Subgroups — C₆₇×#61727 #30740978

Order 17152.

1886 conjugacy classes of subgroups.

The subgroup lattice has 1346 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	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3355	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3346	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3339	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3318	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3309	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3297	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3188	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#480×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	#553×C₆₇	—	2	1	no	—
27	#553×C₆₇	—	2	1	no	—
28	#553×C₆₇	—	2	1	no	—
29	#553×C₆₇	—	2	1	no	—
30	#553×C₆₇	—	2	1	no	—
31	#553×C₆₇	C₂²	1	2	yes	—
32	#553×C₆₇	C₂²	1	2	yes	complemented
33	#553×C₆₇	C₂²	1	2	yes	complemented
34	#553×C₆₇	C₂²	1	2	yes	complemented
35	#553×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#553×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#546×C₆₇	—	2	1	no	—
39	#546×C₆₇	—	2	1	no	—
40	#546×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#546×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	D₄²×C₆₇	—	2	1	no	—
43	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#540×C₆₇	—	2	1	no	—
45	#538×C₆₇	—	2	1	no	—
46	#538×C₆₇	—	2	1	no	—
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	#529×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#126×C₆₇	—	2	1	no	—
50	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	#525×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#123×C₆₇	—	2	1	no	—
54	C₂×#121×C₆₇	—	2	1	no	—
55	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#518×C₆₇	—	2	1	no	—
60	C₂×C₄×D₄×C₆₇	—	2	1	no	—
61	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#490×C₆₇	C₂²	1	2	yes	complemented
68	#488×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#484×C₆₇	C₂²	1	2	yes	complemented
71	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#482×C₆₇	C₂²	1	2	yes	complemented
75	#482×C₆₇	C₂²	1	2	yes	complemented
76	#482×C₆₇	C₂²	1	2	yes	complemented
77	#482×C₆₇	C₂²	1	2	yes	complemented
78	#482×C₆₇	C₂²	1	2	yes	complemented
79	#481×C₆₇	C₂²	1	1	yes	characteristic
80	#481×C₆₇	C₂²	1	2	yes	complemented
81	#481×C₆₇	C₂²	1	2	yes	complemented
82	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#480×C₆₇	C₂²	1	1	yes	characteristic
85	#480×C₆₇	C₂²	1	1	yes	characteristic
86	#480×C₆₇	C₂²	1	2	yes	complemented
87	#480×C₆₇	C₂²	1	2	yes	complemented
88	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#480×C₆₇	C₂²	1	2	yes	complemented
91	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#479×C₆₇	C₂²	1	2	yes	complemented
94	#478×C₆₇	C₂²	1	2	yes	complemented
95	#478×C₆₇	C₂²	1	2	yes	complemented
96	#478×C₆₇	C₂²	1	2	yes	complemented
97	#478×C₆₇	C₂²	1	2	yes	complemented
98	#474×C₆₇	C₂²	1	2	yes	complemented
99	#469×C₆₇	C₂²	1	2	yes	complemented
100	#469×C₆₇	C₂²	1	2	yes	complemented
101	#469×C₆₇	C₂²	1	2	yes	complemented
102	#468×C₆₇	C₂²	1	2	yes	complemented
103	#466×C₆₇	C₂²	1	2	yes	complemented
104	#466×C₆₇	C₂²	1	2	yes	complemented
105	#466×C₆₇	C₂²	1	2	yes	complemented
106	#465×C₆₇	C₂²	1	2	yes	complemented
107	#463×C₆₇	C₂²	1	2	yes	complemented
108	#459×C₆₇	C₂²	1	2	yes	complemented
109	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#449×C₆₇	C₂²	1	2	yes	complemented
111	#449×C₆₇	C₂²	1	2	yes	complemented
112	#447×C₆₇	C₂²	1	1	yes	characteristic
113	#447×C₆₇	C₂²	1	2	yes	complemented
114	#447×C₆₇	C₂²	1	2	yes	complemented
115	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#442×C₆₇	C₂²	1	2	yes	complemented
118	#440×C₆₇	C₂²	1	2	yes	complemented
119	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
120	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	2	yes	complemented
122	#435×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
125	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	2	yes	complemented
128	#428×C₆₇	C₂²	1	2	yes	complemented
129	#427×C₆₇	C₂²	1	2	yes	complemented
130	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
131	#418×C₆₇	C₂²	1	2	yes	complemented
132	#417×C₆₇	C₂²	1	2	yes	complemented
133	#416×C₆₇	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
135	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₇	—	2	1	no	—
143	C₂²×D₄×C₆₇	—	2	1	no	—
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	—	2	1	no	—
146	C₂²×D₄×C₆₇	—	2	1	no	—
147	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
148	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₆₇	—	2	1	no	—
152	C₂³×C₄×C₆₇	—	2	1	no	—
153	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×D₈×C₆₇	C₂³	1	2	yes	—
159	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	#127×C₆₇	—	2	1	no	—
165	#127×C₆₇	C₂³	1	1	yes	characteristic
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	1	no	—
171	#126×C₆₇	—	2	1	no	—
172	#126×C₆₇	—	2	1	no	—
173	#125×C₆₇	—	2	1	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	C₂³	1	2	yes	—
177	#125×C₆₇	C₂³	1	1	yes	characteristic
178	#125×C₆₇	C₂³	1	2	yes	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	—	2	1	no	—
181	#124×C₆₇	—	2	1	no	—
182	#124×C₆₇	C₂³	1	1	yes	characteristic
183	#123×C₆₇	—	2	1	no	—
184	#123×C₆₇	—	2	1	no	—
185	#123×C₆₇	—	2	1	no	—
186	#123×C₆₇	—	2	1	no	—
187	#123×C₆₇	—	2	1	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	—	2	2	no	—
192	#123×C₆₇	—	2	1	no	—
193	#123×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	—	2	1	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	1	no	—
210	#121×C₆₇	—	2	1	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	1	no	—
214	#121×C₆₇	—	2	1	no	—
215	#121×C₆₇	—	2	1	no	—
216	#121×C₆₇	—	2	1	no	—
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	1	no	—
219	#121×C₆₇	—	2	1	no	—
220	#121×C₆₇	C₂³	1	2	yes	—
221	#121×C₆₇	C₂³	1	2	yes	—
222	#121×C₆₇	C₂³	1	2	yes	—
223	#121×C₆₇	C₂³	1	1	yes	characteristic
224	#121×C₆₇	C₂³	1	1	yes	characteristic
225	#121×C₆₇	C₂³	1	1	yes	characteristic
226	#121×C₆₇	C₂³	1	2	yes	—
227	#121×C₆₇	C₂³	1	1	yes	characteristic
228	#121×C₆₇	C₂³	1	1	yes	characteristic
229	#121×C₆₇	C₂³	1	1	yes	characteristic
230	#121×C₆₇	C₂³	1	1	yes	characteristic
231	#121×C₆₇	C₂³	1	1	yes	characteristic
232	#121×C₆₇	C₂³	1	1	yes	characteristic
233	#120×C₆₇	—	2	1	no	—
234	#120×C₆₇	—	2	1	no	—
235	#120×C₆₇	—	2	1	no	—
236	#120×C₆₇	—	2	1	no	—
237	#120×C₆₇	—	2	1	no	—
238	#120×C₆₇	—	2	1	no	—
239	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	1	no	—
243	C₄×D₄×C₆₇	—	2	1	no	—
244	C₄×D₄×C₆₇	—	2	1	no	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	1	no	—
247	C₄×D₄×C₆₇	—	2	2	no	—
248	C₄×D₄×C₆₇	—	2	2	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	2	no	—
251	C₄×D₄×C₆₇	—	2	1	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	—	2	1	no	—
254	C₄×D₄×C₆₇	—	2	1	no	—
255	C₄×D₄×C₆₇	—	2	1	no	—
256	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
257	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
258	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
259	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
260	C₄×D₄×C₆₇	C₂³	1	2	yes	—
261	C₄×D₄×C₆₇	C₂³	1	2	yes	—
262	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
267	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
269	#117×C₆₇	—	2	1	no	—
270	#117×C₆₇	—	2	1	no	—
271	#117×C₆₇	—	2	1	no	—
272	#117×C₆₇	—	2	1	no	—
273	#117×C₆₇	C₂³	1	2	yes	—
274	#117×C₆₇	C₂³	1	1	yes	characteristic
275	#117×C₆₇	C₂³	1	1	yes	characteristic
276	#117×C₆₇	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
290	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
291	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
292	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
293	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	#107×C₆₇	C₂³	1	2	yes	—
303	#107×C₆₇	C₂³	1	2	yes	—
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#107×C₆₇	C₂³	1	2	yes	—
308	#107×C₆₇	C₂³	1	2	yes	—
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	2	yes	—
312	#106×C₆₇	C₂³	1	2	yes	—
313	#106×C₆₇	C₂³	1	2	yes	—
314	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	#103×C₆₇	C₂³	1	2	yes	—
317	#103×C₆₇	C₂³	1	2	yes	—
318	#103×C₆₇	C₂³	1	2	yes	—
319	#102×C₆₇	C₂³	1	2	yes	—
320	#102×C₆₇	C₂³	1	2	yes	—
321	#102×C₆₇	C₂³	1	2	yes	—
322	#102×C₆₇	C₂³	1	2	yes	—
323	#102×C₆₇	C₂³	1	2	yes	—
324	#102×C₆₇	C₂³	1	2	yes	—
325	#102×C₆₇	C₂³	1	2	yes	—
326	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
333	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
340	#97×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	C₂⁴×C₆₇	—	2	1	no	—
343	C₂⁴×C₆₇	—	2	1	no	—
344	C₂⁴×C₆₇	—	2	1	no	—
345	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
346	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
347	#41×C₆₇	—	4	2	no	—
348	#41×C₆₇	—	4	2	no	—
349	#41×C₆₇	—	8	2	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₆₇	—	2	1	no	—
353	C₂×D₄×C₆₇	—	2	1	no	—
354	C₂×D₄×C₆₇	—	2	2	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	1	no	—
357	C₂×D₄×C₆₇	—	2	1	no	—
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	2	no	—
364	C₂×D₄×C₆₇	—	2	2	no	—
365	C₂×D₄×C₆₇	—	2	1	no	—
366	C₂×D₄×C₆₇	—	2	1	no	—
367	C₂×D₄×C₆₇	—	2	1	no	—
368	C₂×D₄×C₆₇	—	2	1	no	—
369	C₂×D₄×C₆₇	—	2	1	no	—
370	C₂×D₄×C₆₇	—	2	1	no	—
371	C₂×D₄×C₆₇	—	2	1	no	—
372	C₂×D₄×C₆₇	—	4	2	no	—
373	C₂×D₄×C₆₇	—	4	2	no	—
374	C₂×D₄×C₆₇	—	4	2	no	—
375	C₂×D₄×C₆₇	—	4	2	no	—
376	C₂×D₄×C₆₇	—	4	4	no	—
377	C₂×D₄×C₆₇	—	4	4	no	—
378	C₂×D₄×C₆₇	—	8	2	no	—
379	C₂×D₄×C₆₇	—	8	2	no	—
380	C₂×D₄×C₆₇	—	8	2	no	—
381	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
385	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₆₇	—	2	1	no	—
390	C₂²×C₄×C₆₇	—	2	1	no	—
391	C₂²×C₄×C₆₇	—	2	1	no	—
392	C₂²×C₄×C₆₇	—	2	1	no	—
393	C₂²×C₄×C₆₇	—	2	1	no	—
394	C₂²×C₄×C₆₇	—	2	2	no	—
395	C₂²×C₄×C₆₇	—	2	2	no	—
396	C₂²×C₄×C₆₇	—	2	1	no	—
397	C₂²×C₄×C₆₇	—	2	1	no	—
398	C₂²×C₄×C₆₇	—	2	1	no	—
399	C₂²×C₄×C₆₇	—	2	1	no	—
400	C₂²×C₄×C₆₇	—	2	1	no	—
401	C₂²×C₄×C₆₇	—	2	2	no	—
402	C₂²×C₄×C₆₇	—	2	2	no	—
403	C₂²×C₄×C₆₇	—	4	2	no	—
404	C₂²×C₄×C₆₇	—	4	2	no	—
405	C₂²×C₄×C₆₇	—	8	2	no	—
406	C₂²×C₄×C₆₇	—	8	2	no	—
407	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	SD₁₆×C₆₇	—	4	2	no	—
421	D₈×C₆₇	—	4	2	no	—
422	D₈×C₆₇	—	4	2	no	—
423	D₈×C₆₇	—	4	2	no	—
424	M₁₆×C₆₇	—	4	2	no	—
425	M₁₆×C₆₇	—	4	2	no	—
426	C₂×C₈×C₆₇	—	4	2	no	—
427	C₂×C₈×C₆₇	—	4	2	no	—
428	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
429	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
430	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
431	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	2	no	—
435	C₄⋊C₄×C₆₇	—	2	2	no	—
436	C₄⋊C₄×C₆₇	—	2	2	no	—
437	C₄⋊C₄×C₆₇	—	2	2	no	—
438	C₄⋊C₄×C₆₇	—	2	2	no	—
439	C₄⋊C₄×C₆₇	—	2	2	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	—	2	1	no	—
442	C₄⋊C₄×C₆₇	—	2	1	no	—
443	C₄⋊C₄×C₆₇	—	2	1	no	—
444	C₄⋊C₄×C₆₇	—	2	1	no	—
445	C₄⋊C₄×C₆₇	—	2	1	no	—
446	C₄⋊C₄×C₆₇	—	2	1	no	—
447	C₄⋊C₄×C₆₇	—	2	1	no	—
448	C₄⋊C₄×C₆₇	—	2	1	no	—
449	C₄⋊C₄×C₆₇	—	2	1	no	—
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
454	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
455	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
457	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
459	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
460	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
461	C₂²⋊C₄×C₆₇	—	2	2	no	—
462	C₂²⋊C₄×C₆₇	—	2	2	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	no	—
464	C₂²⋊C₄×C₆₇	—	2	1	no	—
465	C₂²⋊C₄×C₆₇	—	2	1	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	1	no	—
475	C₂²⋊C₄×C₆₇	—	2	1	no	—
476	C₂²⋊C₄×C₆₇	—	2	2	no	—
477	C₂²⋊C₄×C₆₇	—	2	2	no	—
478	C₂²⋊C₄×C₆₇	—	2	2	no	—
479	C₂²⋊C₄×C₆₇	—	2	2	no	—
480	C₂²⋊C₄×C₆₇	—	2	2	no	—
481	C₂²⋊C₄×C₆₇	—	2	2	no	—
482	C₂²⋊C₄×C₆₇	—	2	1	no	—
483	C₂²⋊C₄×C₆₇	—	2	1	no	—
484	C₂²⋊C₄×C₆₇	—	2	1	no	—
485	C₂²⋊C₄×C₆₇	—	2	1	no	—
486	C₂²⋊C₄×C₆₇	—	2	1	no	—
487	C₂²⋊C₄×C₆₇	—	2	1	no	—
488	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
495	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₆₇	—	2	2	no	—
497	C₄²×C₆₇	—	2	2	no	—
498	C₄²×C₆₇	—	2	1	no	—
499	C₄²×C₆₇	—	2	1	no	—
500	C₄²×C₆₇	—	2	1	no	—
501	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
502	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
503	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
504	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂³×C₆₇	—	2	2	no	—
506	C₂³×C₆₇	—	2	2	no	—
507	C₂³×C₆₇	—	2	2	no	—
508	C₂³×C₆₇	—	2	2	no	—
509	C₂³×C₆₇	—	2	1	no	—
510	C₂³×C₆₇	—	2	1	no	—
511	C₂³×C₆₇	—	2	1	no	—
512	C₂³×C₆₇	—	4	1	no	—
513	C₂³×C₆₇	—	4	1	no	—
514	C₂³×C₆₇	—	4	1	no	—
515	C₂³×C₆₇	—	4	2	no	—
516	C₂³×C₆₇	—	4	2	no	—
517	C₂³×C₆₇	—	4	2	no	—
518	C₂³×C₆₇	—	4	2	no	—
519	C₂³×C₆₇	—	4	2	no	—
520	C₂³×C₆₇	—	8	1	no	—
521	C₂³×C₆₇	—	8	1	no	—
522	C₂³×C₆₇	—	8	1	no	—
523	C₂³×C₆₇	—	8	1	no	—
524	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
525	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
526	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
527	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
528	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
529	Q₈×C₆₇	—	2	2	no	—
530	Q₈×C₆₇	—	8	1	no	—
531	D₄×C₆₇	—	2	2	no	—
532	D₄×C₆₇	—	2	2	no	—
533	D₄×C₆₇	—	2	2	no	—
534	D₄×C₆₇	—	2	2	no	—
535	D₄×C₆₇	—	2	2	no	—
536	D₄×C₆₇	—	2	2	no	—
537	D₄×C₆₇	—	2	2	no	—
538	D₄×C₆₇	—	4	1	no	—
539	D₄×C₆₇	—	4	1	no	—
540	D₄×C₆₇	—	4	2	no	—
541	D₄×C₆₇	—	4	2	no	—
542	D₄×C₆₇	—	4	2	no	—
543	D₄×C₆₇	—	4	4	no	—
544	D₄×C₆₇	—	4	2	no	—
545	D₄×C₆₇	—	4	4	no	—
546	D₄×C₆₇	—	4	2	no	—
547	D₄×C₆₇	—	4	2	no	—
548	D₄×C₆₇	—	4	2	no	—
549	D₄×C₆₇	—	8	1	no	—
550	D₄×C₆₇	—	8	1	no	—
551	D₄×C₆₇	—	8	1	no	—
552	D₄×C₆₇	—	8	2	no	—
553	D₄×C₆₇	—	8	2	no	—
554	D₄×C₆₇	—	8	1	no	—
555	D₄×C₆₇	—	8	1	no	—
556	D₄×C₆₇	—	8	1	no	—
557	D₄×C₆₇	—	8	1	no	—
558	D₄×C₆₇	—	8	1	no	—
559	D₄×C₆₇	—	8	1	no	—
560	C₂×C₄×C₆₇	—	2	2	no	—
561	C₂×C₄×C₆₇	—	2	2	no	—
562	C₂×C₄×C₆₇	—	2	2	no	—
563	C₂×C₄×C₆₇	—	2	2	no	—
564	C₂×C₄×C₆₇	—	2	2	no	—
565	C₂×C₄×C₆₇	—	2	2	no	—
566	C₂×C₄×C₆₇	—	2	1	no	—
567	C₂×C₄×C₆₇	—	2	2	no	—
568	C₂×C₄×C₆₇	—	2	2	no	—
569	C₂×C₄×C₆₇	—	2	1	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	2	no	—
574	C₂×C₄×C₆₇	—	4	1	no	—
575	C₂×C₄×C₆₇	—	4	1	no	—
576	C₂×C₄×C₆₇	—	4	1	no	—
577	C₂×C₄×C₆₇	—	4	1	no	—
578	C₂×C₄×C₆₇	—	4	1	no	—
579	C₂×C₄×C₆₇	—	4	1	no	—
580	C₂×C₄×C₆₇	—	4	1	no	—
581	C₂×C₄×C₆₇	—	4	2	no	—
582	C₂×C₄×C₆₇	—	4	2	no	—
583	C₂×C₄×C₆₇	—	4	2	no	—
584	C₂×C₄×C₆₇	—	4	2	no	—
585	C₂×C₄×C₆₇	—	8	2	no	—
586	C₂×C₄×C₆₇	—	8	2	no	—
587	C₂×C₄×C₆₇	—	8	1	no	—
588	C₂×C₄×C₆₇	—	8	1	no	—
589	C₂×C₄×C₆₇	—	8	1	no	—
590	C₂×C₄×C₆₇	—	8	1	no	—
591	C₂×C₄×C₆₇	—	8	2	no	—
592	C₂×C₄×C₆₇	—	8	2	no	—
593	C₂×C₄×C₆₇	—	8	1	no	—
594	C₂×C₄×C₆₇	—	8	1	no	—
595	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
605	C₈×C₆₇	—	2	2	no	—
606	C₈×C₆₇	—	2	2	no	—
607	C₈×C₆₇	—	2	2	no	—
608	C₈×C₆₇	—	2	2	no	—
609	C₂²×C₆₇	—	2	1	no	—
610	C₂²×C₆₇	—	2	1	no	—
611	C₂²×C₆₇	—	2	1	no	—
612	C₂²×C₆₇	—	2	1	no	—
613	C₂²×C₆₇	—	2	1	no	—
614	C₂²×C₆₇	—	2	1	no	—
615	C₂²×C₆₇	—	2	1	no	—
616	C₂²×C₆₇	—	2	1	no	—
617	C₂²×C₆₇	—	2	1	no	—
618	C₂²×C₆₇	—	2	1	no	—
619	C₂²×C₆₇	—	2	1	no	—
620	C₂²×C₆₇	—	2	1	no	—
621	C₂²×C₆₇	—	2	1	no	—
622	C₂²×C₆₇	—	4	4	no	—
623	C₂²×C₆₇	—	4	1	no	—
624	C₂²×C₆₇	—	4	1	no	—
625	C₂²×C₆₇	—	4	2	no	—
626	C₂²×C₆₇	—	4	1	no	—
627	C₂²×C₆₇	—	4	1	no	—
628	C₂²×C₆₇	—	4	2	no	—
629	C₂²×C₆₇	—	4	1	no	—
630	C₂²×C₆₇	—	4	1	no	—
631	C₂²×C₆₇	—	4	2	no	—
632	C₂²×C₆₇	—	4	1	no	—
633	C₂²×C₆₇	—	4	1	no	—
634	C₂²×C₆₇	—	4	1	no	—
635	C₂²×C₆₇	—	8	2	no	—
636	C₂²×C₆₇	—	8	4	no	—
637	C₂²×C₆₇	—	16	2	no	—
638	C₂²×C₆₇	—	16	2	no	—
639	C₂²×C₆₇	#575	1	2	yes	—
640	C₂²×C₆₇	#576	1	2	yes	—
641	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
642	C₄×C₆₇	—	2	1	no	—
643	C₄×C₆₇	—	2	1	no	—
644	C₄×C₆₇	—	2	1	no	—
645	C₄×C₆₇	—	2	1	no	—
646	C₄×C₆₇	—	2	1	no	—
647	C₄×C₆₇	—	2	1	no	—
648	C₄×C₆₇	—	2	1	no	—
649	C₄×C₆₇	—	2	1	no	—
650	C₄×C₆₇	—	2	1	no	—
651	C₄×C₆₇	—	4	1	no	—
652	C₄×C₆₇	—	4	1	no	—
653	C₄×C₆₇	—	4	2	no	—
654	C₄×C₆₇	—	4	2	no	—
655	C₄×C₆₇	—	4	2	no	—
656	C₄×C₆₇	—	4	1	no	—
657	C₄×C₆₇	—	4	1	no	—
658	C₄×C₆₇	—	4	1	no	—
659	C₄×C₆₇	#585	1	2	yes	—
660	#61727	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
661	C₂×C₆₇	—	2	2	no	—
662	C₂×C₆₇	—	2	2	no	—
663	C₂×C₆₇	—	4	1	no	—
664	C₂×C₆₇	—	4	1	no	—
665	C₂×C₆₇	—	4	1	no	—
666	C₂×C₆₇	—	8	2	no	—
667	C₂×C₆₇	—	8	1	no	—
668	C₂×C₆₇	—	8	1	no	—
669	C₂×C₆₇	—	8	1	no	—
670	C₂×C₆₇	#3485	1	1	yes	characteristic
671	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
672	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
673	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
674	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#3355	C₂×C₆₇	1	2	yes	complemented
676	#3347	C₂×C₆₇	1	2	yes	complemented
677	#3346	C₂×C₆₇	1	2	yes	complemented
678	#3339	C₂×C₆₇	1	2	yes	complemented
679	#3322	C₂×C₆₇	1	2	yes	complemented
680	#3318	C₂×C₆₇	1	2	yes	complemented
681	#3309	C₂×C₆₇	1	2	yes	complemented
682	#3297	C₂×C₆₇	1	2	yes	complemented
683	#3234	C₂×C₆₇	1	1	yes	characteristic, complemented
684	#3232	C₂×C₆₇	1	1	yes	characteristic, complemented
685	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
686	#3192	C₂×C₆₇	1	1	yes	characteristic, complemented
687	#3188	C₂×C₆₇	1	1	yes	characteristic, complemented
688	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
689	#3114	C₂×C₆₇	1	1	yes	characteristic, complemented
690	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
691	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
692	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
693	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
694	C₂×#480	C₂×C₆₇	1	1	yes	characteristic, complemented
695	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
696	C₆₇	#61727	1	1	yes	characteristic, direct product factor, Sylow
697	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#553	—	2	1	no	—
700	#553	—	2	1	no	—
701	#553	—	2	1	no	—
702	#553	—	2	1	no	—
703	#553	—	2	1	no	—
704	#553	C₂²×C₆₇	1	2	yes	—
705	#553	C₂²×C₆₇	1	1	yes	characteristic, complemented
706	#553	C₂²×C₆₇	1	2	yes	complemented
707	#553	C₂²×C₆₇	1	2	yes	complemented
708	#553	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#553	C₂²×C₆₇	1	2	yes	complemented
710	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#546	—	2	1	no	—
712	#546	—	2	1	no	—
713	#546	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#546	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	D₄²	—	2	1	no	—
716	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
717	#540	—	2	1	no	—
718	#538	—	2	1	no	—
719	#538	—	2	1	no	—
720	#532	C₂²×C₆₇	1	1	yes	characteristic
721	#529	C₂²×C₆₇	1	1	yes	characteristic
722	C₂×#126	—	2	1	no	—
723	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	#525	C₂²×C₆₇	1	1	yes	characteristic
725	#525	C₂²×C₆₇	1	1	yes	characteristic
726	C₂×#123	—	2	1	no	—
727	C₂×#121	—	2	1	no	—
728	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
729	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
730	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
732	#518	—	2	1	no	—
733	C₂×C₄×D₄	—	2	1	no	—
734	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
735	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
737	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	#501	C₂²×C₆₇	1	2	yes	complemented
739	#499	C₂²×C₆₇	1	2	yes	complemented
740	#490	C₂²×C₆₇	1	2	yes	complemented
741	#488	C₂²×C₆₇	1	2	yes	complemented
742	#485	C₂²×C₆₇	1	2	yes	complemented
743	#484	C₂²×C₆₇	1	2	yes	complemented
744	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
745	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
747	#482	C₂²×C₆₇	1	2	yes	complemented
748	#482	C₂²×C₆₇	1	2	yes	complemented
749	#482	C₂²×C₆₇	1	2	yes	complemented
750	#482	C₂²×C₆₇	1	2	yes	complemented
751	#482	C₂²×C₆₇	1	2	yes	complemented
752	#481	C₂²×C₆₇	1	1	yes	characteristic
753	#481	C₂²×C₆₇	1	2	yes	complemented
754	#481	C₂²×C₆₇	1	2	yes	complemented
755	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
756	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
757	#480	C₂²×C₆₇	1	1	yes	characteristic
758	#480	C₂²×C₆₇	1	1	yes	characteristic
759	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	#480	C₂²×C₆₇	1	2	yes	complemented
761	#480	C₂²×C₆₇	1	2	yes	complemented
762	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	#480	C₂²×C₆₇	1	2	yes	complemented
764	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	#479	C₂²×C₆₇	1	2	yes	complemented
767	#478	C₂²×C₆₇	1	2	yes	complemented
768	#478	C₂²×C₆₇	1	2	yes	complemented
769	#478	C₂²×C₆₇	1	2	yes	complemented
770	#478	C₂²×C₆₇	1	2	yes	complemented
771	#474	C₂²×C₆₇	1	2	yes	complemented
772	#469	C₂²×C₆₇	1	2	yes	complemented
773	#469	C₂²×C₆₇	1	2	yes	complemented
774	#469	C₂²×C₆₇	1	2	yes	complemented
775	#468	C₂²×C₆₇	1	2	yes	complemented
776	#466	C₂²×C₆₇	1	2	yes	complemented
777	#466	C₂²×C₆₇	1	2	yes	complemented
778	#466	C₂²×C₆₇	1	2	yes	complemented
779	#465	C₂²×C₆₇	1	2	yes	complemented
780	#463	C₂²×C₆₇	1	2	yes	complemented
781	#459	C₂²×C₆₇	1	2	yes	complemented
782	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	#449	C₂²×C₆₇	1	2	yes	complemented
784	#449	C₂²×C₆₇	1	2	yes	complemented
785	#447	C₂²×C₆₇	1	1	yes	characteristic
786	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
787	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
788	#447	C₂²×C₆₇	1	2	yes	complemented
789	#447	C₂²×C₆₇	1	2	yes	complemented
790	#442	C₂²×C₆₇	1	2	yes	complemented
791	#440	C₂²×C₆₇	1	2	yes	complemented
792	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
793	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
794	#436	C₂²×C₆₇	1	2	yes	complemented
795	#435	C₂²×C₆₇	1	2	yes	complemented
796	#435	C₂²×C₆₇	1	2	yes	complemented
797	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
798	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
799	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
800	#428	C₂²×C₆₇	1	2	yes	complemented
801	#428	C₂²×C₆₇	1	2	yes	complemented
802	#427	C₂²×C₆₇	1	2	yes	complemented
803	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
804	#418	C₂²×C₆₇	1	2	yes	complemented
805	#417	C₂²×C₆₇	1	2	yes	complemented
806	#416	C₂²×C₆₇	1	2	yes	complemented
807	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
808	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
809	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
810	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
811	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
812	C₂×#41	—	2	1	no	—
813	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
814	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
815	C₂²×D₄	—	2	1	no	—
816	C₂²×D₄	—	2	1	no	—
817	C₂²×D₄	—	2	1	no	—
818	C₂²×D₄	—	2	1	no	—
819	C₂²×D₄	—	2	1	no	—
820	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
821	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
822	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
823	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
824	C₂³×C₄	—	2	1	no	—
825	C₂³×C₄	—	2	1	no	—
826	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
827	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
828	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
829	C₂×D₈	C₂³×C₆₇	1	2	yes	—
830	C₂×D₈	C₂³×C₆₇	1	2	yes	—
831	C₂×D₈	C₂³×C₆₇	1	2	yes	—
832	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
833	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
834	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
835	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
836	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
837	#127	—	2	1	no	—
838	#127	C₂³×C₆₇	1	1	yes	characteristic
839	#126	—	2	2	no	—
840	#126	—	2	2	no	—
841	#126	—	2	2	no	—
842	#126	—	2	2	no	—
843	#126	—	2	1	no	—
844	#126	—	2	1	no	—
845	#126	—	2	1	no	—
846	#125	—	2	1	no	—
847	#125	—	2	1	no	—
848	#125	—	2	1	no	—
849	#125	C₂³×C₆₇	1	2	yes	—
850	#125	C₂³×C₆₇	1	2	yes	—
851	#125	C₂³×C₆₇	1	1	yes	characteristic
852	#124	—	2	1	no	—
853	#124	—	2	1	no	—
854	#124	—	2	1	no	—
855	#124	C₂³×C₆₇	1	1	yes	characteristic
856	#123	—	2	1	no	—
857	#123	—	2	1	no	—
858	#123	—	2	1	no	—
859	#123	—	2	1	no	—
860	#123	—	2	1	no	—
861	#123	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	#123	—	2	1	no	—
866	#123	—	2	1	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
870	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
871	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
872	#121	—	2	2	no	—
873	#121	—	2	2	no	—
874	#121	—	2	2	no	—
875	#121	—	2	2	no	—
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	—	2	1	no	—
880	#121	—	2	1	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	1	no	—
884	#121	—	2	1	no	—
885	#121	—	2	1	no	—
886	#121	—	2	1	no	—
887	#121	—	2	1	no	—
888	#121	—	2	1	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	—	2	1	no	—
892	#121	—	2	1	no	—
893	#121	C₂³×C₆₇	1	1	yes	characteristic
894	#121	C₂³×C₆₇	1	1	yes	characteristic
895	#121	C₂³×C₆₇	1	1	yes	characteristic
896	#121	C₂³×C₆₇	1	1	yes	characteristic
897	#121	C₂³×C₆₇	1	1	yes	characteristic
898	#121	C₂³×C₆₇	1	1	yes	characteristic
899	#121	C₂³×C₆₇	1	1	yes	characteristic
900	#121	C₂³×C₆₇	1	2	yes	—
901	#121	C₂³×C₆₇	1	2	yes	—
902	#121	C₂³×C₆₇	1	2	yes	—
903	#121	C₂³×C₆₇	1	2	yes	—
904	#121	C₂³×C₆₇	1	1	yes	characteristic
905	#121	C₂³×C₆₇	1	1	yes	characteristic
906	#120	—	2	1	no	—
907	#120	—	2	1	no	—
908	#120	—	2	1	no	—
909	#120	—	2	1	no	—
910	#120	—	2	1	no	—
911	#120	—	2	1	no	—
912	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	1	no	—
915	C₄×D₄	—	2	1	no	—
916	C₄×D₄	—	2	1	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	2	no	—
921	C₄×D₄	—	2	2	no	—
922	C₄×D₄	—	2	2	no	—
923	C₄×D₄	—	2	2	no	—
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	—	2	1	no	—
928	C₄×D₄	—	2	1	no	—
929	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
930	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
931	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
932	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
933	C₄×D₄	C₂³×C₆₇	1	2	yes	—
934	C₄×D₄	C₂³×C₆₇	1	2	yes	—
935	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
936	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
937	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
938	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
939	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
940	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
941	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
942	#117	—	2	1	no	—
943	#117	—	2	1	no	—
944	#117	—	2	1	no	—
945	#117	—	2	1	no	—
946	#117	C₂³×C₆₇	1	2	yes	—
947	#117	C₂³×C₆₇	1	2	yes	—
948	#117	C₂³×C₆₇	1	1	yes	characteristic
949	#117	C₂³×C₆₇	1	1	yes	characteristic
950	C₂×C₄⋊C₄	—	2	1	no	—
951	C₂×C₄⋊C₄	—	2	1	no	—
952	C₂×C₄⋊C₄	—	2	1	no	—
953	C₂×C₄⋊C₄	—	2	1	no	—
954	C₂×C₄⋊C₄	—	2	1	no	—
955	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
959	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
960	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
963	C₂×C₂²⋊C₄	—	2	1	no	—
964	C₂×C₂²⋊C₄	—	2	1	no	—
965	C₂×C₂²⋊C₄	—	2	1	no	—
966	C₂×C₂²⋊C₄	—	2	1	no	—
967	C₂×C₂²⋊C₄	—	2	1	no	—
968	C₂×C₂²⋊C₄	—	2	1	no	—
969	C₂×C₂²⋊C₄	—	2	1	no	—
970	C₂×C₂²⋊C₄	—	2	1	no	—
971	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
972	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
973	C₂×C₄²	—	2	1	no	—
974	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
975	#107	C₂³×C₆₇	1	2	yes	—
976	#107	C₂³×C₆₇	1	2	yes	—
977	#107	C₂³×C₆₇	1	2	yes	—
978	#107	C₂³×C₆₇	1	2	yes	—
979	#107	C₂³×C₆₇	1	2	yes	—
980	#107	C₂³×C₆₇	1	2	yes	—
981	#107	C₂³×C₆₇	1	2	yes	—
982	#106	C₂³×C₆₇	1	2	yes	—
983	#106	C₂³×C₆₇	1	2	yes	—
984	#106	C₂³×C₆₇	1	2	yes	—
985	#106	C₂³×C₆₇	1	2	yes	—
986	#106	C₂³×C₆₇	1	2	yes	—
987	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
988	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
989	#103	C₂³×C₆₇	1	2	yes	—
990	#103	C₂³×C₆₇	1	2	yes	—
991	#103	C₂³×C₆₇	1	2	yes	—
992	#102	C₂³×C₆₇	1	2	yes	—
993	#102	C₂³×C₆₇	1	2	yes	—
994	#102	C₂³×C₆₇	1	2	yes	—
995	#102	C₂³×C₆₇	1	2	yes	—
996	#102	C₂³×C₆₇	1	2	yes	—
997	#102	C₂³×C₆₇	1	2	yes	—
998	#102	C₂³×C₆₇	1	2	yes	—
999	#102	C₂³×C₆₇	1	2	yes	—
1000	#102	C₂³×C₆₇	1	2	yes	—
1001	#102	C₂³×C₆₇	1	2	yes	—
1002	#102	C₂³×C₆₇	1	2	yes	—
1003	#102	C₂³×C₆₇	1	2	yes	—
1004	#102	C₂³×C₆₇	1	2	yes	—
1005	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1006	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1007	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1008	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1009	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1010	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1011	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1012	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1013	#97	C₂³×C₆₇	1	2	yes	—
1014	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1015	C₂⁴	—	2	1	no	—
1016	C₂⁴	—	2	1	no	—
1017	C₂⁴	—	2	1	no	—
1018	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1019	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	#41	—	4	2	no	—
1021	#41	—	4	2	no	—
1022	#41	—	8	2	no	—
1023	C₂×Q₈	—	2	1	no	—
1024	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	2	2	no	—
1028	C₂×D₄	—	2	2	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	1	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	1	no	—
1035	C₂×D₄	—	2	1	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	1	no	—
1041	C₂×D₄	—	2	1	no	—
1042	C₂×D₄	—	2	1	no	—
1043	C₂×D₄	—	2	1	no	—
1044	C₂×D₄	—	2	1	no	—
1045	C₂×D₄	—	4	2	no	—
1046	C₂×D₄	—	4	2	no	—
1047	C₂×D₄	—	4	2	no	—
1048	C₂×D₄	—	4	2	no	—
1049	C₂×D₄	—	4	4	no	—
1050	C₂×D₄	—	4	4	no	—
1051	C₂×D₄	—	8	2	no	—
1052	C₂×D₄	—	8	2	no	—
1053	C₂×D₄	—	8	2	no	—
1054	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1055	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1056	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1057	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1058	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1059	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1060	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1061	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1062	C₂²×C₄	—	2	1	no	—
1063	C₂²×C₄	—	2	1	no	—
1064	C₂²×C₄	—	2	1	no	—
1065	C₂²×C₄	—	2	1	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	2	no	—
1068	C₂²×C₄	—	2	2	no	—
1069	C₂²×C₄	—	2	1	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	1	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	2	no	—
1076	C₂²×C₄	—	4	2	no	—
1077	C₂²×C₄	—	4	2	no	—
1078	C₂²×C₄	—	8	2	no	—
1079	C₂²×C₄	—	8	2	no	—
1080	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1081	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1084	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1085	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1086	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1087	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1088	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1089	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1090	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1091	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1092	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1093	SD₁₆	—	4	2	no	—
1094	D₈	—	4	2	no	—
1095	D₈	—	4	2	no	—
1096	D₈	—	4	2	no	—
1097	M₁₆	—	4	2	no	—
1098	M₁₆	—	4	2	no	—
1099	C₂×C₈	—	4	2	no	—
1100	C₂×C₈	—	4	2	no	—
1101	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1102	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1103	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1104	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	2	no	—
1108	C₄⋊C₄	—	2	2	no	—
1109	C₄⋊C₄	—	2	2	no	—
1110	C₄⋊C₄	—	2	2	no	—
1111	C₄⋊C₄	—	2	2	no	—
1112	C₄⋊C₄	—	2	2	no	—
1113	C₄⋊C₄	—	2	1	no	—
1114	C₄⋊C₄	—	2	1	no	—
1115	C₄⋊C₄	—	2	1	no	—
1116	C₄⋊C₄	—	2	1	no	—
1117	C₄⋊C₄	—	2	1	no	—
1118	C₄⋊C₄	—	2	1	no	—
1119	C₄⋊C₄	—	2	1	no	—
1120	C₄⋊C₄	—	2	1	no	—
1121	C₄⋊C₄	—	2	1	no	—
1122	C₄⋊C₄	—	2	1	no	—
1123	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1124	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1125	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1126	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1127	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1128	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1129	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1130	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1131	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1132	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1133	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	1	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	1	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	1	no	—
1148	C₂²⋊C₄	—	2	1	no	—
1149	C₂²⋊C₄	—	2	2	no	—
1150	C₂²⋊C₄	—	2	2	no	—
1151	C₂²⋊C₄	—	2	2	no	—
1152	C₂²⋊C₄	—	2	2	no	—
1153	C₂²⋊C₄	—	2	2	no	—
1154	C₂²⋊C₄	—	2	2	no	—
1155	C₂²⋊C₄	—	2	1	no	—
1156	C₂²⋊C₄	—	2	1	no	—
1157	C₂²⋊C₄	—	2	1	no	—
1158	C₂²⋊C₄	—	2	1	no	—
1159	C₂²⋊C₄	—	2	1	no	—
1160	C₂²⋊C₄	—	2	1	no	—
1161	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1162	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1163	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1164	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1165	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1166	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1167	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1168	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1169	C₄²	—	2	2	no	—
1170	C₄²	—	2	2	no	—
1171	C₄²	—	2	1	no	—
1172	C₄²	—	2	1	no	—
1173	C₄²	—	2	1	no	—
1174	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1175	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1176	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1177	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1178	C₂³	—	2	2	no	—
1179	C₂³	—	2	2	no	—
1180	C₂³	—	2	2	no	—
1181	C₂³	—	2	2	no	—
1182	C₂³	—	2	1	no	—
1183	C₂³	—	2	1	no	—
1184	C₂³	—	2	1	no	—
1185	C₂³	—	4	1	no	—
1186	C₂³	—	4	1	no	—
1187	C₂³	—	4	1	no	—
1188	C₂³	—	4	2	no	—
1189	C₂³	—	4	2	no	—
1190	C₂³	—	4	2	no	—
1191	C₂³	—	4	2	no	—
1192	C₂³	—	4	2	no	—
1193	C₂³	—	8	1	no	—
1194	C₂³	—	8	1	no	—
1195	C₂³	—	8	1	no	—
1196	C₂³	—	8	1	no	—
1197	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1198	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1199	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1200	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1201	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1202	Q₈	—	2	2	no	—
1203	Q₈	—	8	1	no	—
1204	D₄	—	2	2	no	—
1205	D₄	—	2	2	no	—
1206	D₄	—	2	2	no	—
1207	D₄	—	2	2	no	—
1208	D₄	—	2	2	no	—
1209	D₄	—	2	2	no	—
1210	D₄	—	2	2	no	—
1211	D₄	—	4	1	no	—
1212	D₄	—	4	1	no	—
1213	D₄	—	4	2	no	—
1214	D₄	—	4	2	no	—
1215	D₄	—	4	2	no	—
1216	D₄	—	4	4	no	—
1217	D₄	—	4	2	no	—
1218	D₄	—	4	4	no	—
1219	D₄	—	4	2	no	—
1220	D₄	—	4	2	no	—
1221	D₄	—	4	2	no	—
1222	D₄	—	8	1	no	—
1223	D₄	—	8	1	no	—
1224	D₄	—	8	1	no	—
1225	D₄	—	8	2	no	—
1226	D₄	—	8	2	no	—
1227	D₄	—	8	1	no	—
1228	D₄	—	8	1	no	—
1229	D₄	—	8	1	no	—
1230	D₄	—	8	1	no	—
1231	D₄	—	8	1	no	—
1232	D₄	—	8	1	no	—
1233	C₂×C₄	—	2	2	no	—
1234	C₂×C₄	—	2	2	no	—
1235	C₂×C₄	—	2	2	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	2	no	—
1238	C₂×C₄	—	2	2	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	2	no	—
1241	C₂×C₄	—	2	2	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	2	no	—
1247	C₂×C₄	—	4	1	no	—
1248	C₂×C₄	—	4	1	no	—
1249	C₂×C₄	—	4	1	no	—
1250	C₂×C₄	—	4	1	no	—
1251	C₂×C₄	—	4	1	no	—
1252	C₂×C₄	—	4	1	no	—
1253	C₂×C₄	—	4	1	no	—
1254	C₂×C₄	—	4	2	no	—
1255	C₂×C₄	—	4	2	no	—
1256	C₂×C₄	—	4	2	no	—
1257	C₂×C₄	—	4	2	no	—
1258	C₂×C₄	—	8	2	no	—
1259	C₂×C₄	—	8	2	no	—
1260	C₂×C₄	—	8	1	no	—
1261	C₂×C₄	—	8	1	no	—
1262	C₂×C₄	—	8	1	no	—
1263	C₂×C₄	—	8	1	no	—
1264	C₂×C₄	—	8	2	no	—
1265	C₂×C₄	—	8	2	no	—
1266	C₂×C₄	—	8	1	no	—
1267	C₂×C₄	—	8	1	no	—
1268	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1269	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1270	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1271	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1272	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1273	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1274	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1275	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1276	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1277	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1278	C₈	—	2	2	no	—
1279	C₈	—	2	2	no	—
1280	C₈	—	2	2	no	—
1281	C₈	—	2	2	no	—
1282	C₂²	—	2	1	no	—
1283	C₂²	—	2	1	no	—
1284	C₂²	—	2	1	no	—
1285	C₂²	—	2	1	no	—
1286	C₂²	—	2	1	no	—
1287	C₂²	—	2	1	no	—
1288	C₂²	—	2	1	no	—
1289	C₂²	—	2	1	no	—
1290	C₂²	—	2	1	no	—
1291	C₂²	—	2	1	no	—
1292	C₂²	—	2	1	no	—
1293	C₂²	—	2	1	no	—
1294	C₂²	—	2	1	no	—
1295	C₂²	—	4	4	no	—
1296	C₂²	—	4	1	no	—
1297	C₂²	—	4	2	no	—
1298	C₂²	—	4	1	no	—
1299	C₂²	—	4	1	no	—
1300	C₂²	—	4	2	no	—
1301	C₂²	—	4	1	no	—
1302	C₂²	—	4	1	no	—
1303	C₂²	—	4	1	no	—
1304	C₂²	—	4	1	no	—
1305	C₂²	—	4	1	no	—
1306	C₂²	—	4	2	no	—
1307	C₂²	—	4	1	no	—
1308	C₂²	—	8	2	no	—
1309	C₂²	—	8	4	no	—
1310	C₂²	—	16	2	no	—
1311	C₂²	—	16	2	no	—
1312	C₂²	#575×C₆₇	1	2	yes	—
1313	C₂²	#576×C₆₇	1	2	yes	—
1314	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1315	C₄	—	2	1	no	—
1316	C₄	—	2	1	no	—
1317	C₄	—	2	1	no	—
1318	C₄	—	2	1	no	—
1319	C₄	—	2	1	no	—
1320	C₄	—	2	1	no	—
1321	C₄	—	2	1	no	—
1322	C₄	—	2	1	no	—
1323	C₄	—	2	1	no	—
1324	C₄	—	4	1	no	—
1325	C₄	—	4	2	no	—
1326	C₄	—	4	2	no	—
1327	C₄	—	4	2	no	—
1328	C₄	—	4	1	no	—
1329	C₄	—	4	1	no	—
1330	C₄	—	4	1	no	—
1331	C₄	—	4	1	no	—
1332	C₄	#585×C₆₇	1	2	yes	—
1333	C₂	—	2	2	no	—
1334	C₂	—	2	2	no	—
1335	C₂	—	4	1	no	—
1336	C₂	—	4	1	no	—
1337	C₂	—	4	1	no	—
1338	C₂	—	8	2	no	—
1339	C₂	—	8	1	no	—
1340	C₂	—	8	1	no	—
1341	C₂	—	8	1	no	—
1342	C₂	C₆₇×#3485	1	1	yes	characteristic
1343	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1344	C₂	C₂×#576×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3519	C₂	semidirect
2. C₂×#553×C₆₇	C₂	semidirect
3. C₆₇×#3355	C₂	semidirect
4. C₆₇×#3347	C₂	semidirect
5. C₆₇×#3346	C₂	semidirect
6. C₆₇×#3339	C₂	semidirect
7. C₆₇×#3322	C₂	semidirect
8. C₆₇×#3318	C₂	semidirect
9. C₆₇×#3309	C₂	semidirect
10. C₆₇×#3297	C₂	semidirect
11. C₆₇×#3234	C₂	semidirect
12. C₆₇×#3232	C₂	semidirect
13. C₆₇×#3194	C₂	semidirect
14. C₆₇×#3192	C₂	semidirect
15. C₆₇×#3188	C₂	semidirect
16. C₆₇×#3186	C₂	semidirect
17. C₆₇×#3114	C₂	semidirect
18. C₆₇×#3100	C₂	semidirect
19. C₆₇×#3094	C₂	semidirect
20. C₆₇×#3092	C₂	semidirect
21. C₆₇×#3091	C₂	semidirect
22. C₂×#480×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
24. #555×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
32. #553×C₆₇	C₂²	semidirect
33. #553×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
35. #553×C₆₇	C₂²	semidirect
36. #553×C₆₇	C₂²	semidirect
37. #550×C₆₇	C₂²	semidirect
40. #546×C₆₇	C₂²	semidirect
41. #546×C₆₇	C₂²	semidirect
43. D₄²×C₆₇	C₂²	semidirect
50. C₂×#125×C₆₇	C₂²	semidirect
57. C₂×#121×C₆₇	C₂²	semidirect
58. C₂×#121×C₆₇	C₂²	semidirect
62. C₂×C₄×D₄×C₆₇	C₂²	semidirect
63. C₂×#117×C₆₇	C₂²	semidirect
64. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
67. #490×C₆₇	C₂²	semidirect
68. #488×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #484×C₆₇	C₂²	semidirect
71. #484×C₆₇	C₂²	semidirect
72. #483×C₆₇	C₂²	semidirect
73. #483×C₆₇	C₂²	semidirect
74. #482×C₆₇	C₂²	semidirect
75. #482×C₆₇	C₂²	semidirect
76. #482×C₆₇	C₂²	semidirect
77. #482×C₆₇	C₂²	semidirect
78. #482×C₆₇	C₂²	semidirect
80. #481×C₆₇	C₂²	semidirect
81. #481×C₆₇	C₂²	semidirect
82. #481×C₆₇	C₂²	semidirect
83. #481×C₆₇	C₂²	semidirect
86. #480×C₆₇	C₂²	semidirect
87. #480×C₆₇	C₂²	semidirect
88. #480×C₆₇	C₂²	semidirect
89. #480×C₆₇	C₂²	semidirect
90. #480×C₆₇	C₂²	semidirect
91. #480×C₆₇	C₂²	semidirect
92. #480×C₆₇	C₂²	semidirect
93. #479×C₆₇	C₂²	semidirect
94. #478×C₆₇	C₂²	semidirect
95. #478×C₆₇	C₂²	semidirect
96. #478×C₆₇	C₂²	semidirect
97. #478×C₆₇	C₂²	semidirect
98. #474×C₆₇	C₂²	semidirect
99. #469×C₆₇	C₂²	semidirect
100. #469×C₆₇	C₂²	semidirect
101. #469×C₆₇	C₂²	semidirect
102. #468×C₆₇	C₂²	semidirect
103. #466×C₆₇	C₂²	semidirect
104. #466×C₆₇	C₂²	semidirect
105. #466×C₆₇	C₂²	semidirect
106. #465×C₆₇	C₂²	semidirect
107. #463×C₆₇	C₂²	semidirect
108. #459×C₆₇	C₂²	semidirect
109. #450×C₆₇	C₂²	semidirect
110. #449×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
113. #447×C₆₇	C₂²	semidirect
114. #447×C₆₇	C₂²	semidirect
115. #447×C₆₇	C₂²	semidirect
116. #447×C₆₇	C₂²	semidirect
117. #442×C₆₇	C₂²	semidirect
118. #440×C₆₇	C₂²	semidirect
119. C₄×D₈×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
122. #435×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. #432×C₆₇	C₂²	semidirect
126. #431×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
129. #427×C₆₇	C₂²	semidirect
130. C₂×#107×C₆₇	C₂²	semidirect
131. #418×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×#102×C₆₇	C₂²	semidirect
135. #407×C₆₇	C₂²	semidirect
136. #407×C₆₇	C₂²	semidirect
137. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
138. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
660. #61727	C₆₇	direct (N × H)
673. #3519	C₂×C₆₇	semidirect
674. C₂×#553	C₂×C₆₇	semidirect
675. #3355	C₂×C₆₇	semidirect
676. #3347	C₂×C₆₇	semidirect
677. #3346	C₂×C₆₇	semidirect
678. #3339	C₂×C₆₇	semidirect
679. #3322	C₂×C₆₇	semidirect
680. #3318	C₂×C₆₇	semidirect
681. #3309	C₂×C₆₇	semidirect
682. #3297	C₂×C₆₇	semidirect
683. #3234	C₂×C₆₇	semidirect
684. #3232	C₂×C₆₇	semidirect
685. #3194	C₂×C₆₇	semidirect
686. #3192	C₂×C₆₇	semidirect
687. #3188	C₂×C₆₇	semidirect
688. #3186	C₂×C₆₇	semidirect
689. #3114	C₂×C₆₇	semidirect
690. #3100	C₂×C₆₇	semidirect
691. #3094	C₂×C₆₇	semidirect
692. #3092	C₂×C₆₇	semidirect
693. #3091	C₂×C₆₇	semidirect
694. C₂×#480	C₂×C₆₇	semidirect
695. #2974	C₂×C₆₇	semidirect
696. C₆₇	#61727	direct (N × H)
697. #555	C₂²×C₆₇	semidirect
698. #554	C₂²×C₆₇	semidirect
705. #553	C₂²×C₆₇	semidirect
706. #553	C₂²×C₆₇	semidirect
707. #553	C₂²×C₆₇	semidirect
708. #553	C₂²×C₆₇	semidirect
709. #553	C₂²×C₆₇	semidirect
710. #550	C₂²×C₆₇	semidirect
713. #546	C₂²×C₆₇	semidirect
714. #546	C₂²×C₆₇	semidirect
716. D₄²	C₂²×C₆₇	semidirect
723. C₂×#125	C₂²×C₆₇	semidirect
730. C₂×#121	C₂²×C₆₇	semidirect
731. C₂×#121	C₂²×C₆₇	semidirect
735. C₂×C₄×D₄	C₂²×C₆₇	semidirect
736. C₂×#117	C₂²×C₆₇	semidirect
737. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
738. #501	C₂²×C₆₇	semidirect
739. #499	C₂²×C₆₇	semidirect
740. #490	C₂²×C₆₇	semidirect
741. #488	C₂²×C₆₇	semidirect
742. #485	C₂²×C₆₇	semidirect
743. #484	C₂²×C₆₇	semidirect
744. #484	C₂²×C₆₇	semidirect
745. #483	C₂²×C₆₇	semidirect
746. #483	C₂²×C₆₇	semidirect
747. #482	C₂²×C₆₇	semidirect
748. #482	C₂²×C₆₇	semidirect
749. #482	C₂²×C₆₇	semidirect
750. #482	C₂²×C₆₇	semidirect
751. #482	C₂²×C₆₇	semidirect
753. #481	C₂²×C₆₇	semidirect
754. #481	C₂²×C₆₇	semidirect
755. #481	C₂²×C₆₇	semidirect
756. #481	C₂²×C₆₇	semidirect
759. #480	C₂²×C₆₇	semidirect
760. #480	C₂²×C₆₇	semidirect
761. #480	C₂²×C₆₇	semidirect
762. #480	C₂²×C₆₇	semidirect
763. #480	C₂²×C₆₇	semidirect
764. #480	C₂²×C₆₇	semidirect
765. #480	C₂²×C₆₇	semidirect
766. #479	C₂²×C₆₇	semidirect
767. #478	C₂²×C₆₇	semidirect
768. #478	C₂²×C₆₇	semidirect
769. #478	C₂²×C₆₇	semidirect
770. #478	C₂²×C₆₇	semidirect
771. #474	C₂²×C₆₇	semidirect
772. #469	C₂²×C₆₇	semidirect
773. #469	C₂²×C₆₇	semidirect
774. #469	C₂²×C₆₇	semidirect
775. #468	C₂²×C₆₇	semidirect
776. #466	C₂²×C₆₇	semidirect
777. #466	C₂²×C₆₇	semidirect
778. #466	C₂²×C₆₇	semidirect
779. #465	C₂²×C₆₇	semidirect
780. #463	C₂²×C₆₇	semidirect
781. #459	C₂²×C₆₇	semidirect
782. #450	C₂²×C₆₇	semidirect
783. #449	C₂²×C₆₇	semidirect
784. #449	C₂²×C₆₇	semidirect
786. #447	C₂²×C₆₇	semidirect
787. #447	C₂²×C₆₇	semidirect
788. #447	C₂²×C₆₇	semidirect
789. #447	C₂²×C₆₇	semidirect
790. #442	C₂²×C₆₇	semidirect
791. #440	C₂²×C₆₇	semidirect
792. C₄×D₈	C₂²×C₆₇	semidirect
793. C₄×D₈	C₂²×C₆₇	semidirect
794. #436	C₂²×C₆₇	semidirect
795. #435	C₂²×C₆₇	semidirect
796. #435	C₂²×C₆₇	semidirect
797. C₈×D₄	C₂²×C₆₇	semidirect
798. #432	C₂²×C₆₇	semidirect
799. #431	C₂²×C₆₇	semidirect
800. #428	C₂²×C₆₇	semidirect
801. #428	C₂²×C₆₇	semidirect
802. #427	C₂²×C₆₇	semidirect
803. C₂×#107	C₂²×C₆₇	semidirect
804. #418	C₂²×C₆₇	semidirect
805. #417	C₂²×C₆₇	semidirect
806. #416	C₂²×C₆₇	semidirect
807. C₂×#102	C₂²×C₆₇	semidirect
808. #407	C₂²×C₆₇	semidirect
809. #407	C₂²×C₆₇	semidirect
810. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
811. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3519	2
C₂×#553×C₆₇	2
C₆₇×#3355	2
C₆₇×#3347	2
C₆₇×#3346	2
C₆₇×#3339	2
C₆₇×#3322	2
C₆₇×#3318	2
C₆₇×#3309	2
C₆₇×#3297	2
C₆₇×#3234	2
C₆₇×#3232	2
C₆₇×#3194	2
C₆₇×#3192	2
C₆₇×#3188	2
C₆₇×#3186	2
C₆₇×#3114	2
C₆₇×#3100	2
C₆₇×#3094	2
C₆₇×#3092	2
C₆₇×#3091	2
C₂×#480×C₆₇	2
C₆₇×#2974	2
#61727	67

Subgroups — C67×#61727 #30740978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61727 #30740978