Subgroups — C₆₇×#61738 #30740989

Order 17152.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	1	yes	maximal, characteristic
2	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3352	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3349	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3343	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3336	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3315	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3095	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×#484×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#556×C₆₇	C₂²	1	1	yes	characteristic
25	#554×C₆₇	—	2	1	no	—
26	#552×C₆₇	—	2	1	no	—
27	#552×C₆₇	—	2	1	no	—
28	#552×C₆₇	—	2	1	no	—
29	#552×C₆₇	—	2	1	no	—
30	#552×C₆₇	C₂²	1	2	yes	—
31	#552×C₆₇	C₂²	1	2	yes	—
32	#552×C₆₇	C₂²	1	2	yes	—
33	#552×C₆₇	C₂²	1	2	yes	—
34	#552×C₆₇	C₂²	1	1	yes	characteristic
35	#552×C₆₇	C₂²	1	1	yes	characteristic
36	#551×C₆₇	—	2	1	no	—
37	#551×C₆₇	—	2	1	no	—
38	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	#548×C₆₇	C₂²	1	1	yes	characteristic
40	#548×C₆₇	C₂²	1	1	yes	characteristic
41	#547×C₆₇	C₂²	1	1	yes	characteristic
42	#547×C₆₇	C₂²	1	1	yes	characteristic
43	#546×C₆₇	—	2	1	no	—
44	#542×C₆₇	—	2	1	no	—
45	#539×C₆₇	—	2	1	no	—
46	#539×C₆₇	—	2	1	no	—
47	#533×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	—	2	1	no	—
51	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
52	#525×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#123×C₆₇	—	2	1	no	—
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	—	2	1	no	—
60	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#117×C₆₇	—	2	1	no	—
63	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
64	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#491×C₆₇	C₂²	1	2	yes	complemented
68	#488×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#485×C₆₇	C₂²	1	2	yes	complemented
71	#485×C₆₇	C₂²	1	2	yes	complemented
72	#485×C₆₇	C₂²	1	2	yes	complemented
73	#485×C₆₇	C₂²	1	2	yes	complemented
74	#484×C₆₇	C₂²	1	1	yes	characteristic
75	#484×C₆₇	C₂²	1	1	yes	characteristic
76	#484×C₆₇	C₂²	1	1	yes	characteristic
77	#484×C₆₇	C₂²	1	1	yes	characteristic
78	#484×C₆₇	C₂²	1	1	yes	characteristic
79	#484×C₆₇	C₂²	1	1	yes	characteristic
80	#484×C₆₇	C₂²	1	2	yes	complemented
81	#484×C₆₇	C₂²	1	2	yes	complemented
82	#484×C₆₇	C₂²	1	2	yes	complemented
83	#483×C₆₇	C₂²	1	1	yes	characteristic
84	#483×C₆₇	C₂²	1	1	yes	characteristic
85	#483×C₆₇	C₂²	1	1	yes	characteristic
86	#483×C₆₇	C₂²	1	2	yes	complemented
87	#483×C₆₇	C₂²	1	2	yes	complemented
88	#482×C₆₇	C₂²	1	2	yes	complemented
89	#481×C₆₇	C₂²	1	1	yes	characteristic
90	#481×C₆₇	C₂²	1	1	yes	characteristic
91	#480×C₆₇	C₂²	1	1	yes	characteristic
92	#480×C₆₇	C₂²	1	2	yes	complemented
93	#479×C₆₇	C₂²	1	2	yes	complemented
94	#479×C₆₇	C₂²	1	2	yes	complemented
95	#479×C₆₇	C₂²	1	2	yes	complemented
96	#479×C₆₇	C₂²	1	2	yes	complemented
97	#478×C₆₇	C₂²	1	2	yes	complemented
98	#477×C₆₇	C₂²	1	2	yes	complemented
99	#470×C₆₇	C₂²	1	2	yes	complemented
100	#470×C₆₇	C₂²	1	2	yes	complemented
101	#470×C₆₇	C₂²	1	2	yes	complemented
102	#468×C₆₇	C₂²	1	2	yes	complemented
103	#467×C₆₇	C₂²	1	2	yes	complemented
104	#467×C₆₇	C₂²	1	2	yes	complemented
105	#467×C₆₇	C₂²	1	2	yes	complemented
106	#465×C₆₇	C₂²	1	2	yes	complemented
107	#464×C₆₇	C₂²	1	2	yes	complemented
108	#462×C₆₇	C₂²	1	2	yes	complemented
109	#452×C₆₇	C₂²	1	2	yes	complemented
110	#452×C₆₇	C₂²	1	2	yes	complemented
111	#451×C₆₇	C₂²	1	1	yes	characteristic
112	#451×C₆₇	C₂²	1	1	yes	characteristic
113	#451×C₆₇	C₂²	1	1	yes	characteristic
114	#451×C₆₇	C₂²	1	2	yes	complemented
115	#451×C₆₇	C₂²	1	2	yes	complemented
116	#448×C₆₇	C₂²	1	1	yes	characteristic
117	#441×C₆₇	C₂²	1	2	yes	complemented
118	#440×C₆₇	C₂²	1	2	yes	complemented
119	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	2	yes	—
122	#435×C₆₇	C₂²	1	2	yes	—
123	#435×C₆₇	C₂²	1	2	yes	—
124	C₈×D₄×C₆₇	C₂²	1	2	yes	—
125	#432×C₆₇	C₂²	1	1	yes	characteristic
126	#431×C₆₇	C₂²	1	1	yes	characteristic
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	#419×C₆₇	C₂²	1	2	yes	complemented
132	#417×C₆₇	C₂²	1	2	yes	complemented
133	#416×C₆₇	C₂²	1	2	yes	complemented
134	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
135	#407×C₆₇	C₂²	1	1	yes	characteristic
136	#407×C₆₇	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
138	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
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×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
146	C₂³×C₄×C₆₇	—	2	1	no	—
147	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
156	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	#126×C₆₇	—	2	2	no	—
161	#126×C₆₇	—	2	2	no	—
162	#126×C₆₇	—	2	2	no	—
163	#126×C₆₇	—	2	2	no	—
164	#126×C₆₇	—	2	1	no	—
165	#126×C₆₇	—	2	1	no	—
166	#126×C₆₇	—	2	1	no	—
167	#126×C₆₇	—	2	1	no	—
168	#126×C₆₇	—	2	1	no	—
169	#125×C₆₇	—	2	2	no	—
170	#125×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	1	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	—	2	1	no	—
178	#125×C₆₇	C₂³	1	2	yes	—
179	#125×C₆₇	C₂³	1	2	yes	—
180	#125×C₆₇	C₂³	1	1	yes	characteristic
181	#124×C₆₇	—	2	1	no	—
182	#124×C₆₇	—	2	1	no	—
183	#124×C₆₇	—	2	1	no	—
184	#124×C₆₇	C₂³	1	1	yes	characteristic
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	1	no	—
190	#123×C₆₇	—	2	1	no	—
191	#123×C₆₇	—	2	1	no	—
192	#123×C₆₇	—	2	1	no	—
193	#123×C₆₇	—	2	1	no	—
194	#123×C₆₇	—	2	1	no	—
195	#123×C₆₇	—	2	1	no	—
196	#123×C₆₇	—	2	1	no	—
197	#123×C₆₇	—	2	1	no	—
198	C₂²⋊Q₈×C₆₇	—	2	1	no	—
199	C₂²⋊Q₈×C₆₇	—	2	1	no	—
200	C₂²⋊Q₈×C₆₇	—	2	1	no	—
201	C₂²⋊Q₈×C₆₇	—	2	1	no	—
202	C₂²⋊Q₈×C₆₇	—	2	1	no	—
203	C₂²⋊Q₈×C₆₇	—	2	1	no	—
204	C₂²⋊Q₈×C₆₇	—	2	1	no	—
205	C₂²⋊Q₈×C₆₇	—	2	1	no	—
206	C₂²⋊Q₈×C₆₇	—	2	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	1	no	—
210	C₂²⋊Q₈×C₆₇	—	2	1	no	—
211	C₂²⋊Q₈×C₆₇	—	2	1	no	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	#121×C₆₇	—	2	1	no	—
226	#121×C₆₇	—	2	1	no	—
227	#121×C₆₇	—	2	1	no	—
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	#120×C₆₇	—	2	1	no	—
232	#120×C₆₇	—	2	1	no	—
233	C₄×Q₈×C₆₇	—	2	1	no	—
234	C₄×Q₈×C₆₇	—	2	1	no	—
235	C₄×Q₈×C₆₇	—	2	1	no	—
236	C₄×Q₈×C₆₇	—	2	1	no	—
237	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
239	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	1	no	—
248	C₄×D₄×C₆₇	—	2	1	no	—
249	C₄×D₄×C₆₇	—	2	1	no	—
250	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
251	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
252	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
253	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
254	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
259	#117×C₆₇	—	2	1	no	—
260	#117×C₆₇	—	2	1	no	—
261	#117×C₆₇	—	2	1	no	—
262	#117×C₆₇	—	2	2	no	—
263	#117×C₆₇	—	2	2	no	—
264	#117×C₆₇	—	2	2	no	—
265	#117×C₆₇	—	2	2	no	—
266	#117×C₆₇	—	2	1	no	—
267	#117×C₆₇	—	2	1	no	—
268	#117×C₆₇	—	2	1	no	—
269	#117×C₆₇	C₂³	1	2	yes	—
270	#117×C₆₇	C₂³	1	2	yes	—
271	#117×C₆₇	C₂³	1	1	yes	characteristic
272	#117×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
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	—	2	1	no	—
283	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
284	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
299	C₂×C₄²×C₆₇	—	2	1	no	—
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	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#103×C₆₇	C₂³	1	2	yes	—
324	#103×C₆₇	C₂³	1	2	yes	—
325	#103×C₆₇	C₂³	1	2	yes	—
326	#103×C₆₇	C₂³	1	2	yes	—
327	#103×C₆₇	C₂³	1	2	yes	—
328	#103×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
343	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
344	#41×C₆₇	—	4	2	no	—
345	#41×C₆₇	—	4	2	no	—
346	#41×C₆₇	—	4	4	no	—
347	C₂×Q₈×C₆₇	—	2	1	no	—
348	C₂×Q₈×C₆₇	—	2	1	no	—
349	C₂×Q₈×C₆₇	—	2	1	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	—	4	2	no	—
352	C₂×Q₈×C₆₇	—	4	2	no	—
353	C₂×Q₈×C₆₇	—	4	2	no	—
354	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
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	—	4	2	no	—
364	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	1	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	1	no	—
374	C₂²×C₄×C₆₇	—	2	1	no	—
375	C₂²×C₄×C₆₇	—	2	2	no	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	1	no	—
379	C₂²×C₄×C₆₇	—	2	1	no	—
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	2	1	no	—
382	C₂²×C₄×C₆₇	—	4	2	no	—
383	C₂²×C₄×C₆₇	—	4	2	no	—
384	C₂²×C₄×C₆₇	—	4	4	no	—
385	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	Q₁₆×C₆₇	—	4	2	no	—
399	Q₁₆×C₆₇	—	4	2	no	—
400	Q₁₆×C₆₇	—	4	2	no	—
401	SD₁₆×C₆₇	—	4	2	no	—
402	M₁₆×C₆₇	—	4	2	no	—
403	M₁₆×C₆₇	—	4	2	no	—
404	C₂×C₈×C₆₇	—	4	2	no	—
405	C₂×C₈×C₆₇	—	4	2	no	—
406	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
407	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
409	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	1	no	—
416	C₄⋊C₄×C₆₇	—	2	1	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	1	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	2	no	—
427	C₄⋊C₄×C₆₇	—	2	2	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	—	2	2	no	—
431	C₄⋊C₄×C₆₇	—	2	2	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	1	no	—
438	C₄⋊C₄×C₆₇	—	2	1	no	—
439	C₄⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	1	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
467	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
477	C₂²⋊C₄×C₆₇	—	2	1	no	—
478	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
486	C₄²×C₆₇	—	2	2	no	—
487	C₄²×C₆₇	—	2	2	no	—
488	C₄²×C₆₇	—	2	2	no	—
489	C₄²×C₆₇	—	2	2	no	—
490	C₄²×C₆₇	—	2	1	no	—
491	C₄²×C₆₇	—	2	1	no	—
492	C₄²×C₆₇	—	2	1	no	—
493	C₄²×C₆₇	—	2	1	no	—
494	C₄²×C₆₇	—	2	1	no	—
495	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂³×C₆₇	—	2	2	no	—
500	C₂³×C₆₇	—	2	2	no	—
501	C₂³×C₆₇	—	2	2	no	—
502	C₂³×C₆₇	—	2	1	no	—
503	C₂³×C₆₇	—	4	1	no	—
504	C₂³×C₆₇	—	4	1	no	—
505	C₂³×C₆₇	—	4	1	no	—
506	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
507	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
508	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
511	Q₈×C₆₇	—	2	2	no	—
512	Q₈×C₆₇	—	2	2	no	—
513	Q₈×C₆₇	—	2	2	no	—
514	Q₈×C₆₇	—	2	2	no	—
515	Q₈×C₆₇	—	2	2	no	—
516	Q₈×C₆₇	—	4	2	no	—
517	Q₈×C₆₇	—	4	2	no	—
518	Q₈×C₆₇	—	8	1	no	—
519	Q₈×C₆₇	—	8	1	no	—
520	D₄×C₆₇	—	2	2	no	—
521	D₄×C₆₇	—	2	2	no	—
522	D₄×C₆₇	—	2	2	no	—
523	D₄×C₆₇	—	4	1	no	—
524	D₄×C₆₇	—	4	1	no	—
525	D₄×C₆₇	—	4	2	no	—
526	D₄×C₆₇	—	4	2	no	—
527	D₄×C₆₇	—	4	2	no	—
528	D₄×C₆₇	—	8	1	no	—
529	D₄×C₆₇	—	8	1	no	—
530	C₂×C₄×C₆₇	—	2	2	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	2	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	2	no	—
539	C₂×C₄×C₆₇	—	2	2	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	1	no	—
545	C₂×C₄×C₆₇	—	2	1	no	—
546	C₂×C₄×C₆₇	—	2	2	no	—
547	C₂×C₄×C₆₇	—	4	1	no	—
548	C₂×C₄×C₆₇	—	4	1	no	—
549	C₂×C₄×C₆₇	—	4	1	no	—
550	C₂×C₄×C₆₇	—	4	1	no	—
551	C₂×C₄×C₆₇	—	4	1	no	—
552	C₂×C₄×C₆₇	—	4	1	no	—
553	C₂×C₄×C₆₇	—	4	1	no	—
554	C₂×C₄×C₆₇	—	4	2	no	—
555	C₂×C₄×C₆₇	—	4	2	no	—
556	C₂×C₄×C₆₇	—	4	2	no	—
557	C₂×C₄×C₆₇	—	4	4	no	—
558	C₂×C₄×C₆₇	—	4	2	no	—
559	C₂×C₄×C₆₇	—	4	2	no	—
560	C₂×C₄×C₆₇	—	4	4	no	—
561	C₂×C₄×C₆₇	—	4	2	no	—
562	C₂×C₄×C₆₇	—	4	2	no	—
563	C₂×C₄×C₆₇	—	8	1	no	—
564	C₂×C₄×C₆₇	—	8	1	no	—
565	C₂×C₄×C₆₇	—	8	1	no	—
566	C₂×C₄×C₆₇	—	8	1	no	—
567	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
577	C₈×C₆₇	—	2	2	no	—
578	C₈×C₆₇	—	2	2	no	—
579	C₈×C₆₇	—	2	2	no	—
580	C₈×C₆₇	—	2	2	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	2	1	no	—
583	C₂²×C₆₇	—	2	1	no	—
584	C₂²×C₆₇	—	2	1	no	—
585	C₂²×C₆₇	—	2	1	no	—
586	C₂²×C₆₇	—	2	1	no	—
587	C₂²×C₆₇	—	2	1	no	—
588	C₂²×C₆₇	—	2	1	no	—
589	C₂²×C₆₇	—	2	1	no	—
590	C₂²×C₆₇	—	2	1	no	—
591	C₂²×C₆₇	—	2	1	no	—
592	C₂²×C₆₇	—	2	1	no	—
593	C₂²×C₆₇	—	2	1	no	—
594	C₂²×C₆₇	—	4	4	no	—
595	C₂²×C₆₇	—	4	1	no	—
596	C₂²×C₆₇	—	4	1	no	—
597	C₂²×C₆₇	—	4	1	no	—
598	C₂²×C₆₇	—	8	2	no	—
599	C₂²×C₆₇	#575	1	2	yes	—
600	C₂²×C₆₇	#578	1	2	yes	—
601	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
602	C₄×C₆₇	—	2	1	no	—
603	C₄×C₆₇	—	2	1	no	—
604	C₄×C₆₇	—	2	1	no	—
605	C₄×C₆₇	—	2	1	no	—
606	C₄×C₆₇	—	2	1	no	—
607	C₄×C₆₇	—	2	1	no	—
608	C₄×C₆₇	—	2	1	no	—
609	C₄×C₆₇	—	2	1	no	—
610	C₄×C₆₇	—	2	1	no	—
611	C₄×C₆₇	—	4	2	no	—
612	C₄×C₆₇	—	4	1	no	—
613	C₄×C₆₇	—	4	1	no	—
614	C₄×C₆₇	—	4	1	no	—
615	C₄×C₆₇	—	4	2	no	—
616	C₄×C₆₇	—	4	1	no	—
617	C₄×C₆₇	—	4	2	no	—
618	C₄×C₆₇	—	4	1	no	—
619	C₄×C₆₇	—	4	1	no	—
620	C₄×C₆₇	—	4	2	no	—
621	C₄×C₆₇	—	4	1	no	—
622	C₄×C₆₇	#585	1	2	yes	—
623	#61738	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
624	C₂×C₆₇	—	2	2	no	—
625	C₂×C₆₇	—	2	2	no	—
626	C₂×C₆₇	—	4	1	no	—
627	C₂×C₆₇	—	4	1	no	—
628	C₂×C₆₇	—	4	1	no	—
629	C₂×C₆₇	—	8	1	no	—
630	C₂×C₆₇	#3485	1	1	yes	characteristic
631	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
632	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
633	#3520	C₂×C₆₇	1	1	yes	characteristic
634	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#3352	C₂×C₆₇	1	2	yes	complemented
636	#3349	C₂×C₆₇	1	2	yes	complemented
637	#3343	C₂×C₆₇	1	2	yes	complemented
638	#3336	C₂×C₆₇	1	2	yes	complemented
639	#3327	C₂×C₆₇	1	2	yes	complemented
640	#3315	C₂×C₆₇	1	2	yes	complemented
641	#3312	C₂×C₆₇	1	2	yes	complemented
642	#3300	C₂×C₆₇	1	2	yes	complemented
643	#3236	C₂×C₆₇	1	1	yes	characteristic, complemented
644	#3232	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#3196	C₂×C₆₇	1	1	yes	characteristic, complemented
646	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
647	#3190	C₂×C₆₇	1	1	yes	characteristic, complemented
648	#3189	C₂×C₆₇	1	1	yes	characteristic, complemented
649	#3117	C₂×C₆₇	1	1	yes	characteristic, complemented
650	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
651	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
652	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
653	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
654	C₂×#484	C₂×C₆₇	1	1	yes	characteristic, complemented
655	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
656	C₆₇	#61738	1	1	yes	characteristic, direct product factor, Sylow
657	#556	C₂²×C₆₇	1	1	yes	characteristic
658	#554	—	2	1	no	—
659	#552	—	2	1	no	—
660	#552	—	2	1	no	—
661	#552	—	2	1	no	—
662	#552	—	2	1	no	—
663	#552	C₂²×C₆₇	1	1	yes	characteristic
664	#552	C₂²×C₆₇	1	2	yes	—
665	#552	C₂²×C₆₇	1	2	yes	—
666	#552	C₂²×C₆₇	1	2	yes	—
667	#552	C₂²×C₆₇	1	1	yes	characteristic
668	#552	C₂²×C₆₇	1	2	yes	—
669	#551	—	2	1	no	—
670	#551	—	2	1	no	—
671	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
672	#548	C₂²×C₆₇	1	1	yes	characteristic
673	#548	C₂²×C₆₇	1	1	yes	characteristic
674	#547	C₂²×C₆₇	1	1	yes	characteristic
675	#547	C₂²×C₆₇	1	1	yes	characteristic
676	#546	—	2	1	no	—
677	#542	—	2	1	no	—
678	#539	—	2	1	no	—
679	#539	—	2	1	no	—
680	#533	C₂²×C₆₇	1	1	yes	characteristic
681	#529	C₂²×C₆₇	1	1	yes	characteristic
682	C₂×#126	—	2	1	no	—
683	C₂×#125	—	2	1	no	—
684	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
685	#525	C₂²×C₆₇	1	1	yes	characteristic
686	#525	C₂²×C₆₇	1	1	yes	characteristic
687	C₂×#123	—	2	1	no	—
688	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
689	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
690	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
691	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
692	#520	—	2	1	no	—
693	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
694	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
695	C₂×#117	—	2	1	no	—
696	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
697	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
698	#501	C₂²×C₆₇	1	2	yes	complemented
699	#499	C₂²×C₆₇	1	2	yes	complemented
700	#491	C₂²×C₆₇	1	2	yes	complemented
701	#488	C₂²×C₆₇	1	2	yes	complemented
702	#485	C₂²×C₆₇	1	2	yes	complemented
703	#485	C₂²×C₆₇	1	2	yes	complemented
704	#485	C₂²×C₆₇	1	2	yes	complemented
705	#485	C₂²×C₆₇	1	2	yes	complemented
706	#485	C₂²×C₆₇	1	2	yes	complemented
707	#484	C₂²×C₆₇	1	1	yes	characteristic
708	#484	C₂²×C₆₇	1	1	yes	characteristic
709	#484	C₂²×C₆₇	1	1	yes	characteristic
710	#484	C₂²×C₆₇	1	1	yes	characteristic
711	#484	C₂²×C₆₇	1	1	yes	characteristic
712	#484	C₂²×C₆₇	1	1	yes	characteristic
713	#484	C₂²×C₆₇	1	2	yes	complemented
714	#484	C₂²×C₆₇	1	2	yes	complemented
715	#484	C₂²×C₆₇	1	2	yes	complemented
716	#483	C₂²×C₆₇	1	1	yes	characteristic
717	#483	C₂²×C₆₇	1	1	yes	characteristic
718	#483	C₂²×C₆₇	1	1	yes	characteristic
719	#483	C₂²×C₆₇	1	2	yes	complemented
720	#483	C₂²×C₆₇	1	2	yes	complemented
721	#482	C₂²×C₆₇	1	2	yes	complemented
722	#481	C₂²×C₆₇	1	1	yes	characteristic
723	#481	C₂²×C₆₇	1	1	yes	characteristic
724	#480	C₂²×C₆₇	1	1	yes	characteristic
725	#480	C₂²×C₆₇	1	2	yes	complemented
726	#479	C₂²×C₆₇	1	2	yes	complemented
727	#479	C₂²×C₆₇	1	2	yes	complemented
728	#479	C₂²×C₆₇	1	2	yes	complemented
729	#479	C₂²×C₆₇	1	2	yes	complemented
730	#478	C₂²×C₆₇	1	2	yes	complemented
731	#477	C₂²×C₆₇	1	2	yes	complemented
732	#470	C₂²×C₆₇	1	2	yes	complemented
733	#470	C₂²×C₆₇	1	2	yes	complemented
734	#470	C₂²×C₆₇	1	2	yes	complemented
735	#468	C₂²×C₆₇	1	2	yes	complemented
736	#467	C₂²×C₆₇	1	2	yes	complemented
737	#467	C₂²×C₆₇	1	2	yes	complemented
738	#467	C₂²×C₆₇	1	2	yes	complemented
739	#465	C₂²×C₆₇	1	2	yes	complemented
740	#464	C₂²×C₆₇	1	2	yes	complemented
741	#462	C₂²×C₆₇	1	2	yes	complemented
742	#452	C₂²×C₆₇	1	2	yes	complemented
743	#452	C₂²×C₆₇	1	2	yes	complemented
744	#451	C₂²×C₆₇	1	1	yes	characteristic
745	#451	C₂²×C₆₇	1	1	yes	characteristic
746	#451	C₂²×C₆₇	1	1	yes	characteristic
747	#451	C₂²×C₆₇	1	2	yes	complemented
748	#451	C₂²×C₆₇	1	2	yes	complemented
749	#448	C₂²×C₆₇	1	1	yes	characteristic
750	#441	C₂²×C₆₇	1	2	yes	complemented
751	#440	C₂²×C₆₇	1	2	yes	complemented
752	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
753	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
754	#436	C₂²×C₆₇	1	2	yes	—
755	#435	C₂²×C₆₇	1	2	yes	—
756	#435	C₂²×C₆₇	1	2	yes	—
757	C₈×D₄	C₂²×C₆₇	1	2	yes	—
758	#432	C₂²×C₆₇	1	1	yes	characteristic
759	#431	C₂²×C₆₇	1	1	yes	characteristic
760	#428	C₂²×C₆₇	1	2	yes	complemented
761	#428	C₂²×C₆₇	1	2	yes	complemented
762	#427	C₂²×C₆₇	1	2	yes	complemented
763	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
764	#419	C₂²×C₆₇	1	2	yes	complemented
765	#417	C₂²×C₆₇	1	2	yes	complemented
766	#416	C₂²×C₆₇	1	2	yes	complemented
767	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
768	#407	C₂²×C₆₇	1	1	yes	characteristic
769	#407	C₂²×C₆₇	1	1	yes	characteristic
770	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
771	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
772	C₂×#41	—	2	1	no	—
773	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
774	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
775	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
776	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
777	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
779	C₂³×C₄	—	2	1	no	—
780	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
781	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
783	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
784	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
786	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
787	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
788	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
789	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	2	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#125	—	2	2	no	—
803	#125	—	2	2	no	—
804	#125	—	2	2	no	—
805	#125	—	2	2	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	—	2	1	no	—
810	#125	—	2	1	no	—
811	#125	C₂³×C₆₇	1	2	yes	—
812	#125	C₂³×C₆₇	1	2	yes	—
813	#125	C₂³×C₆₇	1	1	yes	characteristic
814	#124	—	2	1	no	—
815	#124	—	2	1	no	—
816	#124	—	2	1	no	—
817	#124	C₂³×C₆₇	1	1	yes	characteristic
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	1	no	—
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	#123	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
846	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
850	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
851	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
852	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
853	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
854	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	C₂³×C₆₇	1	1	yes	characteristic
862	#121	C₂³×C₆₇	1	1	yes	characteristic
863	#121	C₂³×C₆₇	1	1	yes	characteristic
864	#120	—	2	1	no	—
865	#120	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
871	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
872	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
873	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
874	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
884	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
885	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
886	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
887	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
892	#117	—	2	1	no	—
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	2	no	—
896	#117	—	2	2	no	—
897	#117	—	2	2	no	—
898	#117	—	2	2	no	—
899	#117	—	2	1	no	—
900	#117	—	2	1	no	—
901	#117	—	2	1	no	—
902	#117	C₂³×C₆₇	1	2	yes	—
903	#117	C₂³×C₆₇	1	2	yes	—
904	#117	C₂³×C₆₇	1	1	yes	characteristic
905	#117	C₂³×C₆₇	1	1	yes	characteristic
906	C₂×C₄⋊C₄	—	2	1	no	—
907	C₂×C₄⋊C₄	—	2	1	no	—
908	C₂×C₄⋊C₄	—	2	1	no	—
909	C₂×C₄⋊C₄	—	2	1	no	—
910	C₂×C₄⋊C₄	—	2	1	no	—
911	C₂×C₄⋊C₄	—	2	1	no	—
912	C₂×C₄⋊C₄	—	2	1	no	—
913	C₂×C₄⋊C₄	—	2	1	no	—
914	C₂×C₄⋊C₄	—	2	1	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
921	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
922	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	—	2	1	no	—
926	C₂×C₂²⋊C₄	—	2	1	no	—
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	1	no	—
929	C₂×C₂²⋊C₄	—	2	1	no	—
930	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
931	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
932	C₂×C₄²	—	2	1	no	—
933	C₂×C₄²	—	2	1	no	—
934	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
935	#107	C₂³×C₆₇	1	2	yes	—
936	#107	C₂³×C₆₇	1	2	yes	—
937	#107	C₂³×C₆₇	1	2	yes	—
938	#107	C₂³×C₆₇	1	2	yes	—
939	#107	C₂³×C₆₇	1	2	yes	—
940	#107	C₂³×C₆₇	1	2	yes	—
941	#107	C₂³×C₆₇	1	2	yes	—
942	#106	C₂³×C₆₇	1	2	yes	—
943	#106	C₂³×C₆₇	1	2	yes	—
944	#106	C₂³×C₆₇	1	2	yes	—
945	#106	C₂³×C₆₇	1	2	yes	—
946	#106	C₂³×C₆₇	1	2	yes	—
947	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
948	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
949	#103	C₂³×C₆₇	1	2	yes	—
950	#103	C₂³×C₆₇	1	2	yes	—
951	#103	C₂³×C₆₇	1	2	yes	—
952	#103	C₂³×C₆₇	1	2	yes	—
953	#103	C₂³×C₆₇	1	2	yes	—
954	#103	C₂³×C₆₇	1	2	yes	—
955	#103	C₂³×C₆₇	1	2	yes	—
956	#103	C₂³×C₆₇	1	2	yes	—
957	#103	C₂³×C₆₇	1	2	yes	—
958	#103	C₂³×C₆₇	1	2	yes	—
959	#103	C₂³×C₆₇	1	2	yes	—
960	#103	C₂³×C₆₇	1	2	yes	—
961	#103	C₂³×C₆₇	1	2	yes	—
962	#102	C₂³×C₆₇	1	2	yes	—
963	#102	C₂³×C₆₇	1	2	yes	—
964	#102	C₂³×C₆₇	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
966	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
967	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
968	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
969	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
970	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
971	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
972	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
973	#97	C₂³×C₆₇	1	2	yes	—
974	C₄×C₈	C₂³×C₆₇	1	2	yes	—
975	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
976	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
977	#41	—	4	2	no	—
978	#41	—	4	2	no	—
979	#41	—	4	4	no	—
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	4	2	no	—
985	C₂×Q₈	—	4	2	no	—
986	C₂×Q₈	—	4	2	no	—
987	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	4	2	no	—
997	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
998	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
999	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1000	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1001	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	4	2	no	—
1016	C₂²×C₄	—	4	2	no	—
1017	C₂²×C₄	—	4	4	no	—
1018	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1025	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1030	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1031	Q₁₆	—	4	2	no	—
1032	Q₁₆	—	4	2	no	—
1033	Q₁₆	—	4	2	no	—
1034	SD₁₆	—	4	2	no	—
1035	M₁₆	—	4	2	no	—
1036	M₁₆	—	4	2	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1040	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1112	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1113	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1114	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1115	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1116	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1117	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1118	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1119	C₄²	—	2	2	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	—	2	2	no	—
1122	C₄²	—	2	2	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1129	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1131	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1132	C₂³	—	2	2	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	4	1	no	—
1137	C₂³	—	4	1	no	—
1138	C₂³	—	4	1	no	—
1139	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1140	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1141	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1142	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1143	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1144	Q₈	—	2	2	no	—
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	2	no	—
1147	Q₈	—	2	2	no	—
1148	Q₈	—	2	2	no	—
1149	Q₈	—	4	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	8	1	no	—
1152	Q₈	—	8	1	no	—
1153	D₄	—	2	2	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	4	1	no	—
1157	D₄	—	4	1	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	8	1	no	—
1162	D₄	—	8	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	4	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	4	2	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1207	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1209	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1210	C₈	—	2	2	no	—
1211	C₈	—	2	2	no	—
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	1	no	—
1226	C₂²	—	2	1	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	8	2	no	—
1232	C₂²	#575×C₆₇	1	2	yes	—
1233	C₂²	#578×C₆₇	1	2	yes	—
1234	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	2	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	2	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	#585×C₆₇	1	2	yes	—
1256	C₂	—	2	2	no	—
1257	C₂	—	2	2	no	—
1258	C₂	—	4	1	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	1	no	—
1261	C₂	—	8	1	no	—
1262	C₂	C₆₇×#3485	1	1	yes	characteristic
1263	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1264	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3520	C₂
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
2. C₂×#552×C₆₇	C₂	semidirect
3. C₆₇×#3352	C₂	semidirect
4. C₆₇×#3349	C₂	semidirect
5. C₆₇×#3343	C₂	semidirect
6. C₆₇×#3336	C₂	semidirect
7. C₆₇×#3327	C₂	semidirect
8. C₆₇×#3315	C₂	semidirect
9. C₆₇×#3312	C₂	semidirect
10. C₆₇×#3300	C₂	semidirect
11. C₆₇×#3236	C₂	semidirect
12. C₆₇×#3232	C₂	semidirect
13. C₆₇×#3196	C₂	semidirect
14. C₆₇×#3195	C₂	semidirect
15. C₆₇×#3190	C₂	semidirect
16. C₆₇×#3189	C₂	semidirect
17. C₆₇×#3117	C₂	semidirect
18. C₆₇×#3104	C₂	semidirect
19. C₆₇×#3095	C₂	semidirect
20. C₆₇×#3092	C₂	semidirect
21. C₆₇×#3091	C₂	semidirect
22. C₂×#484×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
67. #491×C₆₇	C₂²	semidirect
68. #488×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #485×C₆₇	C₂²	semidirect
71. #485×C₆₇	C₂²	semidirect
72. #485×C₆₇	C₂²	semidirect
73. #485×C₆₇	C₂²	semidirect
80. #484×C₆₇	C₂²	semidirect
81. #484×C₆₇	C₂²	semidirect
82. #484×C₆₇	C₂²	semidirect
86. #483×C₆₇	C₂²	semidirect
87. #483×C₆₇	C₂²	semidirect
88. #482×C₆₇	C₂²	semidirect
92. #480×C₆₇	C₂²	semidirect
93. #479×C₆₇	C₂²	semidirect
94. #479×C₆₇	C₂²	semidirect
95. #479×C₆₇	C₂²	semidirect
96. #479×C₆₇	C₂²	semidirect
97. #478×C₆₇	C₂²	semidirect
98. #477×C₆₇	C₂²	semidirect
99. #470×C₆₇	C₂²	semidirect
100. #470×C₆₇	C₂²	semidirect
101. #470×C₆₇	C₂²	semidirect
102. #468×C₆₇	C₂²	semidirect
103. #467×C₆₇	C₂²	semidirect
104. #467×C₆₇	C₂²	semidirect
105. #467×C₆₇	C₂²	semidirect
106. #465×C₆₇	C₂²	semidirect
107. #464×C₆₇	C₂²	semidirect
108. #462×C₆₇	C₂²	semidirect
109. #452×C₆₇	C₂²	semidirect
110. #452×C₆₇	C₂²	semidirect
114. #451×C₆₇	C₂²	semidirect
115. #451×C₆₇	C₂²	semidirect
117. #441×C₆₇	C₂²	semidirect
118. #440×C₆₇	C₂²	semidirect
119. C₄×Q₁₆×C₆₇	C₂²	semidirect
120. C₄×Q₁₆×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. #419×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×#103×C₆₇	C₂²	semidirect
623. #61738	C₆₇	direct (N × H)
634. C₂×#552	C₂×C₆₇	semidirect
635. #3352	C₂×C₆₇	semidirect
636. #3349	C₂×C₆₇	semidirect
637. #3343	C₂×C₆₇	semidirect
638. #3336	C₂×C₆₇	semidirect
639. #3327	C₂×C₆₇	semidirect
640. #3315	C₂×C₆₇	semidirect
641. #3312	C₂×C₆₇	semidirect
642. #3300	C₂×C₆₇	semidirect
643. #3236	C₂×C₆₇	semidirect
644. #3232	C₂×C₆₇	semidirect
645. #3196	C₂×C₆₇	semidirect
646. #3195	C₂×C₆₇	semidirect
647. #3190	C₂×C₆₇	semidirect
648. #3189	C₂×C₆₇	semidirect
649. #3117	C₂×C₆₇	semidirect
650. #3104	C₂×C₆₇	semidirect
651. #3095	C₂×C₆₇	semidirect
652. #3092	C₂×C₆₇	semidirect
653. #3091	C₂×C₆₇	semidirect
654. C₂×#484	C₂×C₆₇	semidirect
655. #2974	C₂×C₆₇	semidirect
656. C₆₇	#61738	direct (N × H)
698. #501	C₂²×C₆₇	semidirect
699. #499	C₂²×C₆₇	semidirect
700. #491	C₂²×C₆₇	semidirect
701. #488	C₂²×C₆₇	semidirect
702. #485	C₂²×C₆₇	semidirect
703. #485	C₂²×C₆₇	semidirect
704. #485	C₂²×C₆₇	semidirect
705. #485	C₂²×C₆₇	semidirect
706. #485	C₂²×C₆₇	semidirect
713. #484	C₂²×C₆₇	semidirect
714. #484	C₂²×C₆₇	semidirect
715. #484	C₂²×C₆₇	semidirect
719. #483	C₂²×C₆₇	semidirect
720. #483	C₂²×C₆₇	semidirect
721. #482	C₂²×C₆₇	semidirect
725. #480	C₂²×C₆₇	semidirect
726. #479	C₂²×C₆₇	semidirect
727. #479	C₂²×C₆₇	semidirect
728. #479	C₂²×C₆₇	semidirect
729. #479	C₂²×C₆₇	semidirect
730. #478	C₂²×C₆₇	semidirect
731. #477	C₂²×C₆₇	semidirect
732. #470	C₂²×C₆₇	semidirect
733. #470	C₂²×C₆₇	semidirect
734. #470	C₂²×C₆₇	semidirect
735. #468	C₂²×C₆₇	semidirect
736. #467	C₂²×C₆₇	semidirect
737. #467	C₂²×C₆₇	semidirect
738. #467	C₂²×C₆₇	semidirect
739. #465	C₂²×C₆₇	semidirect
740. #464	C₂²×C₆₇	semidirect
741. #462	C₂²×C₆₇	semidirect
742. #452	C₂²×C₆₇	semidirect
743. #452	C₂²×C₆₇	semidirect
747. #451	C₂²×C₆₇	semidirect
748. #451	C₂²×C₆₇	semidirect
750. #441	C₂²×C₆₇	semidirect
751. #440	C₂²×C₆₇	semidirect
752. C₄×Q₁₆	C₂²×C₆₇	semidirect
753. C₄×Q₁₆	C₂²×C₆₇	semidirect
760. #428	C₂²×C₆₇	semidirect
761. #428	C₂²×C₆₇	semidirect
762. #427	C₂²×C₆₇	semidirect
763. C₂×#107	C₂²×C₆₇	semidirect
764. #419	C₂²×C₆₇	semidirect
765. #417	C₂²×C₆₇	semidirect
766. #416	C₂²×C₆₇	semidirect
767. C₂×#103	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×#3520	2
C₂×#552×C₆₇	2
C₆₇×#3352	2
C₆₇×#3349	2
C₆₇×#3343	2
C₆₇×#3336	2
C₆₇×#3327	2
C₆₇×#3315	2
C₆₇×#3312	2
C₆₇×#3300	2
C₆₇×#3236	2
C₆₇×#3232	2
C₆₇×#3196	2
C₆₇×#3195	2
C₆₇×#3190	2
C₆₇×#3189	2
C₆₇×#3117	2
C₆₇×#3104	2
C₆₇×#3095	2
C₆₇×#3092	2
C₆₇×#3091	2
C₂×#484×C₆₇	2
C₆₇×#2974	2
#61738	67

Subgroups — C67×#61738 #30740989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61738 #30740989