2	yes	complemented
62	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#488×C₆₇	C₂²	1	2	yes	complemented
64	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#486×C₆₇	C₂²	1	2	yes	complemented
66	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#483×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	2	yes	complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	2	yes	complemented
73	#479×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#476×C₆₇	C₂²	1	1	yes	characteristic
77	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#476×C₆₇	C₂²	1	2	yes	complemented
80	#474×C₆₇	C₂²	1	2	yes	—
81	#469×C₆₇	C₂²	1	2	yes	complemented
82	#468×C₆₇	C₂²	1	2	yes	complemented
83	#468×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#466×C₆₇	C₂²	1	2	yes	complemented
86	#465×C₆₇	C₂²	1	2	yes	complemented
87	#463×C₆₇	C₂²	1	2	yes	—
88	#463×C₆₇	C₂²	1	2	yes	complemented
89	#461×C₆₇	C₂²	1	1	yes	characteristic
90	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#460×C₆₇	C₂²	1	2	yes	complemented
92	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#460×C₆₇	C₂²	1	2	yes	complemented
94	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#450×C₆₇	C₂²	1	2	yes	—
96	#450×C₆₇	C₂²	1	2	yes	—
97	#449×C₆₇	C₂²	1	2	yes	complemented
98	#448×C₆₇	C₂²	1	2	yes	complemented
99	#448×C₆₇	C₂²	1	2	yes	complemented
100	#447×C₆₇	C₂²	1	2	yes	—
101	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#442×C₆₇	C₂²	1	1	yes	characteristic
104	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#440×C₆₇	C₂²	1	2	yes	—
106	#440×C₆₇	C₂²	1	1	yes	characteristic
107	#440×C₆₇	C₂²	1	2	yes	complemented
108	#440×C₆₇	C₂²	1	2	yes	complemented
109	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#440×C₆₇	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
118	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	2	yes	complemented
122	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#433×C₆₇	C₂²	1	2	yes	complemented
126	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#427×C₆₇	C₂²	1	2	yes	complemented
129	#419×C₆₇	C₂²	1	2	yes	complemented
130	#418×C₆₇	C₂²	1	1	yes	characteristic
131	#418×C₆₇	C₂²	1	2	yes	—
132	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#405×C₆₇	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	—	2	1	no	—
140	C₂²×D₄×C₆₇	—	2	2	no	—
141	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	—	2	1	no	—
144	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
145	C₂×SD₁₆×C₆₇	—	2	8	no	—
146	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×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	1	yes	characteristic
153	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	—	2	1	no	—
161	C₄⋊Q₈×C₆₇	—	2	1	no	—
162	C₄⋊Q₈×C₆₇	—	2	2	no	—
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	C₂³	1	1	yes	characteristic
168	#127×C₆₇	C₂³	1	2	yes	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#126×C₆₇	—	2	2	no	—
174	#126×C₆₇	D₄	1	2	yes	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	D₄	1	1	yes	characteristic
177	#125×C₆₇	C₂³	1	2	yes	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	2	no	—
180	#124×C₆₇	—	2	2	no	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	—	2	2	no	—
183	#124×C₆₇	—	2	1	no	—
184	#124×C₆₇	D₄	1	1	yes	characteristic
185	#124×C₆₇	C₂³	1	2	yes	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	D₄	1	2	yes	—
191	C₂²⋊Q₈×C₆₇	—	2	1	no	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	—	2	2	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	1	no	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	D₄	1	1	yes	characteristic
213	#121×C₆₇	C₂³	1	2	yes	—
214	#121×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#120×C₆₇	—	2	2	no	—
218	#120×C₆₇	—	2	2	no	—
219	#120×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	—	2	1	no	—
221	C₄×Q₈×C₆₇	—	2	2	no	—
222	C₄×Q₈×C₆₇	—	2	2	no	—
223	C₄×Q₈×C₆₇	—	2	2	no	—
224	C₄×Q₈×C₆₇	—	2	1	no	—
225	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
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	2	yes	—
245	C₄×D₄×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₇	C₂³	1	2	yes	—
250	C₄×D₄×C₆₇	C₂³	1	2	yes	—
251	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
252	#117×C₆₇	—	2	1	no	—
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	—	2	1	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	—	2	2	no	—
257	#117×C₆₇	—	2	2	no	—
258	#117×C₆₇	—	2	1	no	—
259	#117×C₆₇	C₂³	1	1	yes	characteristic
260	#117×C₆₇	C₂³	1	2	yes	—
261	#117×C₆₇	C₂³	1	2	yes	—
262	#117×C₆₇	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	2	yes	—
271	#107×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	2	yes	—
273	#107×C₆₇	C₂³	1	1	yes	characteristic
274	#107×C₆₇	C₂³	1	1	yes	characteristic
275	#106×C₆₇	C₂³	1	1	yes	characteristic
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	1	yes	characteristic
279	#106×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	1	yes	characteristic
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#102×C₆₇	C₂³	1	2	yes	—
292	#102×C₆₇	C₂³	1	1	yes	characteristic
293	#102×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	1	yes	characteristic
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	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₂⁴×C₆₇	—	2	1	no	—
315	C₂⁴×C₆₇	—	2	2	no	—
316	#41×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	4	1	no	—
318	#41×C₆₇	—	8	2	no	—
319	#41×C₆₇	—	8	2	no	—
320	C₂×Q₈×C₆₇	—	2	2	no	—
321	C₂×Q₈×C₆₇	—	2	1	no	—
322	C₂×Q₈×C₆₇	—	2	2	no	—
323	C₂×Q₈×C₆₇	—	2	1	no	—
324	C₂×Q₈×C₆₇	—	2	4	no	—
325	C₂×Q₈×C₆₇	—	4	2	no	—
326	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₆₇	—	2	4	no	—
330	C₂×D₄×C₆₇	—	2	2	no	—
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	1	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	2	2	no	—
342	C₂×D₄×C₆₇	—	4	2	no	—
343	C₂×D₄×C₆₇	—	4	1	no	—
344	C₂×D₄×C₆₇	—	8	2	no	—
345	C₂×D₄×C₆₇	—	8	4	no	—
346	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
351	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	1	no	—
354	C₂²×C₄×C₆₇	—	2	1	no	—
355	C₂²×C₄×C₆₇	—	2	1	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	1	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	2	no	—
361	C₂²×C₄×C₆₇	—	2	2	no	—
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	8	2	no	—
365	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
369	SD₁₆×C₆₇	—	2	4	no	—
370	SD₁₆×C₆₇	—	2	2	no	—
371	SD₁₆×C₆₇	—	2	4	no	—
372	SD₁₆×C₆₇	—	2	4	no	—
373	SD₁₆×C₆₇	—	4	2	no	—
374	SD₁₆×C₆₇	—	4	2	no	—
375	SD₁₆×C₆₇	#41	1	4	yes	complemented
376	D₈×C₆₇	—	2	2	no	—
377	D₈×C₆₇	—	2	2	no	—
378	D₈×C₆₇	—	4	2	no	—
379	M₁₆×C₆₇	—	2	2	no	—
380	M₁₆×C₆₇	—	4	2	no	—
381	M₁₆×C₆₇	—	4	1	no	—
382	C₂×C₈×C₆₇	—	2	4	no	—
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₆₇	—	2	1	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	1	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	1	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	1	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	1	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
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	1	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	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	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄²×C₆₇	C₂⁴	1	2	yes	—
453	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂³×C₆₇	—	2	1	no	—
455	C₂³×C₆₇	—	2	1	no	—
456	C₂³×C₆₇	—	2	2	no	—
457	C₂³×C₆₇	—	2	1	no	—
458	C₂³×C₆₇	—	4	2	no	—
459	C₂³×C₆₇	—	4	4	no	—
460	C₂³×C₆₇	—	4	2	no	—
461	C₂³×C₆₇	—	8	1	no	—
462	C₂³×C₆₇	—	8	2	no	—
463	C₂³×C₆₇	—	8	2	no	—
464	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
465	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₆₇	—	2	2	no	—
467	Q₈×C₆₇	—	2	1	no	—
468	Q₈×C₆₇	—	2	2	no	—
469	Q₈×C₆₇	—	2	2	no	—
470	Q₈×C₆₇	—	4	4	no	—
471	Q₈×C₆₇	—	8	1	no	—
472	Q₈×C₆₇	—	8	2	no	—
473	Q₈×C₆₇	—	8	1	no	—
474	Q₈×C₆₇	C₂×#41	1	2	yes	—
475	D₄×C₆₇	—	2	2	no	—
476	D₄×C₆₇	—	2	1	no	—
477	D₄×C₆₇	—	2	1	no	—
478	D₄×C₆₇	—	2	2	no	—
479	D₄×C₆₇	—	2	1	no	—
480	D₄×C₆₇	—	2	1	no	—
481	D₄×C₆₇	—	2	2	no	—
482	D₄×C₆₇	—	2	1	no	—
483	D₄×C₆₇	—	4	2	no	—
484	D₄×C₆₇	—	4	2	no	—
485	D₄×C₆₇	—	4	4	no	—
486	D₄×C₆₇	—	4	2	no	—
487	D₄×C₆₇	—	4	4	no	—
488	D₄×C₆₇	—	4	2	no	—
489	D₄×C₆₇	—	8	2	no	—
490	D₄×C₆₇	—	8	1	no	—
491	D₄×C₆₇	—	8	2	no	—
492	D₄×C₆₇	—	8	2	no	—
493	D₄×C₆₇	—	8	2	no	—
494	D₄×C₆₇	—	8	2	no	—
495	D₄×C₆₇	C₂×#41	1	2	yes	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	2	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	2	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	4	1	no	—
510	C₂×C₄×C₆₇	—	4	2	no	—
511	C₂×C₄×C₆₇	—	4	4	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	4	2	no	—
514	C₂×C₄×C₆₇	—	4	2	no	—
515	C₂×C₄×C₆₇	—	8	1	no	—
516	C₂×C₄×C₆₇	—	8	1	no	—
517	C₂×C₄×C₆₇	—	8	1	no	—
518	C₂×C₄×C₆₇	—	8	2	no	—
519	C₂×C₄×C₆₇	—	8	2	no	—
520	C₂×C₄×C₆₇	—	8	2	no	—
521	C₂×C₄×C₆₇	—	8	1	no	—
522	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
531	C₈×C₆₇	—	2	2	no	—
532	C₈×C₆₇	—	2	1	no	—
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	—	2	2	no	—
535	C₈×C₆₇	—	2	1	no	—
536	C₈×C₆₇	C₂×#41	1	2	yes	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	2	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	1	no	—
543	C₂²×C₆₇	—	2	2	no	—
544	C₂²×C₆₇	—	4	1	no	—
545	C₂²×C₆₇	—	4	1	no	—
546	C₂²×C₆₇	—	4	2	no	—
547	C₂²×C₆₇	—	4	1	no	—
548	C₂²×C₆₇	—	4	1	no	—
549	C₂²×C₆₇	—	4	1	no	—
550	C₂²×C₆₇	—	4	1	no	—
551	C₂²×C₆₇	—	4	2	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	8	4	no	—
556	C₂²×C₆₇	—	16	4	no	—
557	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₆₇	—	2	1	no	—
559	C₄×C₆₇	—	2	1	no	—
560	C₄×C₆₇	—	2	2	no	—
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	2	no	—
563	C₄×C₆₇	—	2	2	no	—
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	4	2	no	—
567	C₄×C₆₇	—	4	1	no	—
568	C₄×C₆₇	—	4	2	no	—
569	C₄×C₆₇	—	4	2	no	—
570	C₄×C₆₇	—	4	1	no	—
571	C₄×C₆₇	—	4	1	no	—
572	C₄×C₆₇	—	4	1	no	—
573	C₄×C₆₇	#577	1	2	yes	—
574	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
575	C₄×C₆₇	#585	1	1	yes	characteristic
576	#61543	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
577	C₂×C₆₇	—	4	1	no	—
578	C₂×C₆₇	—	4	2	no	—
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	8	1	no	—
581	C₂×C₆₇	—	8	1	no	—
582	C₂×C₆₇	—	8	2	no	—
583	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
584	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
585	C₂×C₆₇	#3585	1	1	yes	characteristic
586	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3518	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3397	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3385	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3362	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3360	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#3350	C₂×C₆₇	1	2	yes	complemented
593	#3341	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#3329	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#3326	C₂×C₆₇	1	2	yes	complemented
596	#3325	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#3324	C₂×C₆₇	1	2	yes	complemented
598	D₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3265	C₂×C₆₇	1	2	yes	complemented
600	#3182	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3179	C₂×C₆₇	1	2	yes	complemented
602	#3126	C₂×C₆₇	1	2	yes	complemented
603	#3118	C₂×C₆₇	1	2	yes	complemented
604	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3101	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2949	C₂×C₆₇	1	2	yes	complemented
608	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
609	C₆₇	#61543	1	1	yes	characteristic, direct product factor, Sylow
610	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
611	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
612	Q₈²	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	#556	—	2	2	no	—
614	#556	—	2	1	no	—
615	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
616	#556	C₂²×C₆₇	1	2	yes	complemented
617	#555	—	2	1	no	—
618	#555	C₂²×C₆₇	1	1	yes	characteristic
619	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
620	#554	C₂²×C₆₇	1	1	yes	characteristic
621	#553	—	2	1	no	—
622	#553	C₂²×C₆₇	1	2	yes	—
623	#550	C₂²×C₆₇	1	1	yes	characteristic
624	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#548	C₂²×C₆₇	1	2	yes	complemented
626	#546	—	2	1	no	—
627	#546	—	2	2	no	—
628	D₄²	C₂²×C₆₇	1	2	yes	—
629	D₄²	C₂²×C₆₇	1	1	yes	characteristic
630	#542	—	2	2	no	—
631	#542	C₂²×C₆₇	1	2	yes	complemented
632	#540	C₂²×C₆₇	1	2	yes	—
633	#538	—	2	2	no	—
634	#533	—	2	1	no	—
635	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	#532	C₂²×C₆₇	1	1	yes	characteristic
637	#529	—	2	1	no	—
638	#529	C₂²×C₆₇	1	1	yes	characteristic
639	#525	—	2	1	no	—
640	C₂×#121	—	2	1	no	—
641	#519	C₂²×C₆₇	1	2	yes	complemented
642	#518	C₂²×C₆₇	1	2	yes	—
643	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
645	#501	C₂²×C₆₇	1	2	yes	complemented
646	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#496	C₂²×C₆₇	1	2	yes	complemented
648	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	#488	C₂²×C₆₇	1	2	yes	complemented
650	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#486	C₂²×C₆₇	1	2	yes	complemented
652	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#485	C₂²×C₆₇	1	2	yes	complemented
654	#483	C₂²×C₆₇	1	2	yes	complemented
655	#482	C₂²×C₆₇	1	2	yes	complemented
656	#482	C₂²×C₆₇	1	2	yes	complemented
657	#482	C₂²×C₆₇	1	2	yes	complemented
658	#482	C₂²×C₆₇	1	2	yes	complemented
659	#479	C₂²×C₆₇	1	2	yes	complemented
660	#479	C₂²×C₆₇	1	2	yes	complemented
661	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#476	C₂²×C₆₇	1	1	yes	characteristic
663	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#476	C₂²×C₆₇	1	2	yes	complemented
666	#474	C₂²×C₆₇	1	2	yes	—
667	#469	C₂²×C₆₇	1	2	yes	complemented
668	#468	C₂²×C₆₇	1	2	yes	complemented
669	#468	C₂²×C₆₇	1	2	yes	complemented
670	#468	C₂²×C₆₇	1	2	yes	complemented
671	#466	C₂²×C₆₇	1	2	yes	complemented
672	#465	C₂²×C₆₇	1	2	yes	complemented
673	#463	C₂²×C₆₇	1	2	yes	—
674	#463	C₂²×C₆₇	1	2	yes	complemented
675	#461	C₂²×C₆₇	1	1	yes	characteristic
676	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#460	C₂²×C₆₇	1	2	yes	complemented
679	#460	C₂²×C₆₇	1	2	yes	complemented
680	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	#450	C₂²×C₆₇	1	2	yes	—
682	#450	C₂²×C₆₇	1	2	yes	—
683	#449	C₂²×C₆₇	1	2	yes	complemented
684	#448	C₂²×C₆₇	1	2	yes	complemented
685	#448	C₂²×C₆₇	1	2	yes	complemented
686	#447	C₂²×C₆₇	1	2	yes	—
687	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#442	C₂²×C₆₇	1	1	yes	characteristic
690	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#440	C₂²×C₆₇	1	2	yes	—
692	#440	C₂²×C₆₇	1	1	yes	characteristic
693	#440	C₂²×C₆₇	1	2	yes	complemented
694	#440	C₂²×C₆₇	1	2	yes	complemented
695	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	#440	C₂²×C₆₇	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
698	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
699	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
700	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
702	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
703	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
704	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
705	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
706	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
707	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#436	C₂²×C₆₇	1	2	yes	complemented
709	#435	C₂²×C₆₇	1	2	yes	complemented
710	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#433	C₂²×C₆₇	1	2	yes	complemented
712	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#427	C₂²×C₆₇	1	2	yes	complemented
715	#419	C₂²×C₆₇	1	2	yes	complemented
716	#418	C₂²×C₆₇	1	1	yes	characteristic
717	#418	C₂²×C₆₇	1	2	yes	—
718	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	#405	C₂²×C₆₇	1	2	yes	complemented
720	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
724	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
729	C₂³×C₄	—	2	1	no	—
730	AGL(1,ℤ/8)	—	2	4	no	—
731	C₂×SD₁₆	—	2	8	no	—
732	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×D₈	C₂³×C₆₇	1	2	yes	—
742	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
745	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	—	2	2	no	—
749	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
753	#127	C₂³×C₆₇	1	1	yes	characteristic
754	#127	C₂³×C₆₇	1	2	yes	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	D₄×C₆₇	1	2	yes	—
761	#125	—	2	1	no	—
762	#125	D₄×C₆₇	1	1	yes	characteristic
763	#125	C₂³×C₆₇	1	2	yes	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	1	no	—
770	#124	D₄×C₆₇	1	1	yes	characteristic
771	#124	C₂³×C₆₇	1	2	yes	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	D₄×C₆₇	1	2	yes	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	D₄×C₆₇	1	1	yes	characteristic
799	#121	C₂³×C₆₇	1	2	yes	—
800	#121	C₂³×C₆₇	1	2	yes	—
801	#121	C₂³×C₆₇	1	2	yes	—
802	#121	C₂³×C₆₇	1	2	yes	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	2	no	—
808	C₄×Q₈	—	2	2	no	—
809	C₄×Q₈	—	2	2	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
814	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
815	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
816	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₆₇	1	2	yes	—
834	C₄×D₄	C₂³×C₆₇	1	2	yes	—
835	C₄×D₄	C₂³×C₆₇	1	2	yes	—
836	C₄×D₄	C₂³×C₆₇	1	2	yes	—
837	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	—	2	2	no	—
844	#117	—	2	1	no	—
845	#117	C₂³×C₆₇	1	1	yes	characteristic
846	#117	C₂³×C₆₇	1	2	yes	—
847	#117	C₂³×C₆₇	1	2	yes	—
848	#117	C₂³×C₆₇	1	2	yes	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
851	C₂×C₂²⋊C₄	—	2	1	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
856	#107	C₂³×C₆₇	1	1	yes	characteristic
857	#107	C₂³×C₆₇	1	2	yes	—
858	#107	C₂³×C₆₇	1	1	yes	characteristic
859	#107	C₂³×C₆₇	1	2	yes	—
860	#107	C₂³×C₆₇	1	2	yes	—
861	#106	C₂³×C₆₇	1	2	yes	—
862	#106	C₂³×C₆₇	1	2	yes	—
863	#106	C₂³×C₆₇	1	1	yes	characteristic
864	#106	C₂³×C₆₇	1	1	yes	characteristic
865	#106	C₂³×C₆₇	1	2	yes	—
866	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
870	#103	C₂³×C₆₇	1	1	yes	characteristic
871	#103	C₂³×C₆₇	1	1	yes	characteristic
872	#103	C₂³×C₆₇	1	2	yes	—
873	#103	C₂³×C₆₇	1	2	yes	—
874	#103	C₂³×C₆₇	1	2	yes	—
875	#103	C₂³×C₆₇	1	2	yes	—
876	#103	C₂³×C₆₇	1	2	yes	—
877	#102	C₂³×C₆₇	1	1	yes	characteristic
878	#102	C₂³×C₆₇	1	1	yes	characteristic
879	#102	C₂³×C₆₇	1	1	yes	characteristic
880	#102	C₂³×C₆₇	1	1	yes	characteristic
881	#102	C₂³×C₆₇	1	2	yes	—
882	#102	C₂³×C₆₇	1	1	yes	characteristic
883	#102	C₂³×C₆₇	1	2	yes	—
884	#102	C₂³×C₆₇	1	2	yes	—
885	#102	C₂³×C₆₇	1	1	yes	characteristic
886	#102	C₂³×C₆₇	1	2	yes	—
887	#102	C₂³×C₆₇	1	2	yes	—
888	#102	C₂³×C₆₇	1	2	yes	—
889	#102	C₂³×C₆₇	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
893	#97	C₂³×C₆₇	1	1	yes	characteristic
894	#97	C₂³×C₆₇	1	1	yes	characteristic
895	#97	C₂³×C₆₇	1	2	yes	—
896	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₆₇	1	2	yes	—
899	C₄×C₈	C₂³×C₆₇	1	2	yes	—
900	C₂⁴	—	2	1	no	—
901	C₂⁴	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	4	1	no	—
904	#41	—	8	2	no	—
905	#41	—	8	2	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	4	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
915	C₂×D₄	—	2	4	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	1	no	—
930	C₂×D₄	—	8	2	no	—
931	C₂×D₄	—	8	4	no	—
932	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
934	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
937	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	8	2	no	—
951	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
955	SD₁₆	—	2	4	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	2	4	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	#41×C₆₇	1	4	yes	complemented
962	D₈	—	2	2	no	—
963	D₈	—	2	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	2	2	no	—
966	M₁₆	—	4	2	no	—
967	M₁₆	—	4	1	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
971	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
974	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₆₇	1	2	yes	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	8	1	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1051	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	4	4	no	—
1057	Q₈	—	8	1	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	C₂×#41×C₆₇	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	C₂×#41×C₆₇	1	2	yes	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1116	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	C₂×#41×C₆₇	1	2	yes	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	8	4	no	—
1142	C₂²	—	16	4	no	—
1143	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	2	no	—
1159	C₄	#577×C₆₇	1	2	yes	—
1160	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1161	C₄	#585×C₆₇	1	1	yes	characteristic
1162	C₂	—	4	1	no	—
1163	C₂	—	4	2	no	—
1164	C₂	—	4	2	no	—
1165	C₂	—	8	1	no	—
1166	C₂	—	8	2	no	—
1167	C₂	—	8	1	no	—
1168	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1169	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1170	C₂	C₆₇×#3585	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3519	C₂	semidirect
2. C₆₇×#3518	C₂	semidirect
3. C₆₇×#3397	C₂	semidirect
4. C₆₇×#3385	C₂	semidirect
5. C₆₇×#3362	C₂	semidirect
6. C₆₇×#3360	C₂	semidirect
7. C₆₇×#3350	C₂	semidirect
8. C₆₇×#3341	C₂	semidirect
9. C₆₇×#3329	C₂	semidirect
10. C₆₇×#3326	C₂	semidirect
11. C₆₇×#3325	C₂	semidirect
12. C₆₇×#3324	C₂	semidirect
13. D₄×SD₁₆×C₆₇	C₂	semidirect
14. C₆₇×#3265	C₂	semidirect
15. C₆₇×#3182	C₂	semidirect
16. C₆₇×#3179	C₂	semidirect
17. C₆₇×#3126	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#3106	C₂	semidirect
20. C₆₇×#3101	C₂	semidirect
21. C₆₇×#2969	C₂	semidirect
22. C₆₇×#2949	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
26. Q₈²×C₆₇	C₂²	semidirect
29. #556×C₆₇	C₂²	semidirect
30. #556×C₆₇	C₂²	semidirect
33. #555×C₆₇	C₂²	semidirect
38. D₄×Q₈×C₆₇	C₂²	semidirect
39. #548×C₆₇	C₂²	semidirect
45. #542×C₆₇	C₂²	semidirect
49. #533×C₆₇	C₂²	semidirect
55. #519×C₆₇	C₂²	semidirect
57. C₄×#41×C₆₇	C₂²	semidirect
59. #501×C₆₇	C₂²	semidirect
60. #500×C₆₇	C₂²	semidirect
61. #496×C₆₇	C₂²	semidirect
62. #492×C₆₇	C₂²	semidirect
63. #488×C₆₇	C₂²	semidirect
64. #487×C₆₇	C₂²	semidirect
65. #486×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #483×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #479×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #477×C₆₇	C₂²	semidirect
77. #476×C₆₇	C₂²	semidirect
78. #476×C₆₇	C₂²	semidirect
79. #476×C₆₇	C₂²	semidirect
81. #469×C₆₇	C₂²	semidirect
82. #468×C₆₇	C₂²	semidirect
83. #468×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #466×C₆₇	C₂²	semidirect
86. #465×C₆₇	C₂²	semidirect
88. #463×C₆₇	C₂²	semidirect
90. #461×C₆₇	C₂²	semidirect
91. #460×C₆₇	C₂²	semidirect
92. #460×C₆₇	C₂²	semidirect
93. #460×C₆₇	C₂²	semidirect
94. #459×C₆₇	C₂²	semidirect
97. #449×C₆₇	C₂²	semidirect
98. #448×C₆₇	C₂²	semidirect
99. #448×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. C₈×Q₈×C₆₇	C₂²	semidirect
104. #442×C₆₇	C₂²	semidirect
107. #440×C₆₇	C₂²	semidirect
108. #440×C₆₇	C₂²	semidirect
109. #440×C₆₇	C₂²	semidirect
110. #440×C₆₇	C₂²	semidirect
114. C₄×SD₁₆×C₆₇	C₂²	semidirect
115. C₄×SD₁₆×C₆₇	C₂²	semidirect
116. C₄×SD₁₆×C₆₇	C₂²	semidirect
117. C₄×SD₁₆×C₆₇	C₂²	semidirect
119. C₄×D₈×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. #433×C₆₇	C₂²	semidirect
126. #431×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #427×C₆₇	C₂²	semidirect
129. #419×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #405×C₆₇	C₂²	semidirect
134. C₄×M₁₆×C₆₇	C₂²	semidirect
375. SD₁₆×C₆₇	#41	semidirect
576. #61543	C₆₇	direct (N × H)
586. #3519	C₂×C₆₇	semidirect
587. #3518	C₂×C₆₇	semidirect
588. #3397	C₂×C₆₇	semidirect
589. #3385	C₂×C₆₇	semidirect
590. #3362	C₂×C₆₇	semidirect
591. #3360	C₂×C₆₇	semidirect
592. #3350	C₂×C₆₇	semidirect
593. #3341	C₂×C₆₇	semidirect
594. #3329	C₂×C₆₇	semidirect
595. #3326	C₂×C₆₇	semidirect
596. #3325	C₂×C₆₇	semidirect
597. #3324	C₂×C₆₇	semidirect
598. D₄×SD₁₆	C₂×C₆₇	semidirect
599. #3265	C₂×C₆₇	semidirect
600. #3182	C₂×C₆₇	semidirect
601. #3179	C₂×C₆₇	semidirect
602. #3126	C₂×C₆₇	semidirect
603. #3118	C₂×C₆₇	semidirect
604. #3106	C₂×C₆₇	semidirect
605. #3101	C₂×C₆₇	semidirect
606. #2969	C₂×C₆₇	semidirect
607. #2949	C₂×C₆₇	semidirect
608. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
609. C₆₇	#61543	direct (N × H)
612. Q₈²	C₂²×C₆₇	semidirect
615. #556	C₂²×C₆₇	semidirect
616. #556	C₂²×C₆₇	semidirect
619. #555	C₂²×C₆₇	semidirect
624. D₄×Q₈	C₂²×C₆₇	semidirect
625. #548	C₂²×C₆₇	semidirect
631. #542	C₂²×C₆₇	semidirect
635. #533	C₂²×C₆₇	semidirect
641. #519	C₂²×C₆₇	semidirect
643. C₄×#41	C₂²×C₆₇	semidirect
645. #501	C₂²×C₆₇	semidirect
646. #500	C₂²×C₆₇	semidirect
647. #496	C₂²×C₆₇	semidirect
648. #492	C₂²×C₆₇	semidirect
649. #488	C₂²×C₆₇	semidirect
650. #487	C₂²×C₆₇	semidirect
651. #486	C₂²×C₆₇	semidirect
652. #486	C₂²×C₆₇	semidirect
653. #485	C₂²×C₆₇	semidirect
654. #483	C₂²×C₆₇	semidirect
655. #482	C₂²×C₆₇	semidirect
656. #482	C₂²×C₆₇	semidirect
657. #482	C₂²×C₆₇	semidirect
658. #482	C₂²×C₆₇	semidirect
659. #479	C₂²×C₆₇	semidirect
660. #479	C₂²×C₆₇	semidirect
661. #477	C₂²×C₆₇	semidirect
663. #476	C₂²×C₆₇	semidirect
664. #476	C₂²×C₆₇	semidirect
665. #476	C₂²×C₆₇	semidirect
667. #469	C₂²×C₆₇	semidirect
668. #468	C₂²×C₆₇	semidirect
669. #468	C₂²×C₆₇	semidirect
670. #468	C₂²×C₆₇	semidirect
671. #466	C₂²×C₆₇	semidirect
672. #465	C₂²×C₆₇	semidirect
674. #463	C₂²×C₆₇	semidirect
676. #461	C₂²×C₆₇	semidirect
677. #460	C₂²×C₆₇	semidirect
678. #460	C₂²×C₆₇	semidirect
679. #460	C₂²×C₆₇	semidirect
680. #459	C₂²×C₆₇	semidirect
683. #449	C₂²×C₆₇	semidirect
684. #448	C₂²×C₆₇	semidirect
685. #448	C₂²×C₆₇	semidirect
687. #446	C₂²×C₆₇	semidirect
688. C₈×Q₈	C₂²×C₆₇	semidirect
690. #442	C₂²×C₆₇	semidirect
693. #440	C₂²×C₆₇	semidirect
694. #440	C₂²×C₆₇	semidirect
695. #440	C₂²×C₆₇	semidirect
696. #440	C₂²×C₆₇	semidirect
700. C₄×SD₁₆	C₂²×C₆₇	semidirect
701. C₄×SD₁₆	C₂²×C₆₇	semidirect
702. C₄×SD₁₆	C₂²×C₆₇	semidirect
703. C₄×SD₁₆	C₂²×C₆₇	semidirect
705. C₄×D₈	C₂²×C₆₇	semidirect
706. C₄×D₈	C₂²×C₆₇	semidirect
707. #436	C₂²×C₆₇	semidirect
708. #436	C₂²×C₆₇	semidirect
709. #435	C₂²×C₆₇	semidirect
710. C₈×D₄	C₂²×C₆₇	semidirect
711. #433	C₂²×C₆₇	semidirect
712. #431	C₂²×C₆₇	semidirect
713. #428	C₂²×C₆₇	semidirect
714. #427	C₂²×C₆₇	semidirect
715. #419	C₂²×C₆₇	semidirect
718. #417	C₂²×C₆₇	semidirect
719. #405	C₂²×C₆₇	semidirect
720. C₄×M₁₆	C₂²×C₆₇	semidirect
961. SD₁₆	#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×#3519	2
C₆₇×#3518	2
C₆₇×#3397	2
C₆₇×#3385	2
C₆₇×#3362	2
C₆₇×#3360	2
C₆₇×#3350	2
C₆₇×#3341	2
C₆₇×#3329	2
C₆₇×#3326	2
C₆₇×#3325	2
C₆₇×#3324	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3265	2
C₆₇×#3182	2
C₆₇×#3179	2
C₆₇×#3126	2
C₆₇×#3118	2
C₆₇×#3106	2
C₆₇×#3101	2
C₆₇×#2969	2
C₆₇×#2949	2
C₄×AGL(1,ℤ/8)×C₆₇	2
#61543	67

Subgroups — C67×#61543 #30740794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61543 #30740794