Subgroups — C₆₇×#61168 #30740419

Order 17152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3308	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3299	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3004	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×#103×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
31	#554×C₆₇	—	2	1	no	—
32	#554×C₆₇	C₂²	1	2	yes	—
33	#553×C₆₇	—	2	1	no	—
34	#553×C₆₇	C₂²	1	2	yes	—
35	#552×C₆₇	—	2	1	no	—
36	#552×C₆₇	C₂²	1	2	yes	—
37	D₄×Q₈×C₆₇	—	2	1	no	—
38	D₄×Q₈×C₆₇	—	2	1	no	—
39	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
40	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
41	#548×C₆₇	—	2	1	no	—
42	#548×C₆₇	—	2	1	no	—
43	#548×C₆₇	C₂²	1	2	yes	—
44	#548×C₆₇	C₂²	1	2	yes	—
45	#547×C₆₇	—	2	1	no	—
46	#547×C₆₇	C₂²	1	2	yes	—
47	#544×C₆₇	C₂²	1	1	yes	characteristic
48	#539×C₆₇	—	2	2	no	—
49	#537×C₆₇	C₂²	1	1	yes	characteristic
50	#536×C₆₇	—	2	2	no	—
51	#536×C₆₇	C₂²	1	1	yes	characteristic
52	#536×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	—	2	2	no	—
54	#525×C₆₇	—	2	2	no	—
55	#525×C₆₇	C₂²	1	1	yes	characteristic
56	#525×C₆₇	C₂²	1	1	yes	characteristic
57	#525×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	C₂²	1	1	yes	characteristic
60	#519×C₆₇	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
62	#491×C₆₇	C₂²	1	2	yes	complemented
63	#489×C₆₇	C₂²	1	2	yes	complemented
64	#488×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#484×C₆₇	C₂²	1	2	yes	—
69	#484×C₆₇	C₂²	1	2	yes	complemented
70	#483×C₆₇	C₂²	1	2	yes	—
71	#483×C₆₇	C₂²	1	2	yes	complemented
72	#481×C₆₇	C₂²	1	2	yes	—
73	#480×C₆₇	C₂²	1	2	yes	—
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#479×C₆₇	C₂²	1	2	yes	complemented
76	#477×C₆₇	C₂²	1	2	yes	complemented
77	#475×C₆₇	C₂²	1	2	yes	complemented
78	#470×C₆₇	C₂²	1	2	yes	complemented
79	#468×C₆₇	C₂²	1	2	yes	complemented
80	#467×C₆₇	C₂²	1	1	yes	characteristic
81	#467×C₆₇	C₂²	1	1	yes	characteristic
82	#467×C₆₇	C₂²	1	2	yes	complemented
83	#466×C₆₇	C₂²	1	1	yes	characteristic
84	#466×C₆₇	C₂²	1	1	yes	characteristic
85	#465×C₆₇	C₂²	1	1	yes	characteristic
86	#465×C₆₇	C₂²	1	1	yes	characteristic
87	#465×C₆₇	C₂²	1	1	yes	characteristic
88	#465×C₆₇	C₂²	1	1	yes	characteristic
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#463×C₆₇	C₂²	1	2	yes	complemented
92	#462×C₆₇	C₂²	1	2	yes	complemented
93	#461×C₆₇	C₂²	1	2	yes	complemented
94	#452×C₆₇	C₂²	1	2	yes	complemented
95	#451×C₆₇	C₂²	1	2	yes	—
96	#451×C₆₇	C₂²	1	2	yes	—
97	#451×C₆₇	C₂²	1	2	yes	complemented
98	#449×C₆₇	C₂²	1	2	yes	complemented
99	#448×C₆₇	C₂²	1	2	yes	—
100	#448×C₆₇	C₂²	1	2	yes	—
101	#448×C₆₇	C₂²	1	2	yes	complemented
102	#441×C₆₇	C₂²	1	2	yes	complemented
103	#440×C₆₇	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
106	#435×C₆₇	C₂²	1	2	yes	—
107	#435×C₆₇	C₂²	1	2	yes	—
108	C₈×D₄×C₆₇	C₂²	1	2	yes	—
109	C₈×D₄×C₆₇	C₂²	1	2	yes	—
110	#428×C₆₇	C₂²	1	1	yes	characteristic
111	#428×C₆₇	C₂²	1	1	yes	characteristic
112	#427×C₆₇	C₂²	1	1	yes	characteristic
113	#424×C₆₇	C₂²	1	1	yes	characteristic
114	#419×C₆₇	C₂²	1	1	yes	characteristic
115	#419×C₆₇	C₂²	1	1	yes	characteristic
116	#419×C₆₇	C₂²	1	2	yes	complemented
117	#417×C₆₇	C₂²	1	1	yes	characteristic
118	#417×C₆₇	C₂²	1	1	yes	characteristic
119	#417×C₆₇	C₂²	1	2	yes	complemented
120	#416×C₆₇	C₂²	1	1	yes	characteristic
121	#416×C₆₇	C₂²	1	1	yes	characteristic
122	#416×C₆₇	C₂²	1	2	yes	complemented
123	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
124	C₂×#103×C₆₇	C₂²	1	2	yes	—
125	C₂×#103×C₆₇	C₂²	1	2	yes	—
126	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
127	C₂×#103×C₆₇	C₂²	1	2	yes	—
128	C₂×#103×C₆₇	C₂²	1	2	yes	—
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	#407×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	—	2	2	no	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	2	yes	—
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₇	—	2	1	no	—
145	C₂²×Q₈×C₆₇	—	2	1	no	—
146	C₂²×Q₈×C₆₇	—	2	1	no	—
147	C₂²×Q₈×C₆₇	—	2	1	no	—
148	C₂²×Q₈×C₆₇	—	2	4	no	—
149	C₂²×Q₈×C₆₇	—	4	2	no	—
150	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
153	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
154	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₆₇	—	2	1	no	—
156	C₂³×C₄×C₆₇	—	2	1	no	—
157	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
158	#137×C₆₇	—	2	4	no	—
159	#137×C₆₇	—	4	2	no	—
160	#135×C₆₇	—	4	2	no	—
161	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
169	#131×C₆₇	—	4	2	no	—
170	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂²×C₈×C₆₇	—	4	2	no	—
174	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
179	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈×C₆₇	—	2	1	no	—
182	C₄⋊Q₈×C₆₇	—	2	2	no	—
183	C₄⋊Q₈×C₆₇	—	2	2	no	—
184	C₄⋊Q₈×C₆₇	—	2	1	no	—
185	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
186	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
187	#126×C₆₇	—	2	2	no	—
188	#126×C₆₇	—	2	2	no	—
189	#125×C₆₇	—	2	2	no	—
190	#125×C₆₇	—	2	2	no	—
191	#125×C₆₇	—	2	1	no	—
192	#125×C₆₇	C₂³	1	2	yes	—
193	#124×C₆₇	—	2	1	no	—
194	#124×C₆₇	—	2	2	no	—
195	#124×C₆₇	—	2	2	no	—
196	#124×C₆₇	C₂³	1	2	yes	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	1	no	—
200	#123×C₆₇	—	2	1	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	—	2	2	no	—
205	#123×C₆₇	D₄	1	2	yes	—
206	C₂²⋊Q₈×C₆₇	—	2	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	—	2	1	no	—
210	C₂²⋊Q₈×C₆₇	—	2	1	no	—
211	C₂²⋊Q₈×C₆₇	—	2	2	no	—
212	C₂²⋊Q₈×C₆₇	—	2	2	no	—
213	C₂²⋊Q₈×C₆₇	—	2	2	no	—
214	C₂²⋊Q₈×C₆₇	—	2	2	no	—
215	C₂²⋊Q₈×C₆₇	—	2	2	no	—
216	C₂²⋊Q₈×C₆₇	—	2	2	no	—
217	C₂²⋊Q₈×C₆₇	—	2	2	no	—
218	C₂²⋊Q₈×C₆₇	—	2	2	no	—
219	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈×C₆₇	D₄	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	2	yes	—
224	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	—	2	2	no	—
229	#121×C₆₇	—	2	2	no	—
230	#121×C₆₇	—	2	2	no	—
231	#121×C₆₇	—	2	2	no	—
232	#121×C₆₇	—	2	1	no	—
233	#121×C₆₇	D₄	1	1	yes	characteristic
234	#121×C₆₇	D₄	1	1	yes	characteristic
235	#121×C₆₇	C₂³	1	1	yes	characteristic
236	#121×C₆₇	C₂³	1	1	yes	characteristic
237	#121×C₆₇	C₂³	1	2	yes	—
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	1	yes	characteristic
240	#120×C₆₇	—	2	1	no	—
241	#120×C₆₇	—	2	1	no	—
242	#120×C₆₇	D₄	1	2	yes	—
243	C₄×Q₈×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	—	2	1	no	—
245	C₄×Q₈×C₆₇	—	2	1	no	—
246	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
248	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	2	no	—
252	C₄×D₄×C₆₇	—	2	2	no	—
253	C₄×D₄×C₆₇	—	2	2	no	—
254	C₄×D₄×C₆₇	—	2	1	no	—
255	C₄×D₄×C₆₇	—	2	1	no	—
256	C₄×D₄×C₆₇	—	2	1	no	—
257	C₄×D₄×C₆₇	—	2	1	no	—
258	C₄×D₄×C₆₇	—	2	2	no	—
259	C₄×D₄×C₆₇	—	2	2	no	—
260	C₄×D₄×C₆₇	—	2	2	no	—
261	C₄×D₄×C₆₇	—	2	2	no	—
262	C₄×D₄×C₆₇	C₂³	1	2	yes	—
263	C₄×D₄×C₆₇	C₂³	1	2	yes	—
264	C₄×D₄×C₆₇	C₂³	1	2	yes	—
265	#117×C₆₇	—	2	1	no	—
266	#117×C₆₇	—	2	2	no	—
267	#117×C₆₇	—	2	2	no	—
268	#117×C₆₇	C₂³	1	2	yes	—
269	#117×C₆₇	C₂³	1	1	yes	characteristic
270	#117×C₆₇	C₂³	1	1	yes	characteristic
271	#117×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
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	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
278	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
281	#107×C₆₇	C₂³	1	1	yes	characteristic
282	#107×C₆₇	C₂³	1	1	yes	characteristic
283	#107×C₆₇	C₂³	1	2	yes	—
284	#107×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	1	yes	characteristic
286	#106×C₆₇	C₂³	1	1	yes	characteristic
287	#106×C₆₇	C₂³	1	2	yes	—
288	#106×C₆₇	C₂³	1	2	yes	—
289	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
290	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	2	yes	—
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	1	yes	characteristic
302	#103×C₆₇	C₂³	1	1	yes	characteristic
303	#103×C₆₇	C₂³	1	1	yes	characteristic
304	#103×C₆₇	C₂³	1	1	yes	characteristic
305	#103×C₆₇	C₂³	1	2	yes	—
306	#103×C₆₇	C₂³	1	2	yes	—
307	#103×C₆₇	C₂³	1	2	yes	—
308	#103×C₆₇	C₂³	1	2	yes	—
309	#102×C₆₇	C₂³	1	2	yes	—
310	#102×C₆₇	C₂³	1	2	yes	—
311	#102×C₆₇	C₂³	1	1	yes	characteristic
312	#102×C₆₇	C₂³	1	1	yes	characteristic
313	#102×C₆₇	C₂³	1	1	yes	characteristic
314	#102×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
319	#97×C₆₇	C₂³	1	2	yes	—
320	C₄×C₈×C₆₇	C₂³	1	2	yes	—
321	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
322	#41×C₆₇	—	2	2	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	4	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	—	4	2	no	—
330	#41×C₆₇	—	4	8	no	—
331	#41×C₆₇	—	4	4	no	—
332	#41×C₆₇	—	8	4	no	—
333	C₂×Q₈×C₆₇	—	2	1	no	—
334	C₂×Q₈×C₆₇	—	2	2	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	—	2	1	no	—
337	C₂×Q₈×C₆₇	—	2	2	no	—
338	C₂×Q₈×C₆₇	—	2	2	no	—
339	C₂×Q₈×C₆₇	—	2	2	no	—
340	C₂×Q₈×C₆₇	—	2	4	no	—
341	C₂×Q₈×C₆₇	—	2	4	no	—
342	C₂×Q₈×C₆₇	—	2	4	no	—
343	C₂×Q₈×C₆₇	—	2	2	no	—
344	C₂×Q₈×C₆₇	—	2	2	no	—
345	C₂×Q₈×C₆₇	—	4	4	no	—
346	C₂×Q₈×C₆₇	—	4	2	no	—
347	C₂×Q₈×C₆₇	—	4	2	no	—
348	C₂×Q₈×C₆₇	—	4	2	no	—
349	C₂×Q₈×C₆₇	—	4	4	no	—
350	C₂×Q₈×C₆₇	—	4	4	no	—
351	C₂×Q₈×C₆₇	—	4	4	no	—
352	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
354	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
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	—	2	1	no	—
364	C₂×D₄×C₆₇	—	2	2	no	—
365	C₂×D₄×C₆₇	—	2	2	no	—
366	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	—	2	2	no	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	1	no	—
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	2	2	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	2	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
387	C₂²×C₄×C₆₇	—	2	2	no	—
388	C₂²×C₄×C₆₇	—	4	4	no	—
389	C₂²×C₄×C₆₇	—	8	2	no	—
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	2	yes	—
396	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	Q₁₆×C₆₇	—	2	4	no	—
398	Q₁₆×C₆₇	—	4	1	no	—
399	Q₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	2	4	no	—
401	SD₁₆×C₆₇	—	4	1	no	—
402	SD₁₆×C₆₇	—	4	1	no	—
403	SD₁₆×C₆₇	—	4	2	no	—
404	D₈×C₆₇	—	4	1	no	—
405	M₁₆×C₆₇	—	2	2	no	—
406	M₁₆×C₆₇	—	2	2	no	—
407	M₁₆×C₆₇	—	4	2	no	—
408	C₂×C₈×C₆₇	—	2	2	no	—
409	C₂×C₈×C₆₇	—	2	2	no	—
410	C₂×C₈×C₆₇	—	4	1	no	—
411	C₂×C₈×C₆₇	—	4	1	no	—
412	C₂×C₈×C₆₇	—	4	1	no	—
413	C₂×C₈×C₆₇	—	4	1	no	—
414	C₂×C₈×C₆₇	—	4	2	no	—
415	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
418	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
419	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	—	2	1	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
425	C₄⋊C₄×C₆₇	—	2	2	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	2	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	1	no	—
437	C₄⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	2	no	—
461	C₂²⋊C₄×C₆₇	—	2	2	no	—
462	C₂²⋊C₄×C₆₇	—	2	2	no	—
463	C₂²⋊C₄×C₆₇	—	2	2	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	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	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
471	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
472	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
473	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
474	C₄²×C₆₇	—	2	2	no	—
475	C₄²×C₆₇	—	2	2	no	—
476	C₄²×C₆₇	—	2	2	no	—
477	C₄²×C₆₇	—	2	2	no	—
478	C₄²×C₆₇	—	2	1	no	—
479	C₄²×C₆₇	—	2	1	no	—
480	C₄²×C₆₇	C₂⁴	1	2	yes	—
481	C₂³×C₆₇	—	2	2	no	—
482	C₂³×C₆₇	—	2	2	no	—
483	C₂³×C₆₇	—	2	2	no	—
484	C₂³×C₆₇	—	2	1	no	—
485	C₂³×C₆₇	—	2	1	no	—
486	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
487	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
488	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
489	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
490	Q₈×C₆₇	—	2	4	no	—
491	Q₈×C₆₇	—	2	2	no	—
492	Q₈×C₆₇	—	2	2	no	—
493	Q₈×C₆₇	—	2	1	no	—
494	Q₈×C₆₇	—	2	2	no	—
495	Q₈×C₆₇	—	2	1	no	—
496	Q₈×C₆₇	—	2	1	no	—
497	Q₈×C₆₇	—	2	2	no	—
498	Q₈×C₆₇	—	2	1	no	—
499	Q₈×C₆₇	—	4	4	no	—
500	Q₈×C₆₇	—	4	4	no	—
501	Q₈×C₆₇	—	4	4	no	—
502	Q₈×C₆₇	—	4	2	no	—
503	Q₈×C₆₇	—	8	2	no	—
504	Q₈×C₆₇	C₂×#41	1	4	yes	—
505	D₄×C₆₇	—	2	4	no	—
506	D₄×C₆₇	—	2	4	no	—
507	D₄×C₆₇	—	2	4	no	—
508	D₄×C₆₇	—	2	2	no	—
509	D₄×C₆₇	—	2	1	no	—
510	D₄×C₆₇	—	2	1	no	—
511	D₄×C₆₇	—	2	1	no	—
512	D₄×C₆₇	—	2	1	no	—
513	D₄×C₆₇	—	4	4	no	—
514	D₄×C₆₇	—	4	2	no	—
515	D₄×C₆₇	—	4	2	no	—
516	D₄×C₆₇	—	4	2	no	—
517	D₄×C₆₇	—	4	2	no	—
518	D₄×C₆₇	—	4	2	no	—
519	D₄×C₆₇	—	4	2	no	—
520	D₄×C₆₇	—	8	2	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	4	no	—
523	C₂×C₄×C₆₇	—	2	2	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	2	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	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	—	4	4	no	—
542	C₂×C₄×C₆₇	—	4	4	no	—
543	C₂×C₄×C₆₇	—	4	4	no	—
544	C₂×C₄×C₆₇	—	4	4	no	—
545	C₂×C₄×C₆₇	—	4	2	no	—
546	C₂×C₄×C₆₇	—	4	4	no	—
547	C₂×C₄×C₆₇	—	4	2	no	—
548	C₂×C₄×C₆₇	—	4	2	no	—
549	C₂×C₄×C₆₇	—	8	2	no	—
550	C₂×C₄×C₆₇	—	8	1	no	—
551	C₂×C₄×C₆₇	—	8	2	no	—
552	C₂×C₄×C₆₇	—	8	1	no	—
553	C₂×C₄×C₆₇	—	8	2	no	—
554	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
561	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
562	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
563	C₈×C₆₇	—	2	2	no	—
564	C₈×C₆₇	—	2	1	no	—
565	C₈×C₆₇	—	2	1	no	—
566	C₈×C₆₇	—	2	1	no	—
567	C₈×C₆₇	—	2	1	no	—
568	C₈×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	8	no	—
570	C₂²×C₆₇	—	2	1	no	—
571	C₂²×C₆₇	—	2	1	no	—
572	C₂²×C₆₇	—	2	1	no	—
573	C₂²×C₆₇	—	2	1	no	—
574	C₂²×C₆₇	—	2	1	no	—
575	C₂²×C₆₇	—	2	1	no	—
576	C₂²×C₆₇	—	2	2	no	—
577	C₂²×C₆₇	—	2	2	no	—
578	C₂²×C₆₇	—	2	2	no	—
579	C₂²×C₆₇	—	4	1	no	—
580	C₂²×C₆₇	—	4	1	no	—
581	C₂²×C₆₇	—	4	1	no	—
582	C₂²×C₆₇	—	4	1	no	—
583	C₂²×C₆₇	—	4	1	no	—
584	C₂²×C₆₇	—	4	1	no	—
585	C₂²×C₆₇	#546	1	2	yes	—
586	C₂²×C₆₇	#577	1	2	yes	—
587	C₂²×C₆₇	#578	1	2	yes	—
588	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₆₇	—	2	1	no	—
590	C₄×C₆₇	—	2	1	no	—
591	C₄×C₆₇	—	2	4	no	—
592	C₄×C₆₇	—	2	2	no	—
593	C₄×C₆₇	—	2	2	no	—
594	C₄×C₆₇	—	2	2	no	—
595	C₄×C₆₇	—	4	1	no	—
596	C₄×C₆₇	—	4	2	no	—
597	C₄×C₆₇	—	4	1	no	—
598	C₄×C₆₇	—	4	2	no	—
599	C₄×C₆₇	—	4	2	no	—
600	C₄×C₆₇	—	4	1	no	—
601	C₄×C₆₇	—	4	1	no	—
602	C₄×C₆₇	—	4	1	no	—
603	C₄×C₆₇	—	4	1	no	—
604	C₄×C₆₇	#546	1	2	yes	—
605	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
606	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	#61168	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
608	C₂×C₆₇	—	2	2	no	—
609	C₂×C₆₇	—	2	2	no	—
610	C₂×C₆₇	—	2	2	no	—
611	C₂×C₆₇	—	4	2	no	—
612	C₂×C₆₇	—	8	1	no	—
613	C₂×C₆₇	—	8	1	no	—
614	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
615	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
616	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
617	#3492	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#3486	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3320	C₂×C₆₇	1	2	yes	complemented
620	#3316	C₂×C₆₇	1	2	yes	complemented
621	#3312	C₂×C₆₇	1	2	yes	complemented
622	#3308	C₂×C₆₇	1	2	yes	complemented
623	#3301	C₂×C₆₇	1	2	yes	complemented
624	#3300	C₂×C₆₇	1	2	yes	complemented
625	#3299	C₂×C₆₇	1	2	yes	complemented
626	#3298	C₂×C₆₇	1	2	yes	complemented
627	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3063	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#3050	C₂×C₆₇	1	1	yes	characteristic, complemented
633	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#3004	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
637	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
639	C₂²×#103	C₂×C₆₇	1	1	yes	characteristic, complemented
640	C₆₇	#61168	1	1	yes	characteristic, direct product factor, Sylow
641	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
642	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
643	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
645	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
646	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
647	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
648	#554	—	2	1	no	—
649	#554	C₂²×C₆₇	1	2	yes	—
650	#553	—	2	1	no	—
651	#553	C₂²×C₆₇	1	2	yes	—
652	#552	—	2	1	no	—
653	#552	C₂²×C₆₇	1	2	yes	—
654	D₄×Q₈	—	2	1	no	—
655	D₄×Q₈	—	2	1	no	—
656	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
657	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
658	#548	—	2	1	no	—
659	#548	—	2	1	no	—
660	#548	C₂²×C₆₇	1	2	yes	—
661	#548	C₂²×C₆₇	1	2	yes	—
662	#547	—	2	1	no	—
663	#547	C₂²×C₆₇	1	2	yes	—
664	#544	C₂²×C₆₇	1	1	yes	characteristic
665	#539	—	2	2	no	—
666	#537	C₂²×C₆₇	1	1	yes	characteristic
667	#536	—	2	2	no	—
668	#536	C₂²×C₆₇	1	1	yes	characteristic
669	#536	C₂²×C₆₇	1	1	yes	characteristic
670	#525	—	2	2	no	—
671	#525	—	2	2	no	—
672	#525	C₂²×C₆₇	1	1	yes	characteristic
673	#525	C₂²×C₆₇	1	1	yes	characteristic
674	#525	C₂²×C₆₇	1	1	yes	characteristic
675	#520	C₂²×C₆₇	1	1	yes	characteristic
676	#520	C₂²×C₆₇	1	1	yes	characteristic
677	#519	C₂²×C₆₇	1	1	yes	characteristic
678	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
679	#491	C₂²×C₆₇	1	2	yes	complemented
680	#489	C₂²×C₆₇	1	2	yes	complemented
681	#488	C₂²×C₆₇	1	2	yes	complemented
682	#487	C₂²×C₆₇	1	2	yes	complemented
683	#485	C₂²×C₆₇	1	2	yes	complemented
684	#485	C₂²×C₆₇	1	2	yes	complemented
685	#484	C₂²×C₆₇	1	2	yes	—
686	#484	C₂²×C₆₇	1	2	yes	complemented
687	#483	C₂²×C₆₇	1	2	yes	—
688	#483	C₂²×C₆₇	1	2	yes	complemented
689	#481	C₂²×C₆₇	1	2	yes	—
690	#480	C₂²×C₆₇	1	2	yes	—
691	#479	C₂²×C₆₇	1	2	yes	complemented
692	#479	C₂²×C₆₇	1	2	yes	complemented
693	#477	C₂²×C₆₇	1	2	yes	complemented
694	#475	C₂²×C₆₇	1	2	yes	complemented
695	#470	C₂²×C₆₇	1	2	yes	complemented
696	#468	C₂²×C₆₇	1	2	yes	complemented
697	#467	C₂²×C₆₇	1	1	yes	characteristic
698	#467	C₂²×C₆₇	1	1	yes	characteristic
699	#467	C₂²×C₆₇	1	2	yes	complemented
700	#466	C₂²×C₆₇	1	1	yes	characteristic
701	#466	C₂²×C₆₇	1	1	yes	characteristic
702	#465	C₂²×C₆₇	1	1	yes	characteristic
703	#465	C₂²×C₆₇	1	1	yes	characteristic
704	#465	C₂²×C₆₇	1	1	yes	characteristic
705	#465	C₂²×C₆₇	1	1	yes	characteristic
706	#465	C₂²×C₆₇	1	2	yes	complemented
707	#464	C₂²×C₆₇	1	2	yes	complemented
708	#463	C₂²×C₆₇	1	2	yes	complemented
709	#462	C₂²×C₆₇	1	2	yes	complemented
710	#461	C₂²×C₆₇	1	2	yes	complemented
711	#452	C₂²×C₆₇	1	2	yes	complemented
712	#451	C₂²×C₆₇	1	2	yes	—
713	#451	C₂²×C₆₇	1	2	yes	—
714	#451	C₂²×C₆₇	1	2	yes	complemented
715	#449	C₂²×C₆₇	1	2	yes	complemented
716	#448	C₂²×C₆₇	1	2	yes	—
717	#448	C₂²×C₆₇	1	2	yes	—
718	#448	C₂²×C₆₇	1	2	yes	complemented
719	#441	C₂²×C₆₇	1	2	yes	complemented
720	#440	C₂²×C₆₇	1	2	yes	complemented
721	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
722	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
723	#435	C₂²×C₆₇	1	2	yes	—
724	#435	C₂²×C₆₇	1	2	yes	—
725	C₈×D₄	C₂²×C₆₇	1	2	yes	—
726	C₈×D₄	C₂²×C₆₇	1	2	yes	—
727	#428	C₂²×C₆₇	1	1	yes	characteristic
728	#428	C₂²×C₆₇	1	1	yes	characteristic
729	#427	C₂²×C₆₇	1	1	yes	characteristic
730	#424	C₂²×C₆₇	1	1	yes	characteristic
731	#419	C₂²×C₆₇	1	1	yes	characteristic
732	#419	C₂²×C₆₇	1	1	yes	characteristic
733	#419	C₂²×C₆₇	1	2	yes	complemented
734	#417	C₂²×C₆₇	1	1	yes	characteristic
735	#417	C₂²×C₆₇	1	1	yes	characteristic
736	#417	C₂²×C₆₇	1	2	yes	complemented
737	#416	C₂²×C₆₇	1	1	yes	characteristic
738	#416	C₂²×C₆₇	1	1	yes	characteristic
739	#416	C₂²×C₆₇	1	2	yes	complemented
740	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
741	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
742	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
743	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
744	C₂×#103	C₂²×C₆₇	1	2	yes	—
745	C₂×#103	C₂²×C₆₇	1	2	yes	—
746	C₂×#103	C₂²×C₆₇	1	2	yes	—
747	C₂×#103	C₂²×C₆₇	1	2	yes	—
748	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
749	#408	C₂²×C₆₇	1	1	yes	characteristic
750	#407	C₂²×C₆₇	1	1	yes	characteristic
751	#405	C₂²×C₆₇	1	1	yes	characteristic
752	2₋¹⁺⁴	—	2	4	no	—
753	2₋¹⁺⁴	—	4	2	no	—
754	C₂×#41	—	2	2	no	—
755	C₂×#41	—	2	1	no	—
756	C₂×#41	—	2	2	no	—
757	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×#41	C₂³×C₆₇	1	2	yes	—
760	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
761	C₂²×Q₈	—	2	1	no	—
762	C₂²×Q₈	—	2	1	no	—
763	C₂²×Q₈	—	2	1	no	—
764	C₂²×Q₈	—	2	1	no	—
765	C₂²×Q₈	—	2	4	no	—
766	C₂²×Q₈	—	4	2	no	—
767	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
768	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
769	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
770	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
771	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
772	C₂³×C₄	—	2	1	no	—
773	C₂³×C₄	—	2	1	no	—
774	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
775	#137	—	2	4	no	—
776	#137	—	4	2	no	—
777	#135	—	4	2	no	—
778	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
785	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
786	#131	—	4	2	no	—
787	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
790	C₂²×C₈	—	4	2	no	—
791	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
792	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
793	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
794	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
795	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
796	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
797	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
798	C₄⋊Q₈	—	2	1	no	—
799	C₄⋊Q₈	—	2	2	no	—
800	C₄⋊Q₈	—	2	2	no	—
801	C₄⋊Q₈	—	2	1	no	—
802	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
803	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#125	—	2	2	no	—
807	#125	—	2	2	no	—
808	#125	—	2	1	no	—
809	#125	C₂³×C₆₇	1	2	yes	—
810	#124	—	2	1	no	—
811	#124	—	2	2	no	—
812	#124	—	2	2	no	—
813	#124	C₂³×C₆₇	1	2	yes	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	1	no	—
817	#123	—	2	1	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	D₄×C₆₇	1	2	yes	—
823	C₂²⋊Q₈	—	2	1	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	—	2	2	no	—
831	C₂²⋊Q₈	—	2	2	no	—
832	C₂²⋊Q₈	—	2	2	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	—	2	2	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
837	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
838	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
839	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	—	2	1	no	—
850	#121	D₄×C₆₇	1	1	yes	characteristic
851	#121	D₄×C₆₇	1	1	yes	characteristic
852	#121	C₂³×C₆₇	1	1	yes	characteristic
853	#121	C₂³×C₆₇	1	1	yes	characteristic
854	#121	C₂³×C₆₇	1	1	yes	characteristic
855	#121	C₂³×C₆₇	1	1	yes	characteristic
856	#121	C₂³×C₆₇	1	2	yes	—
857	#120	—	2	1	no	—
858	#120	—	2	1	no	—
859	#120	D₄×C₆₇	1	2	yes	—
860	C₄×Q₈	—	2	1	no	—
861	C₄×Q₈	—	2	1	no	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
864	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
865	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	2	no	—
878	C₄×D₄	—	2	2	no	—
879	C₄×D₄	C₂³×C₆₇	1	2	yes	—
880	C₄×D₄	C₂³×C₆₇	1	2	yes	—
881	C₄×D₄	C₂³×C₆₇	1	2	yes	—
882	#117	—	2	1	no	—
883	#117	—	2	2	no	—
884	#117	—	2	2	no	—
885	#117	C₂³×C₆₇	1	1	yes	characteristic
886	#117	C₂³×C₆₇	1	1	yes	characteristic
887	#117	C₂³×C₆₇	1	2	yes	—
888	#117	C₂³×C₆₇	1	1	yes	characteristic
889	C₂×C₄⋊C₄	—	2	1	no	—
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	—	2	1	no	—
893	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
896	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
897	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
898	#107	C₂³×C₆₇	1	1	yes	characteristic
899	#107	C₂³×C₆₇	1	1	yes	characteristic
900	#107	C₂³×C₆₇	1	2	yes	—
901	#107	C₂³×C₆₇	1	2	yes	—
902	#106	C₂³×C₆₇	1	1	yes	characteristic
903	#106	C₂³×C₆₇	1	1	yes	characteristic
904	#106	C₂³×C₆₇	1	2	yes	—
905	#106	C₂³×C₆₇	1	2	yes	—
906	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
907	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
908	#103	C₂³×C₆₇	1	2	yes	—
909	#103	C₂³×C₆₇	1	2	yes	—
910	#103	C₂³×C₆₇	1	2	yes	—
911	#103	C₂³×C₆₇	1	2	yes	—
912	#103	C₂³×C₆₇	1	2	yes	—
913	#103	C₂³×C₆₇	1	2	yes	—
914	#103	C₂³×C₆₇	1	2	yes	—
915	#103	C₂³×C₆₇	1	2	yes	—
916	#103	C₂³×C₆₇	1	1	yes	characteristic
917	#103	C₂³×C₆₇	1	2	yes	—
918	#103	C₂³×C₆₇	1	2	yes	—
919	#103	C₂³×C₆₇	1	1	yes	characteristic
920	#103	C₂³×C₆₇	1	1	yes	characteristic
921	#103	C₂³×C₆₇	1	1	yes	characteristic
922	#103	C₂³×C₆₇	1	2	yes	—
923	#103	C₂³×C₆₇	1	2	yes	—
924	#103	C₂³×C₆₇	1	2	yes	—
925	#103	C₂³×C₆₇	1	2	yes	—
926	#102	C₂³×C₆₇	1	1	yes	characteristic
927	#102	C₂³×C₆₇	1	1	yes	characteristic
928	#102	C₂³×C₆₇	1	1	yes	characteristic
929	#102	C₂³×C₆₇	1	1	yes	characteristic
930	#102	C₂³×C₆₇	1	2	yes	—
931	#102	C₂³×C₆₇	1	2	yes	—
932	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
935	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
936	#97	C₂³×C₆₇	1	2	yes	—
937	C₄×C₈	C₂³×C₆₇	1	2	yes	—
938	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
939	#41	—	2	2	no	—
940	#41	—	2	2	no	—
941	#41	—	2	4	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	8	no	—
948	#41	—	4	4	no	—
949	#41	—	8	4	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	1	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	2	4	no	—
958	C₂×Q₈	—	2	4	no	—
959	C₂×Q₈	—	2	4	no	—
960	C₂×Q₈	—	2	2	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	4	4	no	—
963	C₂×Q₈	—	4	2	no	—
964	C₂×Q₈	—	4	2	no	—
965	C₂×Q₈	—	4	2	no	—
966	C₂×Q₈	—	4	4	no	—
967	C₂×Q₈	—	4	4	no	—
968	C₂×Q₈	—	4	4	no	—
969	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
971	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
972	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
984	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
985	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
986	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
987	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	4	4	no	—
1006	C₂²×C₄	—	8	2	no	—
1007	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1013	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1014	Q₁₆	—	2	4	no	—
1015	Q₁₆	—	4	1	no	—
1016	Q₁₆	—	4	2	no	—
1017	SD₁₆	—	2	4	no	—
1018	SD₁₆	—	4	1	no	—
1019	SD₁₆	—	4	1	no	—
1020	SD₁₆	—	4	2	no	—
1021	D₈	—	4	1	no	—
1022	M₁₆	—	2	2	no	—
1023	M₁₆	—	2	2	no	—
1024	M₁₆	—	4	2	no	—
1025	C₂×C₈	—	2	2	no	—
1026	C₂×C₈	—	2	2	no	—
1027	C₂×C₈	—	4	1	no	—
1028	C₂×C₈	—	4	1	no	—
1029	C₂×C₈	—	4	1	no	—
1030	C₂×C₈	—	4	1	no	—
1031	C₂×C₈	—	4	2	no	—
1032	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1034	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1035	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1036	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1037	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1059	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1060	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1061	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1062	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1087	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1088	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1091	C₄²	—	2	2	no	—
1092	C₄²	—	2	2	no	—
1093	C₄²	—	2	2	no	—
1094	C₄²	—	2	2	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	C₂⁴×C₆₇	1	2	yes	—
1098	C₂³	—	2	2	no	—
1099	C₂³	—	2	2	no	—
1100	C₂³	—	2	2	no	—
1101	C₂³	—	2	1	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1104	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1105	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1106	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1107	Q₈	—	2	4	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	1	no	—
1111	Q₈	—	2	2	no	—
1112	Q₈	—	2	1	no	—
1113	Q₈	—	2	1	no	—
1114	Q₈	—	2	2	no	—
1115	Q₈	—	2	1	no	—
1116	Q₈	—	4	4	no	—
1117	Q₈	—	4	4	no	—
1118	Q₈	—	4	4	no	—
1119	Q₈	—	4	2	no	—
1120	Q₈	—	8	2	no	—
1121	Q₈	C₂×#41×C₆₇	1	4	yes	—
1122	D₄	—	2	4	no	—
1123	D₄	—	2	4	no	—
1124	D₄	—	2	4	no	—
1125	D₄	—	2	2	no	—
1126	D₄	—	2	1	no	—
1127	D₄	—	2	1	no	—
1128	D₄	—	2	1	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	4	4	no	—
1131	D₄	—	4	2	no	—
1132	D₄	—	4	2	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	8	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	4	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	4	no	—
1161	C₂×C₄	—	4	4	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	4	no	—
1164	C₂×C₄	—	4	2	no	—
1165	C₂×C₄	—	4	2	no	—
1166	C₂×C₄	—	8	2	no	—
1167	C₂×C₄	—	8	1	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	8	1	no	—
1170	C₂×C₄	—	8	2	no	—
1171	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1172	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1173	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1174	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1177	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1178	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1179	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1180	C₈	—	2	2	no	—
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	2	no	—
1186	C₂²	—	2	8	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	#546×C₆₇	1	2	yes	—
1203	C₂²	#577×C₆₇	1	2	yes	—
1204	C₂²	#578×C₆₇	1	2	yes	—
1205	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	4	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	#546×C₆₇	1	2	yes	—
1222	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1223	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1224	C₂	—	2	2	no	—
1225	C₂	—	2	2	no	—
1226	C₂	—	2	2	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	8	1	no	—
1229	C₂	—	8	1	no	—
1230	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1231	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1232	C₂	C₂×#578×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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3492	C₂	semidirect
2. C₆₇×#3486	C₂	semidirect
3. C₆₇×#3320	C₂	semidirect
4. C₆₇×#3316	C₂	semidirect
5. C₆₇×#3312	C₂	semidirect
6. C₆₇×#3308	C₂	semidirect
7. C₆₇×#3301	C₂	semidirect
8. C₆₇×#3300	C₂	semidirect
9. C₆₇×#3299	C₂	semidirect
10. C₆₇×#3298	C₂	semidirect
11. C₆₇×#3137	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3092	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3063	C₂	semidirect
16. C₆₇×#3050	C₂	semidirect
17. C₆₇×#3046	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3004	C₂	semidirect
20. C₆₇×#2947	C₂	semidirect
21. C₆₇×#2929	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₂²×#103×C₆₇	C₂	semidirect
62. #491×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
69. #484×C₆₇	C₂²	semidirect
71. #483×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #479×C₆₇	C₂²	semidirect
76. #477×C₆₇	C₂²	semidirect
77. #475×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #468×C₆₇	C₂²	semidirect
82. #467×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #463×C₆₇	C₂²	semidirect
92. #462×C₆₇	C₂²	semidirect
93. #461×C₆₇	C₂²	semidirect
94. #452×C₆₇	C₂²	semidirect
97. #451×C₆₇	C₂²	semidirect
98. #449×C₆₇	C₂²	semidirect
101. #448×C₆₇	C₂²	semidirect
102. #441×C₆₇	C₂²	semidirect
103. #440×C₆₇	C₂²	semidirect
104. C₄×Q₁₆×C₆₇	C₂²	semidirect
105. C₄×SD₁₆×C₆₇	C₂²	semidirect
116. #419×C₆₇	C₂²	semidirect
119. #417×C₆₇	C₂²	semidirect
122. #416×C₆₇	C₂²	semidirect
131. C₂×#103×C₆₇	C₂²	semidirect
353. C₂×Q₈×C₆₇	#41	semidirect
607. #61168	C₆₇	direct (N × H)
617. #3492	C₂×C₆₇	semidirect
618. #3486	C₂×C₆₇	semidirect
619. #3320	C₂×C₆₇	semidirect
620. #3316	C₂×C₆₇	semidirect
621. #3312	C₂×C₆₇	semidirect
622. #3308	C₂×C₆₇	semidirect
623. #3301	C₂×C₆₇	semidirect
624. #3300	C₂×C₆₇	semidirect
625. #3299	C₂×C₆₇	semidirect
626. #3298	C₂×C₆₇	semidirect
627. #3137	C₂×C₆₇	semidirect
628. #3097	C₂×C₆₇	semidirect
629. #3092	C₂×C₆₇	semidirect
630. #3082	C₂×C₆₇	semidirect
631. #3063	C₂×C₆₇	semidirect
632. #3050	C₂×C₆₇	semidirect
633. #3046	C₂×C₆₇	semidirect
634. #3013	C₂×C₆₇	semidirect
635. #3004	C₂×C₆₇	semidirect
636. #2947	C₂×C₆₇	semidirect
637. #2929	C₂×C₆₇	semidirect
638. #2898	C₂×C₆₇	semidirect
639. C₂²×#103	C₂×C₆₇	semidirect
640. C₆₇	#61168	direct (N × H)
679. #491	C₂²×C₆₇	semidirect
680. #489	C₂²×C₆₇	semidirect
681. #488	C₂²×C₆₇	semidirect
682. #487	C₂²×C₆₇	semidirect
683. #485	C₂²×C₆₇	semidirect
684. #485	C₂²×C₆₇	semidirect
686. #484	C₂²×C₆₇	semidirect
688. #483	C₂²×C₆₇	semidirect
691. #479	C₂²×C₆₇	semidirect
692. #479	C₂²×C₆₇	semidirect
693. #477	C₂²×C₆₇	semidirect
694. #475	C₂²×C₆₇	semidirect
695. #470	C₂²×C₆₇	semidirect
696. #468	C₂²×C₆₇	semidirect
699. #467	C₂²×C₆₇	semidirect
706. #465	C₂²×C₆₇	semidirect
707. #464	C₂²×C₆₇	semidirect
708. #463	C₂²×C₆₇	semidirect
709. #462	C₂²×C₆₇	semidirect
710. #461	C₂²×C₆₇	semidirect
711. #452	C₂²×C₆₇	semidirect
714. #451	C₂²×C₆₇	semidirect
715. #449	C₂²×C₆₇	semidirect
718. #448	C₂²×C₆₇	semidirect
719. #441	C₂²×C₆₇	semidirect
720. #440	C₂²×C₆₇	semidirect
721. C₄×Q₁₆	C₂²×C₆₇	semidirect
722. C₄×SD₁₆	C₂²×C₆₇	semidirect
733. #419	C₂²×C₆₇	semidirect
736. #417	C₂²×C₆₇	semidirect
739. #416	C₂²×C₆₇	semidirect
748. C₂×#103	C₂²×C₆₇	semidirect
970. C₂×Q₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3492	2
C₆₇×#3486	2
C₆₇×#3320	2
C₆₇×#3316	2
C₆₇×#3312	2
C₆₇×#3308	2
C₆₇×#3301	2
C₆₇×#3300	2
C₆₇×#3299	2
C₆₇×#3298	2
C₆₇×#3137	2
C₆₇×#3097	2
C₆₇×#3092	2
C₆₇×#3082	2
C₆₇×#3063	2
C₆₇×#3050	2
C₆₇×#3046	2
C₆₇×#3013	2
C₆₇×#3004	2
C₆₇×#2947	2
C₆₇×#2929	2
C₆₇×#2898	2
C₂²×#103×C₆₇	2
#61168	67

Subgroups — C67×#61168 #30740419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61168 #30740419