Subgroups — C₆₇×#61173 #30740424

Order 17152.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3315	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3313	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3302	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×#3296	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#467×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3007	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	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×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	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
31	#556×C₆₇	C₂²	1	2	yes	complemented
32	#554×C₆₇	C₂²	1	2	yes	—
33	#552×C₆₇	—	2	2	no	—
34	#552×C₆₇	C₂²	1	2	yes	—
35	#552×C₆₇	C₂²	1	2	yes	complemented
36	#551×C₆₇	—	2	2	no	—
37	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
38	#548×C₆₇	C₂²	1	2	yes	—
39	#547×C₆₇	—	2	2	no	—
40	#547×C₆₇	C₂²	1	2	yes	—
41	#546×C₆₇	—	2	2	no	—
42	#546×C₆₇	C₂²	1	2	yes	—
43	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#542×C₆₇	—	2	1	no	—
45	#541×C₆₇	—	2	1	no	—
46	#537×C₆₇	—	2	1	no	—
47	#537×C₆₇	C₂²	1	1	yes	characteristic
48	#536×C₆₇	—	2	1	no	—
49	#536×C₆₇	C₂²	1	1	yes	characteristic
50	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#533×C₆₇	—	2	1	no	—
52	#529×C₆₇	—	2	1	no	—
53	#525×C₆₇	—	2	1	no	—
54	#525×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×#117×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	#485×C₆₇	C₂²	1	2	yes	complemented
69	#484×C₆₇	C₂²	1	2	yes	—
70	#484×C₆₇	C₂²	1	2	yes	complemented
71	#483×C₆₇	C₂²	1	2	yes	—
72	#482×C₆₇	C₂²	1	2	yes	complemented
73	#480×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#478×C₆₇	C₂²	1	2	yes	complemented
76	#477×C₆₇	C₂²	1	2	yes	complemented
77	#474×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	2	yes	—
81	#467×C₆₇	C₂²	1	2	yes	—
82	#467×C₆₇	C₂²	1	2	yes	complemented
83	#467×C₆₇	C₂²	1	2	yes	complemented
84	#467×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#464×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	2	yes	complemented
88	#462×C₆₇	C₂²	1	2	yes	complemented
89	#462×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	2	yes	—
91	#452×C₆₇	C₂²	1	2	yes	—
92	#452×C₆₇	C₂²	1	2	yes	complemented
93	#452×C₆₇	C₂²	1	2	yes	complemented
94	#451×C₆₇	C₂²	1	2	yes	—
95	#451×C₆₇	C₂²	1	2	yes	complemented
96	#451×C₆₇	C₂²	1	2	yes	complemented
97	#450×C₆₇	C₂²	1	2	yes	—
98	#441×C₆₇	C₂²	1	2	yes	complemented
99	#440×C₆₇	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
102	#435×C₆₇	C₂²	1	2	yes	—
103	#435×C₆₇	C₂²	1	2	yes	complemented
104	C₈×D₄×C₆₇	C₂²	1	2	yes	—
105	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
106	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#419×C₆₇	C₂²	1	2	yes	complemented
113	#417×C₆₇	C₂²	1	1	yes	characteristic
114	#417×C₆₇	C₂²	1	1	yes	characteristic
115	#417×C₆₇	C₂²	1	2	yes	complemented
116	#416×C₆₇	C₂²	1	1	yes	characteristic
117	#416×C₆₇	C₂²	1	1	yes	characteristic
118	#416×C₆₇	C₂²	1	1	yes	characteristic
119	#416×C₆₇	C₂²	1	1	yes	characteristic
120	#416×C₆₇	C₂²	1	1	yes	characteristic
121	#416×C₆₇	C₂²	1	1	yes	characteristic
122	#416×C₆₇	C₂²	1	1	yes	characteristic
123	#416×C₆₇	C₂²	1	1	yes	characteristic
124	#416×C₆₇	C₂²	1	2	yes	complemented
125	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
126	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
127	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#407×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	2	no	—
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	4	no	—
142	C₂×#41×C₆₇	—	4	2	no	—
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	2	yes	—
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₆₇	—	2	1	no	—
150	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
154	C₂²×D₄×C₆₇	—	2	1	no	—
155	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
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	C₂×Q₁₆×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	2	yes	—
164	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
167	#131×C₆₇	—	4	2	no	—
168	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
171	C₂²×C₈×C₆₇	—	4	2	no	—
172	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
179	C₄⋊Q₈×C₆₇	—	2	1	no	—
180	C₄⋊Q₈×C₆₇	—	2	1	no	—
181	C₄⋊Q₈×C₆₇	—	2	2	no	—
182	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
183	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
184	#126×C₆₇	—	2	2	no	—
185	#126×C₆₇	—	2	2	no	—
186	#126×C₆₇	—	2	2	no	—
187	#126×C₆₇	—	2	2	no	—
188	#125×C₆₇	—	2	1	no	—
189	#125×C₆₇	—	2	2	no	—
190	#125×C₆₇	—	2	2	no	—
191	#125×C₆₇	—	2	2	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	2	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	D₄	1	2	yes	—
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	2	no	—
212	C₂²⋊Q₈×C₆₇	—	2	1	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	D₄	1	1	yes	characteristic
219	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
227	#121×C₆₇	—	2	1	no	—
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	D₄	1	1	yes	characteristic
233	#121×C₆₇	D₄	1	1	yes	characteristic
234	#121×C₆₇	C₂³	1	2	yes	—
235	#120×C₆₇	—	2	2	no	—
236	#120×C₆₇	D₄	1	2	yes	—
237	C₄×Q₈×C₆₇	—	2	1	no	—
238	C₄×Q₈×C₆₇	—	2	1	no	—
239	C₄×Q₈×C₆₇	—	2	1	no	—
240	C₄×Q₈×C₆₇	—	2	2	no	—
241	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
243	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	—	2	1	no	—
245	C₄×D₄×C₆₇	—	2	2	no	—
246	C₄×D₄×C₆₇	—	2	2	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	C₂³	1	2	yes	—
251	C₄×D₄×C₆₇	C₂³	1	2	yes	—
252	C₄×D₄×C₆₇	C₂³	1	2	yes	—
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	—	2	1	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	—	2	2	no	—
257	#117×C₆₇	—	2	2	no	—
258	#117×C₆₇	—	2	2	no	—
259	#117×C₆₇	C₂³	1	2	yes	—
260	#117×C₆₇	C₂³	1	1	yes	characteristic
261	#117×C₆₇	C₂³	1	1	yes	characteristic
262	#117×C₆₇	C₂³	1	1	yes	characteristic
263	#117×C₆₇	C₂³	1	1	yes	characteristic
264	#117×C₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
266	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
276	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
277	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
278	C₂×C₄²×C₆₇	—	2	1	no	—
279	#107×C₆₇	C₂³	1	2	yes	—
280	#107×C₆₇	C₂³	1	2	yes	—
281	#107×C₆₇	C₂³	1	2	yes	—
282	#107×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	2	yes	—
284	#106×C₆₇	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	1	yes	characteristic
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	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
322	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	4	no	—
329	#41×C₆₇	—	2	2	no	—
330	#41×C₆₇	—	2	2	no	—
331	#41×C₆₇	—	4	4	no	—
332	#41×C₆₇	—	4	1	no	—
333	#41×C₆₇	—	4	1	no	—
334	#41×C₆₇	—	4	2	no	—
335	#41×C₆₇	—	4	4	no	—
336	#41×C₆₇	—	4	4	no	—
337	#41×C₆₇	—	4	8	no	—
338	#41×C₆₇	#41	1	4	yes	—
339	C₂×Q₈×C₆₇	—	2	1	no	—
340	C₂×Q₈×C₆₇	—	2	1	no	—
341	C₂×Q₈×C₆₇	—	2	2	no	—
342	C₂×Q₈×C₆₇	—	2	1	no	—
343	C₂×Q₈×C₆₇	—	2	2	no	—
344	C₂×Q₈×C₆₇	—	2	2	no	—
345	C₂×Q₈×C₆₇	—	2	4	no	—
346	C₂×Q₈×C₆₇	—	2	2	no	—
347	C₂×Q₈×C₆₇	—	2	2	no	—
348	C₂×Q₈×C₆₇	—	2	2	no	—
349	C₂×Q₈×C₆₇	—	2	2	no	—
350	C₂×Q₈×C₆₇	—	4	1	no	—
351	C₂×Q₈×C₆₇	—	4	2	no	—
352	C₂×Q₈×C₆₇	—	4	4	no	—
353	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
357	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	2	no	—
360	C₂×D₄×C₆₇	—	2	2	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	1	no	—
366	C₂×D₄×C₆₇	—	4	1	no	—
367	C₂×D₄×C₆₇	—	4	4	no	—
368	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
381	C₂²×C₄×C₆₇	—	2	1	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	—	2	2	no	—
387	C₂²×C₄×C₆₇	—	2	1	no	—
388	C₂²×C₄×C₆₇	—	2	1	no	—
389	C₂²×C₄×C₆₇	—	2	1	no	—
390	C₂²×C₄×C₆₇	—	2	2	no	—
391	C₂²×C₄×C₆₇	—	4	4	no	—
392	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₆₇	—	2	4	no	—
400	Q₁₆×C₆₇	—	4	2	no	—
401	Q₁₆×C₆₇	—	4	2	no	—
402	Q₁₆×C₆₇	—	4	2	no	—
403	SD₁₆×C₆₇	—	2	4	no	—
404	SD₁₆×C₆₇	—	4	2	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	1	yes	characteristic
418	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
420	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₆₇	—	2	2	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	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	2	no	—
433	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
441	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	no	—
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	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	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	2	no	—
467	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
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	C₄²×C₆₇	—	2	1	no	—
473	C₄²×C₆₇	—	2	1	no	—
474	C₄²×C₆₇	—	2	1	no	—
475	C₄²×C₆₇	—	2	1	no	—
476	C₄²×C₆₇	—	2	2	no	—
477	C₄²×C₆₇	—	2	2	no	—
478	C₄²×C₆₇	—	2	2	no	—
479	C₄²×C₆₇	—	2	2	no	—
480	C₄²×C₆₇	C₂⁴	1	2	yes	—
481	C₂³×C₆₇	—	2	2	no	—
482	C₂³×C₆₇	—	2	2	no	—
483	C₂³×C₆₇	—	2	1	no	—
484	C₂³×C₆₇	—	2	1	no	—
485	C₂³×C₆₇	—	4	1	no	—
486	C₂³×C₆₇	—	4	2	no	—
487	C₂³×C₆₇	—	4	2	no	—
488	C₂³×C₆₇	—	8	1	no	—
489	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
490	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
491	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
493	Q₈×C₆₇	—	2	2	no	—
494	Q₈×C₆₇	—	2	1	no	—
495	Q₈×C₆₇	—	2	2	no	—
496	Q₈×C₆₇	—	2	2	no	—
497	Q₈×C₆₇	—	2	1	no	—
498	Q₈×C₆₇	—	2	2	no	—
499	Q₈×C₆₇	—	2	2	no	—
500	Q₈×C₆₇	—	2	1	no	—
501	Q₈×C₆₇	—	4	4	no	—
502	Q₈×C₆₇	—	4	2	no	—
503	Q₈×C₆₇	—	4	2	no	—
504	Q₈×C₆₇	—	4	2	no	—
505	Q₈×C₆₇	—	8	2	no	—
506	Q₈×C₆₇	C₂×#41	1	2	yes	—
507	D₄×C₆₇	—	2	4	no	—
508	D₄×C₆₇	—	2	4	no	—
509	D₄×C₆₇	—	2	4	no	—
510	D₄×C₆₇	—	2	2	no	—
511	D₄×C₆₇	—	2	1	no	—
512	D₄×C₆₇	—	2	1	no	—
513	D₄×C₆₇	—	2	1	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	4	no	—
519	D₄×C₆₇	—	4	2	no	—
520	D₄×C₆₇	—	8	2	no	—
521	D₄×C₆₇	C₂×#41	1	2	yes	—
522	C₂×C₄×C₆₇	—	2	2	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	4	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	2	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	2	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	2	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	4	2	no	—
543	C₂×C₄×C₆₇	—	4	2	no	—
544	C₂×C₄×C₆₇	—	4	2	no	—
545	C₂×C₄×C₆₇	—	4	4	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	—	4	2	no	—
550	C₂×C₄×C₆₇	—	4	2	no	—
551	C₂×C₄×C₆₇	—	8	2	no	—
552	C₂×C₄×C₆₇	—	8	2	no	—
553	C₂×C₄×C₆₇	—	8	1	no	—
554	C₂×C₄×C₆₇	—	8	1	no	—
555	C₂×C₄×C₆₇	—	8	1	no	—
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	2	yes	—
559	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
563	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
564	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
565	C₈×C₆₇	—	2	2	no	—
566	C₈×C₆₇	—	2	1	no	—
567	C₈×C₆₇	—	2	1	no	—
568	C₈×C₆₇	—	2	1	no	—
569	C₈×C₆₇	—	2	1	no	—
570	C₈×C₆₇	—	2	2	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	2	no	—
576	C₂²×C₆₇	—	2	1	no	—
577	C₂²×C₆₇	—	2	1	no	—
578	C₂²×C₆₇	—	2	2	no	—
579	C₂²×C₆₇	—	2	2	no	—
580	C₂²×C₆₇	—	2	2	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	4	4	no	—
583	C₂²×C₆₇	—	4	1	no	—
584	C₂²×C₆₇	—	4	1	no	—
585	C₂²×C₆₇	—	4	1	no	—
586	C₂²×C₆₇	—	4	1	no	—
587	C₂²×C₆₇	—	4	1	no	—
588	C₂²×C₆₇	—	8	4	no	—
589	C₂²×C₆₇	#546	1	2	yes	—
590	C₂²×C₆₇	#578	1	2	yes	—
591	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
592	C₄×C₆₇	—	2	2	no	—
593	C₄×C₆₇	—	2	1	no	—
594	C₄×C₆₇	—	2	1	no	—
595	C₄×C₆₇	—	2	2	no	—
596	C₄×C₆₇	—	2	2	no	—
597	C₄×C₆₇	—	2	2	no	—
598	C₄×C₆₇	—	4	1	no	—
599	C₄×C₆₇	—	4	2	no	—
600	C₄×C₆₇	—	4	2	no	—
601	C₄×C₆₇	—	4	1	no	—
602	C₄×C₆₇	—	4	1	no	—
603	C₄×C₆₇	—	4	2	no	—
604	C₄×C₆₇	—	4	2	no	—
605	C₄×C₆₇	—	4	1	no	—
606	C₄×C₆₇	—	4	1	no	—
607	C₄×C₆₇	#546	1	2	yes	—
608	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
609	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	#61173	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
611	C₂×C₆₇	—	2	2	no	—
612	C₂×C₆₇	—	2	2	no	—
613	C₂×C₆₇	—	4	2	no	—
614	C₂×C₆₇	—	4	1	no	—
615	C₂×C₆₇	—	4	2	no	—
616	C₂×C₆₇	—	8	1	no	—
617	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
618	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
619	C₂×C₆₇	#3584	1	1	yes	characteristic
620	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#3489	C₂×C₆₇	1	1	yes	characteristic
622	#3315	C₂×C₆₇	1	2	yes	complemented
623	#3314	C₂×C₆₇	1	2	yes	complemented
624	#3313	C₂×C₆₇	1	2	yes	complemented
625	#3312	C₂×C₆₇	1	2	yes	complemented
626	#3302	C₂×C₆₇	1	2	yes	complemented
627	#3300	C₂×C₆₇	1	2	yes	complemented
628	#3299	C₂×C₆₇	1	2	yes	complemented
629	#3296	C₂×C₆₇	1	2	yes	complemented
630	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
633	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#3063	C₂×C₆₇	1	1	yes	characteristic, complemented
635	C₂×#467	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#3044	C₂×C₆₇	1	1	yes	characteristic, complemented
637	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
639	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
641	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
642	C₂×#416	C₂×C₆₇	1	1	yes	characteristic, complemented
643	C₆₇	#61173	1	1	yes	characteristic, direct product factor, Sylow
644	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
645	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
646	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
647	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
648	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
651	#556	C₂²×C₆₇	1	2	yes	complemented
652	#554	C₂²×C₆₇	1	2	yes	—
653	#552	—	2	2	no	—
654	#552	C₂²×C₆₇	1	2	yes	—
655	#552	C₂²×C₆₇	1	2	yes	complemented
656	#551	—	2	2	no	—
657	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
658	#548	C₂²×C₆₇	1	2	yes	—
659	#547	—	2	2	no	—
660	#547	C₂²×C₆₇	1	2	yes	—
661	#546	—	2	2	no	—
662	#546	C₂²×C₆₇	1	2	yes	—
663	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#542	—	2	1	no	—
665	#541	—	2	1	no	—
666	#537	—	2	1	no	—
667	#537	C₂²×C₆₇	1	1	yes	characteristic
668	#536	—	2	1	no	—
669	#536	C₂²×C₆₇	1	1	yes	characteristic
670	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
671	#533	—	2	1	no	—
672	#529	—	2	1	no	—
673	#525	—	2	1	no	—
674	#525	C₂²×C₆₇	1	1	yes	characteristic
675	C₂×C₂²⋊Q₈	—	2	1	no	—
676	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
677	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
678	#520	C₂²×C₆₇	1	1	yes	characteristic
679	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
682	#491	C₂²×C₆₇	1	2	yes	complemented
683	#489	C₂²×C₆₇	1	2	yes	complemented
684	#488	C₂²×C₆₇	1	2	yes	complemented
685	#487	C₂²×C₆₇	1	2	yes	complemented
686	#485	C₂²×C₆₇	1	2	yes	complemented
687	#485	C₂²×C₆₇	1	2	yes	complemented
688	#485	C₂²×C₆₇	1	2	yes	complemented
689	#484	C₂²×C₆₇	1	2	yes	—
690	#484	C₂²×C₆₇	1	2	yes	complemented
691	#483	C₂²×C₆₇	1	2	yes	—
692	#482	C₂²×C₆₇	1	2	yes	complemented
693	#480	C₂²×C₆₇	1	2	yes	complemented
694	#479	C₂²×C₆₇	1	2	yes	complemented
695	#478	C₂²×C₆₇	1	2	yes	complemented
696	#477	C₂²×C₆₇	1	2	yes	complemented
697	#474	C₂²×C₆₇	1	2	yes	complemented
698	#470	C₂²×C₆₇	1	2	yes	complemented
699	#468	C₂²×C₆₇	1	2	yes	complemented
700	#467	C₂²×C₆₇	1	2	yes	—
701	#467	C₂²×C₆₇	1	2	yes	—
702	#467	C₂²×C₆₇	1	2	yes	complemented
703	#467	C₂²×C₆₇	1	2	yes	complemented
704	#467	C₂²×C₆₇	1	2	yes	complemented
705	#465	C₂²×C₆₇	1	2	yes	complemented
706	#464	C₂²×C₆₇	1	2	yes	complemented
707	#464	C₂²×C₆₇	1	2	yes	complemented
708	#462	C₂²×C₆₇	1	2	yes	complemented
709	#462	C₂²×C₆₇	1	2	yes	complemented
710	#452	C₂²×C₆₇	1	2	yes	—
711	#452	C₂²×C₆₇	1	2	yes	—
712	#452	C₂²×C₆₇	1	2	yes	complemented
713	#452	C₂²×C₆₇	1	2	yes	complemented
714	#451	C₂²×C₆₇	1	2	yes	—
715	#451	C₂²×C₆₇	1	2	yes	complemented
716	#451	C₂²×C₆₇	1	2	yes	complemented
717	#450	C₂²×C₆₇	1	2	yes	—
718	#441	C₂²×C₆₇	1	2	yes	complemented
719	#440	C₂²×C₆₇	1	2	yes	complemented
720	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
721	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
722	#435	C₂²×C₆₇	1	2	yes	—
723	#435	C₂²×C₆₇	1	2	yes	complemented
724	C₈×D₄	C₂²×C₆₇	1	2	yes	—
725	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
726	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
730	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
732	#419	C₂²×C₆₇	1	2	yes	complemented
733	#417	C₂²×C₆₇	1	1	yes	characteristic
734	#417	C₂²×C₆₇	1	1	yes	characteristic
735	#417	C₂²×C₆₇	1	2	yes	complemented
736	#416	C₂²×C₆₇	1	1	yes	characteristic
737	#416	C₂²×C₆₇	1	1	yes	characteristic
738	#416	C₂²×C₆₇	1	1	yes	characteristic
739	#416	C₂²×C₆₇	1	1	yes	characteristic
740	#416	C₂²×C₆₇	1	1	yes	characteristic
741	#416	C₂²×C₆₇	1	1	yes	characteristic
742	#416	C₂²×C₆₇	1	1	yes	characteristic
743	#416	C₂²×C₆₇	1	1	yes	characteristic
744	#416	C₂²×C₆₇	1	2	yes	complemented
745	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
746	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
747	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
749	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
750	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
751	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
752	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
753	#407	C₂²×C₆₇	1	1	yes	characteristic
754	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	2₋¹⁺⁴	—	2	4	no	—
756	2₋¹⁺⁴	—	4	2	no	—
757	C₂×#41	—	2	1	no	—
758	C₂×#41	—	2	2	no	—
759	C₂×#41	—	2	1	no	—
760	C₂×#41	—	2	1	no	—
761	C₂×#41	—	2	4	no	—
762	C₂×#41	—	4	2	no	—
763	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
764	C₂×#41	C₂³×C₆₇	1	2	yes	—
765	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
766	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
767	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
768	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
769	C₂²×Q₈	—	2	1	no	—
770	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
771	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
772	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
773	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
776	C₂³×C₄	—	2	1	no	—
777	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
778	#137	—	2	4	no	—
779	#137	—	4	2	no	—
780	C₂×Q₁₆	—	4	2	no	—
781	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
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×SD₁₆	C₂³×C₆₇	1	2	yes	—
787	#131	—	4	2	no	—
788	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
791	C₂²×C₈	—	4	2	no	—
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	1	yes	characteristic
798	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
799	C₄⋊Q₈	—	2	1	no	—
800	C₄⋊Q₈	—	2	1	no	—
801	C₄⋊Q₈	—	2	2	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	#126	—	2	2	no	—
807	#126	—	2	2	no	—
808	#125	—	2	1	no	—
809	#125	—	2	2	no	—
810	#125	—	2	2	no	—
811	#125	—	2	2	no	—
812	#125	C₂³×C₆₇	1	2	yes	—
813	#124	—	2	1	no	—
814	#124	—	2	2	no	—
815	#124	—	2	2	no	—
816	#124	C₂³×C₆₇	1	2	yes	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	D₄×C₆₇	1	2	yes	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	2	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	—	2	2	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	—	2	2	no	—
837	C₂²⋊Q₈	—	2	2	no	—
838	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
839	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
841	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
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	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
846	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
847	#121	—	2	1	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	D₄×C₆₇	1	1	yes	characteristic
853	#121	D₄×C₆₇	1	1	yes	characteristic
854	#121	C₂³×C₆₇	1	2	yes	—
855	#120	—	2	2	no	—
856	#120	D₄×C₆₇	1	2	yes	—
857	C₄×Q₈	—	2	1	no	—
858	C₄×Q₈	—	2	1	no	—
859	C₄×Q₈	—	2	1	no	—
860	C₄×Q₈	—	2	2	no	—
861	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
862	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
863	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	C₂³×C₆₇	1	2	yes	—
871	C₄×D₄	C₂³×C₆₇	1	2	yes	—
872	C₄×D₄	C₂³×C₆₇	1	2	yes	—
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	—	2	1	no	—
876	#117	—	2	2	no	—
877	#117	—	2	2	no	—
878	#117	—	2	2	no	—
879	#117	C₂³×C₆₇	1	1	yes	characteristic
880	#117	C₂³×C₆₇	1	1	yes	characteristic
881	#117	C₂³×C₆₇	1	1	yes	characteristic
882	#117	C₂³×C₆₇	1	1	yes	characteristic
883	#117	C₂³×C₆₇	1	2	yes	—
884	#117	C₂³×C₆₇	1	1	yes	characteristic
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	—	2	1	no	—
887	C₂×C₄⋊C₄	—	2	1	no	—
888	C₂×C₄⋊C₄	—	2	2	no	—
889	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
894	C₂×C₂²⋊C₄	—	2	1	no	—
895	C₂×C₂²⋊C₄	—	2	1	no	—
896	C₂×C₂²⋊C₄	—	2	1	no	—
897	C₂×C₂²⋊C₄	—	2	2	no	—
898	C₂×C₄²	—	2	1	no	—
899	#107	C₂³×C₆₇	1	2	yes	—
900	#107	C₂³×C₆₇	1	2	yes	—
901	#107	C₂³×C₆₇	1	2	yes	—
902	#107	C₂³×C₆₇	1	2	yes	—
903	#106	C₂³×C₆₇	1	2	yes	—
904	#106	C₂³×C₆₇	1	2	yes	—
905	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
906	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
907	#103	C₂³×C₆₇	1	1	yes	characteristic
908	#103	C₂³×C₆₇	1	1	yes	characteristic
909	#103	C₂³×C₆₇	1	1	yes	characteristic
910	#103	C₂³×C₆₇	1	1	yes	characteristic
911	#103	C₂³×C₆₇	1	1	yes	characteristic
912	#103	C₂³×C₆₇	1	1	yes	characteristic
913	#103	C₂³×C₆₇	1	1	yes	characteristic
914	#103	C₂³×C₆₇	1	1	yes	characteristic
915	#103	C₂³×C₆₇	1	2	yes	—
916	#103	C₂³×C₆₇	1	2	yes	—
917	#103	C₂³×C₆₇	1	2	yes	—
918	#103	C₂³×C₆₇	1	2	yes	—
919	#103	C₂³×C₆₇	1	2	yes	—
920	#103	C₂³×C₆₇	1	2	yes	—
921	#103	C₂³×C₆₇	1	2	yes	—
922	#103	C₂³×C₆₇	1	2	yes	—
923	#103	C₂³×C₆₇	1	2	yes	—
924	#103	C₂³×C₆₇	1	2	yes	—
925	#102	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
931	#102	C₂³×C₆₇	1	1	yes	characteristic
932	#102	C₂³×C₆₇	1	1	yes	characteristic
933	#102	C₂³×C₆₇	1	2	yes	—
934	#102	C₂³×C₆₇	1	2	yes	—
935	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
936	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
939	#97	C₂³×C₆₇	1	2	yes	—
940	C₄×C₈	C₂³×C₆₇	1	2	yes	—
941	C₂⁴	—	2	1	no	—
942	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	4	no	—
949	#41	—	2	2	no	—
950	#41	—	2	2	no	—
951	#41	—	4	4	no	—
952	#41	—	4	1	no	—
953	#41	—	4	1	no	—
954	#41	—	4	2	no	—
955	#41	—	4	4	no	—
956	#41	—	4	4	no	—
957	#41	—	4	8	no	—
958	#41	#41×C₆₇	1	4	yes	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	1	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	4	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	—	2	2	no	—
970	C₂×Q₈	—	4	1	no	—
971	C₂×Q₈	—	4	2	no	—
972	C₂×Q₈	—	4	4	no	—
973	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
975	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
977	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	4	1	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
990	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
991	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
992	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
993	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	4	4	no	—
1012	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1013	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1014	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1019	Q₁₆	—	2	4	no	—
1020	Q₁₆	—	4	2	no	—
1021	Q₁₆	—	4	2	no	—
1022	Q₁₆	—	4	2	no	—
1023	SD₁₆	—	2	4	no	—
1024	SD₁₆	—	4	2	no	—
1025	M₁₆	—	2	2	no	—
1026	M₁₆	—	2	2	no	—
1027	M₁₆	—	4	2	no	—
1028	C₂×C₈	—	2	2	no	—
1029	C₂×C₈	—	2	2	no	—
1030	C₂×C₈	—	4	1	no	—
1031	C₂×C₈	—	4	1	no	—
1032	C₂×C₈	—	4	1	no	—
1033	C₂×C₈	—	4	1	no	—
1034	C₂×C₈	—	4	2	no	—
1035	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1040	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	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	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1063	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
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	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
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	1	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	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	C₂⁴×C₆₇	1	2	yes	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	4	1	no	—
1106	C₂³	—	4	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	8	1	no	—
1109	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1110	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1111	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	1	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	1	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	4	4	no	—
1122	Q₈	—	4	2	no	—
1123	Q₈	—	4	2	no	—
1124	Q₈	—	4	2	no	—
1125	Q₈	—	8	2	no	—
1126	Q₈	C₂×#41×C₆₇	1	2	yes	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	4	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	C₂×#41×C₆₇	1	2	yes	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	4	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	4	2	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	—	8	1	no	—
1176	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1180	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1182	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1183	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1184	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₈	—	2	1	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	2	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	4	4	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	8	4	no	—
1209	C₂²	#546×C₆₇	1	2	yes	—
1210	C₂²	#578×C₆₇	1	2	yes	—
1211	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	2	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	2	no	—
1227	C₄	#546×C₆₇	1	2	yes	—
1228	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1229	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1230	C₂	—	2	2	no	—
1231	C₂	—	2	2	no	—
1232	C₂	—	4	1	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1237	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1238	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3489	C₂
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×#3495	C₂	semidirect
3. C₆₇×#3315	C₂	semidirect
4. C₆₇×#3314	C₂	semidirect
5. C₆₇×#3313	C₂	semidirect
6. C₆₇×#3312	C₂	semidirect
7. C₆₇×#3302	C₂	semidirect
8. C₆₇×#3300	C₂	semidirect
9. C₆₇×#3299	C₂	semidirect
10. C₆₇×#3296	C₂	semidirect
11. C₆₇×#3137	C₂	semidirect
12. C₆₇×#3098	C₂	semidirect
13. C₆₇×#3095	C₂	semidirect
14. C₆₇×#3083	C₂	semidirect
15. C₆₇×#3063	C₂	semidirect
16. C₂×#467×C₆₇	C₂	semidirect
17. C₆₇×#3044	C₂	semidirect
18. C₆₇×#3011	C₂	semidirect
19. C₆₇×#3007	C₂	semidirect
20. C₆₇×#2947	C₂	semidirect
21. C₆₇×#2929	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₂×#416×C₆₇	C₂	semidirect
28. C₂²×Q₁₆×C₆₇	C₂²	semidirect
29. C₂×#131×C₆₇	C₂²	semidirect
31. #556×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
43. #544×C₆₇	C₂²	semidirect
50. #536×C₆₇	C₂²	semidirect
59. #520×C₆₇	C₂²	semidirect
60. #519×C₆₇	C₂²	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
68. #485×C₆₇	C₂²	semidirect
70. #484×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #480×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #478×C₆₇	C₂²	semidirect
76. #477×C₆₇	C₂²	semidirect
77. #474×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #468×C₆₇	C₂²	semidirect
82. #467×C₆₇	C₂²	semidirect
83. #467×C₆₇	C₂²	semidirect
84. #467×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
86. #464×C₆₇	C₂²	semidirect
87. #464×C₆₇	C₂²	semidirect
88. #462×C₆₇	C₂²	semidirect
89. #462×C₆₇	C₂²	semidirect
92. #452×C₆₇	C₂²	semidirect
93. #452×C₆₇	C₂²	semidirect
95. #451×C₆₇	C₂²	semidirect
96. #451×C₆₇	C₂²	semidirect
98. #441×C₆₇	C₂²	semidirect
99. #440×C₆₇	C₂²	semidirect
100. C₄×Q₁₆×C₆₇	C₂²	semidirect
101. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. #435×C₆₇	C₂²	semidirect
105. C₈×D₄×C₆₇	C₂²	semidirect
106. #428×C₆₇	C₂²	semidirect
107. #428×C₆₇	C₂²	semidirect
108. C₂×#107×C₆₇	C₂²	semidirect
109. #424×C₆₇	C₂²	semidirect
110. #419×C₆₇	C₂²	semidirect
111. #419×C₆₇	C₂²	semidirect
112. #419×C₆₇	C₂²	semidirect
115. #417×C₆₇	C₂²	semidirect
124. #416×C₆₇	C₂²	semidirect
127. C₂×#103×C₆₇	C₂²	semidirect
128. C₂×#103×C₆₇	C₂²	semidirect
129. C₂×#103×C₆₇	C₂²	semidirect
132. #408×C₆₇	C₂²	semidirect
134. #405×C₆₇	C₂²	semidirect
610. #61173	C₆₇	direct (N × H)
620. #3495	C₂×C₆₇	semidirect
622. #3315	C₂×C₆₇	semidirect
623. #3314	C₂×C₆₇	semidirect
624. #3313	C₂×C₆₇	semidirect
625. #3312	C₂×C₆₇	semidirect
626. #3302	C₂×C₆₇	semidirect
627. #3300	C₂×C₆₇	semidirect
628. #3299	C₂×C₆₇	semidirect
629. #3296	C₂×C₆₇	semidirect
630. #3137	C₂×C₆₇	semidirect
631. #3098	C₂×C₆₇	semidirect
632. #3095	C₂×C₆₇	semidirect
633. #3083	C₂×C₆₇	semidirect
634. #3063	C₂×C₆₇	semidirect
635. C₂×#467	C₂×C₆₇	semidirect
636. #3044	C₂×C₆₇	semidirect
637. #3011	C₂×C₆₇	semidirect
638. #3007	C₂×C₆₇	semidirect
639. #2947	C₂×C₆₇	semidirect
640. #2929	C₂×C₆₇	semidirect
641. #2898	C₂×C₆₇	semidirect
642. C₂×#416	C₂×C₆₇	semidirect
643. C₆₇	#61173	direct (N × H)
648. C₂²×Q₁₆	C₂²×C₆₇	semidirect
649. C₂×#131	C₂²×C₆₇	semidirect
651. #556	C₂²×C₆₇	semidirect
655. #552	C₂²×C₆₇	semidirect
663. #544	C₂²×C₆₇	semidirect
670. #536	C₂²×C₆₇	semidirect
679. #520	C₂²×C₆₇	semidirect
680. #519	C₂²×C₆₇	semidirect
682. #491	C₂²×C₆₇	semidirect
683. #489	C₂²×C₆₇	semidirect
684. #488	C₂²×C₆₇	semidirect
685. #487	C₂²×C₆₇	semidirect
686. #485	C₂²×C₆₇	semidirect
687. #485	C₂²×C₆₇	semidirect
688. #485	C₂²×C₆₇	semidirect
690. #484	C₂²×C₆₇	semidirect
692. #482	C₂²×C₆₇	semidirect
693. #480	C₂²×C₆₇	semidirect
694. #479	C₂²×C₆₇	semidirect
695. #478	C₂²×C₆₇	semidirect
696. #477	C₂²×C₆₇	semidirect
697. #474	C₂²×C₆₇	semidirect
698. #470	C₂²×C₆₇	semidirect
699. #468	C₂²×C₆₇	semidirect
702. #467	C₂²×C₆₇	semidirect
703. #467	C₂²×C₆₇	semidirect
704. #467	C₂²×C₆₇	semidirect
705. #465	C₂²×C₆₇	semidirect
706. #464	C₂²×C₆₇	semidirect
707. #464	C₂²×C₆₇	semidirect
708. #462	C₂²×C₆₇	semidirect
709. #462	C₂²×C₆₇	semidirect
712. #452	C₂²×C₆₇	semidirect
713. #452	C₂²×C₆₇	semidirect
715. #451	C₂²×C₆₇	semidirect
716. #451	C₂²×C₆₇	semidirect
718. #441	C₂²×C₆₇	semidirect
719. #440	C₂²×C₆₇	semidirect
720. C₄×Q₁₆	C₂²×C₆₇	semidirect
721. C₄×SD₁₆	C₂²×C₆₇	semidirect
723. #435	C₂²×C₆₇	semidirect
725. C₈×D₄	C₂²×C₆₇	semidirect
726. #428	C₂²×C₆₇	semidirect
727. #428	C₂²×C₆₇	semidirect
728. C₂×#107	C₂²×C₆₇	semidirect
729. #424	C₂²×C₆₇	semidirect
730. #419	C₂²×C₆₇	semidirect
731. #419	C₂²×C₆₇	semidirect
732. #419	C₂²×C₆₇	semidirect
735. #417	C₂²×C₆₇	semidirect
744. #416	C₂²×C₆₇	semidirect
747. C₂×#103	C₂²×C₆₇	semidirect
748. C₂×#103	C₂²×C₆₇	semidirect
749. C₂×#103	C₂²×C₆₇	semidirect
752. #408	C₂²×C₆₇	semidirect
754. #405	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×#3495	2
C₆₇×#3489	2
C₆₇×#3315	2
C₆₇×#3314	2
C₆₇×#3313	2
C₆₇×#3312	2
C₆₇×#3302	2
C₆₇×#3300	2
C₆₇×#3299	2
C₆₇×#3296	2
C₆₇×#3137	2
C₆₇×#3098	2
C₆₇×#3095	2
C₆₇×#3083	2
C₆₇×#3063	2
C₂×#467×C₆₇	2
C₆₇×#3044	2
C₆₇×#3011	2
C₆₇×#3007	2
C₆₇×#2947	2
C₆₇×#2929	2
C₆₇×#2898	2
C₂×#416×C₆₇	2
#61173	67

Subgroups — C67×#61173 #30740424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61173 #30740424